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Electrochemical processes within the slimes layer of lead anodes during Betts electrorefining González Domínguez, José Alberto 1991

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t l Electrochemical Processes Within the Slimes Layer of Lead Anodes During Betts Electrorefining by Jose Alberto Gonzalez Dominguez B.Sc. National Autonomous University of Mexico (U.N.AM), 1984 M.Sc. National Autonomous University of Mexico (U.N.AM), 1985 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of Metals and Materials Engineering We accept this thesis as conforming to the required standard The University of British Columbia March 1991 © Jose" Alberto Gonzalez Dominguez, 1991 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada Date DE-6 (2/88) Abstract In the Betts process for lead electrorefining the noble impur i t ies originally present i n the bu l l i on form a strong and adherent layer of s l imes. W i th in this layer the establ ished ionic concentrat ion gradients can lead to secondary react ions. The fol lowing processes were analyzed from a thermodynamic perspective: (A) hydrolys is of the acid (B) precipitat ion of secondary products (C) react ion of noble compounds . The nature of the concentrat ion gradients w i th in the s l imes layer and related secondary processes was studied by us ing transient electrochemical techniques w h i c h inc lude : (A) current interrupt ion, (B) AC impedance, and (C) a var iat ion of S A C V (Small Ampl i tude Cyc l ic Voltammetry) . These studies were complemented by: (A) physico-chemical data on electrolyte properties, (B) "insitu" and "industrially recovered" s l imes electrolyte composit ions, (C) S E M and X-ray diffraction analysis of the s l imes layer. For compar ison purposes the electrochemical behaviour of "pure" Pb electrodes was also studied. U p o n current in ter rupt ion the anodic overpotential decays, f irst abruptly, (as the uncompensated ohmic drop disappears) and then slowly (due to the presence of a back E.M.F. created by ionic concentrat ion gradients that decay slowly). Cu r ren t in ter rupt ion measurements showed that: (A) concentrat ion gradients exist across the s l imes layer, (B) inner so lut ion potentials w i th in the s l imes layer can be larger than those measured f rom reference electrodes located i n the b u l k electrolyte, (C) secondary products can shift the inner so lut ion potential to negative values w h i c h reverse upon re-dissolution and (D) ionic d i f fus ion is seen u p o n current in ter rupt ion bu t it is complex and diff icult to model due to the presence of processes that can support the passage of interna l currents . The anodic polar izat ion components were obtained by analyz ing the potential and current dependance u p o n appl icat ion of a sma l l ampl i tude s inuso ida l waveform. Th i s dependance was found to be l inear i n the low overpotential region (< 250mV) . T h u s , u p o n subtract ion of the uncompensated ohmic drop, the rema in ing polar izat ion is due to the "apparent" ohmic drop of the sl imes electrolyte and to l iqu id j unc t i on and concentrat ion overpotentials. These components are direct ly l i nked to the electrolysis condit ions and to the s l imes layer structure. Fur thermore , the ratio of these components can be used to obta in the point at w h i c h the prec ip i tat ion of secondary products starts. Changes i n th is ratio can also be related to the anodic effects caused by the presence of addi t ion agents. [ii] AC impedance measurements performed i n the presence of a net Faradaic current showed that the impedance increases un i formly as the s l imes layer th ickens u p to the point at wh i ch noble impur i t ies start to react. Three electrical analogue models were used to describe the impedance spectra. A steady-state mathemat ica l model that predicts concentrat ion and potential gradients across the s l imes layer was developed. On ly when a pos i t ion dependent eddy d i f fus ion term was incorporated i n the numer i ca l so lut ion, were reasonable loca l ionic concentrat ions and overpotentials obtained. Table of Contents Abstract ii List of Tables iz List of Figures xi Nomenclature xz Acknowledgments zzv Chapter 1 L i terature Review 3 I Introduct ion 3 II Meta l lurgy of Lead 3 III P lant Practice i n Lead Electroref ining 7 IV The Anodic Process 12 I. Introduct ion 12 II. The phys i ca l metal lurgy of the lead anodes 12 III. Industr ia l practice 14 IV. S l imes electrochemical behavior 15 V The Cathodic Process 22 I. Addit ives control and electrochemistry 22 II. S tar t ing sheet technology 23 III. Ce l l electrolysis parameter opt imizat ion 23 IV. B ipo la r ref in ing of lead 25 Chapter 2 Fundamenta l s of the E lectrochemical Measurement Procedure 26 I. Components of the Anodic Overpotential 26 II. Trans ient E lectrochemica l Techniques 28 A . Cur ren t in ter rupt ion techniques 28 B. A C impedance techniques 31 1. A i m s and l imitat ions of the A C impedance studies 32 Chapter 3: Exper imenta l Procedure 34 I. E lect rochemica l Exper iments 34 A . E lect rochemica l cells 34 1. Beaker Ce l l 34 2. Rectangular cel l 35 [iv] B. E lectrodes 37 1. Work ing electrodes 37 ' (a) Mater ia ls 37 (b) Beaker cel l 38 (I) Pure lead work ing electrodes 38 (II) Lead bu l l i on work ing electrodes 38 (c) Rectangular cel l 38 (I) Pure lead work ing electrodes 39 (II) Lead bu l l i on work ing electrodes 39 2. Reference electrodes 39 3. Counte r electrode 40 C. Electrolyte 41 D. Temperature control 43 E. Instrumentat ion 43 1. Wenk ing potentiostat 43 2. So lar t ron electrochemical interface and frequency response analyzer 47 (a) General i t ies: 47 (b) Descr ipt ion of the experimental set-up 48 II. Electrolyte Physico-Chemical Properties 50 A . p H measurements 50 B. E lect r ica l conduct iv i ty 50 C. K inemat ic v iscosity 50 D. Dens i ty 51 C h a p t e r 4 E lectroref in ing of Lead In A Small-Scale E leclxoref ining Ce l l : A Case S tudy 52 I. Introduct ion 52 IL Presentat ion of Resul ts 54 A . Anod i c overpotential measurements 56 1. Stage I 56 2. Stage H 65 3. Stage m 67 B. Ana ly t i ca l chemistry 69 1. B u l k electrolyte concentrat ions 69 2. Inner s l imes electrolyte concentrat ions 71 C. Character izat ion of the s l imes layer 74 1. Meta l lography of the start ing lead anode 75 2. Ana lys i s of the s l imes layer phases and compounds 80 (a) S E M analys is 80 (b) X-ray diffraction 85 C h a p t e r 5 Anod ic and Rest Potential Behavior of Pure Lead i n H 2 S i F 6 -PbS i F 6 E lectrolytes 86 I. Overview of Pure Lead D isso lu t ion i n H 2 S i F 6 -PbS iF 6 Electrolytes Under Galvanostat ic Condi t ions 86 A . Anod i c overpotential i n the absence of large concentrat ion gradients i n the anode boundary layer 86 B. Corre lat ion between the anodic overpotential and the presence of addi t ion agents 88 C. Corre lat ion between the anodic overpotential and the presence of secondary products that precipitate on the anode surface 89 II. E s tab l i shment of Ionic Concentrat ion Gradients i n the Anode Bounda r y Layer and their Relat ionship to the Anod ic Overpotential 90 A . In the absence of addi t ion agents i n the b u l k electrolyte 92 B. In the presence of addi t ion agents i n the b u l k electrolyte 98 III. A C Impedance 102 A . Introduct ion 102 B. Impedance spectra obtained i n an electrolyte wi thout addi t ion agents 103 C. Impedance spectra obtained i n electrolytes conta in ing addi t ion agents 108 C h a p t e r 6 E lect rochemica l Behavior of Lead bu l l i on Electrodes i n the Presence of S l imes 115 I. Introduct ion 115 II. A C Impedance Character izat ion of the Stort ing Work ing Electrodes 117 A . A C behav iour i n the absence of addi t ion agents i n the b u l k electrolyte 118 B. A C behav iour i n the presence of addit ion agents i n the b u l k electrolyte 120 III. DC and AC S tudies i n Corroded Electrodes 124 A . Studies under galvanostatic, potentiostatic, and current in te r rupt ion condit ions 124 1. Exper imenta l results 124 (a) Var ia t ion of the anodic overpotential as a funct ion of the electrolysis t ime and the current in ter rupt ion t ime 124 (b) Changes i n the impedance as a funct ion of the s l imes layer th ickness and of the current in ter rupt ion time 133 2. Ana l ys i s of the experimental data 151 (a) Re lat ionship between the DC anodic overpotential and the DC current density 151 (I) Da t a analys is 153 (b) Proposed analogue representation of a lead bu l l i on electrode covered w i th a layer of s l imes 161 (I) D a t a analys is 169 (i) Case I: impedance spectra obtained i n the fwesence of a net Faradaic current 170 ii) Case II: impedance spectra obtained i n the absence of a net Faradaic current 183 [vi] C h a p t e r 7 Phys ico-Chemlcal Properties of H 2 S iF 6 -PbSIF 6 Electrolytes and their Re lat ionship to the Transport Processes Across the S l imes Layer 191 I. Introduct ion 191 II. Average S l imes Electrolyte Compos i t ion 191 III. Eh-pH Diagrams 194 A . (F)-Si-H 20 system 195 B. (Pb-F)-Si-H aO system 196 C. (Sb-F)-Si-H 2O f (As-F)-Si-H 20, and (Bi-F)-Si-H 20 systems 199 IV. Phys ico-Chemical Properties of H 2 S i F 6 -PbS iF 6 E lectrolytes 201 A . p H , density, v iscosity, and activity of H 2 S i F 6 so lut ions 201 B. Densi ty , v iscosity, and electrical conduct iv i ty of H 2 S i F 6 -PbS i F 6 electrolytes 203 V. Mathemat i ca l Mode l : Numer ica l So lut ion of the Nemst-P lanck F l u x Equat ions 214 A . Case A : constant y, values 215 B. Case B: constant yt values i n the presence of eddy di f fus ion .... 217 C. Anod ic overpotential values derived from the mathemat ica l model 222 S u m m a r y 226 C o n c l u s i o n s 234 R e c o m m e n d a t i o n s f o r F u r t h e r W o r k 236 B i b l i o g r a p h y 238 Appendices Appendix 1 Mathemat ica l Mode l : Numer ica l So lut ion of the Nernst-Planck F l u x Equat ions and Its Appl i ca t ion to the Betts Process 265 Appendix 2 Ana ly t i ca l So lut ion of the Nernst-Planck F l u x Equat ions 276 Appendix 3 T ime D o m a i n To Frequency D o m a i n Transformat ion: The Four ier T rans form In Cur ren t Step E lectrochemica l Techniques 291 Appendix 4 Ana ly t i ca l Chemis t ry of Electrolyte So lut ions Conta in ing PbS i F 6 -H 2 S i F 6 312 Appendix 5 Computer Interfacing of the Wenk ing Potentiostat: Ca l ib ra t ion of the Rout ines used to Interrupt the Cur ren t 322 Appendix 6 Cur ren t Interruption and AC Impedance Measurements us ing the Solar t ron Devices 330 Appendix 7 So lubi l i ty of P b S i F 6 4 H 2 0 334 Appendix 8 So lu t ion of F ick 's Second Law Equa t ion Under Cur ren t Interrupt ion Condi t ions 337 Appendix 9 Extended Vers ion of Tables Presented i n Chapter 6 348 Appendix 10 Kramers-Kronig Transformat ions of NUD E lements 360 Appendix 11 Programs Used to Generate the Eh-pH Diagrams Presented i n Chapter 7 363 [viii] Lis t of Tables Chapter 1 Table 1.1 Betts lead eleclxorefining i n the wor ld 10 Table 1.2 Chemica l composi t ion and X-Ray diffraction analys is of the lead anode s l imes 19 Chapter 4 Table 4.1 Character is t ics of experiment 1X2 55 Table 4.2 X-ray diffract ion analys is of outer and inner s l imes powder samples 85 Chapter 5 Table 5.1 Resul ts of the analys is of the concentrat ion overpotential increases du r i ng the first second after appl icat ion of the current steps Fick's Second Law approximation 96 Table 5.2 Var i a t ion of the B x and parameters w i th current density .. 107 Chapter 6 Table 6.1 Character is t ics of the experiments presented i n chapter 6 116 Table 6.2 Average t imes required to measure the AC impedance spec t rum 117 Table 6.3 S u m m a r y of the values of the electrical analogue parameters obtained under rest potential condit ions 117 Table 6.4 Ana lys i s of the spikes produced du r ing the appl icat ion of the AC waveform, i n the presence of a net DC current (Exp. C A 2 , Figs. 6.32 to 35) 156 Table 6.5.a Ana l ys i s of the spikes produced dur ing the appl icat ion of the AC waveform, i n the presence of a net DC current (Exp. CA6) 158 Table 6.5.b Ana lys i s of the spikes produced dur ing the appl icat ion of the AC waveform, under current interrupt ion condit ions (Exp. CA6) 159 Table 6.6 Ana lys i s of the spikes produced dur ing the appl icat ion of the AC waveform, i n the presence of a net DC current (Exp. CC1) 159 Table 6.7 Parameters derived from the fitt ing of the impedance data obtained i n Exp . C A 2 to the ZZARC-ZZARC analogue (Circuit A . 2 , Figs. 6.38,39) 175 [ix] Table 6.8 Parameters derived f rom the f itt ing of the impedance spectra obtained i n Exp . C A 2 (Circuit B.2, F igs. 6.40, 41) 179 Table 6.9 Parameters derived f rom the f itt ing of the Impedance data obta ined i n E x p C A 5 to the Z^c-Z^^e analogue (Circuit A.2) 181 Table 6.10 E lect r ica l analogue parameters derived f rom the f i t t ing of the impedance data obtained i n Exp . C A 5 (Circuit B.2) 181 Table 6.11 Parameters derived f rom the fitt ing of the impedance data obta ined i n Exp . C A 2 to the Randies Analogue C i r cu i t (Figs. 6.43, 44) 184 table 6.12 E lectr ica l analogue parameters derived from the F i t t ing of the impedance data obtained i n Exp . C A 5 to the Randies Analogue C i r cu i t (Fig. 6.45) 188 Table 6.13 E lectr ica l Analogue parameters derived f rom the f i t t ing of the A C impedance data obtained i n Exp . C A 4 to the T^SC'^ZJ^ analogue (Circuit A .2 , F ig . 6.47) 190 Chapter 7 Table 7.1 Compos i t ion of the electrolyte samples extracted f rom anode s l imes obtained under indus t r i a l operation o f the B E P (Corninco Ltd.) .. 192 Table 7.2 Va lues of the coefficients A and Q i n Equa t ion 7.17 202 Table 7.3 Changes i n the osmotic and activity coefficients as a funct ion of the Ionic strength 203 Table 7.4 Physico-chemical properties of H 2 S i F 6 -PbS iF 6 electrolytes 204 Table 7.5 Coefficients i n the empir ica l electrical conductiv ity, v iscosity and density correlat ions 206 Table 7.6 Changes i n the ind iv idua l ionic mobil i t ies as a funct ion of the electrolyte composi t ion 212 Summary Table S. 1 S u m m a r y of informat ion that can be derived f rom us ing transient electrochemical techniques 233 [x] Lis t of Figures Chapter 1 F ig . 1.1 F lowsheet for lead extract ion from su lph id ic concentrates 4 F ig . 1.2 A generalized flowsheet for the pyrometal lurgical ref ining of lead 5 F ig . 1.3 A generalized flowsheet for the pyrometal lurgical /electrometal lurgical ref ining of lead 6 F ig . 1.4 Changes i n the anodic overpotential value, r\A,during lead electxorefining 9 F ig . 1.5 Lead anode microstructure 13 F ig . 1.6 Stra ight type hor izonta l lead anode cast ing system 15 F ig . 1.7 B i s m u t h content of the cathodic deposit as a funct ion of the anodic polar izat ion and the electrolysis t ime 17 F ig . 1.8 D imens ions of the anodes used i n Wenzei's experiments showing the pos i t ion and size of the electrolyte sampl ing wells 18 F ig . 1.9 Changes w i th electrolysis t ime of the relative concentrat ions of P t r 2 and H+ w i th in the sl imes layer w i th respect to their b u l k values .... 19 F ig . 1.10 Lead specific weight loss (corrosion) as a funct ion of the immers ion t ime i n a 2 M Pb(BF4)2-1 M H B F 4 so lut ion i n the presence of 0, 2, 5, and 10 m M of B i + 3 21 F ig . 1.11 Con t inuous pur i f icat ion of electrolyte v ia pur i f icat ion co lumn 22 F ig . 1.12 Influence of the cycle length and current reversal ratio on the anodic overpotential value dur ing P C R 24 Chapter 2 F ig . 2.1 E lec t rochemica l cel l arrangement 27 Chapter 3 F ig . 3.1 Assembly used i n the experiments performed w i th the beaker cel l 35 F ig . 3.2 Assemb ly used i n the experiments performed us ing the rectangular cel l 36 F ig . 3.3 Sect ions of the lead bu l l i on anodes used to prepare work ing electrodes 3 7 F ig . 3.4 Deta i l of the Luggin-Haber reference electrode arrangement 4 0 F ig . 3.5 Exper imenta l set-up us ing the Wenk ing potentiostat 4 4 F ig . 3.6 Deta i l of the connect ions required to interrupt the current and to fol low the cel l response 4 5 F ig . 3.7 Cu r ren t step resu l t ing f rom ha l t ing the flow of current to the electrochemical cel l u s ing the Wenk ing potentiostat 4 7 F ig . 3.8 Connect ions f rom the electrochemical cel l to the Solar t ron E lect rochemica l Interface 4 9 Chapter 4 F ig . 4.1 Lead anode top view 5 4 F ig . 4.2 Anod ic overpotential (uncorrected for changes as a funct ion of the s l imes layer th ickness 5 7 F ig . 4 .3 Outer and inner A, B, and C reference electrodes anodic overpotential response to current interrupt ions (during a n otherwise galvanostatic experiment) 5 8 F ig . 4 .4 Deta i l of the TIa response of the inner A reference electrode to current interrupt ions (during the whole electrorefining cycle) 5 9 F ig . 4 .5 Deta i l of the r j A response of the inner B (Fig. A) and inner C (Fig. B) reference electrodes to current interrupt ions (during the whole electrorefining cycle) 5 9 F ig . 4 .6 Deta i l of the r\A response to current interrupt ions measured by the outer reference electrode (at different s l imes layer thickness) 6 0 F ig . 4 .7 Changes In the value of the uncompensated ohmic drop, T|Q , as a funct ion of the s l imes th ickness 61 F ig . 4 .8 Deta i l of the T\A response to current interrupt ions measured by the inner A reference electrode (at different s l imes layer thickness) 6 2 F ig . 4 .9 Deta i l of the i i A response to current interrupt ions measured by the inner B reference electrode (at different s l imes layer thickness) 6 3 F ig . 4 . 1 0 Deta i l of the T\a response to current interrupt ions measured by the inner C reference electrode (at different s l imes layer thickness) .. 6 4 F ig . 4 .11 Anod ic overpotential (corrected for TJQ) changes as a funct ion of the s l imes layer th ickness 6 5 [xii] F ig . 4.12 Anod ic overpotential (uncorrected for i i d changes as a func t ion of the current in ter rupt ion t ime 66 F ig . 4.13 Changes In the value of the anodic overpotential ( uncorrected for TI J as a func t ion of the electrolysis t ime 67 F ig . 4.14 Anod i c overpotential response u p o n current in ter rupt ion (Stage m Table 1 68 F ig . 4.15 Changes i n composi t ion of the b u l k electrolyte as a funct ion of the s l imes layer th ickness 70 F ig . 4.16 Changes i n the b u l k electrolyte composi t ion as a funct ion of the current in ter rupt ion t ime 70 F ig . 4.17 Changes i n the local composi t ion of the s l imes electrolyte as a funct ion of the movement (from the sampl ing point) of the anode/s l imes interfac 71 F ig . 4.18 Changes i n the local concentrat ion of the total S i and F present i n the s l imes electrolyte as a funct ion of the movement (from the sampl ing point) of the anode/sl imes interfac 72 F ig . 4.19 Changes i n the local composi t ion of the s l imes electrolyte as a func t ion of the current in ter rupt ion time 73 F ig . 4.20 Changes i n the local concentrat ion of the total S i and F present i n the s l imes electrolyte as a funct ion of the current in ter rupt ion t ime 74 F ig . 4.21 Sect ion of the lead anode and of the s l imes layer s tudied metal lographical ly 75 F ig . 4.22 Lead anode microstuctures . Anode "A", A i r cooled face. A l l micrographs correspond to the same observation point( point # 1 F ig . 4.21) 76 F ig . 4.23 Lead anode microstuctures . Anode "A" . A l l micrographs correspond to the same observation point( point #2 F ig . 4.21) 78 F ig . 4.24 Lead anode microstuctures . Micrographs correspond to different observat ion points 79 F ig . 4.25 Mic ros t ruc ture of the s l imes layer @2mm away f rom the sl imes/electrolyte interface (position #2 F ig. 4.21) 81 F ig . 4.26 Deta i l of the microstructure of the sl imes layer @2mm away from the sl imes/electrolyte interface (position #2 F ig . 4.21) 82 F ig . 4.27 Micros t ruc ture of the s l imes layer @12mm away f rom the sl imes/electrolyte interface (position #3 F ig . 4.21) 83 F ig . 4.28 Deta i l of the microst ructure of the sl imes layer @12mm away from the sl imes/electrolyte interface (position 3 F ig . 4.21) 84 [xiii] Chapter 5 F ig . 5.1 Potentia l difference between a fixed reference electrode and a corroding anode i n the absence of addi t ion agents 87 F ig . 5.2 Overpotent ia l changes du r ing the galvanostatic d isso lut ion of pure lead (in the presence of excess quantit ies of addi t ion agents) 89 F ig . 5.3 Anod ic overpotential response (uncorrected for TJQ) of pure lead, to the appl icat ion of successive current step 90 F ig . 5.4 Cur ren t step funct ion used to s tudy the establ ishment of concentrat ion gradients i n the anode boundary layer. The rise t ime of the current steps was smal ler than 10 usee 91 F ig . 5.5 Anod ic overpotential response (uncorrected for TIJ of a pure lead electrode to the current steps described i n F ig . 4, i n the presence of addi t ion agents (compare w i th F ig . 5) 92 F ig . 5.6 Changes i n the uncompensated ohmic drop [r\o) as a funct ion of the appl ied current density 93 F ig . 5.7 Anod i c overpotential response (corrected for in i t i a l TIJ of a pure lead electrode to the current steps described i n F ig . 4 94 F ig . 5.8 Changes i n the dimensionless overpotential, <!>!, as a funct ion of the square root of t ime, 96 F ig . 5.9 Decay i n the anodic overpotential (corrected for TJQ) as a func t ion of the in ter rupt ion t ime, t^  97 F ig . 5.10 Anod ic overpotential response (uncorrected for TIJ of a pure lead electrode to the current steps described i n F ig . 4 98 F ig . 5.11 Anod ic overpotential response (corrected for in i t ia l of a pure lead electrode to the current steps described i n F ig . 4 99 F ig . 5.12 Compar i son between the anodic overpotential value obtained r ight after appl icat ion of current (*) and the uncompensated ohmic drop obtained from the h igh frequency intercept of the impedance spec t rum 100 F ig . 5.13 Changes i n the anodic overpotential upon appl icat ion of a current step 101 F ig . 5.14 Changes i n the anodic overpotential as a funct ion of the current in ter rupt ion t ime 102 F ig . 5.15 Impedance d iagram of pure lead under rest potent ia l condit ions (in the absence of addi t ion agents) 104 F ig . 5.16 Deta i l of the impedance curve shown i n F ig . 15 (after subtrac t ing the Rg value) 105 [xiv] F ig . 5.17 Impedance d iagram of pure lead i n the presence of a n anodic current 1=150 A m p m*2 (after subtract ing the Rg value) 107 F ig . 5.18 Impedance d iagram of pure lead under rest potential condi t ions (in the presence of addit ion agents) 108 F ig . 5.19 Impedance diagrams of pure lead under rest potent ia l condi t ions obtained at two different ampl i tudes of the appl ied AC waveform (in the presence of addi t ion agents) 109 F ig . 5.20 Analogue c i rcu i ts used to model the h igh frequency response of the impedance curve shown i n F ig . 15 110 F ig . 5.21 H igh frequency sect ion of the impedance d iagram shown i n F ig . 18 112 F ig . 5.22 Impedance diagrams of pure lead obtained i n the presence and i n the absence of a net Faradaic current (in the presence of addi t ion agents) 113 F ig . 5.23 Deta i l of the impedance diagrams obtained i n the presence of a net Farada ic current (in the presence of addi t ion agents) 114 Chapter 6 F ig . 6.1 Impedance d iagram (Argand plot) of a typical lead bu l l i on electrode (Exp. CC1-6) under rest potential condit ions and i n the absence of addi t ion agents 119 F ig . 6.2 Impedance d iagram (Argand plot) of a typical lead bu l l i on electrode (Exp. CA2-J) under rest potential condit ions and i n the presence of addi t ion agents 120 F ig . 6.3 Deta i l of the h igh frequency region of the impedance d iagram shown i n F ig . 2 121 F ig . 6.4 Deta i l of the h igh frequency regions of the impedance diagrams obtained under rest potent ia l condit ions 122 F ig . 6.5 Impedance spectra obtained under potentiostatic (solid line) and galvanostatic control (dashed line) 123 F ig . 6.6 Overpotent ia l response of a typical lead bu l l i on anode as a func t ion of the s l imes th ickness (Exp. CA2) 125 F ig . 6.7 Anod ic overpotential (corrected for in i t ia l r y measured by the counter and reference electrodes as a funct ion of the s l imes th ickness (Exp. CA5) 127 F ig . 6.8 Cur ren t density changes as a funct ion of the electrolysis t ime and of the amount of lead dissolved (Exp. C A 4 , potentiostatic condit ions £^^,,=220 mV) 128 [xv] F ig . 6.9 Changes i n the anodic overpotential (corrected for TJQ) as a func t ion of the amount of lead dissolved (Exp. CA4) 129 F ig . 6.10 Anod ic overpotential changes u p o n current in ter rupt ion (Exps. C A 2 . C A 5 , and CA4) 130 F ig . 6.11 Anod i c overpotential (corrected for in i t ia l TJQ) as a funct ion of the s l imes th ickness (Exps. C A 6 and CC1) . .: 132 F ig . 6.12 Anod i c overpotential changes u p o n current in ter rupt ion (From Exp . CA6) 133 F ig . 6.13 Impedance spectra obtained dur ing Exp . C A 2 at s l imes layer th ickness between 0.8 and 7.8 m m 134 F ig . 6.14 Impedance spectra obtained dur ing Exp . C A 2 at a s l imes layer th ickness of 8.4 m m 135 F ig . 6.15 Impedance spect rum obtained dur ing Exp . C A 2 at a s l imes layer th ickness of 8.65 m m 136 F ig . 6.16 Changes i n the value of the uncompensated ohmic resistance, Rg, as a funct ion of the s l imes th ickness (Exp. CA2) 137 F ig . 6.17 Impedance spectra obtained dur ing Exp . C A 5 at s l imes layer th ickness between 0.64 and 1.89 m m 138 F ig . 6.18 Impedance spectra obtained dur ing Exp . C A 5 at a s l imes layer th ickness of 2.2 m m (Rg was subtracted from the component of the impedance) 139 F ig . 6.19 Changes i n the value of the uncompensated ohmic resistance, Rg, as a funct ion of the s l imes th ickness (Exp. CA5) 140 F ig . 6.20 Impedance spectra obtained du r ing Exp . C A 4 at s l imes layer th ickness between 0.87 and 2.87 m m 141 F ig . 6.21 Changes i n the value of the uncompensated ohmic resistance, Rg, as a funct ion of the s l imes th ickness (Exp. CA4) 142 F ig . 6.22 A rgand plot showing the changes i n the impedance spectra obtained i n the presence of a layer of s l imes and i n the absence of a net Farada ic current (Exp. CA2) 143 F ig . 6.23 Changes i n the value of the uncompensated ohmic resistance, Rg, as a funct ion of the current interrupt ion time (Exp. CA2) 143 F ig . 6.24 A rgand plot showing the changes i n the impedance spectra obtained i n the presence of a layer of s l imes and i n the absence of a net Farada ic current (Exp. CA5) 144 F ig . 6.25 Changes i n the value of the uncompensated ohmic resistance, Rg, as a func t ion of the current interrupt ion t ime (Exp. CA5) 145 [xvi] F ig . 6.26 A rgand plot showing the changes i n the impedance spectra obtained i n the presence of a layer of s l imes and i n the absence of a net Farada ic current (Exp. CA4) 146 F ig . 6.27 Impedance spectra obtained dur ing Exp . C A 6 at s l imes layer th i ckness between 0.43 and 7.7 m m 147 F ig . 6.28 Impedance spectra obtained dur ing Exp . C C 1 at s l imes layer th i ckness between 0.14 and 5.3 m m 148 F ig . 6.29 Changes i n the value of the uncompensated ohmic resistance, Rs, as a funct ion of the s l imes th ickness (Exps. C A 6 and CC1) . 149 F ig . 6.30 A rgand plot showing the changes i n the impedance spectra obtained i n the presence of a layer of s l imes and i n the absence of a net Farada ic current (Exp. CA6) 150 F ig . 6.31 Changes i n the value of the uncompensated ohmic resistance, Rg, as a funct ion of the current in ter rupt ion t ime (Exp. CA6) 150 F ig . 6.32 Deta i l of the "spikes" observed at -0.8 m m sl imes (Exp. C A 2 , Table 6.4) 154 F ig . 6.33 Var ia t ions i n the anodic overpotential as a funct ion of the anodic current density at var ious s l imes th ickness (Exp. C A 2 , Table 6.4) 155 F ig . 6.34 Changes i n the value of the resistance of the s l imes electrolyte as a funct ion of the s l imes th ickness (Exp. C A 2 , Table 6.4) 157 F ig . 6.35 Changes i n the parameters b and IRn, w i th re lat ionship to the exper imental var iat ions of the anodic overpotential (Exp. C A 2 , Table 6.4) 157 F ig . 6.36 Proposed analogue model representat ion of a lead bu l l i on electrode covered w i th a layer of s l imes 164 F ig . 6.37 E lectr ica l c i rcu i ts used to analyze the impedance spectra 171 F ig . 6.38 Corre la t ion between the experimental and theoretical impedance spectra (Exp. C A 2 , c i rcu i t A .2 , Table 6.7). 174 F ig . 6.39 Var i a t ion of the derived electrical analogue parameters as a funct ion of the s l imes th ickness (Exp. C A 2 , C i r cu i t A .2 , Table 6.7) 177 F ig . 6.40 Deta i l of the impedance spect rum obtained i n Exp . C A 2 at 0.80 m m of s l imes (Exp. C A 2 , c i rcu i t B.l) 178 F ig . 6.41 Var i a t ion of the derived electrical analogue parameters as a func t ion of the s l imes th ickness (Exp. C A 2 , C i r cu i t B.2, Table 6.8) 179 [xvii] F ig . 6.42 Var i a t ion of the m a x i m u m values of the real , Z*. and the imaginary parts , -Zg , of the impedance as a funct ion of the amount of lead dissolved (Exp. CA4) 182 F ig . 6.43 Modif ied Randies analogue c i rcu i t 183 F ig . 6.44 Corre lat ion between the experimental and theoretical impedance spectra (Exp. C A 2 , current interrupt ion condit ions, Table 6.11) 184 F ig . 6.45 Corre lat ion between the experimental and theoretical impedance spectra (Exp. C A 5 , current interrupt ion condit ions, Table 6.12) 186 F ig . 6.46 Argand plot of a typical lead bu l l i on electrode (Exp. CC2) i n the presence of a 2.2 m m layer of s l imes 187 F ig . 6.47 Corre lat ion between the experimental and theoretical impedance spectra (Exp. CA4 , current interrupt ion condit ions, Table 6.13) 189 Chapter 7 F ig . 7.1 Sys tem (F)-Si-H 20 at 25 °C 196 F ig . 7.2 Sys tem (Pb-F)-Si-H 20 at 25 °C 197 F ig . 7.3 Changes i n p H as a funct ion of logaSiF-2 and loga p b + 2 198 F ig . 7.4A System (Sb-F)-Si-H aO at 25 °C 199 F ig . 7.4B System (Bi-F)-Si-H 20 at 25 'C 200 F ig . 7.4C System (As-F)-Si-HaO at 25 °C 200 F ig . 7.5 Changes i n p H as a funct ion of the electrolyte composi t ion 201 F ig . 7.6 E lect r ica l conductiv i ty, density, and viscosity of H 2 S i F 6 -PbS i F 6 electrolytes 207 F ig . 7.8 Changes i n Walden's product as a funct ion of the square root of the ionic strength 213 F ig . 7.8 Va r i a t ion i n the s l imes electrolyte composi t ion as a funct ion of the distance f rom the s l imes/bu lk electrolyte interface, a s suming no changes i n activity coefficients (Case A) 216 F ig . 7.9 Changes i n the potential of the sl imes electrolyte as a funct ion of the distance f rom the anode/sl imes interface 218 F ig . 7.10 Changes i n the potential difference between the outer and inner reference electrodes as a funct ion of the distance from the s l imes/bu lk electrolyte interface 219 [xviii] F ig . 7.11 Var ia t ion of the eddy di f fusion constant, D E, as a funct ion of the distance f rom the s l imes/bu lk electrolyte interface, (oc=lxlO 2 m m and p ^ x l O " 4 c m 2 sec"1) 220 F ig . 7.12 Var i a t ion i n the sl imes electrolyte composi t ion as a funct ion of the distance from the s l imes/bu lk electrolyte interface, when changes i n activity coefficients and i n eddy di f fusion are accounted for (CaseB) 221 F ig . 7.13 Var ia t ion i n the sl imes electrolyte composi t ion as a funct ion of the distance from the s l imes/bu lk electrolyte interface, when changes i n eddy di f fusion are accounted for (Case C) 222 F ig . 7.14 Var i a t ion i n physico-chemical properties of the s l imes electrolyte as a funct ion of the distance f rom the s l imes/bu lk electrolyte interface 223 F ig . 7.15 Compar i son between the experimental (unsteady-state) and predicted (steady-state) anodic overpotentials 225 [xix] Nomenclature a, molar activity coefficient of species i: a, = ^C, apbdXi) Activity of Pb+2 as a function of the distance from the slimes/electrolyte interface. a +2(bulk) Activity of Pb+2 in the bulk electrolyte (i.e. outside the slimes/bulk electrolyte interface). b slope, mV (Eq. 5, Chapter 6). Bj Frequency independent parameter, [Q cm2 sec Vzc], (Eq. 6, Chapter 5) b,b2b0 Frequency independent parameters, [£2cm2sec"1 ]^, (Eq. 10. Chapter 6) bD Dimensionless parameter defined in Eq. 4, Chapter 5. Capacity of the electrical double layer, [uF cm"2] C g Geometrical capacitance, [|xF cm"2] C° t 2 Bulk Pb+2 concentration, [mol cm"3] rb C,o Concentration of species i at the electrode surface (at x=0), [mol cm"3] C, Concentration of species i, [mol cm"3]: Species a: Pb+2 Species b: SiF6"2 Species c: H + C loo Concentration of species i in the bulk electrolyte (at x=°°), [mol cm"3] CPE! Analogue parameter that represents the distributed nature of the anode/slimes and the slimes/slimes electrolyte interface CPE2 Analogue parameter that represents the presence of a distributed capacitance generated by the concentration gradients present in the slimes electrolyte. D Diffusion coefficient, [cm2 sec"1] Dt Diffusion coefficient of species i, [cm2 sec"1] D E Eddy diffusion constant, [cm2 sec"1] DD^2 Mean diffusion coefficient for Pb+2 ions, [cm2 sec"1] D™ Molecular diffusion coefficient of species i, [cm2 sec"1] <Di Overall diffusion coefficient of species i, [cm2 sec"1] : T>i = DT+DE e(t) Potential as a function of time Econtroi Difference in potential between the reference and working electrodes under potentiostatic control. F Faraday's constant. 96487 C eq"1 iron. Steady-state corrosion current density, [Amp m"2] i\, Exchange current density, [Amp m"2] [xx] I& 0 Current density at the electrode surface, [A cm"2]. I (t) Superficial current density at the anode/slimes interface as a function of the electrolysis time, [A cm"2]. It Total molar ionic strength = /, = 0.5{Afu(v,Z2+v^2)+Mm{y& + VjZ2)} = 4x[PbSiF(5] + 3x[H2SiFe] IiHzSifj Molar ionic strength of H2SiF6 in a H2SiF6-PbSiF6 mixture = 3x[H2SiF6] hbsiFj Molar ionic strength of PbSiF6 in a H2SiF6-PbSiF6 rnixture= 4x[PbSiF6] j Imaginary number , V - -T L Characteristic length of the electrode, [cm] mD Slope defined in Eq. 4, Chapter 5, [sec"0 ^  m Molality, [mol of solute/Kg of solvent] M Molarity, [mol/1] N, Water mol fraction with respect to species i. n Number of electrons involved in electrode reaction. I r Ia, I yr 12 Statistical parameters defined in Appendix 9. R, Analogue parameter that represents charge transfer resistances associated with the lead dissolution processes, [Qcm ]. Analogue parameter related to the D C conductivity of the slimes electrolyte, [Qcm2] ra Analogue parameter related to the D C resistance of the slimes electrolyte, [Qcm2] rb Analogue parameter related to the charge transfer resistance associated with the lead dissolution process, [Qcm2] Rb Resistance of the electrolyte present between the reference electrode and the anode boundary layer, [Clem ] R,t Charge transfer resistance, [Qcm2] RD Diffusional (DC) resistance, [Qcm2.] Rata Resistance of the film created by the addition agents, [Qcm2] Rm "Apparent" average resistivity of the electrolyte present across the slimes layer, [Qcm2]. Rp Polarization resistance, [Qcm2] Rs "Uncompensated" ohmic resistance, [Qcm2]. R Universal gas constant, [8.3114 J mol"1 deg"1] s, Stoichiometric coefficient in electrode reaction T Absolute temperature, [K] v+ and v_ Number of cations and anions into which a mole of electrolyte dissociates. w Solution composition, [wt% H2S1F<J x, Distance from the slimes/bulk electrolyte interface at which point D e is to be computed, [ x, < x^], [mm] [xxi] Xjotai Total slimes thickness, [mm] x Mixing fraction (Eq, 22, Chapter 7). Z, Charge number of species i, [eq mol"1] Z(jco) Impedance as a function of frequency,. [Qcm2] Zj Imaginary component of the impedance, [Qcm2] Z* Real component of the impedance, [Qcm2] IZI Absolute value of the impedance, [Qcm2], (| Z |= -N/ZI+Z2) Z a / s e Faradaic impedance at the lead anode/slimes electrolyte interface. Z a / s l Electronic impedance at the lead anode/slimes interface. ZC P E Impedance of the CPE analogue element. Z2/lBC Impedance of the ZARC analogue circuit. ZnJt) Changes in D C impedance as a function of time. Z s l / b e Faradaic impedance at the slimes/bulk electrolyte interface. Z s I / s e Faradaic impedance at the slimes/slimes electrolyte interface. Warburg ionic diffusional impedance in the slimes electrolyte/bulk electrolyte interface. Zw Warburg ionic diffusional impedance throughout the slimes electrolyte. [M™] Ionic concentration of ions M, [Ml. [Mfn]b Ionic concentration of ions M, at the slimes/bulk electrolyte Interface, [Mj. [M+n]e Ionic concentration of ions M, at the anode/slimes electrolyte interface, [Mj. {M+n}r Concentration of ions M at the anode/slimes interface with respect to their [Pfr+^V concentration at the slimes/bulk electrolyte interface (e.g. {Pb+%=—^) It Total molar ionic strength = 4x[PbSiF6l + 3x[H2SiF6] [HaSiFglu H 2SiF 6 concentration at the total molar ionic strength of H2SiF6-PbSiF6 mixtures, [M], [PbSiFg] + [HaSiFJ PbSiF6 and H2SiF6 concentrations in the electrolyte rnixtures, [M], [PbSiFelK PbSiF6 concentration at the total molar ionic strength of H2SiF6-PbSiF6 mixture, [M]. a and p Arbitrary positive constants whose value depends on the electrolysis conditions: a [mm] and (3 [cm2 sec"1] (Eq. 31, Chapter 7). pa Anodic Tafel slope Pc Cathodic Tafel slope. 8 Thickness of the hypothetical Nernst boundary layer, [cm] [xxii] y, Individual molar activity coefficient. Y± Mean activity coefficient AO Migration or "liquid junction" potential, [mV] O e Maximum value of the migration potential for a fixed slimes thickness, [mVj <J>1( 0 2 Dimensionless parameters in Eqs. 4 and 5, Chapter 5. ^zc Fractional element in CPE analogue element A ^ Equivalent conductivity of the H2SiF6-PbSiF6 mixtures, [cm2 eq"1 ft"1] A H ^ and ApK^ Equivalent conductivity of the pure H2SiF6 and PbSiF6 solutions at the total ionic strength of H2SiF6-PbSiF6 mixtures, [cm2 eq"1 CI'1] X, Individual equivalent conductivity of ions i, [cm2 eq'1 Ci'1] T ) a c Activation overpotential, [mV] r)n "Uncompensated" ohmic drop, [mV] •nA Anodic overpotential, [mV] r|c Concentration overpotential. [mV] rj^, Total ohmic drop across the slimes layer, [mV] (Eq. 32, Chapter 7) r\c Concentration overpotential due to Pb+2, [mV] (Eq. 33, Chapter 7). ru Steady-state anodic overpotential from the solution of the Nemst-Planck flux equations, [mV] (Eq. 34, Chapter 7). TI Dynamic viscosity [coefficient q/), [cP] K Electrical conductivity, [mmho cm"1] K [x^ Electrical conductivity changes as a function of the distance from the anode/slimes interface, A* [mmho cm"1] K^ fc Electrical conductivity of H2SiF6-PbSiF6 mixtures, [mmho cm"1] KiPbsiFj,, Electrical conductivity of PbSiF6 at the total ionic strength of H2SiF6-PbSiF6 mixtures, [mmho cm"1.] K_ Bulk electrolyte electrical conductivity, [mmho cm"1] H, Absolute ionic mobility of ion i, [cm2 sec"1 volt"1] v Kinematic viscosity [coefficient oJ), [cSt]. pm Specific electrical resistivity of the electrolyte entrapped within the slimes layer, [ftcm]. p Solution density, [g cm"3] ov Warburg Coefficient, [CI cm2 sec"05] x Relaxation time, [sec] tD Dielectric relaxation time of the bulk electrolyte, [sec], TD=Cg.Rb xf Relaxation time of the Faradaic reaction taking place upon discharge of the double layer, [sec] [xxiii] 0) ©min ©max AAS AC BEP cd C.P.V. CPE DC E.M.F. EPMA FFT FRA PCR RM.S. SACV SEI SSM SEM SSR Relaxation time of the diffusional processes across the hypothetical Nemst boundary layer, [sec]. Relaxation time required to equilibrate the charge of the electrical double layer, [sec] Frequency, [rad sec"1] Minimum frequency at which the AC impedance was acquired (or analyzed), [rad sec"1] Maximum frequency at which the AC impedance was acquired (or analyzed), [rad sec"1] Abbreviations Atomic Absorption Spectroscopy Alternating current Betts electrorefining process Current density Cathode polarization voltage Constant phase angle element Direct current Electromotive force Electron probe microanalysis. Fast Fourier transform. Frequency Response Analyzer Periodic current reversal Root mean square Small amplitude cyclic voltammetry Solartron Electrochemical Interface Secondary solidified material Scanning Electron Microscopy Solid State Relay [xxiv] Acknowledgments I want to express my sincere appreciation to my research advisor, Dr. Ernest Peters who guided me constantly throughout my stay at U.B.C. I want to thank him for all his teachings, and most of all for having the persistence of bearing with me. My stay at U.B.C. was made possible due to scholarships from; Universidad National Autonoma de Mexico (U.NJLM.) and The University of British Columbia, and through supplementary funding from the Natural Sciences and Engineering Research Council of Canada. I want to thank these institutions for their support. I want to express my gratitude to Dr. R.C. Kerby (Corninco Ltd.) and Dr. C.C.H. Ma (Dept. of Electrical Engineering, U.B.C.) for providing me with a variety of new ideas. My sincere thanks to Dr. Charles Cooper for taking the task of proofreading the thesis and contributing with constructive comments. I want to thank my beloved wife, Diana, whose positive and encouraging attitude gave me the strength to accomplish this work. I also would like to thank my parents and brothers for giving me moral support throughout this work. [xxv] Introduct ion The Betts process for lead electrorefining treats lead bu l l i on contair i ing 1-4% impur i t ies . Ant imony , arsenic, b i smu th , and a variety of m inor metals inc lud ing si lver and gold are amongst these impur i t ies . The bu l l i on is cast into anodes of about 1 m 2 , weighing between 200 and 300 kg . These anodes are electrolytically corroded w i th the s imul taneous p lat ing of relatively pure lead (>99.99% Pb) on cathodes (pure lead start ing sheets) of about the same area as the anodes. The electrolyte is typical ly an aqueous lead f luosi l icate so lut ion (0.2 to 0.5 M PbSiFg) conta in ing excess f luosi l ic ic acid (0.5 to 0.8 M HaSiFg). The impur i t ies are largely retained on the anode scrap as an adher ing sl ime. Betts ref in ing is the preferred lead ref in ing process when b i s m u t h mus t be separated f rom lead. S ince b i smu th forms a sol id so lut ion w i th lead at concentrat ions normal ly found i n lead bu l l ion , it is necessary for the anode sl imes to adhere so that they can cement out the b i s m u t h f rom the electrolyte after it has corroded w i th l e a d 1 . Th i s s tudy was designed to obta in a fundamenta l unders tand ing of the anodic processes that take place u p o n electrochemical d isso lut ion of lead anodes as used i n the Betts process. D u r i n g the ref ining of lead by the Betts process, ideally, only lead wou ld dissolve and the noble impur i t ies wou ld rema in unreacted and attached to the anode forming a strong, adherent, and h igh ly porous s l imes layer. The extent to w h i c h th is ideal operation can be achieved i n practice is a complex funct ion of the lead anode phys ica l metal lurgy and of the electrolysis condit ions. Th i s dissertat ion has focused on s tudy ing how the electrolysis condit ions affect the behavior of typical lead anodes. The ma in objectives of th is research were: 1) To analyze f rom a thermodynamic perspective, the condit ions under wh i ch hydrolys is of the ac id, precipi tat ion of secondary products , and d isso lut ion of noble compounds can take place. 2) To obta in the components of the anodic polar izat ion and relate them wi th : (a) t ransport processes across the sl imes layer (b) hydrolys is and secondary products prec ip i tat ion (c) noble compounds d isso lut ion (d) b u l k electrolyte composi t ion ( inc luding addi t ion agents) (e) current density. 3) To formulate a mathemat ica l model that can be used to predict concentrat ion and potential gradients across the sl imes layer. 1 If bismuth does not corrode with lead it would enrich at the anode surface until lead corrosion is stopped. [1] The single, most important parameter to study was found to be the ionic concentration gradients in the electrolyte entrapped within the slimes layer. One of the direct effects of the presence of these concentration gradients is the precipitation of secondary products within the slimes layer. The characterization of these secondary products and their effect on the dissolution of noble compounds was studied by several methods. Among these, transient DC (direct current) and AC (alternating current) electrochemical techniques were used to find the extent to which precipitation of secondary products and entrapped electrolyte concentration gradients affect the refining cycle. The electrolyte composition within the slimes and the accompanying potential gradient were obtained by mcorporating tap holes in typical lead anodes. The study and characterization of this entrapped electrolyte required the use of several analytical procedures, including titTimetic analysis and atomic absorption spectroscopy. The characterization of the physico-chemical properties of this entrapped electrolyte was achieved by measuring the electrical conductivity, viscosity, and density of synthetically prepared solutions whose compositions approximated those of inner electrolytes as found from anode tap holes or calculated from theory. In addition to this, sampling of the slimes layer and characterization of the contained secondary products was an important part of this work. Scanning electron microscopy and X-ray diffraction techniques were employed to detect the phases and elements in the slimes layer. A mathematical model based on the Nernst-Planck flux equations was developed to describe the establishment of concentration gradients within the slimes layer. This model predicts these gradients when combined with relationships between concentrations and fundamental solution properties (i.e. activities, mobilities, diffusion coefficients). The full application of this model will occur only when more experimental data on these fundamental properties become available. To explain the presence of secondary products and their stability range from a thermodynamic perspective, computer generated Eh-pH diagrams were drawn. [2] Chapter 1 L i terature Review I Introduct ion This chapter deals mainly with the Betts electrorefining process for lead, as described in the literature. In this process lead bullion is purified by transferring most of the lead from a soluble anode to a cathode through a lead-containing electrolyte while leaving behind impurities in an adherent anode slime. The electrochemistry of this process involves the properties of anode slimes and of entrained electrolyte. Thus, the processes of anodic corrosion of lead and transport of lead ions through the entrained electrolyte are essential to the understanding of the Betts process. In this chapter, the physical metallurgy of lead anodes, which affects the slimes adherence is also discussed. n Metal lurgy of Lead Lead is an ancient metal. It was used by the Romans for components of their water distribution systems, and for that purpose it had to be malleable and ductile IH. The ancients made lead of acceptable purity probably by smelting lead ores under conditions that prevented arsenic, antimony, and other hardening elements from reducing to the metallic phase. This could be accomplished in most cases by producing high lead slags such as those still produced in fire assaying. In those days it was necessary to avoid excessive copper in the ore, but arsenic, antimony, bismuth, nickel, iron, etc. were reliably held in the slag by maintaining the high oxidizing conditions of lead silicate based slags. Lead recoveries were low - not better than 85% from the highest grade hand picked galena ore. When high lead recoveries were found to be obtainable by coke-based blast furnace reduction, lead so produced was too hard, usually because of its copper, antimony, and arsenic content. The function of lead refining became both a softening process and a method of recovering silver and gold [2]. Nowadays the extraction process can be conveniently portrayed in the two-step flowsheet shown in Fig. 1. The first step involves bullion production from the sulphide concentrate and the second step the refining of bullion to the final product. The conventional route for bullion production requires sintering of the concentrate to produce a lead oxide containing product, which is then reduced in a blast furnace with metallurgical coke to produce lead bullion. The KTVCET [3] Metallurgy of Lead and QSL processes represent two relatively recent commercial developments 131 that replace both the sintering - blast furnace combination with a single furnace that treats concentrates, and reduce both the costs of lead smelting and the environmental impact. The KIVCET [4] process replaces the sintering/blast furnace operations with a flash smelting step. In this process, lead sulphide is oxidized to lead bullion and sulphur dioxide in a stream of oxygen. In a second step, the bullion and slag flow under a weir to an electrically heated settling hearth where coke breeze or coal is added to reduce the residual lead oxide in the slag and produce a final bullion (for refining) as well as a low-lead slag. Lead Sulphide Concentrate Bullion Lead Bullion Production • Sulphur Dioxide Refining of Bull ion Residues Fig. 1 Flowsheet for Lead Extraction from Sulphidic Concentrates. 99.99+ %Pb Byproduct Metals The QSL [5] process consists of a long, horizontal, tubular, brick-lined converter in which lead concentrates are pelletized and injected near one end into a bath containing lead bullion, lead oxide - containing slag, and lead sulphide matte. Oxygen is blown into the bath in the feed injection (and lead - bullion discharge) zone where it ultimately oxidizes sulphide sulphur to sulphur dioxide gas. Slag is tapped from the far end of the reactor after passing through a zone where reducing coal-air mixtures are injected through tuyeres to lower its lead oxide content. [4] Metallurgy of Lead The refining of bullion is carried out by either a pyrometallurgical route or a combined pyrometallurgical/electrometallurgical route. Comparisons between these two routes show that the pyrometallurgical route is usually used when ores with low Bi content are treated 17,81. The generalized pyrometallurgical flowsheet is shown in Fig. 2 \ This process consists of a series of steps which capitalize on a complex series of phase relationships to extract all the impurities contained in the lead bullion down to very low levels. Reviews on the chemistry and technology of these refining steps are available in the literature [4,6,9-11]. LEAD BULLION <Co,Sb.At.SnrAg,Au.Bf) [F»^n3/*.01 T DROSSING COPPER DROSS OR MATTE 1 T SOFTENING ANTIMONIAL SLAG l [Sb] T Fig. 2 A Generalized Flowsheet for the Pyrometallurgical Refining of DESILVERISING ZINC-SILVER CRUST L e a d [6]. 1 (ZnS) IS>I T 0 brackets indicate a major impurity component DEZINCING METALLIC ZINC i (Bi) T [] brackets indicate a minor impurity component DEBISMUTHISING • BISMUTH DROSS 1 <C.Mg) IZnJb) T FINAL REFINING CAUSTIC DROSS T MARKET LEAD > 99.99% Pb The combined pyrometallurgical/electrometallurgical route is shown in Fig. 3. Here, copper dressing is performed to remove the bulk of the copper as a combination of matte and arsenide - antimonide for further treatment, thus allowing for the removal of some arsenic and antimony. Arsenic and antimony are sometimes reduced further as sodium arsenate - antimonate dross by oxidizing in the presence of caustic soda, because their levels in bullion must be controlled to produce suitable anodes for successful electrorefining practice. 1 Fig. 2 was taken as is from the literature and does not contain inputs required for material balances. [5] Metallurgy of Lead Molten .crude lead f Slag and matte Cu recovery Continuous drossina tumace Decopperized lead I Casting kettle I Anode casting machine Electrolyte Anode 7 3 _ J c I Electrolytic cell Scrap anode Mechanical scraper I Starling sheet kettle i I . Starling sheel machine ^ m Starling sheet Scrap I Filtrate-Deposit cathodes T Wa Fig. 3 A Generalized Flowsheet for the Pyrometallurgical /Electrometallurgical Refining of Lead [22]. Cenlrituge Slime T Precious metals recovery 1 Pig castin p kettle 1 1 Casting machine 1 Pig lead Electrorefining is carried out in either a fluosilicic, fluoboric or sulphamic acid electrolyte and produces a commercial lead cathode product and an anode with an adhering slime [12] \ The purity of the produced lead is usually higher than 99.99% [131. The slimes, representing only 2 to 4% of the anode weight, are treated by a variety of processes to recover silver, copper, antimony, gold, bismuth, and sometimes tin and indium [ 14-21]. Processes that entirely avoid smelting (and its attendant gas and dust treatment systems and associated environmental risks), utilizing hydrometallurgical/ electrometallurgical flowsheets, have also been proposed to replace the current technology [23]. These include (a) the U.S. Bureau of Mines ferric chloride leach process [24] which recovers lead via the molten salt electrolysis of PbCl2, (b) the Minemet Recherche ferric chloride leach process [25] which recovers lead from chloride leach solutions using aqueous electrolysis and (c) the U.S. Bureau of Mines process [26] for leaching lead concentrates in waste fluosilicic 1 Nitric acid media are not suitable because, in the presence of free acid, nitrate is reduced (to nitric oxide gas) at the cathode, preferentially to plating of lead. At higher pH, where the nitrate ion is much more inert to reduction, the electrical conductivity of the electrolyte is much too low for an economic practice. [6] Plant Practice in Lead Electrorefining acid with an oxidant (hydrogen peroxide or lead peroxide) followed by aqueous electrolysis from the fluosilicic acid leach solution. All of these processes have been piloted, but none has been commercialized \ HI Plant Pract ice i n Lead Electroref in ing A detailed description of the Betts Electrorefining Process (BEP) can be found in Betts' book [271 and numerous patents [28-32]. The fundamentals of the process described there remain applicable to all the plants which electrorefine lead nowadays. The BEP process is used in Canada [33-36], China [22,37,38], East Germany [39], Italy [40-42], Japan [43-51], Peru [52-541, Rumania [55.56], Russia [57-591, U.S.A. [60] and West Germany [61-63]. The average annual production of lead by BEP is approximately 1,000,000 tons. Since the production of refined lead in the non-socialist countries (for which good figures are available) is close to 4,700,000 tons per year [64], it can be assumed that up to about 20% of the world lead production is refined by the BEP. Two variations of the BEP, the sulphamic acid and the fluoboric acid processes are operated in Italy 141] and in West Germany [61] respectively. The Betts Electrorefining Process normally utilizes a fluosilicic acid (HaSiFe) electrolyte containing lead fluosilicate to electrorefine impure lead anodes into pure lead cathodes. The fluoborate and the sulphamate processes are identical to the fluosilicate process except for the substitution of the electrolyte. Fluoboric acid has not been used extensively due to its relatively high cost. HBF 4is a stable acid with a good electrolytic conductivity and a high solubility of the lead salt. It is also used in lead plating baths [65-67], lead fluoborate-fluoboric acid rechargeable batteries and in the recovery of lead from spent batteries [68-72]. The sulphamic acid process has two main limitations when compared to the fluosilicic acid process [40,58,73]: firstly, sulphamic acid decomposes rapidly at current densities larger than 100 Amp/m 2 resulting in high reagent replacement cost; secondly, the free acid is a crystalline solid of limited solubility, and limited ionization in aqueous solution, leading to a low conductivity of sulphamic acid solutions (at most, half of the conductivity of equivalent fluosilicic acid solutions). This results in larger power costs in refining. The significant advantage of the 1 Commercialization of any new lead processes faces a lack of need for plant expansion in this industry and so must be justified on the basis of conversion or replacement of existing capacity. [7] Plant Practice in Lead Electrorefining sulphamic acid process is that it is the most efficient process for the removal of tin from impure lead (Sn remains in the slimes) [74-77]. Plants that use the fluosilicic process remove Sn prior to electrolysis by using the Harris process 1781. When anodes containing significant Sn concentrations are refined by the Betts process, tin dissolves with lead at the anode and co-deposits at the cathode. The lead - tin alloy may be sold, or some post treatment of the cathodes is necessary to remove Sn [79]. The wide use of H 2 SiF 6 in lead electrorefining is due to its low cost. Fluosilicic acid is produced as a by-product of the treatment of phosphate rock in fertilizer manufacture [801. Fluorides and silica contained in phosphate rock form fluosilicate and are separated from the fertilizer product. Fluosilicic acid is also produced as a by-product during the dissolution of apatite with sulphuric acid [54,80]. During the electrorefining operation, fluosilicic acid is consumed by entrapment in the anode slimes and by volatilization from the surface of the electrolyte. The acid develops significant vapour pressures through volatile decomposition products according to the reaction, H2SiF6^2HF(g) + SiF4(g) SiF 4and HF are both corrosive and toxic and are removed from the tankhouse atmosphere by adequate ventilation. Table 1 shows some of the operating parameters of various lead electrorefining plants. The wide variation in electrolysis conditions seen in this table does not seem to have a strong influence on the final quality of the refined lead. For example, lead concentrations in the electrolyte can be varied between 30 and 270 g/1 without affecting seriously the refined lead quality. The electrolyte recirculation rates are also varied widely, with no apparent correlation to other operating parameters. Extremely high electrolyte velocities might improve mass transfer across electrode boundary layers, but can also nullify the additive effects, worsening the deposit quality and causing short circuits [81]. Table 1 also shows that the current densities employed in the Betts process fall in the range of 120 to 230 Amp/m 2. Higher current densities have been achieved through the use of galvanodynamic techniques such as current modulation and periodic current reversal (PCR). The current modulation technique consists of decreasing the current density (e.g. from 220 to 160 Amp/m2) in small steps [33,87]. Each constant current density step is determined on the [8] Plant Practice in Lead Electrorefining (a) ft a G Q C 0) u J-l 3 O Va 200 <u o 120 ft IH > o 80 o •3 o 40 JH < 30 60 90 120 ISO 180 Electrorefining Time, hrs a in Q C 9) IH IH U (b) l c , extrapolated curve l c, current modulation program > a a) C 4! o ft IH > o T l O c < 60 90 120 150 180 Electrorefining Time, hrs Fig. 4 Changes in the anodic overpotential value, riA,during lead electrorefining [87] (a) Conventional galvanostatic process (b) Galvanodynamic process in which the cell current is continuously decreased during the refining cycle to fix the value of T | A . basis of an anode overpotential value which increases as the slimes layer thickens and decreases when the current density is reduced. The upper limit for the anode overpotential is usually deterrnined by Bi dissolution from the anode. Fig. 4 shows the current density program that can be applied to the elechrorefiriing circuit without reaching the critical overpotential value for Bi dissolution. The higher average current density possible with current modulation reflects in a shorter electrorefining cycle and higher refinery production. Periodic current reversal (PCR) in lead electrorefining is widely employed in China {381. PCR involves frequent short reversals of the electrolysis current direction 188]. This reduces the concentration polarization in the slimes layer and levels the cathodic deposit by selectively dissolving projections. High current efficiencies, good cathode quality, low electrolyte losses, low energy consumption and a decrease in the number of short circuits have been reported through the use of PCR [22]. A 16% increase in free acid was found in the slimes layer due to PCR. [22] [9] Plant Practice in Lead Electrorefining T A B L E 1 . B e t t s l e a d e l e c t r o r e f i n i n g i n t h e w o r l d Takehara. Japan U3] Chiglrlshlma Japan 1471 Harima, Japan 1*6] Shenyang Smelter, China [sal Electrolyte: Pb. g/1 Total HjSiF,. g/1 Free HjSlFj, g/l Others: rag/1 Additives Consumption: Aloes, g/ton Ligniri Sulphonate, g/ton Glue, g/ton Others, g/ton Temperature, C Circulation Apparatus 236-270 52-61 2-5 Bi. 0.5-2 Cu, 1-2 As, 130-200 Sb 600-1100 28-43 75 135 35-38 90-100 110-115 1000 40-43 1.8 m'/min x 20 m Head 74 104-124 38-58 400 Sb, 800 Fe, 110 As, 28 Zn. 290 Sn. 0.2 Ag 300-450 200-300 32-45 Pressure Tank with centrifugal copper pump 18-25 1.5-1.7 Recirculation Rate, 1/min Add loss. Kg/ton 30 1.6-2.7 40 2.3 30 4 Current: Amp/m1, Cathode Cdf Voltage, V Current, Kw per Generator Current Efficiency. % Energy Consumption Kwh/ton Pb: Electrolysis Mechanical 120-140 0.5-0.6 15000 Amp S70V 95.6-98.7 154-157 17.8-20.7 147 0.47 10000 Amp 9200V 93 143 30 185 0.55 5000 amp ® 50v 13000 amp 8 50v 93 175-180 154-172 0.46 2800-3500 96.30 120-130 30-40 Anodes: Casting Technique Composition Length,Width,Thickness, mm3 Mode of Suspension Life, Days Scrap. % Anode Spacing, mm Weight, Kg Casting Wheel, 18 Moulds .98% Sb. 0.5% Bi. 0.02% Cu. 0.02% Sn. 0.01% As, 67 oz/ton Ag. 0.4 oz/ton Au 1150x1000x25-39 Cast Lugs 8 (half cycle scrubbing) 380-440 Vertical Casting With Water Cooling On Top Of The Mould 1.25% Sb. 0.12% Bi, 0.06% Cu, 65 oz/ton Ag. 0.07 oz/ton Au 1200x800x24 cast lugs 7 30 100 250 Casting Wheel With Water Cooing On Top And Bottom Of The Mold. 15 Mould .5%Sb. 0.13% Bl. <. 1% Cu. 0.05% Sn. 0.05% As 970x740x35 cast lugs 8 26.5 110 280 Casting Wheel .68% Sb. 0.073% Cu. 0.044% Sn 920x620x23 Suspended Lugs 20-25 95 140±3 Cathodes: Starting Sheet Production Technique Thickness, mm Weight, Kg Life, days 0.6-1.0 10-20 4-5 .8 10 7 1 10 4 .8-1. 8-11 2.5 Anode Slimes: Composition Removed After ? days Percentage of Anodes Scrubbing Technique 36.9% Sb. 17.4% Bl, 12.1%Pb. 3.1% Cu. 0.1% Sn. 0.4% As. 8.9% Ag. 0.06% Au 2.4-3.6 Rotating Brush 45% Sb. 4% Bi. 12% Pb. 3%Cu. 7-10% Ag, 3.22 oz/ton Au. 30% H^ O 7 2.9 1.3 12-15% Pb, 8-12% Bl. 0.2-0.4% Te 2.5 1.1-1.4 Tanks: Length, Width. Depth, cm' Number of Anodes, cathodes Construction Materials 500x130x155 42, 43 prefabricated concrete, PVC lining 300x100x150 28. 29 vinyl chloride with steel frame 1150x920x1450 (inner size) asphalt lined reinforced concrete tank 320x75x120 32, 33 Reinforced Concrete with asphalt or PVC lining Pb Annual Production, ton Pb Average Content % 45000 99.999 68000 99.999 27000 99.999 54450 99.99+ [10] Plant Practice in Lead Electrorefining T A B L E 1 . Betts lead electrorefining i n the world (continuation)  Cominco, Canadaiss] "Albert Funk", East GermanytM] Cerro dd Pasco, Peru [881 Kamloka. Japan [so] Electrolvte: Pb.g/l Total H,S1F„ g/1 FreeH,SiF,.g7l Others: mg/1 Additives Consumption: Aloes, g/ton Lignin Sulphonate, g/ton Glue, g/ton Others, g/ton Temperature, T! Circulation Apparatus Recirculation Rate, 1/min Add loss. Kg/ton 75 (60-80) 141 90 (90-100) 8 Bi. 65 Sb, 4000 SiO,. 1.6 Cu, 12 Sn. 5 As, 17 In, 70 Tl 170 (Aloin) 250 (Calcium) 40 (38-43) Centrifugal Pumps 27 (27-45) 2 30-50 120 100 600 35 Storage tank with epoxy lined^gump 15 (32% pure) 75 120 60 600 HF. 5. Sb. 0.5 BL 0 SlOj. solids 550 (Calcium) 550 40 Centrifugal Pumps 12 3 75 130 75 1 Bi. 150 Sb 180 600 35-45 Volte Pump 18.5Kw x 2 40 2 Current: Amp/m1, Cathode CellVoltaBe. V Current, Kw per Generator Current Efficiency. % Energy Consumption Kwh/ton Pb: Electrolysis Mechanical 230 (max) .3-.5 6300 Amp(5 day), 5400 Amp(7 day) 1000 kw 90-95 168 50 185 0.45 150 92 195 90 156 0.5-0.6 Mercury Rectifier 1520 Motor generator 360 90 143 35 135 0.55 20000 Amp O60V 96 165 130 Anodes: Casting Technique Composition Open Mould Casting Wheel 1.2-1.4% Sb, 0.4 %As, 0.15%BL0.05%Cu, 100 oz/ton Ag Casting Wheel, 12 Mould 0.5% Sb. 0.3% Ag. 0.3% Bi, 0.1% Cu, 0.002% Sn Casting Wheel 1.8% Sb. 0.15% As, 1.5% Bi. 0.05% Cu. 0.01% Sn. 0.07 oz/ton Au. 140 oz/ton Ag 940x690x25 Horizontal Casting With Horizontal Mould 0.4% Ag. 0.3% BL 0.1% Cu. 0.6% As, 0.6% Sb Length.Width.Thickness, mm3 864x660x30 730x710x25 (immersed surface) Suspended Lugs 1140x990x20 Mode of Suspension Lugs Designed into Casting 5 25 100 206 Suspended Lugs Shoulder Type Life. Days Scrap, % Anode Spacing, mm Weight, Kg 6 40 130 200 4 49 100 150 6 45 110 Cathodes: Starting, Sheet Production Technique Continuous Drum Casting Mechanized production with on line casting of ribbon Continuous Drum Casting Direct Method Machine Thickness, mm Weight, Kg 1 6.3 1 60-70 (Final Wdght) .6 80 (Final Wdght) .7 13 Life, days 5 or 7 3 4 6 Anode Slimes: Composition Removed After ? days Percentage of Anodes Scrubbing Technique 40% Sb, 16% As, 13% Pb. 2.5% Cu, 2500 oz/ton Ag 5 or 7 3 Conveyed By Monorail Between Rubber Scrapers 15% Pb. 25% Sb. 15% Ag. 10% Bi, 5%Cu 6 1% (solids) pneumatic stripping 28% Sb. 10% As. 24% Bi. 10% Ag. 1.2% Cu. 0.07%^e, 0.52 %Te, 18% Pb, 38.4% HjO. 0.4% SIO, 4 4 Water Sprays 10% Pb, 15% Ag. 15% Bi, l%Cu. 20% As, 20% Sb 6 1.4 Rotating Brush Tanks: Length, Width, Depth, cm3 Number of Anodes, cathodes Construction Materials 268x82x112 24. 25 Asphalt Lined Concrete (old) Polymer Concrete (new) 230x80x120 (inner size) 16, 17 Rubberized steel plates 455x95x130 40, 41 Glue Lined Concrete 500x130x160 43, 44 Vinyl Chloride Resin and Concrete Pb Annual Production, ton Pb Average Content % 144000 99.99 15000 99.99 72000 99.99 30000 99.99 [11] Introduction TV The Anod ic Process A . Introduct ion The Betts process, as practiced by all refineries, depends on the formation of an adherent, porous anode slimes layer during electrolysis. The slimes layer consists of undissolved impurities which are removed mechanically from anode scrap after the anodes are withdrawn \ If the slimes do not adhere to the anode during electrolysis they will settle through the solution and to some extent be mechanically entrained in the cathode deposit. There is no indication in the literature of a lead refining process in which (as in copper refining) slimes fall is encouraged. Further, the recovery of slimes from the bottom of the cell (as in copper refining) is perceived to be more costly. To form an adherent slimes layer, certain elements (mainly As, Sb, and Bi) must be controlled within a narrow composition range and/or ratio in the anode, and the anode casting process must be designed to control the rate of solidification to optimize the microstructure of the cast bullion. B. The phys ica l metal lurgy of the lead anodes The lead anode microstructure that is desired for optimum slimes structure during electrorefining is known as the honeycomb structure, because it consists of uniform size grains of lead surrounded by impurities on the grain boundaries (Fig. 5). As the lead grains dissolve they leave behind a skeleton of slimes which resembles a honeycomb. Any non-uniformity of the matrix will lead to non-adherence of the slimes layer, and any precipitates present in this matrix material will contribute to slimes detachment because of their extra weight. There are four elements present in the lead anodes that seem to exert a strong influence on the anodic process: As, Sb, Bi and Ag. The interaction of these impurities with each other and with lead can be deduced from the available binary and ternary phase diagrams [89-93], which show that both intermetallic compounds and eutectic structures maybe present. Three different slime forming systems have been identified and classified from studies on synthetic anodes [94]. 1 During normal lead electrorefining practice some slimes do fall, and are cleaned out of the cells at very infrequent intervals (months). [12] The Physical Metallurgy of the Lead Anodes Fig. 5 Lead anode microstructure. From an anode currently being used by Cominco Ltd. Chemical composition as described in Table 1. Top view, air cooled side. 1) Impurity phases of the solid solution type (SST): the Pb-Bi system. 2) Impurity phases of the precipitation type (PT): the Pb-Sb system. 3) Impurity phases of the eutectic type (ET): the Pb-As and the Pb-Ag systems. The strength of slimes adhesion to the anode was quantified by Tanaka [94] through observations of slimes fall and slimes morphology. Tanaka summarized the results of these studies with the following relationships: 1) The greatest slimes adherence is obtained when impurity phases of the SST type are present in the anode in concentrations greater than 0.23% wt. A SST concentration lower than this critical value produced a slime that easily slides off the anode. 2) The addition of a third element to the eutectic systems increases significantly the slimes adherence. 3) Water quenching of the anodes increase slimes adhesion particularly in [13] Industrial practice the FT and ET systems. However, the very small slimes particles formed during quenching may also promote slimes detachment and mechanical entrainment in the cathodes. The increase of slimes adhesion by water quenching relates directly to the lead anode solidification rate, which influences the growth and distribution of impurity-containing phases. Especially important are the eutectic forming systems where it is known that the solidification parameters (growth velocity, temperature gradient in the liquid and growth mechanism) and system parameters (volume fraction and impurities content) can lead to anomalous eutectic structures 1951. Such structures have been reported to occur in the following systems (95]1 : Ag-Pb and Ag-Bi: broken lamellar structure type Pb-Bi: complex structure type Pb-Sb: complex regular structure and irregular structure type. It must be emphasized that even though the physical metallurgy of the lead anodes is of great importance to the Betts process, there remains a lack of knowledge in this area. C. Industr ial pract ice As Table 1 shows, the range of anode impurities used in lead refining varies from plant to plant. In every refinery the anode composition is kept vrittiin narrow limits to obtain an adherent slimes layer. The need for production of anodes with homogeneous properties has led to control methods for cooling rates and casting techniques. In addition to the use of a casting wheel, straight horizontal 144-46] and vertical [47] anode casting systems are employed. Fig. 6 shows the straight type horizontal lead anode casting system currently used in Japan. Although the vertical and horizontal casting processes were originally developed to save space (over that occupied by a casting wheel), they were carefully designed to achieve uniform cooling rates during the casting of the 1 A broken lamellar structure consists of a near regular array of "broken" plates and occurs in systems that contain less than 10% of the faceting phase [95]. The complex structure consists of an array of plates that are regular over small areas around a well defined spine [95]. [14] Slimes electrochemical behavior Anode Conveying System Anod* 01 ID i i I I T I J C Casting Mould Lifter Cooling Lifter 1 Fig. 6 Straight Type Horizontal Lead Anode Casting System [44] Electrode Assembling Machine anodes. Such new techniques for anode casting as well as for optimizing heat treatment have been patented by Japanese companies 1961, but no information was found that would indicate the nature of changes in microstructure resulting from these newer techniques. D . S l imes e lectrochemical behavior The slimes layer formed in the BEP undergoes structural and chemical changes during its growth. As the slimes layer thickens, the different phases and compounds present react with the entrained electrolyte creating secondary products. The Ej, - pH diagram for the PbSiF 6-H 2SiF 6 system (ion indicates that both lead fluoride and silica can precipitate at higher pH values. This has been related to the effect of electrolysis parameters on secondary processes (such as these precipitations) that take place witxiin the slimes layer during electrolysis [97-1001. The transport processes within the slimes layer in the context of these secondary reactions have also been the subject of several studies [102-108]. A simple physical model to study the role of the slimes layer during anodic dissolution rate in electrorefining systems was developed by Reznichenko et al. [1091. In this model, the slimes layer was represented by a silver gauze diaphragm (representing the noble impurity) electrically connected to the anode (a highly pure base metal) and placed at a (variable) distance from the anode corresponding to the slimes - electrolyte interface. The distance between the anode and the gauze was varied to simulate the effect of an increasing ohmic drop between the anode and the slimes layer. During electrolysis, concentration gradients normally [15] Slimes electrochemical behavior present in a slimes layer were replaced by a simple concentration difference between the solutions on the two sides of the gauze, and this was related to a modified Nernst equation: where: [A/eJ , /^ concentration and valence of noble metal [Me,],nx = concentration and valence of base metal A<t> = ohmic drop between the base metal and the noble metal gauze = rest potential of the metal to be refined E2° = rest potential of the noble metal Equation 1 shows that the larger the ohmic drop the larger the equilibrium concentration of ions of the noble metal and the larger its dissolution rate. Although this model oversimplifies the different phenomena taking place within a slimes layer, it provides an insight as to the effect of ohmic drop buildup in the slimes layer and the dissolution rate of noble impurities normally left in the slimes. Reznichenko et al. 11091 applied their model to the study of the Cu-Ag system in which they found a logarithmic relationship between the dissolution rate of noble impurities and the ohmic drop potential. Early research on the behavior of BEP slimes has focused on relating the anodic overpotential to the cathode purity [lio.ni]. Among the impurities most closely followed in the cathodic deposit is Bi [112.1131. Even though the BEP has a large selectivity for the removal of Bi, it has been found that towards the end of the electrorefining cycle such selectivity can be lost. It seems that the buildup of concentration gradients and the precipitation of secondary products within the slimes layer can initiate steep increases or discontinuities in the anodic overpotential at a certain slimes thickness. This would produce a large increase in the rate of dissolution of such impurities, and subsequently in the deposition of impurities in the cathodic deposit. Fig. 7 shows how Bi contamination in the cathode increases with anodic overpotentials above a critical value (about 200 mV). This has been recognized as a general behaviour for bismuth in lead refining by the BEP [33,87,110, ill]. On the other hand, the use of periodic current reversal (PCR) [39,98] has been found to increase the minimum anodic overpotential at which noble impurities start to dissolve. ...1 [16] Slimes electrochemical behavior 500 Electrorefining Time, hrs Table 1 shows that the slimes layer weight is only 1 to 4% of the original anode weight; yet, the slimes occupy the whole of the original anode volume. This indicates that the porosity of the slimes layer exceeds 92% and may be as high as 98% (taking into account a density for slimes phases of about half that of the bullion). Concentration gradients in the electrolyte confined within this highly porous layer and the slimes electrochemistry are closely linked. Wenzel et al. [97,114,1151 measured the change in composition of the electrolyte contained in the slimes layer as a function of time and of slimes thickness. Fig. 8 shows the sampling method used by Wenzel, utilizing sampling wells at different distances from the anode surface. Small amounts of electrolyte were withdrawn through these wells at carefully selected times (to avoid perturbing appreciably the system). According to their results, using a range of anode compositions (Bi from 0 to 1.74% and Sb from 0.45 to 3.01%), the more the amount of secondary solidified material (SSM) present in the anode, the steeper the pH and the Pb+ 2 concentration gradient throughout the slimes layer. Also they found that the thicker the slimes layer the steeper the concentration gradients. Fig. 9 shows these changes in concentration for two different anode compositions. Wenzel et al.proposed that [17] Slimes electrochemical behavior 62 Bath level o CO o CM Fig. 8 Dimensions of the anodes used in Wenzel's experiments showing the position and size of the electrolyte sampling wells [97]. All measurements in mm. 4 98 i®:: i : : e - -tj * i -e- -Q-" T T T * 8 due to the pH increase several reactions may occur: SiF6"2 decomposition to SiF 4 and F" (pH > 3); precipitation of Sb 2 0 3 (pH > 4.9) and precipitation of PbO (pH > 7). Table 2 shows the results of chemical and diffraction analysis, which seems to indicate the presence of these secondary compounds within the slimes layer l. From an analysis of the concentration of noble impurities in the entrapped electrolyte, Wenzel et al.were able to conclude that when the SSM exceeded 5%, as determined from the Pb-Bi-Sb ternary diagram, permissible impurities in the anode were too high to obtain an acceptable impurity level in the refined lead. 1 Note that since slimes oxidize rapidly in air, the analysis may indicate oxide phases where metallic phases were present in the in-situ slimes. [18] Slimes electrochemical behavior Fig. 9 Changes with electrolysis time of the relative concentrations of Pb*2 and H* within the slimes layer with respect to their bulk values [97,115]. Bulk electrolyte composition: [PbSiFJ = 0.4 M, [HjSiFJ^ = 0.6 M, T= 35 *C, I = 200 Amp/m2, Stationary Electrodes. Vertical Axis: Pb+2 and H* concentration ratio between the electrolyte sampled within the slimes layer and the bulk electrolyte. (a) Anode with 0.46% Sb and 0.24% Bi (= 1.73% SSM) (b) Anode with 0.92% Sb and 0.24% Bi (= 3.80% SSM) Note: No extrapolation of the inner electrolyte concentrations at zero slimes thickness done here. Table 2 Chemical Composition and X-ray Diffraction Analysis of the Lead Anode Slimes [97] Sample No. Anode Composition %wt,(rest Pb) Slimes Chemical Analysis %wt X-ray Diffraction Analysis Pb Sb Bi F Si 1 0.46% Sb, 0.24% Bi 56.98 7.62 3.95 11.97 6.66 PbO, SbaOg, PbF2, Bi 20 3 2 0.46% Sb, 0.24% Bi 58.02 9.40 4.28 14.09 3.33 PbO, Sb203, PbF2, Pb4Si04. BtjOg 3 0.92% Sb, 0.24% Bi 56.57 6.81 5.55 11.27 6.65 PbO, Sb203, PbF2, BiaOg 4 0.92% Sb, 0.24% Bi 53.77 9.37 9.20 12.22 4.19 PbO. Sb203. PbF2, BisOa [19] Slimes electrochemical behavior Wenzel's X-ray diffraction analysis on the slimes products agree with the findings of Isawa et al. 1116,117], who studied the slimes composition of synthetic and industrial lead anodes and found the presence of the following compounds1 Metallic Bi: In the Pb-Bi, Pb-Bi-As, Pb-Bi-Sb, and Pb-Bi-As-Ag systems Metallic As: In the Pb-As, Pb-Bi-As, and Pb-Bi-As-Ag systems Metallic Ag: In the Pb-Ag and Pb-Bi-As-Ag systems Also the presence of the Bi-Sb solid solution, of the e and e' phases of the Ag-Sb system, and of water soluble As and Sb (identified as As 20 3 and of Sb203) was found in some of the above mentioned systems and in the slimes obtained from industrial anodes [Ii6,ii7]. One compound that has been difficult to characterize is AgaSb 194], whose presence has been detected in both synthetic and industrial lead anodes. The morphology of this compound has been found to be a function of the anode cooling rate and of the electrolysis conditions. The electrolyte used in lead electrorefining contains impurities whose concentration ranges from a few ppm and several g/1, and have their origin in the anode from which they are dissolved (i.e. Cu + 2 , Sn+2) or from the acid manufacturing process (i.e. phosphorus species). Their steady state concentrations in the electrolyte depend on the electrolysis parameters and slimes thickness. They can affect both the anodic and cathodic processes through changes in fundamental electrochemical parameters such as the exchange current density [Q, the symmetry factor (a), and the electrical double layer capacity (CdJ \ Measurement of these parameters usually involve transient electrochemical techniques, such as polarization scans, current interruptions, and AC impedance studies. Miyashita et al. [118-1231 have studied extensively the influence of minor impurities and addition agents in the electrolyte used in lead refining. These studies focused on the determination of the fundamental electrochemical 1 The term electrical double layer is used to describe the arrangment of charges and oriented dipoles constituting the interphase region at the boundary of an electrolyte [144, p.630] The exchange current density, i0, is a measure of the rate of equilibrium potential and sensitivity to interference [145, P.IO] The symmetry factor, a, determines what fraction of the electrical energy resulting from the displacement of the potential from the equilibrium value affects the rate of electrochemical transformation [144, P.923] [20] Slimes electrochemical behavior parameters [i^, e.d.l., and a) as a function of Sn + 2, Fe+ 3, Zn + 2 and glue, using a single current step transient method [118]. He found that under an oxygen atmosphere the presence of the above ionic species increased the anodic overpotential value. Thus, they may inhibit the dissolution of some noble species including lead. F i g . 10 Lead specific weight loss (corrosion) as a function of the immersion time in a2M Pb(BF4)2-l M HBF 4 solution in the presence of 0,2,5, and 10 mM of Bi*3 [66]. 50 100 150 200 Immersion Time, hrs When noble impurities present in the lead anodes transfer to the electrolyte they can be redeposited by cementing on less noble elements. While such redeposition is obscured during anodic dissolution, it can be inferred from corrosion measurements in the absence of a current. For example, the weight loss rate for a lead sample in the presence of dissolved bismuth has been observed in the HBF4-Pb(BF4)2 system [661. Fig. 10 shows how Bi concentrations as low as 2 mM enhance the corrosion rate of lead. During the dissolution of the lead anodes in the BEP, bismuth and other noble impurities accumulate in the proximity of the slimes/bulk electrolyte interface as well as in the bulk electrolyte [39,124]. Since these noble impurities will deposit on the cathode at their limiting mass transfer rate, the permitted [21] Additives control and electrochemistry electrolyte concentration is related to cathode purity specifications (0.12 mM of bismuth will typically lead to 10 ppm Bi in the cathode! 124]). They can be removed by one of two methods: a) Continuous cementation [125.126] through a column filled with lead particles (Fig. 11). b) Electrodeposition in a separate electrolysis circuit [124]. The purified electrolyte is then sent to the main electrolyte stream. This method is being used in Japan [43]. The majority of plants that electrorefine lead do not purify their electrolyte, but rather operate under conditions where the dissolution of noble impurities from the anode is limited to tolerable levels. Fig. 11 Continuous purification o f electrolyte v i a purification column [125,126]. Continuous Purification of Electrolyte via Purification Column V The Cathodic Process A . Addi t ives contro l and electrochemistry In the absence of additives, lead deposits with a very small overpotential, and tends to form rough, porous deposits or dendrites that result in short circuits. To obtain deposits that are flat, smooth, and free from projections, special reagents are added to the electrolyte. These "addition agents" increase the cathodic overpotential (actually called "inhibition"), and change the kinetic parameters (to, a, and e.d.l.) under comparable electrolysis conditions [120-123]. [22] Starting sheet technology Polarization measurements have been used for controlling and monitoring the concentration of additives in lead electrorefining circuits [81.127-129], as well as for screening of additives in the electrolytic refining of Cu and for the testing of impurity levels in the electrowinning of Zn [130-135]. A polarization technique for determining lignin sulphonate in lead plating baths has also been described [136]. Long term studies and years of industrial practice, especially by Cominco researchers [81,129] have led to a sufficient understanding of the levelling mechanisms of lignin sulphonate and aloes, to permit the use of polarization measurements for controlling the concentration of these species in the industrial electrolyte for lead refining. This additives control is achieved by keeping the cathode polarization voltage (C.P.V.) within preset limits, and adjustments are made by either new additions or by regeneration (in the case of aloes) with a thiosulphate salt [128]. The level of additives present at a given time is directly related to the C.P.V. B. S tar t ing sheet technology The cathode starting sheets used in the BEP are usually cast on a rotary drum casting machine. The stiffness of these sheets is increased by adding approximately 15 ppm Sb to the melt and by impressing wrinkles on the cathodes right after they are produced [791. Procedures to avoid dross incorporation in the lead cathodes have also been developed [137]. In this section of the electrorefining process high levels of automation have been achieved [138]. C. Ce l l electrolysis parameter opt imizat ion The overall electrorefining process has been studied using statistical correlations of some of the variables measurable in an operating plant [39.54.98]. To optimize the electrolysis parameters when the BEP is run at high current densities (> 200 Amp/m2), factorial design of experiments at three levels for four variables has been used by Lange et al.[98]. They varied PbSiF6 and H 2SiF 6 concentrations, temperature, and current density, at constant values of addition agent (glue), anode composition, cell geometry, and electrolyte recirculation. The influence of these parameters on the average anodic and cathodic polarization, on the cell voltage, and on the specific energy consumption was obtained by employing regression analysis correlations. In addition, changes in these parameters were correlated with the cathode quality and appearance as well as [23] CeH electrolysis parameter optimization with the consumption of glue. The optimum electrolysis parameters found for a current density increase (from 200 to 300 Amp/m2) were a Pb + 2 concentration of 60 g/1 (down from 80 g/1), a glue addition maximum of 1500 g/ton Pb (up from 1250 g/1), a free H 2 SiF 6 content of 120 g/1 (no change) and an electrolyte temperature of 35 to 40°C. Under these electrolysis conditions, Lange et al. found that Sb and Bi slimes layers could be subjected to anodic polarizations as high as 280 mV without serious impairment of the cathode quality. 140 120 cO 100 CO ti 80 c u > O 4 0 o • r H T3 20 O ti - : ; : (*) i . . . i . . . i . . . i . . . i . . . Fig. 12 Influence of the cycle length and current reversal ratio on the anodic overpotential value during PCR [39]. Bulk composition and temperature: [PbSiFJ = 0.29 M, [HjSiFj] = 0.84 M, T= 37.5 ' C . W^f—1 = = 10 sec < * ) ^ = £ r ^ = 20.ec 1 backward 1 20 40 60 80 100 120 140 Electrorefining Time, hrs Optimization of the BEP through half cycle anode slimes scrubbing and cathode exchange was also investigated by Lange et al. [98]. Not only did the specific energy consumption decreased by the implementation of this procedure, but highly pure cathodes were assured by avoiding anodic overpotentials in excess of the preset limits for impurities dissolution. On the other hand, the exchange of cathodes and the half cycle scrubbing of the anodes incorporates labour increases making implementation difficult. The use of this technique is necessary when anodes containing high impurity levels (>5%) are to be treated. For example, in Russia [57], lead anodes containing as much as 15% Bi are scrubbed every 48 [24] Bipolar refining of lead hours during the 6-day long anode cycle. In addition to this, cathodes are exchanged daily to avoid short circuits and to obtain a deposit of acceptable purity [57]. Lange et al. also studied the use of PCR in the BEP. Fig. 12 shows the anodic overpotential dependance on the PCR parameters. Thiet [39] found that the use of PCR decreased the anodic overpotential values. The reduction in the anodic overpotential values did not reflect in lower PCR energy consumption probably because it was offset by unproductive energy consumption during the reverse current phase of the cycle. Thiet also showed that the quality of the PCR cathode deposits was very high [39]. D. Bipolar ref in ing of lead Among other alternatives to optimize the lead electrorefining process, the use of a bipolar configuration looks most promising. In this configuration only the terminal electrodes are connected to the source of current. Between these electrodes a large number of bipolar electrodes can be incorporated. One side of these electrodes will corrode anodically, while pure lead will deposit on the other side. The Impurities will be left behind as a slimes layer on the anodic side. The advantages of operating the BEP in a bipolar mode include PCR, C.P.V., optimum lead and free acid contents, and the use of jumbo electrodes (~4m2, possible because there are no bus-bar connections)\ The process has been operated in a pilot plant where it proved to be superior to the parallel process [1421. The rationale for the current use of the parallel system is that a high economic investment is required for the substitution and implementation of the bipolar process. If new plants to electrorefine Pb are to be constructed in the future, very likely they will be assembled on the bipolar configuration. 1 In the bipolar mode by-pass currents are reduced by increasing the area of the electrodes so that the ratio of bypass to electrode area in the cell decreases. [25] Chapter 2 Fundamentals of the E lect rochemica l Measurement Procedure Early in the development of this project it was found that the form of ionic concentration gradients within the lead anode slimes layer needed to be studied. To study these concentration gradients without causing major disruptions to the system, "in-situ" experimental techniques were considered. Among these, transient electrochemical techniques appeared to be particularly advantageous and consequently were used extensively in this work. The study of the electrochemical response of typical lead anodes was complemented by measurements on the physico-chemical properties of H 2SiF 6-PbSiF 6 electrolytes. What follows in this chapter is a description of the electrochemical parameters germane to this work, and of the transient techniques that were used. I. Components of the Anodic Overpotential The anodic overpotential was measured by following the difference in potential between the lead anode ("working electrode") and a suitable reference electrode. A high purity lead wire located within a Luggin capillary and contacted with cell electrolyte was chosen as the reference electrode. Its use was possible because of the high reversibility of lead in the H 2SiF 6-PbSiF 6 electrolyte system. Furthermore, the amount of current that passes through the reference electrode is limited to the current drain of the meter (a few nanoamperes). The "anodic overpotential" \ T\A, measured by such an electrode would also be free of any junction potential between its tip and the slimes/electrolyte interface provided the bulk electrolyte is well mixed. In the present work (unless specified) all potentials are given with reference to such an electrode. The third electrode (a lead foil counter electrode) is required to complete the electrical circuit. The electrochemistry of this counter electrode is of no importance to the anodic processes. Fig. 1 shows a simplified view of this three electrode arrangement. The anodic overpotential measured under constant current conditions increases continuously as the slimes layer thickens during the refining cycle. The build up of concentration gradients in the proximity of the anode/slimes interface 1 This "anodic overpotential", r\Al or potential difference between the anode and the reference electrode, includes an ohmic component, x\a, and long range potential gradients as well as interfacial overpotential components. [26] changes the value of T|A mainly through changes in its migration and concentration overpotential components. Additionally, an ohmic contribution is included in this TJa measurement. F ig . 1 Electrochemical Cell Arrangement The importance of the ohmic component in electrochemical measurements is evident by the number of studies that have been conducted in order to assess its effect [1-91. According to Vetter [ioi the ohmic component is not a real overpotential because its presence does not have any influence on the rate or type of electrochemical processes under investigation. Ohmic drop or resistance polarization can be separated from migration and concentration overpotentials only in regions where the electrolyte composition is uniform as between the reference electrode tip and the slimes/electrolyte interface. Concentration overpotential, ric, is the Nernst potential generated due to activity differences of the electroactive ion. Its presence is primarily due to the limitation in the ionic transport of species moving from or towards the working electrode surface. When this concentration overpotential occurs in the presence of concentration gradients of non-electroactive ionic species, a migration potential [27] gradient \ AO, is generated. The migration potential arises concurrently to TJC. Thus, by subtracting the value of r|Q from the r\A measurement, an overpotential value consisting of T]C and AO is obtained. An additional contribution to the anodic overpotential, the activation overpotential, t|ac, is a function of the transport rate of charge carriers across the electrical double layer. The larger the hindrance for this transport process, the larger T|A C will be. By measuring the difference in potential between the working electrode and a point located very near its surface, the value of T]AC is obtained. The presence of other contributions to T|A (crystallization, reaction) will not be described here, as they are unimportant for lead. Vetter [io] establishes the conditions upon which these components are to be taken into consideration. We assume that the contributions of these overvoltages to T|A are either negligible or can be incorporated within T]AC or r\c. n. Transient E lect rochemica l Techniques The amount of information that non-transient electrochemical techniques are able to provide is rather limited [ 11-14]. Significant enhancements in electronics in the last 25 years have supplied the electrochemist with a wide range of transient techniques. Reviews on the use, applications, and limitations of these techniques are available [11.15-21]. Among these transient techniques, current interruption and AC impedance were used extensively in this work. These techniques were chosen due to their potential for resolving the T\A components. A . Current interruption techniques Current interruption techniques go back as far as 1937 [221. The original driving force for their implementation was to obtain the value of the uncompensated ohmic drop, T| N . Further research has demonstrated that by studying the polarization decay curves and their dependance with time, kinetic and mass transport information can be obtained [23-30]. When several phenomena are superimposed, interpretation of the current interruption decay curves is not straightforward. For example, Newman [7,31] and other researchers [3,27,32] have stressed the fact that upon current interruption, internal currents may not be 1 The migration potential, <t>, can be calculated by solving the Nernst-Planck flux equations. Appendixes 1 and 2 describe how these equations can be solved. A4> can be neglected in the presence of a substantial excess of supporting electrolyte. [28] halted instantaneously. This will be the case if contained electrical double layers are not uniformly charged \ The relaxation time required for the double layer to equilibrate can be estimated from the following relationship 2 : TD = . . . 1 * K The discharge of the double layer can also take place through Faradaic reaction. The time constant for this reaction can be estimated using the following equation: T/ Ft. - Z The third major process that can take place upon current interruption is the relaxation of concentration gradients. The time constant for this unsteady state process can be estimated from the following relationship: X" = D - 3 Upon disappearance of the external current, r\a will vanish almost immediately (in < IO"2 msec) [3413. On the other hand, residual charge arrangements in a supposedly uniform charged electrolyte may affect the rate at which i]a vanishes. Typical values for xf and xR are close to 0.5 msec [7]. Thus, the electrical double layer will be equilibrated and discharged in approximately 1 msec. After this time, concentration gradients will relax. The larger the time constant the longer it will take for the system to reach its open-circuit or equilibrium potential. Another process that can take place upon current interruption is the dissolution and/or re-precipitation of secondary products within the slimes layer. This process may originate one or several potential arrests [351 *. 1 Double layers may not be uniformly charged if the difference in potential at the electrode/solution interface is not uniform. 2 L is the characteristic length that controls the current distribution [20,33]. 3 In electrolytes of uniform composition, potential drops upon current interruption have time constants of the order of 7x10* msec . 4 These potential arrests are sometimes referred as Flade potentials. [29] An estimation of the time required to relax the concentration gradients present within the slimes layer can be done by using Eq. 3. Assuming that the entire slimes layer can be considered as a "nearly" stagnant environment and that D is of the order of 10"5 cm2/sec, we get for a 0.1 cm slimes thickness a value of V of 1000 sec. This shows that long relaxation times are required for the levelling of the concentration gradients present within the slimes layer. Thus, current interruption for short periods of time (~ 0.3 sec) during the galvanostatic dissolution of lead anodes was not expected to change the system appreciably. The information provided by analyzing short interruptions was supplemented by following, for selected cases, the decay in potential over extended periods of time (several days). The experimental set-up (using a Wenking potentiostat) allowed the decay potential to be followed from about 0.5 msec after current was interrupted. Oscilloscope traces at shorter times after current interruption showed that the potential at time zero could be obtained by linear or exponential approximation of the decay curves in the vicinity of the current interruption. These studies resulted in a semi-quantitative picture of the transport processes taking place within the lead anode slimes layer. It has been shown [1,36-39] that analysis of the potential decay curves obtained upon current interruption is more easily accomplished when the time-domain data 1 are transferred into the frequency-domain through the use of Fourier transformations. Both analytical and numerical transformation of the time-domain generated data can be performed. Matching transformations on equivalent electrical circuits selected by trial and error must be found to interpret the data in terms of electrical components such as resistors and capacitors. The input and output signals are subjected to Fourier transformation (i.e. one-sided Laplace transformation) and a transfer function is obtained. In the case of a current interruption experiment, both potential, e(t) and current, i(t) are Fourier transformed to obtain the system impedance from their ratio. Appendix 3 shows how the response to current pulses of a simple RC circuit was analyzed in the frequency domain. Numerical Fourier transformation of some of the current interruption data generated in this work was carried out by using the Fast Fourier 1 The time domain data refers to the potential and current transients dependance with time. When these data are Fourier transformed, the frequency spectrum of the system is obtained (time-domain o frequency-domain). For a more complete description of this transformation see appendix 3. [30] Transform (FFT) algorithm [40-43]. The software packages used in this work incorporate this algorithm1. Knowledge of the FFT algorithm, its application range and limitations, are required to understand the data generated. Appendix 3 reviews some of the relevant steps required for implementing the Fourier transformation. B. AC impedance techniques The use of AC impedance to study electrochemical systems spans over a period of more than 100 years. Kohlrausch, as early as 1854 [44] proposed its use for the determination of the electrical conductivity of electrolytes. Later, with an AC bridge, he obtained the conductivities of a large number of electrolytes [45], Contributions by Warburg [46] and Randies [47] set the theoretical and experimental foundations from which AC impedance measurements have evolved. Nowadays, the technique is routinely used for the analysis of a wide range of electrochemical systems [48-54]. Electrical engineering theory has been heavily used by electrochemists to interpret the results, and reviews on its characteristics, advantages, limitations, and implementation can be found in the literature [14.19,48.55-57]. In a typical AC impedance experiment, a small sinusoidal signal (either voltage or current) is applied to an otherwise DC system. The AC output response is followed as the frequency of the input signal is changed. The ratio of the input and output signals is known as the transfer function [58,59]. Thus, the impedance, Z(jco), is a transfer function. The system response can be assumed to be linear by limiting the amplitude of the input signal to a few mV (or a few mA). The possibility of obtaining an electrical analogue circuit by using AC impedance is a strong driving force for its application. Knowledge of this analogue allows the modelling and prediction of the output signal when the input is known. The linkage between current interruption and AC impedance techniques arises through the use of the transfer function. Theoretically, upon Fourier transformation of the current interruption data, the transfer function obtained should match the one obtained by AC impedance. That this connection exists is shown in appendix 3. On the other hand, experimental artifacts make the analysis of data generated in the time-domain valid only for a very limited frequency range 1 Asyst* version 2.10 and Asystant* version 1.02. [31] [40,60-62]. In addition to this, the time span required for an AC measurement is several orders of magnitude larger than the one required for a current Interruption measurement. AC impedance is the best technique available for the determination of i\a [64]. The resistance polarization value obtained using this technique should coincide with the value obtained from current interruption experiments [65]. Kinetic and mass transfer information can also be readily obtained using this technique [53,66-68].On the other hand, most of the impedance theory developed so far has been focused on the study of very dilute solutions [191 and solid electrolytes [16]. / . Aims and limitations of the AC impedance studies AC impedance studies are aimed at finding an electrical analogue that can be used to study how different physico-chemical (and in some cases mechanical) parameters affect the response of a system given a certain input function. A comprehensive analogue model ought to be able to incorporate as many parameters as variables are in the system. It also should predict the output of the system given the characteristics of the input function. Like any other mathematical model, an analogue model is established using assumptions which are based on prior knowledge of some of the fundamental properties of the system. A wide variety of electrical analogue circuits can match the response of the system but only a few could represent the physico-chemical process involved (without accounting for different interpretations for the same circuit). An indication that the model is appropriate is that the electrical parameters ought to change as the physical variables are altered. Thus, the main limitationoi the impedance studies is a function of how ambiguous are the parameters involved in the circuit. Other limitations arise in unstable systems in which the parameters change faster than the AC measurement, decreasing the frequency in which the AC spectra can be accurately measured. The search of an electrical analogue that matches the response of the system has also been extensively pursued using DC transient techniques such as current interruption [8,69,64] and small amplitude cyclic voltammetry (SACV) [70,71]. DC and AC studies have been used concurrently to better characterize the system under study [15,72]. In the Betts process, AC impedance measurements were made across the slimes layer at preset slimes thickness. Changes in the impedance values were related to concentration gradients, precipitation of secondary products, and dissolution of noble compounds. From these studies, kinetic parameters [32] (exchange current densities, double layer capacities) were determined. Linearity in the system response was assumed by limiting the amplitude of the input sinewaves to very small values (less than 5 mV R.M.S. for potential controlled experiments and less than 35 Amp/m 2 R.M.S. for current controlled experiments). r\a values were obtained from both AC impedance measurements and a current interruption routine built into the Solartron electrochemical interface. The search of electrical analogues that match the response of the system and have physical meaning is strongly pursued in this thesis. [33] Chapter 3: Exper imental Procedure I. E lec t rochemica l Exper iments A. Electrochemical cells 1. Beaker Cell A I L wide mouth (0=11 cm) polyethylene 1 beaker was adapted to function as electrochemical cell (Fig. 1). This cell was used to study the anodic behavior of small working electrodes (i.e. working electrodes whose geometric area 2 was between 1.4 and 3 cm2). A Lucite tight cover was used to hold the electrodes in a fixed position and to avoid loss of water due to electrolyte evaporation. The cover had holes through which the electrical connections to the electrodes and the tubes used for electrolyte sampling were taken out of the cell. Previous to each experiment the cell was thoroughly washed several times using deionized water. After the cell was dried, the electrodes 3 were firmly positioned In the cell. Then the electrolyte was introduced to the cell through a plastic tube. During the experiment, this tube was used to obtain bulk electrolyte samples. Electrolyte was added only at the beginning of the experiment in volumes that ranged between 320 and 400 ml. Mixing of the bulk electrolyte was by either magnetic stirring4 or recirculation5,6. Electrolyte recirculation provided the best experimental reproducibility and was preferred to magnetic stirring. After the electrodes were positioned and the electrolyte introduced, the cell was covered and sealed using generous amounts of silicone rubber 7 . Only after the silicone rubber had "dried to touch" (i.e. after approximately 2 Hrs.) was the cell immersed in the constant temperature water bath. 1 H2SiF6 containing solutions can etch glass [1]. Thus, glass laboratory ware was avoided as much as possible. 2 Geometric areas do not consider surface rugosities. 3 Electrodes were immersed in a 10% Vol HN03 solution and washed with deionized water prior to their introduction to the cell. 4 Magnetic stirrer bar coated with Teflon* (1=2.54 cm, 0=0.95 cm) spinning at low speed by using a Tek-stir magnetic stirrer model S8250-1. 5 As illustrated in Fig. 1 electrolyte was recirculated through plastic tubes located at opposite sides of the cell and at different electrolyte depths. 6 Electrolyte recirculation rates were between 5 and 6 ml/min. A Masterflex pump catalogue No. 7553-20 and Masterflex Tygon tubing catalogue No. 6409-14 were used. 7 100% silicone rubber, RTV Silastic 732. [34] Rectangular cell F i g . 1 Assembly used in the experiments performed with the beaker cell (A) W o r k i n g electrode (B) Counter electrode ( C ) Reference electrode (D) C u wire (E) Plastic tube used to withdraw bulk electrolyte samples (F) Electrolyte recirculation inlet (G) Electrolyte recirculation outlet. 2. Rectangular cell Rectangular Lucite cells were used to study the electrochemical behavior of working electrodes whose exposed geometrical area ranged between 30 and 40 cm2. Fig. 2 describes the dimensions and design features of this kind of cell \ A Lucite tight lid was used to cover the cell. In this lid, holes of appropriate size were drilled. Through these holes, the electrical connections to the electrodes and the tubes used for electrolyte sampling were taken out of the cell. Bulk electrolyte was recirculated2 using lateral cell inlet and outlet facilities. 1 Cell dimensions were modified according to the characteristics of the experiment. Fig. 2 shows the actual dimensions of the electrochemical cell employed in experiment LC2 to be discussed extensively in Chapter 4. 2 Electrolyte recirculation rates were between 5 and 6 ml/min. [35] Rectangular cell Electrolyte from the top of the cell was brought to the bottom continuously. During the electrolysis of lead electrodes, electrolyte samples taken at different cell locations showed no significant concentration differences. Fig. 2 Assembly used in the experiments performed using the rectangular cell (A) Working electrode (B) Counter electrode (C) Reference electrode (D) Cu wire (E) Plastic tube used to withdraw bulk electrolyte samples (F) Electrolyte recirculation inlet (G) Electrolyte recirculation outlet (H) Lucite side walls (I) Lucite strips. Drawings are not scaled. All measurements in mm. (A) Cell tridimensional view (B) Lateral view (C) Frontal view. Fig. 2 shows the position of the two small Lucite strips used to support the anode. The presence of these strips allowed the electrolyte entrapped within the slimes layer to flow downwards. Additionally, wide Lucite strips were used to center the anode in the cell and to improve current distribution. Electrolyte volumes were fixed at the begirining of the experiment and ranged between 300 and 400 ml. When bulk electrolyte samples were withdrawn from the cell, electrolyte of the initial composition was added to the cell to maintain constant the electrolyte volume. As in the beaker cell case, after the electrodes were placed and electrolyte added, the lid was fitted to the cell and sealed afterwards using silicone rubber. Again, only after the silicone rubber had dried to touch, was the cell immersed in the constant temperature bath. [36] Materials B. Electrodes 1. Working electrodes (a) Materials Working electrodes were produced from pure lead 1 and from typical lead bullion anodes provided by Cominco Ltd. Typical anodes used in the Betts electrorefining process were taken from the anode refining wheel and some of its sections were sent to UBC. No particular details regarding the anodes cooling rates or about the pyrometallurgical steps previous to their casting were provided. According to Cominco, the anodes were cast under normal operating conditions and that's where the term "typical" comes from. The electrochemical studies here pursued required the anodes to form strong and adherent slimes. As was later found, this set of anodes did produce slimes which did not fall from the electrodes and remained attached to them during the dissolution stages. Anode "A" A.1 Anode " B " B.1 B.2 Fig. 3 Sections of the lead bullion anodes used to prepare working electrodes. Fig. 3 shows the anode sections that were cut from the anodes and sent to UBC. The anode A strip was sent in July 1986. This strip was cut in smaller pieces and from the area indicated in Fig. 3A, electrodes were produced. Sections of anode B were sent in March 1987. From anode B, electrodes were produced mainly from its center part (section B- l shown in Fig. 3B). The working electrodes were prepared so as to study the electrochemical behavior of the 1 Pure lead working electrodes were made out of Tadanac ingots (Pb >99.99%) [37] Pure lead working electrodes "mould" cooled anode face and the "air" cooled anode face. Thus, electrodes were fabricated by cutting perpendicular sections of the anodes. Depending on the type of electrochemical cell employed, different electrode sizes were used. (b) Beaker cell Small working electrodes whose exposed geometric area ranged between 1.4 and 3 cm 2 were prepared as follows: (I) Pure lead working electrodes Electrodes were made by cutting small pieces of the pure lead ingot. These pieces were machined to form rectangular shaped electrodes. The machining marks on the electrode sides were removed by pohshing the electrode using the 600 grit. The electrical contact was incorporated by soldering a Cu wire to the back of the electrode. Subsequently, the electrode was encapsulated with epoxy resin 1 exposing the electrode surface by polishing away the unwanted resin. The exposed surface was polished again using the 600 grit. (II) Lead bullion working electrodes Rectangular shaped electrodes were cut and machined out of the anode sections previously described. The electrode face to be exposed directly to the electrolyte (either the air cooled or the steel cooled face), was not machined. The deformed layer produced by the cutting and machining operations was removed by polishing2. Electrical contact was made by either soldering a Cu wire to the back of the electrode or by pressure contact. The later technique was preferred due to the fact that the soldering process through heating, may affect the phases originally present in the anode. The pressure contact electrical connection consisted of manually pressing a bundle of the Cu wire strands to the back of the electrode and using acrylic tape to sustain the contact. The electrode was then mounted in epoxy resin and the unwanted resin was polished away. The exposed electrode surface was polished with the 600 grit. (c) Rectangular cell Medium size electrodes whose exposed geometric area ranged between 30 and 40 cm 2 were prepared as follows: 1 Acrylic plastic resin: Quick mount® self-setting resin 2 The deformed layer was measured metallographically and in some cases was as thick as 0.1 mm. [38] Relgrence electrodes (I) Pure lead working electrodes Electrodes were cut and machined out of pure lead ingots as in the beaker cell case. The machining marks were removed by polishing using the 600 grit. Electrical contact was made by using two Cu rods. These were screwed-in to the top of the electrode. One of these rods was used to carry current and the other to measure the electrode potential. The lateral electrode surfaces were covered with silicone rubber. The bottom, top, and one of the electrode faces were not coated with silicone rubber. Thus, only the bottom of the electrode and one of its sides were directly exposed to the electrolyte. (//) Lead bullion working electrodes Electrodes were prepared out of the anode sections in the same way pure lead anodes were produced. To sample the electrolyte present in the slimes layer, and to follow the inner slimes electrode potentials, holes were drilled in top of the anode \ Though these holes, plastic tubes were inserted. These tubes were used either to extract small amounts of electrolyte 2 or to insulate the pure lead wires. Additionally, one of these holes was used to insert a Pt wire. This wire was used to study the electrical conductivity of the slimes layer3. The Pt wire did not have any insulation and during some experiments it was moved to other locations where slimes were present. 2. Reference electrodes A pure lead wire 4 was used to measure the difference in potential between the bulk electrolyte and the working electrode. This wire was mounted in a plastic tube (0=2 mm). The tube was bent at one end, and a plastic tip 5 was inserted there. Fig. 4 illustrates this Luggin-Haber reference electrode arrangement. The reference electrode tip was placed between 2 and 5 mm away from the original position of the working electrode. This distance remained constant during the 1 Size and location of the holes is provided when specific experiments in which electrolyte samples were taken and inner potentials obtained are analyzed. 2 From the inner slimes layer 100 ul of electrolyte were slowly extracted (over a period of 3-6 hours). A 100 u.L Unimetrics removable needle syringe was used to withdraw the inner electrolyte samples. 3 The difference in potential between this wire and the anode was used as an indication of the slimes layer conductivity. 4 Johnson Matthey, 99.95% Pb, 0=1.0 mm. 5 Eppendorf pipette tips 5-100 |xL [39] Counter electrode experiment. The tip of the reference electrode was located facing the geometrical center of the working electrode. After the cell was assembled and the bulk electrolyte had penetrated the reference electrode compartment, this was sealed by using silicone rubber. Thus, the electrolyte surrounding the lead wire had the same composition, temperature, and atmosphere as the bulk electrolyte. A / Fig. 4 Detail of the Luggin-Haber reference electrode arrangement B / (A) Pure lead wire / (B) Plastic Tube / (C) Eppendorf plastic tip. 0!=1.3±O.2 mm, 02=0.5+0.2 mm c 1 .. « ,*«H J In the experiments1 in which the difference in potential between the electrolyte solution present in the slimes layer 2 and the working electrode was followed, pure lead wires were also used. Plastic tubes (0=1.3 mm) were inserted in the previously drilled holes up to @2 mm away from the bottom of the holes. Then, the lead wires were inserted up to @2mm away from the lower end of the plastic tubes. This particular set-up was chosen to avoid prohibitive corrosion of the lead wires during the dissolution of the working electrode. 3. Counter electrode Pure lead foils 3 were used as counter electrodes. In the beaker cell case the lead foil surrounded the working electrode 4 whereas in the experiments which 1 This sort of experiments were only carried out using the rectangular electrochemical cell in which the size of the working electrode was large enough to incorporate these potential measuring probes. 2 The electrolyte entrapped within the slimes layer will be called "slimes electrolyte". 3 Lead foils whose lead content was greater than 99.95% 4 The working electrode was concentrically placed with respect to the counter electrode. [40] Electrolyte used the rectangular cell, the lead foil was located facing the working electrode and @42 mm away from it. In both cases, the area of the counter electrode was larger than the area of the working electrode. This was done to improve the current distribution and also to avoid formation of dendrites. When the beaker cell set-up was used, the geometric area of the counter electrode was between 10 and 15 times larger than the exposed geometric area of the working electrode. In the experiments performed using the rectangular cell, counter electrode areas were between 1.2 and 1.4 times larger than their working electrodes counterpart. In all the experiments, electrical contact was incorporated by soldering a Cu wire to the counter electrode. The place where the electrical contact was made was isolated from the electrolyte by a silicone rubber coating. C. Electrolyte Technical H 2 S i F 6 1 obtained as a by-product of the treatment of phosphate rock [2] 2 was neutralized with either PbC0 3 or PbO to prepare mother electrolyte solutions. The reactions that take place upon neutralization of the acid are: H2SiF6+PbC03 => PbSiF6 + H20+C02 . . .1 H2SiF6 + PbO => PbSiF6 + H20 ...2 Upon neutralization, several insoluble compounds precipitate3. These precipitates were removed by filtering using Whatman paper #40. After this operation, a nearly transparent electrolyte solution is obtained. Depending on the acid strength of this solution, S i0 2 nH 2 0 colloidal particles may be observed 13-7] *. 1 Acid composition: 2.03 M H2SiF6 and 0.40 M Si02. This acid was provided by Cominco Ltd. 2 Phosphate rock is treated with H2S04 to produce HF which is later contacted with Si02 to produce H2SiF6. The sequence of reactions that take place is [2]: Ca]0(PO4)sF2+10//2SO4+20//2O => \0CaSOt-2H2O+6H^POi+2HF ...a 6HF + Si02 => H2SiF6 + 2H20 ...b H£iF6 => SiFA T +2HF ...c 3SiFt + 2H20 => H2SiF6 + Si02 ...d 3 Depending on the extent of the neutralization of the acid, a mixture of lead oxides and fluorides in addition to silica compounds can precipitate. 4 The presence of colloidal Si02nH20 in this system has been reported in the literature [3-7]. [41] Electrolyte A titrimetic analysis routine was set up to analyze the electrolyte for H 2SiF 6, Si0 2, HF, and PbSiF6. In this routine, Pb is analyzed via complexometric titration with EDTA [8,9]. H 2SiF 6 , Si0 2, and HF (if present) are determined by titration with LiOH. Details of this procedure are provided in Appendix 4. To obtain electrolytes of the set compositions, the mother electrolyte solutions were diluted with H 2SiF 6 and deionized water \ Additives were added to the electrolyte in selected experiments. The additives used were aloes 2 and calcium lignin sulphonate 3 . These additives were added from a mother solution at the beginning of the experiment. Precipitates formed due to the additives addition were removed by filtering the electrolyte prior to its introduction to the electrochemical cell. The electrolyte samples withdrawn from the slimes layer were analyzed by using Atomic Absorption Spectroscopy (AAS)4 and specific ion electroanalytical techniques. In these samples, Pb was determined via AAS using the absorption line at 283.3 nm. In the Sb determination via AAS, matrix effects can affect the analysis [ioi. Thus, Sb standard solutions were prepared by adding known amounts of PbSiF6 and H 2 SiF 6 so as to match the lead and acid content of the samples. The absorption line at 231.1 nm was used to determine Sb via AAS. The total Si content5 of the entrapped electrolyte was also determined via AAS. Si was determined using the absorption line at 251.6 nm and a nitrous oxide - acetylene flame. Three different standard solutions were prepared as follows: a) From a 1000 ppm Si solution prepared by dissolving 5.056 g of Na metasilicate (Na2Si03.9 HaO) in @300 ml of deionized water, adding sufficient HCl to bring the pH to about 5 and diluting up to 500 ml using deionized water. b) From H 2 SiF 6 technical solutions diluted so as to obtain standard solutions with less than 1000 ppm Si. c) From PbSiF 6-H 2SiF 6 solutions diluted so as to obtain standard solutions with less than 1000 ppm Si. 1 Deionized water with electrical conductivity lower than 12 u.mhos/cm. 2 Resin from the leaves of certain species of aloes plant native to South Africa. 3 Organic additive obtained as a by-product from wood pulping operations 4 Perkin Elmer Atomic absorption Spectrophotometer model 303. 5 The total Si content corresponds to the total amount of Si present in the electrolyte as H2SiF6, PbSiF6, and Si02. [42] Wenking potentiostat The total amount of fluorine ions present In the entrapped electrolyte was estimated by using an ion sensitive electrode \ Standards were prepared by using NaF solutions. Additionally, calibration curves were obtained using H 2 SiF 6 and PbSiF 6-H 2SiF 6 standards. Gran's plot and standard addition techniques were incorporated in these measurements [11,12]. D. Temperature control The electrochemical cells previously described were immersed in a constant temperature water bath. This bath had a volume of @9 L and was covered with styroform. The bath was stirred using magnetic bars and/or air sparging. The bath temperature was controlled by using a YSI model 71 temperature controller. A thermistor probe 2 was used to monitor the bath temperature and immersion heaters 3 were used to maintain it. This experimental set-up allowed temperature control within ±1.5 °C of the set point. After the bath had reached the set temperature, the assembled electrochemical cell was introduced and at least 3 hours were allowed for the cell to reach thermal equilibrium before the electrochemical experiment began. E. Instrumentation The electrochemical instrumentation involved the use of a variety of electronic equipment. A Wenking potentiostat was used in the first half of this work and a Solartron Electrochemical Interface together with a Solartron Frequency response analyzer were used in the second half. The improvements in the electronics of the Solartron devices enable complex experiments to be performed. What follows is a description of the different electrochemical arrangements used. Also, computer control of the electrochemical experiments and data acquisition will be explained. /. Wenking potentiostat A Wenking potentiostat model 70 HV1/90 was connected to an IBM XT personal computer. A Data Translation board DT 2805 was installed in one of the computer slots. This card allowed the computer to interact with the potentiostat and with the electrochemical cell. A Data Translation DT707 screw 1 An Orion Fluoride electrode model 94-09 together with a double junction reference electrode Orion model 90-02 filled with 1M NaN03 in the outer chamber was used in these measurements. 2 Thermistor probe YSI model 402. 3 Vycor* immersion heaters with 100 to 500W of power. [43] Wenking potentiostat terminal panel was used to address the DT2805 board. This panel acts as an extension of the DT2805 card and simplifies the process of computer interfacing. All the electrical connections are done in the DT707 terminal panel which sends and receives information from and to the DT2805 board. Besides from this terminal panel, a control panel was also used to link the potentiostat, computer, and electrochemical cell connections. OSCILLOSCOPE DT 7 0 7 SCREW TERMINAL PANEL ELECTROCHEMICAL CELL CONTROL P A N E L IBM XT COMPUTER A S Y S T / A S Y S T A N T S O F T W A R E DT 2805 BOARD Fig. 5 Experimental set-up using the Wenking potentiostat WENKING POTENTIOSTAT Fig. 5 shows a simplified view as to how the computer interfacing process was carried out. The flow of digital and analogue data from the computer to the system under study and vice versa was controlled by using specialized software \ A number of programs were written to control the digital and analogue operations performed by the DT2805 board . The complexity of these programs varied depending on the characteristics of the experiment to be conducted. A storage oscilloscope 2 was used to test the performance of these programs and to follow the response of the system when required. A digital voltmeter 3 was also used to check the computer measurements. 1 Asystant® menu-driven software version 1.02, and Asyst® command-driven software version 2.10. 2 Tektronix analogue oscilloscope model 5115 3 Beckman 31/2 digit multimeter model TECH 300. [44] 0 Wenking potentiostat Fig. 6 Detail of the connections required to Interrupt the current and to follow the cell response (A) Three terminal cell (B) Four terminal cell [45] Wenking potentiostat The Wenking potentiostat was used either as a potentiostat or as a galvanostat. Potentiostatic operation was converted to galvanostatic by connecting a resistor of suitable power rating between the working and reference electrode terminals \ It was in this configuration that most of the experiments were conducted. During galvanostatic operation, current was interrupted by short-circuiting the internal battery that controls the flow of current to the cell. This was done by using a mercury wetted relay2 activated by the computer at preset times. The connections required to interrupt the current and to follow the cell response are shown in Fig. 6. As Fig. 6 shows, the current going through the cell and the difference in potential between the working and the reference electrodes were continuously logged. Figs. 6A and 6B differ only in the number of connections made to the working electrode. When two connections are used (Fig 6B), one of them is used for conveying current and the other is used for measuring potential. Experiments in which large amounts of current are involved or when contact resistances are to be avoided call for this particular electrode arrangement. Calibration of the routines used for interrupting the current was done by using "dummy" cell electrical circuits. Appendix 5 provides a description of these measurements. The algorithm used in the computer programs to perform the current interruptions is also described in Appendix 5. By doing these calibration runs, it was found that the Wenking potentiostat halts the flow of current to the cell almost immediately (within 10 (isec3). On the other hand, after the short circuit was opened it was found that the current did not immediately recover its previous value. The rise time of this process was of the order of milliseconds and was dependent of the current going through the cell (e.g. see Fig. 7). In addition, due to hardware and software limitations, the data acquisition system was able to follow the decay in potential only within 1 msec after current interruption4. Subsequent points were sampled at various acquisition rates. This resulted in the current interruption routine being able to resolve decays whose time 1 As shown in Fig. 6, the reference terminal of the Wenking potentiostat is no longer used for connecting the reference electrode of the electrochemical cell. 2 Mercury wetted relay Elect-trol model 31511051. 3 Value obtained from oscilloscope readings. 4 Depending on the complexity of the data acquisition program, the interval of time between current interruption and the first set of data points sampled was between 0.14 msec and 1.0 msec. Oscilloscope readings were used to verify these measurements. [46] Generalities: constants were larger than 10 msec. As the time constant of the diffusion processes under study were several orders of magnitude larger than 10 msec, this instrumental constraint was not critical. 158 i — Fig. 7 Current step resulting from halting the flow of current to the electrochemical cell using the Wenking potentiostat Current was halted within -10 usee. .88 68. 128 188 Tine, usee 248 380 2. Solartron electrochemical interface and frequency response analyzer (a) Generalities: A 1286 Solartron Electrochemical Interface (SEI) and a 1250 Frequency Response Analyzer (FRA) were connected to an IBM XT personal computer by using the IEEE-488 interface built into these instruments. To link these instruments to the computer, an IEEE compatible board 1 was installed in one of its slots. This board enables the computer to act as a "controller" of the flow of information. All the electrical connections of the electrochemical cell were attached directly to the SEI front panel. 1 Scientific Solutions IEEE 488 LM board. [47] Description ol the experimental set-up Prograinining of the IEEE-488 interface is simpler than programming of the Data translation interface previously described. All analogue to digital conversions are done directly in the IEEE apparatus. This results in all the data communications being digital. IEEE instruments are controlled by a series of pre-established commands. As these commands are executed they send information to the control device (in this case the computer). This information instructs the control device with respect to the status of the instrument. The SEI is a complex and powerful instrument that can be used as a stand alone electrochemical device. In its simplest configuration, it can function either as a potentiostat or as a galvanostat. By pressing a button In its control panel (or by sending a command from the computer) switching between these two operating modes can easily be incorporated. Among other features, the SEI offers several ways of obtaining the value of the uncompensated ohmic drop IRg \ Among these, the SEI has built in a procedure ("sampled'TR,, compensation) which allows the potential to be sampled a few microseconds before and after current is interrupted. However, this IR, drop compensation routine operates only under potentiostatic conditions. When galvanostatic experiments are performed, this limitation can be circumvented by switching from galvanostatic to potentiostatic operation, mteirupting the current, and switching back to galvanostatic control. Under computer control the whole process takes @5 sec. The FRA is also a complex instrument. One of its fundamental functions is to generate waveforms. Sinusoidal, triangular, or square waves in the frequency range between 10 |iHz and 65.5 Khz can be generated by this device. The frequency and amplitude of these waveforms can easily be modified. Another of the FRA main functions is to analyze the gain and phase characteristics of sinusoidal waveforms. The system transfer function can be obtained by analyzing concurrently two sinusoidal signals. This is obtained by using two channels for simultaneous measurements at any two points in the system. (b) Description of the experimental set-up Both DC and AC experiments were carried out using the SEI together with the FRA. Fig. 8 describes the electrical connections that were used in these experiments. Furthermore, Appendix 6 illustrates the implementation of the 1 This uncompensated ohmic drop IRS is equivalent to i i n described in Chapter 2. [48] Description of the experimental set-up technique using durnmy circuits to simulate the response of electrochemical cells. The experimental data generated using these dummy circuits was used to calibrate the electrochemical set-up. WE RE1 RE2 CE Solartron Electrochemical Interface Working Fig. 8 Connections from the electrochemical cell to the Solartron Electrochemical Interface. The dissolution of pure lead and of typical lead anodes was studied using the beaker electrochemical cell previously described. In these studies, all leads were shielded to avoid pick-up noise. During the galvanostatic and potentiostatic experiments current was interrupted using the "sampled" IRg compensation routine built into the SEI. In these measurements, only the value of the uncompensated resistance was obtained . The AC impedance of pure lead and of typical lead anodes was measured under a variety of experimental conditions. Impedance measurements were made under rest potential conditions, in the absence and in the presence of a slimes layer, and in the absence and presence of DC current1. All the AC impedance spectra were obtained using sampling rates and integration times set to 200 cycles per frequency followed by a 5 sec break 2 . The SEI bandwidth 1 The difference in potential between the working and reference electrodes and the current flowing to the cell are continuously recorded by the SEI. During the AC experiments, the SEI removes the DC component (if present) from the potential and current waveforms before sending them to the FRA. The fundamental frequency of these waveforms was used to obtain the impedance of the system. 2 Integration times were reduced by using the auto-integration routine built-in the FRA. A long integration cycle was chosen (1% error with 90% confidence) [49] pH measurements type chosen for experiments under potentiostatic control was the type E (maximum bandwidth 24kHz) and for experiments under galvanostatic control the type B (bandwidth >100KHz). n. E lectro lyte Phys ico -Chemica l Properties A . pH measurements The pH of H 2SiF 6 containing solutions was measured using a liquid membrane pH electrode1 and a double junction reference electrode2. Measurements were made at room temperature. In these measurements, no attempts were made to correct for liquid junction potentials. pH measurements were also performed using pH sensitive paper. B. Electrical conductivity The electrical conductivity of H 2SiF 6-PbSiF 6 electrolytes was measured using a Radiometer conductivity meter model CDM2 and a YSI conductivity cell 3 model 3417. A Digital voltmeter was connected to the conductivity meter to assist in the reading of the conductivity measurements. The electrical conductivity of individual solutions4 was measured by immersing the samples in a water bath whose temperature was controlled to within 0.2°C. Two thermocouples 5 were used to monitor the bath temperature at different positions in the water bath. The thermocouples were connected to a computer which was used as a temperature control device. Temperature was maintained within the set limits by using heating elements controlled by the computer via solid state relays (SSR)6. C. Kinematic viscosity Kinematic viscosity of H 2SiF 6-PbSiF 6 solutions was measured using Cannon-Fenske routine viscometers for transparent liquids. The viscometers were 1 Orion pH electrode model 93-01. 2 Orion double junction reference electrode model 90-02. The inner filling solution used in this electrode (Orion 90-00-02) matches the characteristics of the standard KCI calomel electrode. In the outer chamber a 1 M NaN03 solution was used. 3 Cell constant = 1.05. Cell constant was obtained by measuring the electrical conductivity of a NaCl saturated solution and of a 0.100 M KCI solution at different temperatures. 4 Sample volumes vary between 25 and 30 ml. 5 Thermocouples type E Chromel(+)-Constantan(-). A 0 "C reference junction was used during the temperature measurements. 6 Omega DC controlled solid state relay (SSR) model SSR 240 D10. Control voltage 2-32 Voc. [50] Density immersed in a constant temperature water bath 1 and calibrated using deionized water. Temperature was controlled within 0.2°C. From 5 to 12 viscosity measurements2 were made until average flow times3 readings were within 0.20 sec. D. Density The density of H 2SiF 6-PbSiF 6 solutions was measured using 25 mL Binghmam-Type pycnometers. Pycnometers were calibrated by measuring the density of deionized water. Measurements were made at room temperature. From 3 to 5 density measurements were made until the obtained mean density values were within 0.2%. 1 Cylindrical water bath with @2L volume. 2 Viscosity measurements were made using 10 ml sample volumes. 3 Flow times measured by using a digital stopwatch. Parallax errors were diminished by using a magnifying glass. [51] Introduction Chapter 4 E lectroref in ing of Lead i n a Smal l -Scale Electroref in ing Ce l l : A Case Study I. Introduct ion During the electrorefining of lead by the Betts electrorefining process, ionic concentration gradients become established within the slimes layer due to the restriction that the slimes layer presents to the movement of ions. Additionally, the presence of the electric field created by the passage of current contributes to the formation of concentration gradients within this layer. The Betts electrorefining process is carried out under nearly galvanostatic conditions. Under these conditions, a constant flux of lead ions is generated at the anode/slimes interface. These ions are driven towards the cathode by diffusion, migration, and convection. In the absence of a slimes layer, mixing of electrolytes removes the migration and diffusion restrictions. Thus, if pure lead were to be dissolved, the concentration gradients generated would be present only within 100 to 1000 |im of the anode/bulk electrolyte interface where mixing disappears. On the other hand, during the refining of lead bullion, the slimes layer generates an environment in which ionic concentration gradients can be present over distances larger than 10 mm. These concentration gradients contribute to gradients in electrode potential applied to slimes filaments, and thereby affect the dissolution of noble impurities. Primarily, this gradient arises due to the larger concentration of lead ions in the vicinity of the anode interface with respect to their concentration in the bulk electrolyte. Lead ions move out of the slimes layer mainly by diffusion and migration. As lead ions are released, their positive charge must be neutralized to achieve local electroneutrality. This leads to reverse movement of SiF 6 2 and repulsion of H + from the anode/slimes interface. Electrical neutrality has to be observed throughout the slimes layer and this dictates a strong relationship between the SiF6"2, H \ and Pb + 2 concentration gradients. Given the previous relationships, the slimes layer will have a large average concentration of Pb + 2 and SiF6"2 ions and a small average concentration of H + ions with respect to their bulk electrolyte values. Moreover, there will be gradients of their concentrations throughout the slimes depending on the slimes thickness and the current density. The interrelationship between the diffusion coefficients, ionic mobilities, and activity coefficients of the above ions plays a significant role [52] Introduction in the shape of these concentration gradients. In addition, migration will promote the movement of anions from the bulk electrolyte towards the anode interface and would act in the opposite direction for cations. Diffusion will carry Pb + 2 out of the slimes layer and SiF6"2 and FT towards it. Convection will affect the movement of all the ions and depending on the electrode size, it can affect significantly the shape of the concentration gradients. The establishment of ionic concentration gradients within the slimes layer can shift secondary equilibria that can lead to both new solutes and precipitates such as fluoride and oxyfluoride ions, hydrated silica, and lead fluorides. The precipitates can create further hindrances (in addition of those caused by anode impurity filaments) to the convection of electrolyte and to the diffusion and migration of solutes. The stability of the slimes layer and its adherence to the anode surface is a complex function of the lead anode physical metallurgy and of the electrolysis conditions. Upon passage of current, lead is selectively removed from the bullion and a metallic structure of noble impurities is left behind. This structure is established as a "slimes layer". The success of the Betts process relies on this structure remaining unreacted during the electrorefining cycle. By limiting the potential difference across the slimes layer to less than 200 mV, this condition is practically fulfilled. On the other hand, the complex chemistry of this layer and the presence of ionic concentration gradients within it, can affect the extent to which this potential gradient can be observed. If, due to the presence of large concentration gradients, secondary products precipitate, the slimes layer can detach. Under these conditions, the noble compounds harbored in the slimes layer may no longer remain unreacted, and depending on shifts in electrode potentials, noble impurities can be transferred to the electrolyte, then to the cathode. In this chapter, a study of the dissolution of a typical lead anode under galvanostatic conditions is presented. The establishment of concentration gradients within the slimes layer, the precipitation of noble compounds, and the physical metallurgy of the lead anode and the produced slimes layer are reviewed in this case study. Current interruption techniques were used to find the link between the above mentioned phenomena. [53] n. Presentat ion of Results Presentation ol Results The study of the dissolution of a typical lead anode under galvanostatic conditions was done by using the rectangular electrochemical cell described In Fig. 3.2. 42 ^ Inner Electrolyte Sampling Well Potential Sensing Probe »// maaauremontm In mm Fig. 1 Lead anode top view. The location of the holes in which the inner reference electrodes A, B. and C were inserted, is indicated In this diagram. The position of the well used to extract electrolyte samples from the slimes electrolyte is also shown. Fig. 1 is a top view of the lead anode showing the locations where the potentia sensing probes were incorporated as well as the point from which electrolyte samples from the inner slimes electrolyte were withdrawn. Particular characteristics of this experiment are provided in Table 1. Current interruption at preset slimes thickness was implemented by using the circuit described in Figs. 3.5 and 3.6. Experiment LC2 was carried out in three stages which are described in the following paragraphs: Stage I: Galvanostatic dissolution during 300 Hrs. During this stage, current flow to the cell was halted for 138 msec every 3 Hrs. Stage II : Long current interruption for 190 Hrs Stage HI: Further galvanostatic dissolution for 30 min., during which current was halted every 10 min for 1.8 sec. [54] Presentation of Results During these stages, electrolyte samples were taken from the bulk electrolyte and from the inner slimes solution at preset times. After the completion of stage m, current was halted and the corroded anode was left standing in the cell for 48 Hrs. After this time, the electrolyte was slowly drained and a dilute H 2SiF 6 solution (pH =1.5) was used to displace the concentrated solution in the slimes layer. Afterwards, the corroded anode was removed and dried in a vacuum oven at low temperature (t < 40°C). Slimes samples for observation in the SEM were prepared by using a low viscosity resin and a vacuum imbibition technique 11,21 2 . Unsupported samples of the same slimes were analyzed by X-ray diffraction. Table 1 Characteristics of Experiment LC2 Anode Composition (Anode A Fig. 3.6) 0.01% Sn, 0.02% Cu, 0.14% Bi, 0.25% As, 1.12% Sb, 81 oz/ton Ag. (Air cooled face exposed to the electrolyte) Anode Dimensions 69 mm1,42 mm", 29.5 mm' Cathode Pure lead foil >99.95% Pb 75 mm1,62 mm*, 2 mm' Reference Electrodes: Pure lead rods, >99.95% Pb: Outer: Located in the bulk electrolyte, =5mm away from the slimes/electrolyte interface Inner A, B, and C: Located within the lead anode at =3,6, and 8.5 mm away from the slimes/electrolyte interface. Initial Bulk Electrolyte Composition [H2SiFs] = 0.74 M, [PbSiF6] = 0.28 M, [SiOJ = 0.12 M Additives Concentration =2 g/1 aloes, =4 g/1 of lignin sulphonate (added only at the beginning of the experiment) Electrolyte Volume 320 ml Electrolyte Temperature 40±1.5' C Electrolyte Recirculation Rate 6 m 1/min Current Density during stages I and III (from geometric surface area) 139 Amp/m2 Stage I Current Interruption Length and Frequency 138 msec every 3 Hrs Stage m Current Interruption Length and Frequency 1800 msec every 10 min Instrumentation Wenking potentiostat-DT 2805 Data acquisition Board-IBM XT computer 1 Spurr low-viscosity embedding media, 11 = 60 cP 2 In the imbibition technique, penetration of the epoxy resin is encouraged by extracting the air within the sample using a pressure difference (i.e. a vacuum). [55] Stage I A. Anodic overpotential measurements 1. Stage I The anodic overpotential response of electrode LC2 under galvanostatic conditions is shown in Fig. 2. As can be seen from all four reference electrodes, T)A increases quasi linearly as the slimes layer thickens. At the same time, r)A measured by the inner reference electrode A shows that steep excursions in the potential of the solution inside the slimes layer also can be present, although, they do not seem to affect the r\A value measured by the outer reference electrode. The relatively uniform slope of these measurements suggests that the same reaction and the same ions are being seen by all the reference electrodes \ The anodic overpotential response of the outer and inner reference electrodes to current interruptions are shown In Fig. 3. Details of the r|A behavior of the inner reference electrodes A, B, and C are provided in Figs. 4 and 5. In these figures current interruptions 43 to 47 are not shown as oscilloscope readings taken during that time interval required detachment of the current interruption triggering device on the data acquisition board 2 . 1 Measurements on the slimes electrical conductivity were made by following the difference in potential between a bare Pt wire inserted in the slimes layer and the lead anode. In these measurements, it was found that the difference in potential between the Pt wire and the lead anode was negligible. The Pt wire and the anode appeared to be short-circuited indicating the high electrical conductivity of the slimes filaments. 2 Oscilloscope readings were consistent with computer measurements. [56] Stage/ 3 X 180 160 140 * 120 n +» 9 100 +» o ft 5 80. 0 0 60. 0 c « 40. 20. 00 * Outer — Inner A X Inner B + Inner C tttt tt I— * . tt » tt I I I I I I I I I I I I I I ^ 1 + + + + 1 .0 2. 4. 6. 8. 10 Slimes Thickness, MM 12 14 16 Fig. 2 Anodic overpotential (uncorrected for TJQ) changes as a function of the slimes layer thickness. Stage I in Table 1. Position of the reference electrodes: Outer: Located in the bulk electrolyte, =5mm away from the slimes/electrolyte Interface Inner A, B, and C: Located within the lead anode at =3, 6, and 8.5 mm away from the slimes/electrolyte Interface [57] Stage I 2 0 0 > a o & > O o 150 -1 0 0 40 60 Current Interruption Number 1 0 0 Fig. 3 Outer and inner A, B, and C reference electrodes anodic overpotential response to current interruptions (during an otherwise galvanostatic experiment). Abscissa values reflect current interruption number. Current interruption measurements where made every 3 Hrs. (i.e. every 0.138 mm slimes). The first current interruption was made in the absence of slimes and the 100th current interruption was made at a 13.8 mm slimes thickness. [58] Stags/ (A) (B) 1.1 | , "0 I 1 1 2 0 4 0 8 0 8 0 100 20 «1 80 80 100 Current Interruption Number Current Interruption Number Fig. 4 Detail of the response of the inner A reference electrode to current interruptions (during the whole electrorefining cycle). Fig. (B) is the same data presented in (A) with an expanded vertical scale. (A) (B) M 60 ?0 SO 80 100 S3 " 80 90 100 Current Interruption Number Current Interruption Number Fig. 5 Detail of the rfo response of the inner B (Fig. A) and inner C (Fig. B) reference electrodes to current Interruptions (during the whole electrorefining cycle). [59] Stage I 6 1 . 1 2 8 1 8 8 2 4 0 3 8 8 . 8 8 6 8 , 1 2 8 1 8 8 2 4 8 3 8 8 1 2 8 1 8 8 2 4 8 8 6 8 . 1 2 8 1 8 8 2 4 8 3 8 8 Fig. 6 Detail of the response to current Interruptions measured by the outer reference electrode (at different slimes layer thickness). X axis: Time, msec Y axis: Anodic overpotential, mV The response of the outer reference electrode to current interruption is shown in Fig. 6 for different slimes thickness. Upon current interruption, the r\A value first drops abruptly, then decays slowly. The abrupt overpotential decay is nearly equal to the so-called uncompensated ohmic drop, r\a. Furthermore, upon application of current back to the cell, it can be seen that, the thicker the slimes layer, the longer it takes to attain the rjA value observed prior to current interruption (Fig. 6). [60] Stage/ 30. i-23. 20. IS. 10. S.0 .00 ^ ^ ^ ^ Fig. 7 Changes in the value of the uncompensated ohmic drop, r\a, as a function of the slimes thickness. From the T | A response of the outer reference electrode to current interruptions. i i i 1 .00 2.0 4.0 6.0 8.0 10. Slines Thickness, nn 12. 14. 16. As shown in Fig. 7, r\a remains between 14 and 16 mV during the whole experiment. Only during the first interruption of current (at zero slimes thickness) does a larger potential drop appear. The decrease in this value results from changes in the electrolyte concentration in the near proximity of the slimes/electrolyte interface. Within a few milliseconds, steady state is attained and r|n no longer changes. Upon interruption of current, the concentration gradients present within the slimes layer begin to relax towards equilibrium. H + moves from the bulk electrolyte towards the slimes layer and Pb + 2 and SiF6"2 move in the opposite direction. This process is currentless and will cause interaction between the diffusion and migration fluxes so that the potential gradient decays in the same way as the concentration gradients. The response of the inner reference electrode A to current interruptions is different than that observed by the outer reference electrode. Depending on the slimes thickness, TJa measured by this electrode can show a random behavior (see Fig. 4A). Thus, for example Figs. 8A and 8F show that upon current interruption T)A jumps towards higher values rather than decreasing. There is no unambiguous explanation for such jumps. The other curves in Fig. 8 show that [61] Stage/ upon current interruption r|A decays linearly. The amplitude of this decay is smaller than that shown by the outer reference electrode at similar slimes thickness (see Fig. 3). Additionally, there is no initial steep decay in rjA upon current interruption. This is an indication that between this electrode and the lead anode the inner slimes electrolyte does not have a uniform composition. 1 2 0 1 8 0 2 4 0 3 0 O 0 0 6 0 . 1 2 0 1 8 0 2 4 0 Fig. 8 Detail of the response to current Interruptions measured by the inner A reference electrode (at different slimes layer thickness). X axis: Time, msec Y axis: Anodic overpotential, mV [62] The inner reference electrode B response to current interruptions is shown in Fig. 9. Upon interruption of current, a very small decrease in r|A takes place (see also Fig. 5A). This electrode is very close to the lead anode/slimes interface and the concentration of Pb + 2 in its vicinity is expected to be very high \ As this interface moves away from this reference electrode, the region over which concentration gradients span grows and so decays in riA of larger amplitude can take place upon current interruption (see Fig. 5A). 300 42 . 38 . • * * • * • 34 . - • « 38. 26 . 22 . : , . 1 . . 1 10.2 M M .80 60 . 74 . 70 . 66 . 62 , 58 , 54 . - » 128 188 248 388 13.7 M M 1 300 .00 60 . 120 180 240 300 Fig. 9 Detail of the response to current interrupuons measured by the inner B reference electrode (at different slimes layer thickness). X axis: Time, msec Y axis: Anodic overpotential, mV The response of the inner reference electrode C to current interruption is depicted in Fig. 10. This electrode does not show any significant decrease in its r\A value upon current interruption (see Fig. 5B). Furthermore, the amplitude of the potential decay shown by this electrode is the smallest among all the other 1 The reference electrode potential is related to the lead ion concentration. Knowledge of the activity coefficients of the various species that are in the vicinity of these electrodes is required to estimate these ionic concentrations. [63] Stage / reference electrodes (see Figs. 3 and 5B). The presence of a highly concentrated Pb + 2 region between this electrode and the anode/slimes layer interface can account for this behavior. 13 9.8 5.0 1.0 -3.0 j rfWuuum1VBSBuuuin1WSMi -7.8 8.1 nn .88 60 , 40 . 36 . 32 . 28 . 24 . 20 . 120 180 240 300 12.3 nn i l i i I i i I 26 . 22 . 18 . 14 . 10 . 6.0 49 . 45 . 41 . 37 . 33 . 29 . <B> 10.2 nn .00 60 , 120 180 240 300 13.7 nn .00 60 , 120 180 240 300 .00 60 . 120 180 240 300 Fig. 10 Detail of the T | a response to current Interruptions measured by the inner C reference electrode (at different slimes layer thickness). X axis: Time, msec Y axis: Anodic overpotential, mV A plot of the anodic overpotential values obtained right after current interruptions for the four reference electrodes is shown in Fig. 11. By comparison with Fig. 2, the correlation between the n.A curves becomes more evident. Fig. 11 shows that the activities of the lead ions at fixed positions change as the anode/slimes interface moves, reflecting variations in the inner slimes electrolyte composition. Furthermore, the lines for the various reference electrodes are almost parallel, indicating a near steady-state in the solution gradients between any two reference electrodes. [64] Stage II 180. I— 2.08 4.00 6.00 8.00 10.0 SI i lies Thickness, nn 12.0 16.0 Fig. 11 Anodic overpotential (corrected for riJ changes as a function of the slimes layer thickness. Stage I in Table 1. Position of the reference electrodes: Outer: Located in the bulk electrolyte, =5mm away from the slimes/electrolyte interface Inner A, B, and C: Located within the lead anode at =3, 6, and 8.5 mm away from the slimes/electrolyte interface 2. Stage II After forming a 13.8 mm thick slimes layer, current was interrupted for 190 Hrs and the lead anode polarization was followed as a function of time. By [65] mterTupting the current for an extended period of time, the concentration gradients present within the slimes layer are expected to disappear. Changes in these concentration gradients are reflected in the polarization values which decrease as a function of time. x — x outer 0 D — a inner A inner B inner C Outer Inner B -40 i- i.i.i. crrri vrw, m 0 20 40 60 80 100 120 140 160 180 200 Time Since Current Interruption, Hrs Fig. 12 Difference in potential (uncorrected for r\^) between the reference electrodes and the lead anode as a function of the current interruption time. Stage II in Table 1. After anodic dissolution up to a 13.8 mm thick layer of slimes (Fig. 2) current was halted for 190 Hrs and the polarization was followed as a function of time. The arrows indicate the polarization values prior to current interruption. Details of the polarization decay in the first milliseconds after current interruption can be seen in Figs. 6H, 8H, 9D, and 10D. Fig. 12 shows how the difference in potential between the reference electrodes and the lead anode decays during current interruption. The outer and inner A reference electrode polarizations decay to values close to zero within a few hours. On the other hand, the potential difference measured by inner reference electrodes B and C is negative. Furthermore, after a certain time has elapsed, the polarization displayed by these electrodes jumps to near zero values. The closer the reference electrode is to the anode/slimes interface, the longer it takes for this polarization jump to occur. This rise in potential difference is [66] Stage III attributed to dissolution of precipitated products that result from changes in electrolyte composition in the inner slimes layer. Mixed electrochemical processes that can support internal currents in the absence of an external current, such as the reduction of an oxidized ion, also can account for the negative polarization values displayed by these electrodes \ 3. Stage III After allowing the concentration gradients present within the slimes layer to relax during the long current interruption, current was applied back to the cell during 30 min (Fig. 13). > < .03 '•+-> C CD -t-> O Q. i_ 0) > O o T3 O C < 100 90 80 70 60 50 40 30 20 10 0 -10 '-: } : i • '-'- 1 '-/ \ ••**•' ; .^.......\~*-r f | \ - f - Outer; * •••!'• Inner fA t : j - I I I ! • F Inner iC i , i , Fig. 13 Changes in the value of the anodic overpotential ( uncorrected for as a function of the electrolysis time. Stage m in Table 1. After interrupting the current for 190 Hrs (Fig. 13), current was applied back to the cell and the T | A values shown in this plot were obtained. 10 15 20 Time, min 25 30 1 Among these mixed electrochemical processes are: (a) local concentration cells (b) cementation reactions (c) Re-dissolution of PbF2: PbF2+2e~ = Pb*2+2F~ [67] Stage III Fig. 14 Anodic overpotential response upon current interruption (Stage m Table 1) Current interruptions were applied at different electrolysis times as indicated by the arrows shown in each plot: (1) 0.01 min (2) 10 min (3) 20 min (4) 30 min Each plot indicates the overpotential response measured by a different reference electrode: (A) Outer (B) Inner A (C) Inner B (D) Inner C [68] Bulk electrofytB concentrations Fig. 13 shows how the anodic overpotential values increased during the application of current back to the cell. Concentration gradients within the slimes layer become established very rapidly: In 30 min only =0.02 mm of slimes were formed yet the T)a values increased by more than 40 mV 1 . This shows that the slimes layer does hinder appreciably the flow of ions. Current interruptions during 1.8 sec were applied during this stage to study the characteristics of these concentration gradients (Fig. 14). At time zero no significant decay in potential is observed upon current interruption in any of the reference electrodes. As concentration gradients become established, larger overpotential drops can be observed upon current interruption. B. Analytical chemistry 1. Bulk electrolyte concentrations The changes in composition in the bulk electrolyte during Stage I are shown in Fig. 15. A continuous depletion of Pb + 2 in the bulk electrolyte is seen to take place during the formation of the slimes layer. As the current efficiency for the refining process was close to 100%, this depletion can only be associated with Pb + 2 concentration enrichment in the electrolyte within the slimes layer. Concurrently to the Pb + 2 depletion, there is a continuous, yet small increase in acid concentration which is related to H + depletion within the slimes layer2. No major changes in the bulk electrolyte concentration of hydrolyzed Si0 2 were detected during this stage 3 . The changes in the bulk electrolyte composition during Stage n are shown in Fig. 16. Upon current interruption, there is an increase in the Pb+ 2 bulk electrolyte composition, and a decrease in the acid concentration. Once current is interrupted, Pb + 2 and SiF6"2 diffuse out of the slimes layer while H + diffuses in. 1 In the same period of time, the outer anodic overpotential rose by less than 2 mV in the absence of the slimes layer (Fig. 2), as compared to a 65 mV rise in the presence of a 13.8 mm thick layer of slimes (Fig. 11). 2 Material balances indicated that the slimes electrolyte can have average [PbSiF6] higher than 1 M while [H2SiFe] can be lower than 0.5 M. 3 Si02 as determined by titration via the LiF-LiOH technique described in Appendix 4 is merely a composite of all dissolved species containing at least 1 oxygen atom. The general formula Six(OH)yFzq" with 1<y<4, and'- < 6 accounts for the existence of these species. [69] Bulk electrolyte concentrations o E 0.9 0.8 ! 0.7 - .a... 2 0.6 c CD O c o O 03 2 TS LU m 0.5 0.4 \ ° " 7 [H2SiF6] [Pb+2] [Si02] A-/S/02/ "~~"~-©-0 _1 I I I I I I I I I I I I I I I I I I I I I I I I I 1 I 1 I L. Fig. 15 Changes in composition of the bulk electrolyte as a function of the slimes layer thickness. Stage I in Table 1. At preset electrolysis times bulk electrolyte samples were withdrawn from the bulk electrolyte and analyzed for the species shown in this plot From chemical analysis data 2 4 6 8 10 12 14 1< Slimes Thickness, mm 0.9 _ 0.8 o E o 08 c CD O e o O CD 9 TJ a LU CO. 0.7 0.6 0.5 0.4 O GL . [H2SiF6] [PbSiF6] -X-[Si02] i 11 i i i i i i i i i i i 11 11 i i i i i i i i i i i i i 11 Fig. 16 Changes in the bulk electrolyte composition as a function of the current interruption time Stage II in Table 1. From chemical analysis data 20 40 60 80 100 120 140 160 180 200 Time Since Current Interruption, Hrs [70] Inner slimes electrolyte concentrations. 2. Inner slimes electrolyte concentrations. Some information about local ionic concentrations within the slimes layer was obtained by withdrawing small amounts of electrolyte (=100 |il) from a fixed point located =3mm away from the slimes/electrolyte interface (as shown in Fig. 1). Fig. 17 Changes in the local composition of the slimes electrolyte as a function of the movement (from the sampling point) of the anode/slimes interface Stage I in Table 1. From a fixed point located ~3 mm away from the slimes/bulk electrolyte interface (Fig. 1) electrolyte samples were withdrawn at preset times and analyzed for the species shown in the plot. From chemical analysis data 0 2 4 6 8 10 Distance From the Anode/slimes interface, mm Fig. 17 shows the changes in the composition of the inner slimes electrolyte during stage I as the anode/slimes interface moves away from the sampling point. As can be seen, Pb+ 2 concentrations at this point are not as high as the average values predicted from mass balance computations. Furthermore, the acid balance is also somewhat larger than expected . However, Pb+ 2 concentrations were found to be between 3 and 6 times larger than the corresponding bulk electrolyte values. Differences between mass balances and local compositions, may be due to presence of precipitates and also to the fact that sampling was made only at one point within the slimes layer. Fig. 17 also shows that negative changes in the acid concentration accompany positive PbSiF6 variations. This indicates that SiF6"2 exerts an influence in the transport processes within the slimes layer. The Si0 2 concentrations shown in Fig. 17 indicate that large amounts of these species are contained in the inner slimes electrolyte. [71] Inner slimes electrolyte concentrations Analysis of ionic species of noble impurities in this electrolyte showed that AsO+ was present in concentrations of -0.17 m M whereas [BiO+] was lower than 0.01 m M . Additionally, [SbO+] in the entrapped electrolyte was of the order of 0.2 m M . Furthermore, no major changes in the concentration of these noble species were detected during the refining cycle. These small amounts of noble impurities in the inner electrolyte indicate that they do not react significantly at the corresponding overpotential levels shown in Fig. 12 \ ( A ) (B) 1.9 1.8 1.6 ^ 1 5 E 5f 1 4 1.2 ^ from Chemical Analysis from AAS- H2SIF6 Standards - - from AAS-PbSiF6-H2SiF6 Standards i i l I—' ' i I i I I I i i i O E -< —A \ \ -\ \ \ v -Chemical Analysis " -o — JSE and Gran's Plot technique _ ..0. ISE and Standard Addition technique , , I , 3 2 4 6 8 10 Distance from the Anode/slimes Interface, mm 0 2 4 6 8 10 Distance from the anode/slimes interface, mm Fig. 1 Changes in the local concentration of the total Si and F present in the slimes electrolyte as a function of the movement (from the sampling point) of the anode/slimes interface Stage I in Table 1. Electrolyte samples taken from a fixed point located -3 mm away from the slimes/bulk electrolyte interface were analyzed for total Si and F using three different analytical techniques. (A) Changes in the total concentration of Si-bearing species (B) Changes in the total concentration of F-bearing species From chemical analysis data 1 Analysis of the cathode at the end of stage III confirmed that impurities dissolution was not significant. Cathode impurities concentrations were: 0.0003% Cu, 0.0010% Sb, 0.0016% Bi, <0.0003% Sn, <0.0001% Ag, and <0.0001% Tl. [72] Inner slimes electrolyte concentrations. 1.2 1 -S 0.8 o E c o «3 0.6 [H2SiF6J - 0 1 3 - •fZT" /S/027 [PbSiF6] Fig. 19 Changes in the local composition of the slimes electrolyte as a function of the current interruption time. Stage II in Table 1. From a fixed point located ~3 mm away from the slimes/bulk electrolyte interface electrolyte samples were withdrawn at preset times and analyzed for the species shown in the plot. From chemical analysis data 40 80 120 160 Time Since Current Interruption, Hrs 200 Chemical analysis of total Si and F in the inner slimes electrolyte during stage I are provided in Fig. 18. Si and F total concentrations decrease as the slimes layer thickens. Changes in the local composition of the slimes electrolyte are unexpected under steady state anode dissolution conditions. Time dependent processes such as changes in convection due to movement of the anode/slimes interface and/or gradual precipitation of secondary compounds can account for the Si and F decrease at a fixed point such as observed in Fig. 18. Changes in the composition of the inner slimes electrolyte during stage n are depicted in Fig. 19. Although no major changes in Pb + 2 concentration are observed during the long current interruption, a significant enhancement in the acid concentration is observed. Also, a sudden decrease in [SbO+] concentration seems to occur just a few hours after current interruption. As expected, the total Si and F concentrations increase during the current interruption stage (see Fig. 20). Thus, as concentration gradients disappear, the driving force for convection decreases continuously and redissolution of precipitates can take place. [73] Characterization of the slimes layer (A) (B) 1.2 O [Si] from Chemical Analysis -o - - [Si] from AAS- H2SiF6 Standards -£}• [SI] from AAS-PbSIF6-H2SiF6 Standards I 7.5 | - O O 6.5 5.5 p o 7 / 13 X Chemical Analysis —£^ ISE and Gran's Plot technique ISE and Standard Addition technique _L _J_ 20 40 60 80 100 120 140 160 180 200 Time Since Current Interruption, Hrs 0 20 40 60 80 100 120 140 160 180 200 Time Since Current Interruption, Hrs Fig. 20 Changes in the local concentration of the total Si and F present in the slimes electrolyte as a function of the current interruption time. Stage n in Table 1. Electrolyte samples taken from a fixed point located -3 mm away from the slimes/bulk electrolyte interface were analyzed for total Si and F using three different analytical techniques. Total Silica and total fluorine were calculated by adding the concentrations of all the Si and F-bearing species. (A) Changes in the total concentration of Si-bearing species (B) Changes in the total concentration of F-bearing species From chemical analysis data C. Characterization of the slimes layer As described in the previous section, the total concentration of noble impurities present in the cathodic deposit was lower than 30 ppm. Thus, no significant dissolution of noble phases and compounds present in the original lead anode should take place. The relationship between the phases and compounds present in the uncorroded lead anode and those found in the slimes layer was studied by using metallographic techniques. Electron probe microanalysis (EPMA) of these samples was done by using energy dispersive spectrometry. Additionally, X-ray diffraction was used to study the distribution and presence of these phases and compounds within the slimes layer. [74] Metallography ol the staring lead anode 1. Metallography of the starting lead anode Fig. 21 shows the section of the lead anode used in the metallographic analysis, and the observation points chosen to correspond to locations where the slimes layer structure was later studied. Uncorroded electrode Corroded electrode de/slimes Interface F i g . 21 Section of the lead anode and of the slimes layer studied metallographically. The observation points in the uncorroded specimen were chosen to correspond to matching locations in the slimes layer. Air cooled face Fig. 22 shows the microstructure of the lead anode ("air" face, location #1 in Fig. 21) \ A variation of the so-called "honeycomb" structure can be observed in Fig. 22. As found from EPMA 2 , the inner grains in this microstructure have a large concentration of lead-rich phases, whereas the grain boundaries are somewhat depleted in lead and can contain large concentrations of noble elements (Sb, As, Bi, Ag). EPMA performed in this sample (Fig. 22C) shows significant variations in elemental concentrations along the grains and the grain boundaries. 1 This sample was prepared by polishing up to 600 grit followed by 5 urn alumina. Afterwards, the sample was chemically etched with a polishing-etching solution of the following composition: 20 ml CH3COOH (concentrated), 42 ml H2Oj, (30%), 40 ml HN03 (concentrated), and 70 ml of glycerine [6 -8 ] . 2 EPMA in etched samples is not recommended as irregular absorption of x-rays resulting from topography affects the analysis. Thus, the electron probe microanalysis shown in Fig. 22C only indicates qualitative changes in concentrations. [75] (C) Fig. 22 Lead anode microstuctures. Anode "A", Air cooled face. All micrographs correspond to the same observation polnt( point #1 Fig. 21). Secondary Electron Images Specimen was polished up to grit 600 and subsequently chemically polished/etched EPMA Fig. C. %wt Point Cu As Ag Sb Pb Bi 1 0 6 1 2 87 3 2 0 13 5 31 51 0 3 0 14 2 23 62 0 4 0 5 0 2 80 14 5 0 11 4 3 82 0 6 0 9 0 2 81 8 7 0 9 2 3 83 2 [76] Metallography ol the starting lead anode The changes in the anode microstructure at different parts of the lead anode can be seen in Figs. 23 and 24 (locations #2 and #3 respectively of Fig. 21) \ EPMA 3 performed on this sample shows that there is less Pb in the grain boundaries than inside the grains. Furthermore, Bi seems to be present with lead throughout the whole microstructure. This analysis also shows a eutectic phase that is rich in As and Sb (points 6 and 7) whereas Sb and Ag-rich phases can be observed In the proximities of the grain boundaries (points 8 and 9) and in some cases within the grains. The precipitates within the grains have a random composition. Most of these precipitates are Pb-rich compounds. Additionally, Cu-As compounds (not identified in Fig. 23) can also be seen inside the grains. The microstructures compared in Fig. 24, show the continuity of the honeycomb structure throughout the sample. 1 These samples were not etched. They were prepared by polishing up to 600 grit followed by using 0.5 urn alumina. Backscattered electrons were used to reveal the anode microstructure. 2 As these samples were not etched, relative changes in the probe microanalysis are significant and represent semi-quantitative changes in the elemental composition of the samples. [77] Fig. 23 Lead anode microstuctures. Anode "A". All micrographs correspond to the same observation point( point #2 Fig. 21). Backscattered Electron Images Specimen was polished up to grit 600 followed by using 0.5 um alumina (sample was not etched or chemically polished). EPMA Fig. C. %wt Point Cu As Ag Sb Pb Bi 1 0 8 0 1 87 5 2 0 7 0 1 87 5 3 0 7 0 1 88 4 4 0 7 0 1 89 4 5 0 7 0 0 89 4 6 0 12 2 6 77 4 7 0 11 1 13 73 3 8 0 4 28 10 54 3 9 0 6 23 7 62 2 10 0 8 0 1 87 5 Metallography ol tie Starting Lead Anode [78] Metallography ol the Starting Lead Anode Fig. 24 Lead anode microstuctures. Micrographs correspond to different observation points (A) and (B) Observation point #2 Fig. 21 (C) and (D) Observation point #3 Fig. 21 Backscattered Electron Images Specimens were polished up to grit 600 followed by using 0.5 urn alumina (samples were not etched or chemically polished) SEM analysis 2. Analysis of the slimes layer phases and compounds (a) SEM analysis The slimes microstructure1 =2 mm away from the slimes/bulk electrolyte interface is shown in Fig. 25 a. The Pb-rich phases inside the grains have dissolved and the noble phases are left behind. The dissolution of the Pb-rich phases near the grain boundaries can be seen in Fig. 26. EPMA showed that large concentrations of noble elements are present along the former grain boundaries and that there are gradients in their concentrations (e.g. compare points 1 and 2). Additionally, noble compounds and various segregates were detected in these inicrostructures (see points 3 and 4). Fig. 26C shows the form of the precipitates of noble phases originally present inside the lead anode grains which report to the slimes layer. The slimes layer microstructure1 =12 mm away from the slimes/bulk electrolyte interface is shown in Fig. 27. Evidence for the presence of Si-rich compounds is the major difference between this microstructure and the microstructures shown in Figs. 25 and 27. As can be seen in Fig. 28, Si surrounds the former grain boundaries and appears randomly throughout the structure. Si is expected to result from the hydrolysis of SiF6"2 which should be more severe near the anode/slimes interface. 1 Total slimes thickness =13.8 mm. 2 Samples were mounted using a vacuum imbibition technique and a low viscosity resin. Careful polishing using the 0.5u.m cloth grit was used to remove the excess of resin. Samples were coated with graphite previous to their observation in the SEM. [80] SEM ana/ysis Fig. 25 Microstructure of the slimes layer @2mm away from the slimes/electrolyte interface (position #2 Fig. 21) Backscattered Electron Image [81] 016929 30KV X 4 0 0 7 5 u m Fig. 26 Detail of the microstructure of the slimes layer © 2 m m away from the slimes/electrolyte Interface (position #2 Fig. 21) Backscattered Electron Images EPMA Fig. C, %wt Point As Ag Sb Pb Si 1 12 8 56 25 2 6 - 79 14 -3 3 56 40 0 -4 20 8 35 36 -[82] Fig. 27 Microstructure of the slimes layer @12mm away from the slimes/electrolyte interface (position #3 Fig. 21) Backscattered Electron Image SEM analysis [83] SEM analysis ( B ) 016924 30KV X400"'' '75um Fig. 28 Detail of the microstructure of the slimes layer @ 12mm away from the slimes/electrolyte Interface (position 3 Fig. 21) Backscattered Electron Images EPMA Fig. C, %wt Point 1 2 Si Cu As Ag Sb 44 1 8 - 47 23 - 9 6 62 - - 15 3 63 Pb 19 [84] X-ray diffraction (b) X-ray diffraction Table 1 shows the results of the X-ray diffraction analysis of unsupported slimes samples Table 1 X-ray Diffraction Analysis of Outer and Inner Slimes Powder Samples Outer Slimes (=2 mm from the slimes-electrolyte interface) Inner Slimes (=12 mm from the slimes-electrolyte interface) PbF2 X XXX Si0 2 X XX Sb 20 3 X XXX S b A X XX Bi X XX Sb X XX PbO (yellow) -Ag3Sb XX Cu3Sb XX A s A - X PbSiOj Bi 2 0 3 X XX . Phase presence is dubious - Phase detected in very small concentrations X Phase detected in low concentrations XX Phase detected in medium concentrations XXX Phase detected in large concentrations The presence of PbF2 in these samples and its relative larger concentration in the inner slimes is a supplementary indication to the presence of Si detected by EPMA that hydrolysis of SiF6"2 takes place. The presence of metallic Bi, and Sb, together with some of their oxides was as expected from electron probe microanalysis 2 . The presence of mtermetallic compounds (i.e. A^Sb and Cu3Sb) was also expected from these analysis. 1 With multiple phases present there were overlapping peaks that caused problems with positive, unambiguous identification. 2 The presence of oxides can be the result of oxidation of the slimes after they were dried. [85] Chapter 5 Anod ic and Rest Potent ia l Behavior of Pure Lead i n HaSiFe-PbSiFe Electrolytes I. Overview of Pure Lead Dissolut ion i n H 2 S i F 6 - P b S i F 6 E lectrolytes Under Galvanostat ic Condit ions In this chapter the dissolution of a pure lead electrode is discussed in terms of DC and AC electrochemical measurements. A qualitative analysis of the controlling mechanisms for lead dissolution is presented. The different components of the anodic overpotential are related to phenomena taking place in the electrode boundary layer. In the case of pure lead, there are no complications due to the presence of slimes. A. Anodic overpotential in the absence of large concentration gradients in the anode boundary layer During the galvanostatic dissolution of the lead bullion anode described in Chapter 4, the value of the uncompensated ohmic resistance, r|n, remained nearly constant during the whole electrorefining cycle (Fig. 4.7). In this case, the presence of large ionic concentration gradients within the slimes layer results in a counter E.M.F. that is responsible for the failure of the anodic overpotential to decay to zero upon current interruption. When pure lead is dissolved, T|Q increases continuously with time as seen in Fig. 1, as a result of the progressive ohmic resistance created by the movement of the anode/electrolyte interface. Increases in rj n reflect changes in the distance between the reference electrode and the anode/electrolyte interface which directly affect the Rg 1 value. Under these conditions, rjQ appears to be the only source of potential between the lead anode and the reference electrode. By subtracting the calculated ohmic resistance from the r)A measurements, the extent to which concentration gradients become established in the anode boundary layer can be studied. As Fig. IA shows, the corrected anodic overpotential value remains constant during the dissolution of lead, indicating a constant thickness of the boundary layer across which concentration gradients persist. Concentration overpotential can be considered to be the only source of potential under these circumstances, as lead dissolution 1 As explained in Chapters 2 and 4, R, [Qcm2] is the specific resistance of the electrolyte and is related to T\a by the following relationship: Tin=IRs. [86] Anodic overpotential in the absence of large concentration gradients in the anode boundary layer occurs nearly reversibly (n,ac=0 mV) \ The small magnitude of the generated concentration overpotential indicates that large concentration gradients are not established a . (A) (B) 80 i I I I | I i I | I I i | i i i | i i i | i i i | i i i | i i i | i I I | i i i > Fig. 1 Potential difference between a fixed reference electrode and a corroding anode In the absence of addition agents. Experimental conditions: Galvanostatic Experiment, Current Density= 200 Amp m"2, Electrode Area 1.50 cm2, [PbSiF6l=1.31 M , [H2SiF6]=0.30 M . T=4Q±1.5"C, bulk electrolyte electrical conductivity K=220 mmhos cm"1. Beaker electrochemical cell, electrolyte volume =300ml, stationary electrolyte. Wenking potentiostat-Data Translation Board-IBM XT computer. (A) f\A variation during the dissolution of pure lead (B) T\a changes obtained by interrupting the current at preset times. 1 iiae determination was done by using AC impedance techniques described in section III. 2 In the case shown in Fig. 1 concentration gradients in the Nernst boundary layer span over a region between 100 and 1000 urn thick. By comparison, during the refining of impure lead, concentration gradients are present throughout the whole slimes layer (i.e. the Nernst boundary layer spans over several mm). [87] Correlation between the anodic overpotential and the presence ol addition agents. B. Correlation between the anodic overpotential and the presence of addition agents. During the refining of lead, addition agents (i.e. aloes and lignin sulphonate) are normally used to modify cathodic reactions. The presence of addition agents can also affect anodic reactions through complex adsorption mechanisms [lj. In general, the r|A values observed during the galvanostatic dissolution of pure lead were found to increase in the presence of addition agents in the bulk electrolyte1. Moreover, when an excess of these additives is added to the electrolyte, to the extent that suspended material is visible, they collect on the anode and promote very large overpotential values. This behavior is shown in Fig. 2A where it can be seen that in a few hours T|A rises from 0 to =1000 mV. In this case, current interruption measurements indicate thatTjQ accounts for most of the overpotential values (Fig. 2B). In the presence of purely resistive films in the anode surface, T) 0 can be described by the following equation: T]a = IRs=I(Rb+RfiJ ...1 Rt was found to be equal to 1.4 Qcm2 from the ohmic drop value obtained a few seconds after the electrolysis began. Any extra increases in TI q are due to the presence of Rflim. The T j n produced by this film along with its resistance are plotted in Fig. 2B. It seems as if the addition agents form or generate a highly resistive film that may be counter productive to the refining process a . Furthermore, the presence of this film favours the development of concentration gradients in the anode/electrolyte interface. Thus, the rjA values obtained upon current interruption increase continuously with time (see inset Fig. 2A) indicating that the stagnant zone at the anode surface is thickening. 1 See section ll.b. 2 Visual observation of the anode after the refining process showed that a yellowish film adhered to the anode surface. Such a film was visible only when the amount of undissolved addition agents was large. In electrolyte solutions where the electrolyte was filtered prior to its introduction to the cell, the addition agent film was not visible at naked eye. The amount of suspended solids produced by excess additives (aloes and lignin sulphonate) seem to increase with increasing lead concentrations in the electrolyte. Techniques for increasing the dissolution of these and other additives are reported in the literature [2]. [88] Correlation between the anodic overpotential and the presence of secondary products that precipitate on the anode surface (A) (B) Fig. 2 Overpotential changes during the galvanostatic dissolution of pure lead (in the presence of excess quantities of addition agents) Experimental conditions: Current Density = 180 Amp m"2. Electrode Area 31.0 cm2, [PbSiF6]=1.31 M , [H2SiF6]=0.30 M , =2 g 11 aloes and =4 g 11 lignin sulphonate (suspended material was visible), T=40±1.5°C. Rectangular electrochemical cell, electrolyte volume =320ml, bulk electrolyte recirculation rate =6 ml min"1. Wenking potentiostat-Data Translation Board-IBM XT computer. (A) T|A increases as a function of the electrolysis time (B) Changes in the and R^, as a function of the electrolysis time. Left, axis: T | Q due to the presence of a colloidal film of "undissolved" addition agent [r\a ,fflm). Right axis: Ram obtained from the following relationship: Rfi!m = C. Correlation between the anodic overpotential and the presence of secondary products that precipitate on the anode surface Increases in the anodic overpotential values as a result of changes in its ohmic component also can be due to the precipitation of nearly insoluble salts such as PbF2 and Si0 2. The precipitation of these salts can be observed if sufficiently large concentration gradients in the anode boundary layer become established. The presence of these compounds in the anode surface would hinder the movement of ions and induce even larger concentration gradients as well as increase TJq . If the concentration gradients are large enough, even the highly 189] Establishment of Ionic Concentration Gradients in (he Anode Boundary Layer and their Relationship to the Anodic Overpotential soluble PbSiF 6.4H 20 salt can precipitate \ Fig. 3 shows how the formation of secondary products can be promoted by dissolution of the anode using high current densities. rjQ is the main component of the anodic overpotential values shown in Fig. 3. Moreover, TJq is related to the porosity and tortuosity factors resulting from the presence of precipitated products in the anode vicinity. Concentration overpotential also contributes to the rjA increases shown in Fig. 3. 6 0 0 0 5 0 0 0 -4 0 0 0 CM E \ CL E < ' ( / ) 3 0 0 0 c Q c OJ 1_ 13 O 2 0 0 0 1 0 0 0 Anodic Overpotential • Current Density 0) o > < 5^  c OJ -1—' o CL i_ OJ > O o T5 O C < 1 4 0 0 2 8 0 0 i . _ i o 4 2 0 0 Time, sec Fig. 3 Anodic overpotential response (uncorrected for TJQ) of pure lead to the application of successive current steps Experimental conditions: Electrode area 2.34 cm2, [PbSiFJ^.35 M, [HjSiFd^.SO M, [SiOJ=0.13 M, =2 g 1 aloes and =4 g l' 1 lignin sulphonate, T=40±1.5'C, bulk electrolyte electrical conductivity K=330mmhos cm"1. Beaker electrochemical cell, electrolyte volume =300ml, bulk electrolyte recirculation rate =6 ml min"1. Solartron Electrochemical Interface-IEEE Card-IBM XT computer Left axis: Current steps applied as a function of time Right axis: Anodic overpotential response (uncorrected for r\^) EL. Establ ishment of Ionic Concentrat ion Gradients i n the Anode Boundary Layer and their Relat ionship to the Anodic Overpotent ial In the previous section it was shown that during the dissolution of pure lead, T| A increases almost exclusively due to changes in its ohmic component. By subtracting rjQ from n,A, the activation and concentration overpotentials can be 1 The maximum solubility of pure PbSiF6.4H20 at 40 °C is 5 M (see Appendix 7). [90] Establishment ol Ionic Concentration Gradients in the Anode Boundary Layer and their Relationship to the Anodic Overpotential obtained \ The division of the anodic overpotential in its ohmic, activation, and concentration components was attempted by studying the anodic response of pure lead to current steps. Prior to the experiment -0.5 mm of the exposed surface of the working electrode was removed by anodic dissolution at low current density. This aided in obtaining reproducible results. Variation in rjA as a result of the presence of addition agents was studied using the same cell and electrodes 2 . The thickness of the hydrodynamic boundary layer was not controlled, yet, by fixing the recirculation rate of the bulk electrolyte, reproducible results were obtained 3 . c CD Q c CD v_ i_ (J Fig. 4 Current step function used to study the establishment of concentration gradients in the anode boundary layer. The transient period for both current rise and fall was smaller than 10 usee. The time tj marks the onset of the current interruption. Time Fig. 4 shows the characteristics of the current steps used to study the anodic behavior of pure lead. After the application of each current step, current was 1 As described in Chapter 2, concentration overpotential,T\C, develops due to the establishment of concentration gradients in the anode boundary layer and is a function of the current density and the hydrodynamic conditions. Activation overpotential, T^, develops due to the transport hindrance that the charge carriers find during their movement across the Helmholtz electrical double layer, can be determined accurately in the absence of concentration gradients and only when it is controlling the reaction rate. 2 The experiment started by analyzing the T]a changes using an additives-free electrolyte. Subsequently, this electrolyte was slowly substituted with an electrolyte of matching composition but containing addition agents. 3 The hydrodynamic conditions in the vicinity of the anode/electrolyte interface are more nearly a product of convection than of electrolyte recirculation. However, electrolyte recirculation assured uniform electrolyte composition between the reference electrode and the anode/electrolyte interface. [91] In the absence of addition agents in the bulk electrolyte interrupted and the decay potential was followed until it reached its former rest potential value (=0 mV). Then, the current density was increased and the next current step was applied. A. In the absence of addition agents in the bulk electrolyte Fig. 5 shows the changes in rjA due to the application of the current steps. Right after current is applied there is an abrupt change in n,A \ This steep overpotential change arises due to the presence of the n Q 2 and can be described by the following relationship (see also Fig. 6) : r\A (immediately after application of current) = IRS = rjn ...2 Fig. 5 Anodic overpotential response (uncorrected for T|n) of a pure lead electrode to the current steps described in Fig. 4, in the absence of of addition agents (compare with Fig. 5). Experimental conditions: electrode area 2.34 cm2, [PbSiFsl^.35 M, [ H j S i F J ^ ^ M, [SiOJ=0.13 M, T=40±1.5*C, beaker electrochemical cell, electrolyte volume =300ml, bulk electrolyte recirculation rate =6 ml min . Solartron Electrochemical Interface-IEEE Card-IBM XT computer. Current steps were applied only after the electrode had reached rest potential conditions (T|A=0 mV). Overpotential readings were taken 0.10 sec after the application of each current step. Each curve corresponds to the T | A response to a different current density, as follows (from bottom to top): 10, 50,100,150,206,250,300, 500, 800,1000,1400, and 1600 Amp m'2. 300 > E < c OJ -*-> o Q . i _ CD > o o x> o c: < 250 200 •-150 100 50 Each Curve corresponds to the TJA response to a different current density step from tower to higher current densities Increasing Current Density I i i i I 10 15 20 Time, sec 25 30 1 The first T I a reading was taken 100 msec after the application of the current step. Oscilloscope measurements at shorter times indicated that the T | A value at time zero could be obtained by extrapolation of the measured data. 2 tin prior to and during the application of the current step was determined by using AC impedance techniques (see Section III). In addition the ohmic drop compensation routine built-in the electrochemical interface was used to obtain r\a (see Appendix 6). [92] In the absence ol addition agents in the bulk electrolyte The Rg value obtained from the slope of the plot shown in Fig. 6, was nearly equal to the R g value obtained prior to the application of the current steps. The activation overpotential, if present, would be observable by a non-zero intercept or as a curvature near the origin. Evidently, activation overpotential is not controlling the dissolution of the lead anode. The T|A values compensated for the initial r|n (Fig. 6) are presented in Fig. 7. The overpotential obtained immediately after application of current is very close to zero (which implies that rjac=0 mV) 1 . Subsequent increases in the anodic overpotential are due to changes in the concentration of ionic species within the anode boundary layer2. Thus, increases in r|A are nearly equal to changes in its rjc component. 300 240 > E CL o o E O • «—IL ohmic drop right after applying the current step -; I/" /7 i i i i i i i i i i I i i i i i i 1 i i i : i i i 1 i i i i i i i 1 i i i Fig. 6 Changes in T)Q as a function of the applied current density. Tin values derived from the data shown in Fig. 5. T|n values obtained from high frequency AC measurement (under rest potential conditions) were consistent with these readings 400 800 1200 1600 Current Density, Amp.rrf2 200 1 As described by Eq. 2, at time t=0, T | C = 0. Thus, the overvoltage at t=0 becomes equal to the initial value of the activation overpotential [3,p. 356]. 2 As the anode dissolves, an extra increment to t\a can also be present in these measurements. n,n changes can be neglected during the first seconds after the application of current. [93] In the absence of addition agents in the bulk electrolyte 40 r i i i i i i i i i | | -U 1 1 1 1 < ^ j_ Each Curve corresponds to the T J A <r 35 j- response to a different current density step f from lower to higher current densities S  3 0 ~~~~ " f r t o c : / "—~~ . ^ Fig. 7 Anodic overpotential response (corrected for initial T|Q) of a pure lead electrode to the current steps described in Fig. 4. . — : / — i increasing ~£ U / T Current I OJ j- f / ' Density From the rjA data shown in Fig. 5 the T ) N values shown in Fig. 6 were subtracted. Each curve corresponds to the T | A values obtained at different current densities, as follows (from bottom to top): 10, 50,100, 150,206,250, 300, 500, 800, 1000, 1400, and 1600 Amp m'2. u • • • • • 0 5 10 15 20 25 30 T i m e , s e c The anodic overpotential response during the first seconds after the application of the current step was modelled by using the analytical solution of Fick's diffusion equation under unsteady state conditions. To solve this equation the following assumptions were used: 1) Absence of Migration 2) Absence of Convection 3) Unit Activity coefficients 4) Dissolution of lead is not controlled by kinetics (r|ac=0). 5) Linear semi-infinite conditions Description of the boundary conditions required to solve this equation are provided in Appendix 8 along with its analytical solution. From this solution, the following relationship between the concentration overpotential and the square root of time should be observed if the dissolution process is dorninated by diffusion: eXP[ RT J nFCbp.+2y By defining: [94] In the absence ol addition agents in the bulk electrolyte O, =exd 1 *|_ RT 21 1 Eq. 3 can be expressed as a linear equation: <bx=mD-jrx+bD ...4 Thus, by plotting d>j vs.'V^a straight line with slope, mo, and intercept, should be obtained. By using the data shown in Fig. 7, and assuming that rjJO.tJ^A, the plots shown in Fig. 8 were obtained. In this figure, a linear relationship between <J>j and the square root of time is limited to times smaller than 1 sec \ From curve fitting these data to Eq. 4, the data shown in Table 1 were obtained. Correlation coefficients close to 1 were obtained in almost the whole range of current densities studied. The average diffusion coefficient, Dpb+2, agrees with the values reported in the literature a . This diffusion coefficient, while dominated by the movement of Pb+ 2, also includes the effects of other ions (SiF6 2 and H + among others). Changes in the transference number of the lead ions will take place when concentration gradients are fully developed and this will affect the absolute value of this coefficient3. The presence of these concentration gradients is observable in the analyzed data, as departures from linearity and as changes in the value of the intercept from unity4. The agreement between the solution of Fick's equation and the results of the current step experiments confirms that in the absence of addition agents, the lead dissolution process is controlled by diffusion. 1 As seen in Fig. 8, the larger the applied current density the smaller the linear region between the square root of time and O,. 2 Diffusion coefficients for lead in HCI04-Pb(CI04)2 electrolytes at 25 "C reported in the literature are: D r o + 1 = 9.4x10"* cm2/sec [1]; Dp4+1 = 4.8X10"6 cm2/sec [4j. 3 The solution of Fick's second law presented in Appendix 8 implies that the transference number of lead is zero. Any departures from this transference number will affect the obtained diffusion coefficient. 4 Notice also that bD decreases as the current density increases. [95] In the absence of addition agents in the bulk electrolyte Fig. 8 Changes in <&, as a function of the square root of time, -v/f^  From the data presented in Fig. 7. Each curve corresponds to the <t>! values obtained at different current densities, as follows (from bottom to top): 10,50,100,150,206, 250, 300, 500, 800, 1000, 1400, and 1600 Amp m"2. Table 1 Results of the analysis of the concentration overpotential increases during the first second after application of the current steps. Fick's Second Law approximation. Current Fitting Parameters of Eq. 4 Density, TUry Regression D +2 Amp-m"2 Coefficient, r 2 cm2-sec 1 50 1.00 0.0371 0.927 5.1E-06 100 0.99 0.0720 0.979 5.4E-06 150 0.983 5.0E-06 250 ^ ^ ^ ^ ^ ^ 0.1614 """"""""""" 6.7E-06 300 0.97 0.1946 ii/iiiiiiiiiiii 6.6E-06 400 0.96 0.2775 0.957 5.8E-06 500 0.95 0.3624 0.963 5.3E-06 800 0.91 0.5672 0.951 5.6E-06 1002 0.89 0.8205 0.964 4.2E-06 1398 0.83 1.1494 0.959 4.1E-06 1598 0.80 1.1921 0.940 5.0E-06 5 . 3 ± 0 . 8 x l 0 6 [96] In the absence ol addition agents in the bulk electrolyte If concentration overpotential is the only source of potential (after subtracting riJ its presence will be observed after interrupting the current. This can be seen in Fig. 9 which shows the decay in the anodic overpotential corrected for ohmic drop obtained after interrupting the current \ 3 0 > E < V— c cu c> CL i_ <D > O o TJ O C < Fig. 9 Decay in the anodic overpotential (corrected for TIQ) as a function of the interruption time, t2. t1-t2=460 sec (see Fig. 4 for a description of the relationship between tt and t^ . Other experimental conditions as described in Fig. 5. Each curve corresponds to the T | A value obtained after the interruption of the applied current density. Applied current densities were as follows (from bottom to top): 10,50,100,150,206, 250, 300, 500, 800, 1000, 1400, and 1600 Amp m"2. i i i i i i i i i i i i i i i i i i i i i i i i i i i i 4 6 8 10 Time, sec By solving Fick's equation under current interruption conditions (see Appendix 8), the following linear relationship should be observed: 0>2 = mD[V^-VS + ^  ...5 where: 0 2 = exp RT with rrto and bD as defined by Eq. 4. Eq. 5 is applicable only when ti is very small (less than 1 sec) because convection will stop the thickening of the anode boundary layer. Fick's second law could not be used to analyze the T| A response upon current interruption 1 T|n was measured prior to the interruption of current by measuring the impedance at high frequencies and by using the current interruption routine built into the SEI. Upon current interruption, the observed ohmic drop coincided with that obtained in these measurements. [97] In the presence ol addition agents in the bulk electrolyte because the boundary conditions are not known precisely. Nevertheless, what the data in Fig. 9 show is that, upon current interruption, concentration gradients relax and this relaxation can be followed by monitoring the anodic overpotential dependance with time. B. In the presence of addition agents in the bulk electrolyte If addition agents are added to the bulk electrolyte, the rjA response changes (Fig. 10). Upon subtracting the initial T|Q value from the r\A readings, the remaining overpotential was positive (Fig. 11). This rjA value decreased during the first milliseconds after the application of current. After this initial decrease, changes in TJa were a function of the applied current density. In any case, TJa increased only up to the point at which convection stops the thickening of the boundary layer. > E < .K5 - 4 — ' C OJ - 4 — ' o CL OJ > O u TJ O C < 200 175 150 125 100 75 50 25 Each Curve corresponds to the 77A response to a different current density step from lower to higher current densities Increasing Current Density Fig. 10 Anodic overpotential response (uncorrected for T|Q) of a pure lead electrode to the current steps described in Fig. 4. conditions: 2.34 cm2, Experimental electrode area [PbSiFs]=0.37 M, [H2SiF6]=0.82 M, [SiOJ=0.13 M, T=40±1.5"C, =2gl"1 aloes and =A g l'1 lignin sulphonate, beaker electrochemical cell, electrolyte volume =310ml, bulk electrolyte recirculation rate =6 ml min"1. Solartron Electrochemical Interface-IEEE Card-IBM XT computer. i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 i i 11 1 1 i 1 1 11 1 1 i i 1 1 1 11 i 11 1 1 11 i i 5 10 15 20 25 30 Time, sec Current steps were applied only after the electrode had reached rest potential conditions (r|x=0mV). Overpotential readings were taken 0.10 sec after the application of each current step. Each curve corresponds to the T | A response to a different current density, as follows (from bottom to top): 10, 50, 100, 150, 200, 250, 300, 400, 500,600 Amp m"2. The differences in the r\A and T| N values at the beginning of the application of the current steps where consistent throughout the range of current densities studied (see Figs. 12 and 13). Such differences are the result of the presence of an adsorbed film of addition agents in the electrode interface. Such a film extends [98] In the presence of addition agents in the bulk electrolyte (A) (B) 18.8 r- 18.8-688. Mr11 i l i 1111 11 l 1111 i i 11 i 1111 i i 111 i I 11111 111 .888 28.6 48.8 (1.8 88.8 188. • B88t"' ' ' I ' • • I ' ' ' I ' ' • I ' • ' I ' ' • I • • ' I • ' ' I ' ' ' I ' • ' I .888 6.88 12.8 18.8 24.8 38.8 Time, sec Time, sec Fig. 11 Anodic overpotential response (corrected for initial T|J of a pure lead electrode to the current steps described in Fig. 4 From the data shown in Fig. 10 the T|Q values shown in Fig. 12 were subtracted. Each curve corresponds to the values obtained at different current densities (in Amp m"2) as shown to the left of every curve. For the different current densities applied, TJA values at t=0 were as follows: Current density. Amp m 2 50 150 250 406 600 T|A corrected for T|Q (at t=0), 10 8.2 9.6 11.5 9.1 mV (A) Long range variation of the TIA response (corrected for initial TIJ. T|a increases up to the point at which convection stops the thickening of the boundary layer. (B) Detail of the rjA increases. the region where concentration gradients can be found. Upon passage of current, concentration gradients become established, changing the resistance of the film and the kinetics for lead dissolution. The non-zero intercept of the anodic overpotential curves indicates that inhibition is present as a result of this adsorbed film. On account of the synergistic effect between addition agents, activation overpotential, and concentration overpotential, no simple analysis of the T] A transients can be performed. Yet, the riA response indicates clearly that the addition agents affect the anodic reaction for lead in such a way that r|a c can no longer be considered to be zero. [99] In the presence of addition agents in the bulk electrolyte 288. - * Anodic O v e r p o t e n t i a l ( r i g h t a f t e r a p p l y i n g c u r r e n t s tep) —0 lineonpensated Ohnic Drop ( f r o n AC neasuranent) 168 128 , 88.8 48.8 .888 i ' i I I I _I_I_L 1 I I I .888 488 688, 128. 248 . 368. Current Density, Amp/m2 Fig. 12 Comparison between the anodic overpotential value obtained right after application of current (*) and the uncompensated ohmic drop obtained from the high frequency intercept of the impedance spectrum (O) TJA values derived from the data presented in Fig. 10. T | F T values obtained from the high frequency AC measurements under rest potential conditions (i\n = IRJ. [100] In the presence of addition agents in the bulk electrolyte 1 8 8 . 8 8 . 8 1 T3 C -M o & 4 8 . 8 c5 a -a o <2 2 8 . 8 MM M M H M M M M - * M M » » « M » » cd = 4 8 8 . AMP/M 1 1 2 . 8 -9 . 6 8 7 . 2 8 4 . 8 8 -2 . 4 8 ,0004^-L. . 8 8 8 O v e r p o t e n t i a l decay caused by the presence of a d d i t i o n agents tmu»»ii*i 1 • • • 1 • ' ' 1 ' ' ' 1 ' ' ' 1 ' ' • 1 ' •' 1 ' • • 1 • • • 1 ' ' 1 1 . 6 8 8 1 . 2 8 1 . 8 8 2 . 4 8 3 . 8 8 • BOO-j- 1 1 1 I 1 1 1 I 1 1 1 I 1 1 1 I 1 1 1 I 1 1 1 I 1 ' 1 I 1 1 1 I 1 1 1 I 1 1 1 I . 8 8 8 . 6 8 8 1 . 2 8 1 . 8 8 2 . 4 8 3 . 8 8 Time, sec Fig. 13 Changes in the anodic overpotential upon application of a current step. From the data presented in Fig. 10. Applied current density: 400 Amp m~2. Upon application of current TJA increases from 0 to 96 mV and decreases slowly afterwards. From A C measurements under rest potential conditions an Rg value of 2.09 £2cm2 was found. Thus, Tln=2.09£2cm 2 * 40 mAmp cm 2 =83.6 mV The inset plot shows the changes in r\A (mV) as a function of time (sec) after correcting the anodic overpotential for r\a. Finally, the ohmic drop measured by either fast current interruption or high frequency AC impedance measurements predicted T)a values which were slightly larger than measured (Fig. 14). The difference between these values is partially due to the presence of a film resistance, (so-called "film inhibition'). [101] Introduction s c II «• 0 a. >. a » o i • 20 .0 -* i 6 . 0 Y •Unaccounted • the p r e s e n c e o h n i c d r o p c a u s e d 1>«J at a d d i t i o n a g e n t s 88. e 12 .0 8 . 8 8 -i 66 .0 4 .aa -.000+' 1 .eee 1 1 1 » 1 1 1 1 1 1 1 1 1 1 1 1 .800 1.60 i l i i * 1 i i i 1 i i i 1 i i i 1 i i t 1 2.40 3.20 4 . 8 8 44 . 0 cd= 400. •8 | 22 .8 Fig. 14 Changes In the anodic overpotential as a function of the current Interruption time. Experimental conditions as described in Fig. 10. After applying current (1=400 Amp m"2) for 320 sec (trt2=320 sec) current was halted and the overpotential decay was followed as a function of time. Upon current interruption % decreases abruptly (from 105 to 12 mV). From AC measurements prior to the interruption of current an R, value of 2.17 Qcm2 was found. Thus. Tin=2.17flcm2 * 40 mAmp cm 2 =86.8 mV. The inset plot shows the changes in T | A (mV) as a function of time (sec) after subtracting T | Q from the first r^ reading. HI. A C Impedance A . Introduction In the previous section, DC (direct current) transient techniques were used to study the dissolution of pure lead and its relationship to the components of the anodic overpotential. In this section, a complementary study using AC techniques is presented1. 1 For a description of the implementation of the AC techniques see Appendix 6. [102] Impedance spectra obtained in an electrolyte without addition agents In the absence of a net DC current, application of an AC voltage at low frequencies (axlO3 rad/sec) generates sinusoidal concentration gradients whose amplitudes decrease exponentially from the electrode surface towards the bulk electrolyte [5,61. These concentration gradients cause a characteristic AC energy absorption. As the AC frequency is increased (up to 105 rad/sec), ionic diffusion cannot keep up with the change in direction and so energy absorption disappears to be replaced by a phase angle characteristic of a capacitor which represents processes in the vicinity of the electrical double layer. At extremely high frequencies (larger than 105 rad/sec) only the movements of ions and dipoles in solution, representing dielectric properties, can keep up with changing potentials {7,811. This phenomenon is rarely seen because such high frequency measurements in liquid electrolytes are experimentally difficult or inaccessible. AC impedance studies in the presence of a net Faradaic current are analogous to the impedance studies in the absence of a net DC bias provided the electrochemical processes under investigation behave linearly. If conditions at the electrode/electrolyte interface change due to the passage of current, they will be reflected in the AC impedance spectrum. For example, nonlinearities in the response of the system can produce a net rectification current and a rectified voltage. The presence of these nonlinearities and their effect on the related electrochemical processes have been studied by using Faradaic Rectification Techniques 16,9]. In highly reversible systems where diffusion controls the dissolution process (such as lead dissolution in H 2SiF 6-PbSiF 6 electrolytes), AC studies in the presence of a DC current can provide a better insight as to the extent to which concentration gradients become established in the anode boundary layer. Also, information on the effects produced by the presence of addition agents can be derived from AC studies. B. Impedance spectra obtained in an electrolyte without addition agents The AC behaviour of pure lead under rest potential conditions (i.e. in the absence of a net Faradaic DC current) is shown in Fig. 15 2 . The straight line 1 The bulk electrolyte has a uniform composition and its properties are a function of its geometrical capacitance C g and bulk resistance Rb. From these values, the dielectric relaxation time of the bulk electrolyte, T d , can be obtained (xD=RbC8) [7]. 2 A sinusoidal current waveform with an amplitude of 21.3 Amp/m2 R.M.S. was swept from lower to higher frequencies while the impedance was measured at every frequency. Application of DC currents of the same order of magnitude of the amplitude of the AC waveform (see Fig. 7) resulted in overpotentials lower than 5 mV. [103] Impedance spectra obtained in an electrolyte without addition agents obtained indicates that diffusion in the electrode boundary layer is the only mechanism controlling the dissolution/deposition of Pb+ 2. At high frequencies, the interception of the impedance curve with the Z% axis is equal to the value of the uncompensated ohmic resistance, R g 1 . When this value was subtracted from the impedance curve, a 45° straight line was observed in the impedance diagram (Fig. 16) 2. U 4 £ N I 120 — . B9B . 060 . 030 1—xE 0 ra<l/sco - 1 .00 - • 2 . 50 — • 6 . 28 z D IS . 78 z_ • 39 . 63 - -4 99 . 58 — 6 298 . — O 628 . - • 1378 . - * 1771 . . 000 . O0O . 320 . 640 .968 Z r a * l ft-CM* 1 .28 1 .60 Fig. 15 Impedance diagram of pure lead under rest potential conditions (in the absence of addition agents) Experimental conditions: electrode area 2.34 cm2, [PbSiFel=0.35 M, [H2SiF6]=0.84 M, [SiO2]=0.13 M, T=40±1.5"C, beaker electrochemical cell, electrolyte volume =300ml, bulk electrolyte recirculation rate =6 ml min"1. Solartron Electrochemical Interface-IEEE Card-IBM XT computer. Impedance curve obtained under galvanostatic control, A C waveform amplitude 21.3 Amp m'2 RM.S. A total of 65 experimental points are plotted. Some of the frequencies (In rad sec"1) at which these points were sampled are indicated in the diagram From the high frequency intercept of this plot with the Zg, axis, the Rg value can be obtained (Rg= 1.40 Qcm2). 1 For a fixed distance between the reference and the working electrodes, this value was very reproducible (variations were less than 0.5%). These Rs values were used to obtain r\n prior to the application of the current steps (see section ll.b). 2 Impedance diagrams in which the real part of the impedance is the abscissa, Z„, and the negative of the imaginary part of the impedance is the ordinate, -Z,, are also known as Argand plots. In an Argand plot the AC frequencies at which the impedance was measured are also shown. [104] Impedance spectra obtained in an electrolyte without addition agents iaer-xE a .896 -.872 N .848 .824 .eee Experimental — Analogue node I rad/sec A i.ee * 2.58 • 6.28 • 15.78 • 39.65 « 99.58 6 258. 0 628. • 1578. 1771. Fig. 16 Detail of the impedance curve shown in Fig. 15 (after subtracting the R, value). Some frequencies (in rad sec'1) are shown for both the experimental (solid line) and the regressed data (dotted line). The impedance curve was fitted to a CPE element (Z„,E = ^ (/cof'") from which the following values were obtained: B , ^ . 139 Qcm2sec** and Ta^O.50. Quality of Fit Parameters (65 experimental points were fitted to the CPE analogue): r 2„=0.951, Iyj2=2.19xl0'3 Q 2cm 4 r23=0.962 Iy3?=1.70xl0"3 £rcm* ^=0.958 ly J 2=3.75xl0 3 Q W i i i .eee .824 .848 .872 Zreal fi-CM" .896 xE 8 i i i I .128 To model the diffusion processes that take place in the electrode boundary-layer, distributed elements have been used [81112. Among these distributed elements, the Constant Phase Angle Element (CPE) has been used extensively [71. The impedance of the CPE element can be described by the foUowing equation: When the fractional exponent, ^zc , approaches a value of 0.5, the CPE element describes a serin-infinite diffusional process. Under these conditions the 1 All real electrical analogue elements are distributed in space, i.e. their absolute value changes with position due to their finite size. Diffusion processes are distributed over the electrode boundary layer, and constitute a classical example of a distributed element [8]. 2 A "distributed element" is a component in an analogue model that represents properties of the system distributed over macro distances, such as ionic concentration gradients across the Nernst diffusion layer. [105] Impedance spectra obtained in an electrolyte without addition agents impedance of the CPE element is equal to the so-called Warburg impedance [7.10,11] \ The Warburg impedance for the serru-infinite diffusion case is defined as [7.8.12]: Zw,~ = ^ (/"w)^ 5 ...7 When *¥7jC =0.5 the Warburg coefficient can be obtained from the Bj value (Bj = ov). Thus, ^ is a subset of the generalized CPE response. For the Pb/Pb + 2 equilibrium reaction ov is given by the following equation: °V, - = RT (n ^°-5 (nF)2 Cpb«Dpb« RT 1 ..8 When is different than 0.5 a generalized representation of the Warburg coefficient 113-15]2 can be obtained from the following equation: The impedance curve shown in Fig. 16 was curve fitted to Eq. 6 from which the following values were obtained: Bx= 0.139 Q cm2 sec'Vzc and ^ 20=0.5. When these values were incorporated in Eq. 8, Dpb+2 was found to be equal to 2. lxlO"6 cm2/sec. For different experiments this number varied by as much as one order of magnitude 3 . Nevertheless, it was always observed that diffusion was the only controlling mechanism for lead dissolution/precipitation. Activation polarization if present would have been observed in the Argand diagram as an arc from which 1 Warburg studied the establishment of concentration gradients in the electrode boundary layer upon application of an AC voltage. By solving Fick's second law under AC conditions, Warburg found that a square root frequency dependance of the impedance should be observed if the process was controlled by diffusion. This square root dependance is equivalent to observing a 45" relationship between the real and the imaginary components of the impedance (or a value of 0.5). The assumptions under which Warburg solved Fick's second law are similar to those described in the previous section to solve the DC transient case: presence of a supporting electrolyte, unit activity coefficients, absence of convection. Any departures from these conditions will be reflected in departures from the predicted theory. 2 Notice that Warburg impedance is strictly valid only when 4*^ =0.5. Unfortunately, in the study of diffusion processes by AC techniques, ^  values of 0.5 are the exception rather than the rule [13]. By introducing a generalized form of the Warburg impedance the physical meaning of each of the involved parameters may change. For example, variations in the *FZC value have been related to the presence of irregularities in the electrode surface at the micrometer level. Also, DM + 2 no longer represents an absolute diffusional coefficient but rather an integral value related to all the ionic species present across the diffusion layer. 3 Lack of well-defined hydrodynamic conditions could be attributed to this large variation in the observed diffusion coefficients. As can be seen in Eq. 9 when 4^ departs from 0.5 it is not possible to obtain the diffusion coefficient unless the thickness of the Nernst boundary layer is known. [106] Impedance spectra obtained in an electrolyte without addition agents 6.eS |-xE-2 i.ee • 2.SB • 6.28 • 13.78 D 39.65 4 99.58 a 258. 0 628. • 888. 4> 1487. xE-2 Fig. 17 Impedance diagram of pure lead in the presence of an anodic current 1=150 Amp m'2 (after subtracting the R, value). Experimental conditions: as described in Fig. 15. Some frequencies (in rad sec"1) are shown for both the experimental (solid line) and the regressed data (dotted line). The impedance curve was fitted to a CPE element from which the following values were obtained: B,=0.066 Q cm1 sec"y2C and Vv-OAL Quality of Fit Parameters (63 experimental points were fitted to the CPE analogue): rV=0.973, ly.l^.OSxlO^ Q2cm4 r23=0.988 Iy3r=8.95xl0"5 Q2cm4 ^=0.988 ly J2=2.33xl0^ ftW 4.88 6.88 the exchange current density, i^, and the double layer capacitance, C^, could have been obtained (to obtain the so-called Randies circuit [161). Evidently, for lead dissolution in the absence of addition agents rjac->0 (i.e. *«-*»). Table 2 Variation of the B, and ^Vjc fitting parameters with current density Current Density, Amp/m2 0 0 100 150 150 200 Bi, Qcm2secyzc 0.139 0.139 0.074 0.066 0.070 0.056 0.50 0.50 0.43 0.43 0.43 0.43 AC impedance curves obtained ~2000 sec after the application of the set current density. The amplitude of the applied AC waveform was set to 21.3 Amp/m2 RM.S. The experimental impedance curves were fitted to Eq. 6 using between 60 and 66 points Regression coefficients and residuals for the regression curves were ( l<co<2000 rad/sec ]: r29t>0.96 with 1 y„ 1 a< IO"3 Q2cm4 r23>0.95 with 1 y 3 1 2< 10 4 Q2cm4 AC impedance curves obtained while a net anodic DC current was applied were similar to those observed under rest potential conditions (Fig. 17). Upon application of current the AC impedance decreases with respect to the impedance [107] Impedance spectra obtained in electrolytes containing addition agents observed In the absence of a net DC current. Straight lines with slopes close to 39° were obtained (i.e. *Fzc~0.43) while the B x values were between 0.07 and 0.05 Q cm2 sec'** and appear to change with current density (see Table 2). C. Impedance spectra obtained in electrolytes containing addition agents Addition agents are known to affect the electrochemistry of lead fundamentally through changes in its kinetic parameters [1.17.18]. The 'levelling" phenomenon found in electrodeposits and attributed to additives is partially due to a re-distribution of current from changes in the inhibition intensity [19,20] \ 3 .00 I — 2 . 40 V I « 81 <* C ... N I X . 8 0 1 . 20 .688 .000 r a d / s e c .863 « . 48 • 2 . se • I S .78 • 99 .38 •4 628 . 396S . O 25815. 137834. * 198786. .888 Fig. 18 Impedance diagram of pure lead under rest potential conditions (in the presence of addition agents) Experimental conditions: electrode area 2.34 cm2, [PbSiF6]=0.37 M, [H2SiFe]=0.82 M, [SiO2]=0.13 M, T=40±1.5°C, =2 g l" 1 aloes and =4 g l" 1 lignin sulphonate, beaker electrochemical cell, electrolyte volume =310ml, bulk electrolyte recirculation rate =6 ml min'1. Solartron Electrochemical Interface-IEEE Card-IBM XT computer. Impedance curve obtained under galvanostatic control, AC waveform amplitude 21.3 Amp m"2 RM.S. A total of 130 experimental points were obtained. Some of the frequencies (in rad sec"1) at which these points were sampled are indicated in the diagram (^ =1.74 Qcm2). 1 "Inhibition intensity" in Winand's terms [19,20] includes activation overvoltage as well as other polarizations caused by addition agents. [108] Impedance spectra obtained in electrolytes containing addition agents The impedance spectrum obtained when addition agents are present in the bulk electrolyte is shown in Fig. 18. There are big differences between this spectrum and that obtained in the absence of addition agents (compare Figs. 15 and 18). The presence of two weU-defined arcs can be seen in Fig. 18. The arc observed at large frequencies (a»4000 rad/sec) is related to the charge transfer for the Pb/Pb + 2 reaction [i^, C )^ whereas the arc which spans over frequencies smaller than 4000 rad/sec is associated with the presence of an adsorbed layer of addition agents that affect the movement of ions from/towards the electrode surface (and the region where concentration gradients can be present) \ The Rg value was not affected by the presence of the addition agents. u I Ci 91 t £ ... N I 8 . 0 8 i — 6 . 4 0 — 4 . 8 8 — 3 . 2 8 1 . 6 8 . 0 0 0 r a d / s e c A . 8 6 3 • . 4 0 • 2 . 5 0 • 1 5 . 7 8 • 9 9 . 3 8 -4 6 2 8 . 6 3 9 6 5 . O 2 5 0 1 5 . • 1 5 7 8 3 4 . * 2 2 2 9 5 3 . 2 1 . 3 Anp/n2 4 . 3 A M P / M 1 J I L . 8 8 8 4 . 8 8 7 . 2 0 Z r e a l ft-CM* 9 . 6 0 1 2 . 0 Fig. 19 Impedance diagrams of pure lead under rest potential conditions obtained at two different amplitudes of the applied AC waveform (in the presence of addition agents) Experimental conditions: as described in Fig. 18. The AC amplitude values shown in the plot refer to their RM.S. value A total of 130 experimental points were obtained. Some of the frequencies (in rad sec ]) at which these points were sampled are indicated in the diagram. Ra. was subtracted from both impedance curves. 1 This low frequency arc was only observed after a small Faradaic current was applied (less than 50 Amp/m2 for 400 sec), after which, it was always present in the impedance curves obtained under rest potential conditions. [109] Impedance spectra obtained in electrolytes containing addition agents Under rest potential conditions, a decrease in the amplitude of the applied AC waveform produced a decrease in the size of the low frequency arc while the high frequency arc remained virtually unchanged (Fig. 19) . It appears as if by decreasing the amplitude of the AC waveform, the size of the region where concentration gradients are present expands resulting in apparent increases in the impedance. (A) (B) Fig. 2 0 Analogue circuits used to model the high frequency response of the Impedance curve shown In Fig. 15. The analogue shown in (B) is obtained when Z C P E - ^ . This will happen at high frequencies or small values of the Bj parameter. (A) Analogue used to represent the high frequency region of the impedance spectrum: Z(j(6) = R,+ — l+/?aC^O'(0) + C^iO'<fl) (B) Analogue used to represent processes taking place in the electrical double layer: [110] Impedance spectra obtained in electrolytes containing addition agents Analysis of the impedance spectrum obtained at high frequencies (co>500 rad/sec) was done by using the electrical analogue shown in Fig. 20. In this circuit, Ret represents the charge transfer resistance which is related to i„ through the following equation [21] The impedance of the analogue circuit shown in Fig. 20A can be described as follows 2 : Z(/co)=/?,+ lVJ — ...11 The CPE included in the analogue shown in Fig. 20A is used only to subtract the high frequency part of the arc observed at low frequencies from the charge transfer arc. This CPE is not intended to represent any particular process but only to subtract the higher frequency data. The values of the analogue elements obtained from the curve fitting process are as follows (Fig. 21): Rct= 1.665 Qcm2 (±5%), Cd,=20.6 fiF/cm 2 (±3%), B!=149.25 Qcm2 sec>l'zc (±5%), and ^ =0.74(12%). From the Revalue ^ was found to be equal to 82 Amp/m 2 (±5%). For the same electrode these values were reproduced within 15%. On the other hand, small changes in the bulk electrolyte composition, electrolyte temperature, bulk electrolyte recirculation rate, and electrode roughness appreciably affected the and C^  values. In any case, for a fixed electrolyte composition, i„ values were not smaller than 70 Amp/m 2 (70<(o<500 Amp/m2) whereas C^  values were between 18 and 30 |±F/cm 2 . Since in the absence of addition agents a charge transfer arc was not found (io-x»), it is concluded that the presence of the addition agents affects significantly the kinetics for the Pb/Pb + 2 equilibrium reaction. The decrease in the *<, values as a result of the presence of addition agents can be attributed to: (A) changes in the 1 The Stern-Geary equation has also been used to relate the steady-state corrosion current density, 4 and the polarization resistance, Rp [25]: \ P'P< I ' 1_N ^corr 2.303(8, + BC) 2 Analytical representation of the impedance was obtained by using the Laplace plane techniques described in Appendix 3. [ I l l ] Impedance spectra obtained in electrolytes containing addition agents Fig. 21 High frequency section of the impedance diagram shown In Fig. 18. Impedance curve was fitted to the electrical analogue shown In Fig. 20A (R. was computed from the high frequency Intercept of the Impedance curve with the Z, axis). From the curve fitting process, the following values were obtained: B,= 149.250 Q cm2 sec"¥zc, ^=0.741, F^l.SSSQcm2, 0^ =20.6 uF cm2. Some frequencies (in rad sec"1) are shown for both the experimental (solid line) and the regressed data (dotted line). Quality of Fit Parameters (51 experimental points were fitted to obtain the values of 4 parameters): rVO.973, l y a l ^ ^ x l O 1 Q2cm4 rVO.941 I y312=6.16xl0"2 Q2cm4 ^=0.985 ly^l^l . iexlO^Q'cm 4  electrochemically active surface area and (B) variations in the current distribution in the anode vicinity. An effective decrease in the value (considering that the electxochemlcally active surface area is the same in the cases presented in Figs. 16 and 21) would mean that the kinetics for lead dissolution and deposition have become "less" reversible. [112] Impedance spectra obtained in electrolytes containing addition agents The AC arc observed at co<4000 rad/sec is more difficult to model by an electrical analogue. Its presence is associated with abounded concentration region created by addition agents, some of which adsorb on the electrode surface changing the and values. The "spikes" observed during the application of the current steps (see Section Il.b) are undoubtedly associated with the phenomena displayed by the AC impedance curves. 2 .ae 1 .68 — Y 1 .28 a 91 £ N .888 , 488 .888 r a d / s e c A .863 • .48 • 2 .58 • 15 .78 • 99 .38 4 628 . 3965 . 0 25815. 157834. * 198786. Re s t P o t e n t i a l C o n d i t i o n s c d = 8 In the p r e s e n c e of a c d = 188 flny/h' .A J L_l_ - i I L_ I I I I I .888 . 788 .48 2.18 Z r e a l ft-CM* 2 .88 3 .58 Fig. 22 Impedance diagrams of pure lead obtained in the presence and in the absence of a net Faradaic current (in the presence of addition agents) Experimental conditions: As described in Fig. 18. The AC amplitude was the same in both cases (21.3 Amp m 2 RM.S) Rs was subtracted from both impedance curves. In the presence of a net anodic current, the impedance decreases significantly (Fig. 22). As the current density increases, the size of the arc observed at high frequencies decreases while the low frequency arc does not change to the same extent (Fig. 23). Eventually, at high current densities (cd >200 Amp/m2) the high frequency arc vanishes and only one arc related to diffusion in the anode boundary layer is observed. Thus, it appears as if during the anodic dissolution of lead the polarization created by the addition agents decreases as the current density [113] Impedance spectra obtained in electrolytes containing addition agents increases *' a. The decrease in the size of the low frequency arc may be the result of a defined boundary layer whose size has compacted due to the presence of a fixed electric field created by the passage of a net Faradaic current3 . I a 91 £ •p. N . s e e A r i d / t i c .863 • .31 _ • • 1 .58 7.91 . 168 - • 4 39 .63 199 . a 996 . — O 4991 . • 9959 . . 128 - * 15783. . 888 .848 .888 In the p r e s e n c e of a c d = 58 Anp/n> In the p r e s e n c e of a c d = IBB fthp/h' I I l .888 . 868 TJ 128 .188 Z r e a l ft-CM* , 248 . 388 Fig. 23 Detail of the Impedance diagrams obtained In the presence of a net Faradaic current (in the presence of addition agents) Experimental conditions: As described in Fig. 18. The AC amplitude was the same in both cases (21.3 Amp m"2 R.M.S) R, was subtracted from both impedance curves. 1 The exchange current density is also a function of the concentration of the electroactive ion in the electrode surface [22-24]. 2 Notice how the radius of the high frequency arc obtained in the presence of a net Faradaic current (^-.08 Qcm2, Fig. 23) is at least 20 times smaller than under rest potential conditions (Ret~1 -6 Qcm2, Fig. 21). The "apparent" charge transfer resistance decreases until at high current densities Rc t~0. The term "apparent" charge transfer resistance refers to the R* values that may be observable upon passage of a net Faradaic current when studying irreversible systems using AC techniques. 3 Notice that addition agents are also dispersed by the anodic process because: (A) the interface is retreating, and (B) there is a flux of Pb+2 in the opposite direction. Thus, decreases in the size of the low frequency arc as the current density increases can be due to a depletion of addition agents in the anode boundary layer. [114] Chapter 6 E lec t rochemica l Behavior of Lead bu l l ion Electrodes i n the Presence of S l imes I. Introduct ion In the previous Chapter it was shown that in the absence of addition agents in the bulk electrolyte, the Pb/Pb + 2 system behaves nearly reversibly (i.e. PboPb+2+2e~ with i,,-**0). The presence of addition agents in the bulk electrolyte decreases the reversibility of the system through small increases in the activation overpotential. Moreover, the addition agents were found to enhance the concentration gradients at the electrode/solution interface through the formation of specifically and/or electrostatically absorbed films. This Chapter deals with the establishment of concentration gradients within the slimes layer and their relationship to the anodic overpotential observed in the presence and in the absence of a net Faradaic current. All experiments shown in this Chapter were performed atT=40±l .5°C . using the beaker electrochemical cell (Fig. 3.1) and the Solartron equipment (Fig. 3.8). Data acquisition and control of the experiment were performed using an IBM XT personal computer via the IEEE interface (Fig. 3.7). Electrodes were prepared from the same anode1 (anode A, Fig. 3.3) as described in section 3.1 .B. Electrolyte was recirculated continuously at 6 rnl/min (cell volumes varied between 300 and 320 ml). The geometrical area of the electrodes2 was used to compute the current density and the impedance per unit area. In experiments in which addition agents were added to the electrolyte, any insoluble precipitates were removed prior to the introduction of the electrolyte to the cell. The assumed concentration of addition agents prior to the filtering operation was 2 g/1 aloes and 4 g/1 lignin sulphonate. The compositions of the electrolytes used in the various experiments presented in this Chapter are shown in Table 1. 1 Anode composition: 0.01% Sn, 0.02% Cu, 0.14% Bi, 0.25% As, 1.12% Sb, 81 oz/ton Ag. 2 The geometrical area of the electrodes was 1.44±0.02 cm2. [115] Introduction T a b l e 1 Characteristics of the experiments presented in chapter 6 Experiment Number Bulk Electrolyte Composition Bulk electrolyte Conductivity, K,atT=40#C, mmhos/cm Characteristics of the experiment Electrode Face Addition Agents [PbSiF6] mol/1 [HaSiFe] mol/1 [SiOJ mol/1 CA2 mould yes 0.27 0.69 0.14 300 Galvanostatic dissolution at 1=200 Amp/m2 CA4 mould yes 0.45 0.77 0.14 315 Potentiostatic dissolution at Econtn>l=220 mV CA5 mould yes 0.45 0.76 0.14 315 Galvanostatic dissolution at 1=800 Amp/m2 CA6 mould yes 0.45 0.73 0.14 320 Galvanostatic dissolution at 1=200 Amp/m2 CC1 air no 0.35 0.84 0.09 345 Galvanostatic dissolution at 1=200 Amp/m2 CC2 air no 0.36 0.83 0.09 345 Galvanostatic experiment. In the presence of a net Faradaic current the impedance spectra were obtained under galvanostatic control except in Exp. CA4 in which the curves were obtained under potentiostatic control. Under current interruption conditions all the impedance spectra were obtained under Galvanostatic control. The AC impedance was obtained in a wide frequency range (0.063<co<4xl05 .. rad/sec) 1 under either potentiostatic or galvanostatic control. The amplitude of the applied AC waveform was set to 5 mV R.M.S. and 35 Amp/m 2 R.M.S. respectively. In either case, 20 data points were obtained per decade of frequency swept2. All impedance spectra are reported with respect to the time at which the AC measurement started. Typical AC measurement times are shown in Table 2. 1 Under galvanostatic conditions application of AC frequencies in excess of 3x104 rad/sec often resulted in phase shifts produced by the Solartron Electrochemical Interface due to bandwidth limitations. On the other hand, under potentiostatic control, frequencies as high as 4x10s rad/sec could be applied without observing phase shifts. A phase shift is a displacement of the capacitative component of the impedance curve towards negative values [1-3]. 2 For example if 0.063<ox6300 there are log^j = 6 decades of frequency swept and the impedance is measured at 6x20=120 discrete points. [116] AC Impedance Characterization of the Starting Working Electrodes. T a b l e 2 Average times required to measure the AC impedance spectrum Frequency Range Time, Hrs O W rad/sec o w . rad/sec 0.063 408407 l . l 0.63 408407 .30 n. A C Impedance Character izat ion of the Star t ing Working Electrodes. Prior to the anodic dissolution of lead bullion electrodes their impedance was obtained under rest potential conditions. Table 3 summarizes the characteristics of the obtained spectra 1 . The differences between the various spectra are explained in the next paragraphs. Table 3 Summary of the values of the electrical analogue parameters obtained under rest potential conditions Frequency Range Derived Analogue Parameters Experiment Addition Pot/Gal R., Ra, On, ^zc and Sweep Agents Control rad/sec rad/sec Qcm2 Qcm2 uFcm 2 Qcm2 sec'" Amp/m2 Number CA2-7 yes Gal 560 99588 1.42 0.501 64 23.71 0.64 269 CA4-7 yes llltllll 315 250159 1.02 llliill i i ls l i i ! 1X45 0.39 72 CA5-7 yes Pot 560 111740 1.19 0.725 65.30 23.90 0.64 186 CA5-4 yes Gal 560 111740 48.9 liiiilll 0.56 157 CA6-2 yes Gal 177 157834 1.20 1.916 32.6 35.5 0.55 70 CC1-5 no Gal 628 15783 0.90 llliill 0.57 CC1-6 no Gal 628 44482 0.89 - : 2.88 0.45 CC2-7 no Gal 560 17709 0.85 1.88 0.59 CC2-2 no Gal 560 28067 0.85 - - 1.88 0.59 Different electrodes were used in every experiment. Impedance curves were obtained either under Potentiostatic (Pot) control or Galvanostatic (Gal) Control. Changes in the R, values reflect differences in the distance between the reference electrode and the working electrode. The spectra obtained in the absence of addition agents were curve fitted to the impedance function described by Eq. 1 while the spectra obtained in the presence of addition agents was fitted to the function described by Eq. 2. 1 The statistical parameters related to the quality of the curve fitting procedure are presented in Appendix 9. [117] AC behaviour in the absence of addition agents in the bulk electrolyte A. AC behaviour in the absence of addition agents in the bulk electrolyte The AC impedance spectrum of a typical lead anode (in the absence of slimes) under rest potential conditions and in the absence of addition agents is presented in Fig. 1 a * 3 . The uncompensated ohmic resistance, Rg, has been removed in this impedance diagram by subtracting it from the component of the impedance 4 . This impedance spectrum is similar to the obtained using a pure lead electrode (see Fig. 5.16) and can be described by a Warburg serni-infinite diffusion element which follows the response of a CPE element 5 : The impedance curve shown in Fig. 1 was curve-fitted to Eq. 1 to obtain the Bi and values. B x and *¥zc were found to be equal to 2.88 Q. cm2 sec*Vzc and 0.45 respectively. By comparing these values with those obtained when pure lead was studied (Bi-0.14 Qcm2sec"M'ZC7 and ^^-0.5) it is seen that remains practically unchanged, while Bj shows a marked increase in its absolute value 5 . The increase 1 Due to software limitations in the graphics program the axes of the Argand plots are not marked and -Zj as in the main text but as Zreal and -Zimag respectively. 2 An impedance diagram is also known as an Argand plot. 3 FL=0.90 Qcm2. Rs was obtained from the high frequency interception of the impedance curve with the real axis. 4 For a description of the relationship between the CPE element and the semi-infinite Warburg impedance see Chapter 5 (section III.B, Eqs. 6 to 9). 5 Different CPE analogues may have the same slope but quite different B, values. By using de Moivre's theorem, the impedance of the CPE analogue can be expressed as follows: thus, Z a ^ w ^ c o s ^ V z c Z 3 = -B 1 (o" ¥ z c ysin^ 2 c and the slope, m, between Zj, and -Zj is given by: Jt m = tan-Yzc from which: 2 i V z c = -tan m Thus, it can be seen that *PZC does not depend on B, which is only a multiplying factor (i.e. the impedance curve shrinks or contracts according to its value). [118] ZaB = BlV0i)* = Bl<Q AC behaviour in the absence of addition agents in the bulk electrolyte . 138 p i t 8 . 128 — E x p e r i M e n t a l — • f l n a l o o u t n o d e l A. • • a a 0 • 6 2 8 . 1 1 1 7 . 1 9 8 7 . 3 5 3 3 . £ 2 8 3 . 11173 19869 33333 28866 44482 .888 .888 J L ' • • ' I • • ' I ' ' ' I ' ' ' I .128 . 168 .288 Zred, Qcm2 Fig. 1 Impedance diagram of a typical lead bullion electrode (Exp. CC1-6) under rest potential conditions and In the absence of addition agents. R, was subtracted from the Z* component of the impedance (Fv=0.89 Qcm2). Some frequencies (in rad/sec) are shown for both the experimental (solid line) and the curve fitting data (dotted line). The impedance curve was fitted to a CPE element from which the following values were obtained B!=2.88 Qcm2sec"* ^=0.45.  in the B x value is attributed to differences in the roughness and electjochemically active surface areas between these electrodesl. Also, the distinct electrochemical characteristics of the impure lead bullion electrodes may account for the observed increases in the Bx values. As indicated in Table 3 (see sets CC1 and CC2), the Bj values change significantly from one experiment to the next but remain within 0.2 iicm 2 during the same experiment. The relatively constant values of the exponent (0.40<*FZC<0.60) is a clear indication that diffusional processes are the only ones being observed in the impedance spectra. While quantitative values of 1 As a result of surface irregularities at the micrometer level, the thickness of the electrode boundary layer may not be uniform and that results in increases in the B, value. 1119] AC behaviour in the presence of addition agents in the bulk electrolyte the diffusion coefficients cannot be obtained 1 the shape of the impedance curves unequivocally indicates that there are no charge transfer limitations for the dissolution/precipitation of Pb + 2 from/to the lead bullion electrodes. B. AC behaviour in the presence of addition agents in the bulk electrolyte The AC spectrum obtained in the presence of addition agents is shown in Fig. 2. Three different regions can be identified depending on the frequency range: a) A high frequency arc (co>4000 rad/sec) assigned to the charge transfer process taking place across the electrode Helrnholtz double layer. The point where the arc intercepts the Z% axis is equal to the Rg value. b) A distorted arc observed at medium range frequencies (100<co<4000 rad/sec) assigned to addition agents effects in the diffuse double layer. c) A quasi-linear impedance region (at ox 100 rad/sec) assigned to diffusional processes in the hypothetical Nernst boundary layer. r a d / s e c A * 0 6 3 * .40 * 2 .50 • 1 5 . 7 8 • 9 9 . 5 8 4 6 2 8 . a 3 9 6 5 . O 2 3 8 1 3 . • 6 2 8 3 2 . * 9 9 5 8 8 . I I I I I I I I I I I I I I l_l I I I I I I I I I I ' I I ' ' I ' ' ' I i i ' I 1.28 1.88 2 . 4 8 3 . 8 8 3 . 6 8 4.28 Fig. 2 Impedance diagram (Argand plot) of a typical lead bullion electrode (Exp. C A2-7) under rest potential conditions and in the presence of addition agents (R, was not subtracted from Z^) A . D O 1 .68 S i . 4 8 8 ana 1 The lack of knowledge of the electrochemically active surface area poses a serious hindrance for the computation of the diffusion coefficient: the penetration depth of the AC wave and the thickness of the boundary layer have to be uniform across the electrode in the whole range of frequencies for meaningful diffusion coefficient values to be obtained. [120] AC behaviour in the presence ol addition agents in the bulk electrolyte Analysis of the impedance spectra obtained at co>200 rad/sec was carried out using the electrical analogue shown in Fig. 5.20. The impedance of this analogue can be described by the following equation l - 2 : Z(/co) =/?,+-^ e , + fl1(/Q>) The Rg values were obtained directly from the high frequency intercept of the impedance curves with the axis. The four remaining parameters in Eq. 2 (R^, C^, B l t and ^ zc). were obtained by curve fitting the experimental data to Eq. 2. S u a So 1 csf 3 6 8 . 1 1 . 1 7 . • 2 2 2 9 . a 4 4 4 8 . • 8 B 7 6 . •* 1 7 7 B 9 . a 3 3 3 3 3 . o 71364. >• 6 2 B 3 2 . * 9 9 3 3 9 . a a ' ' ' ' _L_i_ J I I I I I I I I L _ ' . . . ' . . . I . 42 ,2 Z^,, Qcm2 Fig. 3 Detail of the high frequency region of the Impedance diagram shown in Fig. 2 Rg was subtracted from the Z* component of the impedance (Rs=1.42 Qcm2). Some frequencies (in rad/sec) are shown for both the experimental (solid line) and the curve fitting data (dotted line). The impedance curve was fitted to the analogue circuit shown in Fig. 5.20 from which the following values were obtained B,=23.71 Q cm2 sec'*^. ^ =0.64, Fc^O.501 Qcm2, and 0^=64 uF cm'2. As can be seen in Figs. 3 and 4, the analogue model describes accurately the experimental data. The values of the analogue parameters varied from one 1 For a description of the characteristics of this circuit see Chapter 5 section III.c. 2 Again, it is worth repeating that the presence of a CPE in the circuit shown in Fig. 5.20 does not represent a purely diffusional process and is included only to aid in the curve fitting procedure to obtain the Rd and Cd, values. [121] AC behaviour in the presence of addition agents in the bulk electrolyte G B I — x E B Ol 8 r A d / f i c sea. * 1 1 1 7 . • 3 3 3 9 . D 4 4 4 8 . • 8 8 7 6 . 4 1 7 7 B 9 . a 3 3 3 3 5 . a 7 8 9 8 4 . 7 0 3 8 4 . * 1 1 1 7 4 0 . x E 8 -J—1—I—l—l—l—1—l—l—l I l I 1 I I I I I l l I I l l l I l l l I l l l I l l i _ J . 0 0 . 2 0 . 4 8 . 6 8 . 8 0 l . O Fig. 4 Detail of the high frequency regions of the impedance diagrams obtained under rest potential conditions (A) Exp. CA4-I fB) Exp. CA5-J The values of the derived analogue values are shown In Table 3. experiment to the next. Nevertheless, the impedance curves reproduced within 10% the indicated parameter values in the same experiment (i.e. for the same electrode and electrolyte composition). [122] AC behaviour in the presence of addition agents in the bulk electrolyte In experiments CA4, CA5, and CA6 the electrolyte composition was kept constant, yet, the derived kinetic parameters varied widely \ These variations can be attributed to differences in the electrode roughness among the different electrodes a . In any case, the exchange current densities were not lower than 70 Amp/m 2 (70<io<270 Amp/m2) while the double layer capacitances varied between 25 and 66 |±F/cm 2 3 . These large values of ^ indicate that dissolution of the lead present in the lead rich phases takes place under nearly reversible conditions and that the noble impurities present in the lead bullion are not significantly affecting the kinetics for lead dissolution (or deposition). a a rad/se o . B63 . 4 a • 2 . 30 - IS . 78 e a - • 99 . s e - 4 £28 . z 3965 . O 238 13. »- 63833. -*- 99388. . 4 o e — Potvirit i os-t.-axt.ic: Control - GAIvAnosiatlo Control Zrea,, Qcm2 Fig. 5 Impedance spectra obtained under potentiostatic (solid line) and galvanostatic control (dashed line). From Exp. CAS (Sweeps CA5-1 and CA5-4 in Table 3). Finally, the impedance spectrum obtained under potentiostatic control was found to be a variation of that obtained under galvanostatic control (Fig. 5). As in the pure lead case, the observed changes are related to different concentration 1 The same electrolyte was used in Exps. CA4, CA5, and CA6 but since the amount of solids filtered prior to the introduction of electrolyte to the cell varied in each case, the final addition agent content may vary. 2 Small changes in the bulk electrolyte recirculation rate, electrode microstructure, and cell temperature may also produce the observed changes in the parameter values. 3 Notice that large capacitance values are associated with high exchange current densities indicating that electrochemically active surface areas are different in every case. [123] Variation of trie anodic overpotential as a function of the electrolysis time and the current interruption time waves created by the different amplitude of the perturbating signal \ The parameters obtained from both curves are close to each other indicating that similar information was obtained from both techniques (see Table 3, Exp. CA5 sets 1 and 4). HI. DG and AC Studies i n Corroded Electrodes A. Studies under galvanostatic, potentiostatic, and current interruption conditions. 1. Experimental results Lead bullion working electrodes were either galvanostatically or potentiostatically dissolved. The movement of the anode/slimes interface was computed assurning that 100% of the current flow was at that interface 2 . During the dissolution process, the AC impedance was measured at preset slimes thicknesses. After dissolving the electrodes up to a certain slimes thickness the overpotential decay was followed as a function of time. During this decay, the AC impedance was also measured. The DC current and anodic overpotential recorded during the AC measurements were analyzed to obtain the components of the concentration overpotential. (a) Variation of the anodic overpotential as a function of the electrolysis time and the current interruption time Fig. 6A shows the anodic overpotential response observed during the galvanostatic dissolution of lead at a current density of 194.44 Amp/m 2 (Exp. CA2 in Table 1). The cell potential follows closely the recorded anodic overpotential values (Fig. 6B). Upon subtraction of the initial T ] Q from both measurements, it is seen (Fig. 6C) that even though a net current was being passed through the counter electrode (a pure lead cathode), it can act very well as a reference electrode due to the high reversibility of lead in this system. 1 Theoretically both curves should have been identical if the processes under study behaves linearly. Instrumental artifacts (i.e. Potentiostat bandwidth) may also contribute to the observed discrepancies. 5 mV R.M.S does not exactly produce a sinusoidal current waveform of 35 Amp/m2 of amplitude and vice versa. 2 The fraction of electronic current going through the slimes filaments was assumed to be negligible compared to the amount of current crossing the anode/slimes interface. The validity of this assumption was confirmed by measuring the distance between the anode/slimes electrolyte interface and the slimes/bulk electrolyte interface at the end of the experiment which was in agreement with the computed value. Furthermore, the slimes composition does not seem to change much with slimes thickness. [124] Variation of the anodic overpotential as a function of the electrolysis time and the current interruption time (A) (B) 1 a cu -M o & 1> o o 1.88 3.SB 3.4B 7.28 9.88 -.BBS 1.88 3.68 3,48 7.28 9.88 mm Slimes (C) mm Slimes I 73 C -M o & Si o o o 70B . 3 6 0 4 2 0 2 0 0 . — 140 . — . 0 0 Fig. 6 Overpotential response of a typical lead bullion anode as a function of the slimes thickness (Exp. CA2). The AC impedance was measured at preset slimes thicknesses indicated by the spikes shown in the curves. CA) Anodic overpotential as a function of the slimes thickness (uncorrected for initial (B) Cell potential as a function of the slimes thickness (uncorrected for initial TIJ. (C) Anodic overpotential measured by the counter and reference electrodes as a function of the slimes thickness (corrected for Initial TIJ. [125] Variation of the anodic overpotential as a function of the electrolysis time and the current interruption time Further analysis of Fig. 6 shows that as the anode dissolves, T|A increases quasi-linearly up to the point at which impurities dissolution occurs at a significant rate (at ~8 mm slimes and -350 mV) \ At this point, increases in riA are also the result of the precipitation of secondary products (such as PbF2 and SiCy which hinder the movement of ions and increase the concentration gradients across the slimes layer. In Fig. 6, the small departures of the anodic overpotential (so-called "spikes") result from the application of the AC waveform used to measure the impedance of the system at preset slimes thicknesses. Such overpotential changes were detected only at low AC frequencies (ox6.3 rad/sec). Potential variations produced by the AC waveform at higher frequencies were either very small or were undetected by the potentiostat digitized readings a . Fig. 7 shows the anodic overpotential changes (corrected from initial rj J observed during the dissolution of lead at a current density of 800 Amp/m 2 (Exp. CA5 in Table 1) . By comparing the r|A response at low and high current densities (Figs. 6C and 7 respectively), it can be seen that increasing the current density resulted in decreasing the time required for impurities to dissolve at excessive rates 3 . Moreover, increases in current density do not appear to have a significant effect on the critical point at which the anodic overpotential rises exponentially. This indicates that if impurities are to dissolve to a large extent, a minimum overpotential value must be overcome. The large T|A values obtained at high current densities as compared to those values obtained at lower current densities, arise primarily as the result of changes in the concentration of the slimes electrolyte. Also, at high current densities steeper concentration gradients become established. This results in potential differences that increase monotonically with the concentration gradients. Steeper concentration gradients develop larger potential differences 1 Abrupt dissolution of phases containing noble impurities was not observed in the case study presented in Chapter 4 because a low current density was applied, the electrode was larger, only a 14 mm thick slimes layer was formed, and the maximum value of T|a was <200 mV. 2 The potentiostat follows continuously (among other parameters) the difference in potential between the reference electrode and the current. At finite sampling times (i.e once every 3 min.), these data are digitized and saved as "DC" data. If during the digitization process the AC waveform was being applied, a net DC overpotential and DC current may be observed as "spikes". 3 A 400% increase in the current density (from 200 to 800 Amp/m2) resulted in a corresponding reduction in the amount of lead that could be removed before impurities dissolve at an excessive rate (i.e. at similar T1A values, the equivalent amount of lead dissolved is ~4 times smaller). [126] Variation of tie anodic overpotential as a function ol the electrolysis time and the current interruption time .88 .aa .68 1.2 1.8 rnrn Slimes 2 . 4 3 . 8 Fig. 7 Anodic overpotential (corrected for initial TIJ measured by the counter and reference electrodes as a function of the slimes thickness (Exp. CAS). Galvanostatic conditions 1=800 Amp-m2 Detween the slimes and the electrolyte promoting their earlier dissolution. In addition, passage of larger currents increases the "ohmic" drop component of the anodic overpotential \ Fig. 8A shows the changes in current density as a function of the electrolysis time during a potentiostatic experiment (Exp. CA4 in Table 1). In this experiment the dissolution of noble impurities present in the slimes layer was restricted by liiinting the potential difference between the reference electrode and the lead anode to 220 mV. From the numerical integration of the data presented in Fig. 8A, the amount of lead dissolved as a function of the electrolysis time was found (Fig. 8B). At short electrolysis times, large current densities can flow because ionic transport proceeds relatively unhindered. As the slimes layer thickens, its presence restrains the flow of current up to the point at which only very small currents can flow through the cell. These decreases in current are 1 See section III.2.a [127] Variation ol the anodic overpotential as a function of the electrolysis time and the current interruption time ( A ) ( B ) 2.S <r£'3< . 0 0 . E a 1 .2 JL . 8 2 . 4 3 . a mm Dissolved Fig. 8 Current density changes as a function of the electrolysis time and of the amount of lead dissolved (Exp. CA4. potentiostatic conditions Econtrol=220 mV) IA) Changes in the anodic current density as a function of the electrolysis time (B) Changes in the amount of lead dissolved as a function of the electrolysis time. This curve was obtained from numerical integration of the data presented in CA) (C) Current density changes as a function of the amount of lead dissolved [128] Variation of the anodic overpotential as a function of the electrolysis time and the current interruption time also the result of the presence of secondary products which block the movement of ions even further until the lead dissolution process is nearly halted (Fig. 8C). At long electrolysis times, lead ions are still being generated whereas concentration overpotential no longer changes and the precipitation of secondary products must take place for rj c to remain constant. During experiment CA4 the difference in potential between the reference and working electrodes was kept constant and equal to 220 mV (£^^ ,=220 mV). As a result of the presence of r|n between such electrodes, the potential difference applied between the working electrode and the slimes/bulk electrolyte interface is not constant. The anodic overpotential changes as a function of Rg and of the current density can be described by the following equation: TjA changes as a function of the amount of lead dissolved are shown in Fig. 9 1 . The anodic overpotential increases continuously as the current density decreases, up to the point at which current flow is negligible and r|A = Eco ,^ . Fig. 9 Changes in the anodic overpotential (corrected for iln) as a function of the amount of lead dissolved (Exp. CA4). mm Dissolved 1 R„ was obtained from AC impedance measurements at preset electrolysis times. 1129] Variation of the anodic overpotential as a function of the electrolysis time and the current interruption time (B) 786 548 1 f - H S <u o & I u o 228 68.1 -188 788 568 428 281 148 .88 .32 .64 .96 1.3 1.6 .u.!...,.»M; f M 24.8 48.8 72.8 Time, Hrs. ( C ) I 73 fi <u -M O & I T3 O .88 18. 28. 38. 46. 38. Time, Hrs. Time, Hrs. Fig. 10 Anodic overpotential changes upon current interruption (Exps. CA2, CA5, and CA4). T | n prior to current interruption was not subtracted from these measurements The AC impedance was measured at preset times indicated by the spikes shown in the curves. (A) From Exp. CA2 (B) From Exp. CA5 (C) From Exp . CA4 [130] Variation of the anodic overpotential as a function ol tie electrolysis time and the current interruption time Changes in anodic overpotential upon c u r r e n t i n t e r r u p t i o n for the three cases described previously (Exps. CA2. CA5, and CA4) are shown in Fig. 10. A steep decrease in the overpotential is observed at the beginning of the interruption cycle. This steep change is followed by a quasi-exponential decrease in the r|A value. On the other hand, the shape of the r\A decay at times smaller than 1.6 Hrs is different for the three cases shown in Fig. 10. This indicates that upon current interruption, processes with different time constants can take place. The presence of these processes appears to be a function of the r\A value and the electrode's history. In the three previous cases AC impedance measurements did not seem to affect the pseudo-equilibrium present within the slimes layer. On the other hand, when the impedance measurements were made more frequently, transient excursions in the anodic overpotential were observed (in Exps. CA6 and CC1, see Fig. 11). As in the case study presented in Chapter 4, these potential excursions cannot be unambiguously explained. These excursions in potential were reproducible and indicate that the changes created by the AC waveform induce a shift of part of the Faradaic current towards the slimes filaments l . The fraction of the current going to the slimes filaments may be insignificant; yet it increases the corrosion potential of the electrode. The transient character of these excursions and the fact that after a certain time the overpotential decreases to a value that can be obtained by extrapolation of the r|A curve (see Fig. 1 IA), indicates that the reaction at the anode/slimes interface was taking place at its normal rate even during the excursions in potential. Finally, upon current interruption, the anodic overpotential decay did not indicate any abrupt changes related to the potential excursions observed during the passage of current (Fig. 12). 1 The AC wave may have changed the conditions at the anode/slimes electrolyte interface by promoting precipitation and/or hydrolysis reactions at that interface. Under these conditions, Faradaic currents can divert to the slimes filaments and cause the excursions in potential shown in Fig. 11. [131] Variation of the anodic overpotential as a function ol the electrolysis time and the current intenvption time (A) 7 8 0 c -(B) 7 B B . pr 5 6 8 , 4 2 0 e *» o a. 01 2 8 0 » O 9 . 0 . 0 0 0 t — L . 0 0 0 _J I I I I I 1_ i . . 8 0 3 . 6 0 S . 4 0 S l l n e s T h i c k n e s s , nn Fig. 11 Anodic overpotential (corrected for initial r\^j as a function of the slimes thickness (Exps. CA6 and CC1). (A) From Exp. CA6 (B) From Exp. CC1 [132] Changes in the impedance as a function ol the slimes layer thickness and of the current interruption time 788 r 560< r Z 428 S I ¥ 0 J 288 J 0 1481 668 . 548' 428 388 189; 68. .88 .82 .84 .86 .88 .18 Fig. 12 Anodic overpotential changes upon current interruption (From Exp. CA6) T|Q prior to current interruption was not subtracted from these measurements The AC impedance was measured at preset times indicated by the spikes shown in the curves. 128 Tine, Hrs (b) Changes in the impedance as a function of the slimes layer thickness and of the current interruption time The AC spectra obtained at different slimes thickness are presented in Fig. 13 (Exp. CA2). Each spectrum was taken in the p r e s e n c e of a net Faradaic current and at different stages of the electrolysis cycle (see Fig. 6). Both the reactive (Z*) and the capacitative (-Zg) parts of the impedance increase as the slimes layer grows. The impedance spectra in Fig. 13 show the presence of a low frequency arc which at high frequencies bends quasi-linearly towards the axis. AC impedance spectra obtained in the overpotential region above 350 mV are shown in Figs. 14 and 15 . These spectra are significantly different from those presented in Fig. 13. The presence of high frequency arcs (i.e. arcs whose time constant is at least of the order of msec) shown in the respective Bode plots (Figs. 14B and 15B) indicates that reaction of noble compounds present in the slimes layer takes place in this region. 1133] Changes in the impedance as a function olthe slimes layer thickness and ol the current interruption time I ft c N I 4 . 0 r* ad/s e c — •m- .31 • 1 . 56 • 7.91 3 . 2 a 39 . 65 < 199 . £* 996 . O 4991 . »- 15783. 25015. 2 . 4 1 . 6 M M SI i ne -s A 0 . 8 B 1 . 6 C 2 . 2 n 3 . 1 E 3 . 7 F 4 . 7 G 5 . 3 H 6 . 0 I 6 . 6 J 7 . 2 K 7 . 8 000 5 . 40 ft-CM* 00 F i g . 1 3 Impedance spectra obtained during Exp. CA2 at slimes layer thicknesses between 0.8 and 7.8 mm. Each impedance curve was obtained at a different slimes thickness as indicated in this Argand plot [134] Changes in the impedance as a function ol the slimes layer thickness and ol the current interruption time (A) 2 . a a x . 6 8 Y 1 . 2 B a Dl t N . 8 0 0 r a d / s e a . 0 6 3 * . 3 5 • 1 . 3 9 a 1 1 . 1 7 a 6 2 . 8 3 -« 3 5 3 . 1 9 8 7 . O 1 1 1 7 4 . 3 9 6 4 7 . 6 2 8 3 2 . 1 . 2 8 . 4 0 0 8 0 0 1 — 1 » '—I—I—I—1—1—I—I—I 1 I I I I I I I I I I I I I I I I 1_ (B) - . 8 3 0 1 5 8 •0 1 u 91 Fig. 14 Impedance spectra obtained during Exp. CA2 at a slimes layer thickness of 8.4 mm i (A) Argand plot (B) Bode plot 1 In a Bode plot, the high frequency arcs are better resolved by analyzing the variations in the phase angle (dotted line, right vertical axis) as a function of the logarithm of the frequency. [135] Changes in the impedance as a function ol the slimes layer thickness and of the current interruption time (A) 2 . 0 0 X . 6 0 M U 1 . 2 8 r A d / l • c A . 0 6 3 » . 4 4 • 3 . 1 3 n 2 2 . 2 9 a 1 5 8 . 4 1 1 1 7 . ti 7 9 1 1 . O 3 6 8 8 2 . ¥• 2 2 2 9 3 3 . * 3 5 3 3 5 4 . 1 « bi 4 E N . 0 0 0 1 1111 11111 11 s~"~~^ / . 4 0 0 . 0 0 0 2 . \ • i l i i i l i i 1 i i i 1 i i i 1 i i i 1 i i i 1 i i i 1 i i • 1 i i i 4 0 4 . 0 8 5 . 6 8 7 . 2 8 8 . 8 8 1 8 Z r e a l ft-CM* (B) . 4 1 0 . " i " — ^ . 0 3 0 8 . 8 _ M 5 T • 2 1 a N a . 6 - » ^ ^ ' * t 1 - 1 - ' ' - . 0 3 0 / f ~ "~ " ' " - ^ _ \ - - o^fo - X . t x ** X . t X / X . - . , 1 5 0 x > ^ ' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Phase Angle, rad 4 . a % — > \ ' S 1 * \ . ' — *- ^ ' ^ 1 1 II 1 2 . 4 - 1 . - 1 1 1 1 1 1 1 1 • i i i i i i i i i i i i i i t t i i i i i i i i i i i i i i 4 8 - . 8 8 8 1 . 4 8 2 . 8 8 4 . 2 0 5 . L O G < F r e < i , r a d / s e c ) 6 0 Fig. 15 Impedance spectrum obtained during Exp. CA2 at a slimes layer thickness of 8.65 mm l. CA) Argand plot (B) Bode plot 1 In a Bode plot, the high frequency arcs are better resolved by analyzing the variations in the phase angle (dotted line, right vertical axis) as a function of the logarithm of the frequency. Thus, for example, in Fig. 15B a hump can be observed at log oo = 4.20. Thus, x= 6.3x10s sec (t is the time constant, x = co"1). [136] Changes in the impedance as a function of the slimes layer thickness and ol the current interruption time The high frequency intercept of the impedance curves with the axis was used to find the changes in Rg as a function of the slimes thickness. As Fig. 16 indicates, the Rg values measured by AC impedance were in agreement with those obtained by current interruption l i 2 . Discrepancies between the Rg values were only observed at slimes thicknesses larger than 8 mm. s X o •0" 41 *» < * s tl & s e o e 3.90 1 — 3 .38 — 2 .70 2 . 10 1 . SO * F r a n OC D * t * O F r o n C u r r e n t I n t e r r u p t i o n •= ft 6 6 6 6 i .90S - .000 1.80 3.60 5.40 S I i n e s T h i c k n e s s , n n 7 .20 9 . 00 Fig. 16 Changes In the value of R,, as a function of the slimes thickness (Exp. CA2). From the AC and DC data obtained in Exp. CA2. AC impedance measurements done while the anode was being galvanostatically dissolved at 800 Amp/m 2 (Exp. CA5) are shown in Figs. 17 and 18. Changes in Rg as a function of the slimes thickness are plotted in Fig. 19. Rg changes the most at slimes thickness larger than 2 mm where dissolution of noble impurities takes place. The small changes in the Rg values at small slimes thickness are partially due to changes in the concentration of the electrolyte between the reference electrode and the slimes/bulk electrolyte interface as a result of the large current density applied. 1 Current interruption was done prior to obtaining the AC impedance spectrum. Appendix 6 describes how the current interruption measurement was implemented. 2 The invariability of the R, values at slimes thicknesses smaller than 8 mm confirms the results obtained in Chapter 4 in which upon current interruption t\a remained constant (Fig. 3.8). [137] Changes in the impedance as a function ol the slimes layer thickness and ol the current interwption time 1 . 2 I ft c N I . 96 72 — A. 6 . 3 - * ±7 . 7 — • 49 . 9 • 141 . • 396 . 1117 . — & 3149 . — O 8876 . •> 14067 . - * 22295. — 48 n n S I i M G S ft 0 . 64 B 1 . 20 C 1 . 76 D 1 . 89 - J * 0.63 rad/sec 000 400 800 1.20 Zreal , ft —CM 2 1 . 60 2 . 00 F ig . 17 Impedance spectra obtained during Exp. CA5 at slimes layer thicknesses between 0.64 and 1.89 mm. Each impedance curve was obtained at a different slimes thicknesses as indicated in this Argand plot. R, was subtracted from the Z„ component of the impedance. [138] Changes in the impedance as a function of the slimes layer thickness and of the current interruption time (A) (B) .Mr-; riJAtc - A 63 > J.M .64 - • 9.96 D 39,63 • a 158. _ 4 628. • & 2381. 0 9959, .48 • 39646. t S68B2. 3.8 r-Q f I I I I I I I I I I I I I I I I I I 1 I I I I I I I t I I I I I I I I I I I I I .888 .248 .488 .728 .968 ,2 1.28 1.8L -.588 4.58 .588 1.58 2.58 3.58 Z^j, flcm2 Log (Freq, rad/sec) Fig. 18 Impedance spectra obtained during Exp. CA5 at a slimes layer thickness of 2.2 mm (R, was subtracted from the Z* component of the Impedance). (A) Argand plot fB) Bode plot Fig. 19 Changes in the value of R, as a function of the slimes thickness (Exp. CA5). From the AC data obtained in Exp. CA5. i.ee .eee .6ee l.ae l.se Slimes Thickness, mm 2.48 3.98 [139] Changes in the impedance as a function ol the slimes layer thickness and of the current intanvption time (A) I— r a d l / s e c 1 . 68 1 . 28 . 888 . 488 .888 .63 • A .99 • 6 .28 • 19 . 87 a 62 . 83 4 199 . 628 . O 1987 . 6284 . * 7911 . n n D i s •» o I v e dl ft 8 . 87 B 1 .39 C 1 .77 n 2 . 86 E 2 . IS F 2 . 52 . 888 1 . 28 2 . 48 3 . 68 Zreal. ftcm* (B) 4 . 88 6 . 88 688 , - nn D i t t o l va«1 _ G 2 . 76 — H 2 . 834 — I 2 . 837 J 2 . 841 K 2 . 865 368 . 248 . A. . 863 . 44 • 3 . 15 • 22 . 29 • 158 . 4 1117 . tk 7911 . O 56882. »- 396469. 4> 488487. I I I I I I _L 208 . 880 , 488. 608. Fig. 20 Impedance spectra obtained during Exp. CA4 at slimes layer thickness between 0.87 and 2.87 mm. Each impedance curve was obtained at a different slimes thickness as indicated in this Argand plot. Ft, was subtracted from the Z* component of the impedance. [140] Changes in tie impedance as a function of the slimes layer thickness and of the current mtemiption time While the impedance curves obtained during Exps. CA2 and CA5 increased uniforrnly with the slimes thickness, those obtained during Exp. CA4 showed marked increases and variations in their magnitude and shape (Fig. 20). This different behaviour is believed to be the result of the precipitation of secondary products across the slimes layer. Thus, impedance arcs whose time constant is large are present throughout the whole electrolysis cycle1. The absence of high frequency arcs is a clear indication that Faradaic dissolution of noble impurities did not occur in this experiment. 1.30 r-"a U 1.24 o a 8 1.18 cj O J . . J . 2 T 3 I o C 1.06 1.00 Fig. 21 Changes in the value of the R, as a function of the slimes thickness (Exp. CA4). From the AC data obtained in Exp. CA4. j i_ _] L J l_ I I .000 .600 1.20 1.80 mm Dissolved 2.40 3.00 Changes in Rg as a function of the amount of lead dissolved are shown in Fig. 21 2 . Again, minor variations in the Rg values result from changes in the concentration of the electrolyte between the reference electrode and the slimes/bulk electrolyte interface. As lower currents go through the cell Rg returns to its original value because such variations in concentration disappear. 1 As indicated by the frequency values at which the capacitative pan" (i.e. the imaginary part) of the impedance reaches a maximum value, the relaxation processes nave very large time constants (of the order of sec). 2 These changes in R9 were used to compute the anodic overpotential as a function of the amount of lead dissolved (Fig. 9). [141] Changes in tie impedance as a function of the slimes layer thickness and of the current interruption time 2 .00 r a d / s e c 17 .7 • 62 .8 • 223 . • 791 . 1 .£0 • 2807 . - 4 99S9 . — a 3S33S. a 125375. — • 222953. - 353354. 1 .28 .880 .488 .000 A A f t e r 8 . 17 Hrs B A f t e r 86 .9 Hrs A 6- 4 - - - - ' - Q -J l_ I • • • I 2 .88 2 .68 3.28 3.88 Z r e a l ft-CH* 4.48 5 .88 Fig. 22 Argand plot showing the changes in the impedance spectra obtained in the presence of a layer of slimes and in the absence of a net Faradaic current (Exp. CA2). The anode was corroded up to the formation of -8.7 mm of slimes (Fig. 6). Subsequently, current was halted for -115 hrs (Fig. 10A). During this period, impedance spectra were obtained at preset times as indicated in this Argand plot. Curve A was obtained -0.17 Hrs after current interruption Curve B was obtained -86.9 Hrs after current interruption The AC impedance spectra obtained in the a b s e n c e of a net Faradaic current (i.e. under current interruption conditions) are significantly different from those obtained during the passage of a net DC current. The impedance curves indicate the presence of a linear region which bends towards a small arc as high frequencies are approached (Fig. 22, Exp. CA2). The impedance decreases as a function of the current interruption time and the anodic overpotential. Also, Rg decreases up to a liiniting value often higher than observed at the beginning of the experiment (compare Figs. 16 and 23). Such a difference arises partially as a result of the prior reaction of the slimes compounds which changed the microstructure of the slimes layer. The impedance spectra obtained at the end of Exp. CA5 (Fig. 24) are siinilar to those obtained in Exp. CA2 (Fig. 22). The decrease in Rg in this experiment follows the pattern previously explained because dissolution of the slimes layer also took place in this experiment (Fig. 25). [142] Changes in the impedance as a function of tie slimes layer thickness and of the current interruption time o , . s . OJ 4-1 CO s. 6 o o 3 .28 2.98 O 2 . 6 8 i 2.38 2.88 S .888 Fig. 23 Changes in the value of R, as a function of the current interruption time (Exp. CA2) From AC data obtained in Exp. CA2. 24.8 48.8 72.8 Time, Hrs. 96.8 128 . . s a r a d / s e a . 6 3 * 2 . 5 0 : • 9 . 9 6 3 9 . 6 5 . 4 0 • 4 1 3 8 . 6 2 8 . _ 2 5 0 1 . o 9 9 5 9 . 3 9 6 4 6 . . 3 0 * 4 4 4 8 5 . . 2 8 . 1 0 . 0 0 A A f t a r 0 . 6 3 H r s B A f t e r 7 . 8 8 H r s C A f t e r 3 8 . 4 H r s 1 . 4 1 . 7 2 . 0 2 . 2 2 . 5 2 . 8 Z^u, Qcm2 Fig. 24 Argand plot showing the changes in the impedance spectra obtained in the presence of a layer of slimes and in the absence of a net Faradaic current (Exp. C A5). The anode was corroded up to the formation of -2.2 mm of slimes (Fig. 7). Subsequently, current was halted for -46 hrs (Fig. 10B). During this interval, impedance spectra were obtained at preset times as indicated in this Argand plot. Curve A was obtained -0.63 Hrs after current interruption Curve B was obtained -7.88 Hrs after current interruption Curve C was obtained -38.4 Hrs after current interruption [143] Changes in the impedance as a function of the stones layer thickness and of the current interruption time In experiment CA4 slimes dissolution was restricted by holding the anodic overpotential at values lower than 220 mV (Fig. 9). This resulted in nearly constant Rg values during both the potentiostatic dissolution (Fig. 21) and the current interruption cycle1. During current interruption, ionic concentration gradients within the slimes layer relax. This results in re-dissolution of precipitates and in ensuing impedance decreases (Fig. 26 Exp. CA4). The shape and magnitude of the impedance arcs are different from those observed in Exps. CA2 and CA5 as the precipitated products can generate an electrical double layer which affects the dielectric properties of the slimes filaments and of the lead electrode through changes in their relative permittivity a . This results in impedance arcs with a large capacitative component. Fig. 25 Changes in the value of R, as a function of the current interruption time (Exp. CA5) From AC data obtained in Exp. CAS. 18.a 2 a . a 3e . e Time, Hrs. 48.a s e . e 1 During current interruption conditions, R, remained nearly constant (1.09<R,<1.13 Qcm2). 2 The (static) relative permittivity is defined as t„=§-C is the capacitance of a parallel plate condenser with plates of large area separated by a small gap, the whole being in a vacuum whereas C 0 is the capacitance of a parallel plate condenser when an isotropic material is present between the plates [5]. [144] Changes in the impedance as a function of the slimes layer thickness and ol the current interruption time Fig. 26 A r g a n d plot s h o w i n g the changes In the Impedance spec t ra ob ta ined In the presence o f a l ayer o f s l imes a n d In the absence o f a ne t F a r a d a i c c u r r e n t (Exp. C A 4 ) T h e a n o d e was cor roded u p to the fo rmat ion o f - 2 . 8 m m o f s l imes (Fig. 9). Subsequen t ly , c u r r e n t w a s ha l t ed for - 2 3 h r s (Fig. IOC). D u r i n g th i s in te rva l , i m p e d a n c e spec t ra were ob ta ined at preset t imes a s ind ica ted i n th i s A r g a n d plot. C u r v e A was ob ta ined - 0 . 2 7 H r s after c u r r e n t i n t e r rup t ion C u r v e B was ob ta ined - 2 . 0 8 H r s after cu r r en t in te r rup t ion [145] Changes in the impedance as a function of the slimes layer thickness and of the current mtenvption time (A) a . e s a 1 . 2 . 8 0 . 4 0 r a d / s e c . 6 3 » 2 . s a • 9 . 9 6 a 3 9 . 6 5 a 1 5 8 . 4 6 2 8 . 2 5 8 1 . a 9 9 5 9 . *- 1 V 7 8 9 . • 2 8 8 6 8 . r t n S I t n e s A . 4 3 B . 9 8 1 . 4 7 C D 2 . 3 9 E 3 . B 6 F S . 3 7 G 5 . 7 9 H 6 . 3 2 I 6 . 6 4 J 7 . 8 6 X 7 . 4 9 J i i i L—J i i L 5 . 0 (B) Z ^ , Ocm2 (C) Zreai, Qcm 2 Fig. 27 Impedance spectra obtained during Exp. CA6 at slimes layer thicknesses between 0.43 and 717 mm. Each impedance curve was obtained at a different slimes thickness as indicated in this Argand plot. R, was subtracted from the component of the impedance. (A) Impedance spectra acquired in the region where potential excursions where not observed (Fig. 11A). OB) Impedance spectrum obtained at ~3.7 mm of slimes (C) Impedance spectrum obtained at ~7.7 mm of slimes [146] Changes in the impedance as a function of the slimes layer thickness and of the current interwption time As previously described, In Exps. CA6 and CC1 excursions in potential appeared to be triggered by the AC measurements (Fig. 11) 1 . The impedance spectra obtained in Exp. CC1 are shown in Fig. 27 while those obtained in Exp. CA6 are shown in Fig. 28. The spectra measured in the region in which no potential excursions were observed increase uniformly as the slimes layer thickens (Figs. 27A and 28A). On the other hand, the impedance spectra measured in the region where the potential excursions were observed indicate the presence of arcs whose time constant is of the order of 10"5 sec 2 . These spectra were reproducible and did not show any large changes in magnitude at different electrolysis times. Such high frequency phenomena can only be related to very fast processes such as found across the Helmholtz electrical double layer. In Exps. CA6 and CC1, changes in Rg were observed only in the region where the anodic overpotential excursions occur (Fig. 29). Upon current interruption, the impedance spectra show the presence of high frequency arcs whose size decreases as the current interruption time increases (Fig. 30). Also, Rg decreases as a function of the current interruption time up to a limiting value which in the case of Exp. CA6 is nearly equal to that observed at the beginning of the experiment (compare Figs. 29A and 31). 1 Exps. CA6 and CC1 were performed using working electrodes from different sides of the lead anode and in the presence and absence of addition agents (see Table 1). In both experiments the potential excursions appeared at about the same slimes thickness (-3.2 mm). Consequently, the outset of the excursions in potential must be related to changes in the slimes electrolyte rather than in the slimes layer or in the anode. 2 In Figs. 27B, 27C, 28B and 28C, the maximum of the imaginary part occurs at 2x104<co<3x103 rad/sec, thus 5x10"5 <T<3.3X10^ sec. [147] Changes in the impedance as a function olthe slimes layer thickness and of the current interruption time (A) 1.08 r— .880 S .608 a .480 .280 i r « d / s e c A 6.3 • 17 .7 • 49 .9 • 141 . • 396 . 4 1117 . 3149 . O 8876 . • 11174 . * 17789. nn S i t H I S A . 14 B .51 C 1 .37 D 2 .22 E 3 .50 «i 8.63 r a d / s e c .8884 • i I i i i I i i i I i i i I . 000 .330 .640 . 960 1 . 28 1 .60 s CJ C! 8.68 rid/sec 6.3 • t 25.8 • 99.6 • 396. 6.48 0 1378. • 4 6283. 6 25813. 0 99582. • 396463, * 488487 4.88 3.28 -1.68 -(B) AC tueei dene it 4.5 m Slinei Z ^ . Qcm2 a a 8,88 rid/sec 6.3 « 25.8 • 99.6 • 396. 6.48 0 1378. 4 6283. • 0 2581S. 0 99582. • 396463, * 488487 4.88 3.28 1.68 (C) AC tvtep dene it 5.3 nn Slinet 12.8 I I I I I I 12.8 Z ^ . Qcm2 Fig. 28 Impedance spectra obtained during Exp. CC1 at slimes layer thicknesses between 0.14 and 5.3 ,8001 1 1 1 1 ' 1 ' 1 ' ' ' 1 ' ' ' 1 ' ' ' ' 1 ' 1 1 ' ' ' 1 ' ' ' .888 2.48 4.88 7.28 9.68 mm. Each impedance curve was obtained at a different slimes thickness as indicated in this Argand plot. R, was subtracted from the component of the impedance. (A) Impedance spectra acquired in the region where potential excursions where not observed (Fig. 11B) (B) Impedance spectrum obtained at -4.5 mm of slimes (C) Impedance spectrum obtained at -5.3 mm of slimes [148] Changes in the impedance as a function of the slimes layer thickness and of the current interruption time Fig. 29 Changes in the value of the R, as a function of the slimes thickness (Exps. CA6 and CCD. (A) From the AC and DC data obtained in Exp. CA6 (B) From the AC data obtained in Exp. CC1 [149] Changes in the impedance as a function oltte slimes layer thickness and of the current interruption time CJ . 3 . 6 3 - * 3 . I S • • 1 3 . 7 8 7 9 . 1 1 . e n 4 3 9 6 . 1 9 8 7 . — 9 9 3 9 . o 4 9 9 1 8 . — 1 3 7 8 3 4 . . s 3 3 8 1 3 2 . 1 . 8 . 8 8 A A4> t « r- 8 . 6 3 H r . B A f t e r 2 . 4 4 H r s C A f t a r 1 1 2 . 8 H r » Fig. 30 Argand plot showing the changes In the Impedance spectra obtained in the presence of a layer of slimes and in the absence of a net Faradaic current [Exp. CA6). The anode was corroded up to the formation of -8 mm of slimes (Fig. 11A). Subsequently, current was halted for -113 hrs (Fig. 12). During this interval, impedance spectra were obtained at preset times as indicated in this Argand plot. Cury.e A was obtained -0.63 Hrs after current interruption Curve B was obtained -2.44 Hrs after current interruption Curve C was obtained -112.8 Hrs after current interruption M6 9 ee ; u a o 4 0 8 ! s 3 ea i Ohrj \ •a 2 ea r V ns U P . S 1 o C J ' a P .08 2 4 . 4 8 . 72. Time. Hrs. 96. 120 Fig. 31 Changes in the value of R, as a function of the current interruption time (Exp. CA6). From AC data obtained in Exp. CA6. [150] Relationship between the DC anodic overpotential and the DC current density 2. Analysis of the experimental data In the study of the establishment.of concentration gradients across the slimes layer an electrical analogue could be used to describe how these gradients affect the dissolution of noble impurities present in the slimes layer. This analogue has to evolve from fundamental DC and AC studies and must include parameters that provide a physico-chemical insight of the system. In the following section the main characteristics of such a model are introduced. The DC data are analyzed prior to the AC data to provide a framework for the elaboration of the analogue model. Subsequently, this model is used to relate the experimental DC and AC behavior of lead bullion electrodes covered with a layer of slimes. (a) Relationship between the DC anodic overpotential and the DC current density As shown in Chapter 4, concentration gradients produce concentration overpotentials which can be linked to the resistivity of the electrolyte present within the slimes layer. Concentration overpotential is also the major component of the r)A curves presented in this Chapter. According to Newman 123,24] concentration overpotential can be defined as follows x > 2 : Eq. 4 can be expressed as a linear equation: T]c=IRm + b ...5 With 1 Despite the different definitions of concentration overpotential available in the literature there is no conclusive evidence that any of them describes accurately the physical phenomena involved, yet, there is an agreement that because of the presence of concentration gradients, an ohmic drop is included in the concentration overpotential measurement (Compare refs. [23-24] and [8-9]). 2 The ohmic part in Eq. 5 of TI0 has more physical meaning when it is equal to / I = 0 t h a n when it is equal to i^Jj^-^dx [151] Relationship between the DC anodic overpotential and the DC current density Eq. 4 indicates that rjc is composed of at least 2 contributions: (A) an ohmic drop due to variations of conductivity in the diffusion layer and (B) the potential difference of a concentration cell. In Chapter 4 the determination of the electrical conductivity of the slimes electrolyte was attempted by using current interruption techniques. Such measurement was not really applicable because as Eq. 4 indicates, even though the ohmic term ought to disappear upon current interruption (I-»0), the relaxation of concentration gradients creates a counter E.M.F. that avoids the direct measurement of the conductivity of the slimes electrolyte \ Under steady state conditions a , Eq. 4 indicates that small changes in the applied current density ought to result in changes in TJc due exclusively to the ohmic component of the slimes electrolyte 3 . If linearity between applied current density and the observed concentration overpotential is observed, the average resistivity of the slimes electrolyte, F^, could be obtained from Eq. 5. In addition, the parameter b should provide complementary information about the extent to which concentration gradients vary across the slimes layer4. The validity of Eq. 5 in the determination of the resistivity of the slimes electrolyte is studied in this section by analyzing the current and anodic overpotential changes observed during the application of a small amplitude sinusoidal waveform 5 . Thus, these changes are analyzed according to Eq. 5 using the following assumptions: 1) Upon subtracting TJq from the anodic overpotential observed upon the dissolution of lead, the main component of the remaining overpotential is due to the presence of concentration overpotential. 1 As explained in Chapter 4, even though the external current may had been halted, processes that support the passage of internal currents may still be present after current interruption. 2 Steady state conditions are such that the concentration gradients across the slimes layer remain constant during the measurement of the T|C-I relationship. 3 As Eq. 4 indicates, Ohm's law is not useful in a region where concentration gradients are present. Nevertheless, in such a region, an integral value of the changes in conductivity can be obtained. 4 Notice that Rm and b are a function of the local electrolyte conductivity and concentration gradients across the slimes layer. 5 AC and DC currents and overpotentials are terms that can easily be confused: An AC wave varies sinusoidally as a function of time and can be described by the following equation: /(f,a)) = M<)sin((iM + (|)) where: Me is the amplitude of the waveform, co is its frequency, * is the phase angle, and t is the time. By knowing M0, ©, and <B, the DC "instantaneous" component of the AC waveform can be obtained. [152] Data analysis 2) Upon application of a small amplitude sinusoidal current waveform (less than 35 Amp/m2) at low frequencies (ox6.3 rad/sec) and for a short period of time, ionic concentrations and concentration gradients throughout the slimes electrolyte remain unchanged \ 3) The only overpotential increase that results in a linear dependance between potential and current is that due to the ohmic drop of the slimes electrolyte (Rn, term in Eq. 5). 4) The restriction to ionic flow caused by the slimes can be obtained from the R,, , value and its dependance with the electrolysis conditions. 5) The part of the overpotential that does not depend on the current density is due to the presence of concentration gradients across the slimes electrolyte (b term in Eq. 5) and to related increases on the corrosion potential of the lead anode. 6) The lead dissolution process proceeds urihindered ( R ^ O ) whereas the slimes layer remains unreacted (Ret-***) 2 7) Ionic concentration gradients are present throughout the slimes layer (i.e. 5 is equal to the thickness of the slimes layer). Furthermore, these gradients are only observed in the direction normal to the anode. (I) Data analysis The steps that were followed to analyze the rjA spikes produced by the AC current waveform are as follows: A) From the TJa readings obtained during the application of the AC current waveform, r)n 3 , was subtracted *. B) The resulting anodic overpotential and the current density were curve-fitted to a straight line according to Eq. 5. 1 The exact values for the amplitude and frequency of the waveform may change depending on whether a oc current is applied or not. 2 This is equivalent to implying that all the current flow is at the anode/slimes interface without any significant Faradaic current crossing the slimes/electrolyte interface. 3 R, is known prior to and after the application of the current steps. An average Ft, value can be used to correct the r\A readings. 4 Notice that the anodic overpotentials shown in Figs. 6C, 7, and 11 are all corrected only for the initialr\a Onn=IR«)- The approach in this section is to analyze the anodic overpotential corrected forr|n present at the local time the current sweeps were applied. [153] Data analysis (A) (B) 268. 236. 2 1 2 , C cu Q ti U 1 8 8 , 1 6 4 . M.lr i i i t I i i i I i i i I i i i I i t i I i i i I i i i I i i i I i i i I 12,1 1 2 . 3 1 2 . 6 1 2 . 9 1 3 . 2 Time, Hrs. (C) 1 3 . 5 3 8 . 8 33,0' i i i i i i i i i i i i i i i 1 2 . 8 1 2 . 3 1 2 . 6 1 2 . 9 1 3 . 2 1 3 . 3 Time, Hrs. 38.8 r >-> 48.8 •a C 38.8 <U o & I... O ^ 11" * * MIr 111111111111 ' ' ' ' ' ' 1 1 1 1 1 1 1 1 1 1 1 1 ' .888 52.8 184. 156. 288. 268. Current Density, Amp/m 2 Fig. 32 Detail of the "spikes" observed at -0.8 mm slimes (Exp. CA2, Table 4). From Exp. CA2 (see Fig. 6) The data points shown in (A) and (B) were linked using cubic splines interpolation. Had more points been available these curves would have looked like distorted sinusoidal waveforms with equal amplitudes. (A) Variation of the anodic current density as a function of time (B) T | A variation as a function of time (corrected for tin)-(C) Current density vs anodic overpotential curve [obtained from the data shown in (A) and (B)] [154] Data analysis The current density changes observed during the application of one of the AC sweeps (Exp. CA2) are shown in Fig. 32A. The anodic overpotential spikes (corrected for TJQ) that result from variations in the cell current are shown in Fig. 32B. The linear relationship between these two quantities can be seen in Fig. 32C. This relationship was found to be frequency independent, indicating nearly steady state conditions. Further analysis of the r\A spikes produced during the application of the AC waveform at different slimes thickness showed that linearity was observed only up to anodic overpotentials smaller than 250 mV (Fig. 33). 2 4 0 . r 2 0 0 . -1 6 0 . h 1 2 0 . 8 B . e 4 0 . 0 1 4 0 . 3 6 0 . r 3 2 0 . 2 8 0 . 2 4 0 . 2 0 0 . 1 6 0 . 1 6 4 . 1 8 8 . 2 3 6 . 2 6 1 1 i I • i • 2 3 6 . 2 6 0 . 1 4 0 . 1 6 4 , 1 8 8 . 2 1 2 . 2 3 6 . 3 6 0 . Fig. 33 Variations in the anodic overpotential as a function of the anodic current density at various slimes thickness (Exp. CA2, Table 4). X axis: Anodic current density, Amp/m2 Y axis: Anodic overpotential (corrected for TIJ Each curve corresponds to the analysis of the spikes observed at the following slimes thickness: (A) 1.6 mm (B) 4.7 mm (C) 6.6 mm (D) 8.6 mm [155] Data analysis Table 4 Analysis of the spikes produced during the application of the A C waveform, in the presence of a net DC current (Exp. CA2, Figs. 32 to 35) Parameters Derived from Regression Analysis Computations From Eq. 4 Experimental Slimes Thickness mm Slope Qcm2 Intercept, b, (mV) |y r| 2,mv 3 b_ IR, pm, Qcm IR.. mV mV mV 0.80 2.23 3.10 5 33 5.95 6.56 7.18 7 79 8.41 8 65 0.62 1.45 2.15 3 93 4.57 5 23 5.71 7 22 4.96 9 40 30.8 45.8 54.4 75.3 82.4 93.1 113.9 124.9 361.0 360.6 0.850 0 986 0.988 0.981 0.961 0.920 0.905 0888 0.051 0.558 6.8 6.4 12.6 59.8 163.7 375.1 633.5 1192.5 4386.0 5688.7 2.54 1.63 1.30 098 0.93 092 1.03 089 3.74 1.97 7.78 6.48 6.93 7.38 7.68 7.98 7.95 9.27 5.90 10 86 12.1 28.1 41.8 76 5 88.8 1017 110.9 140 3 96.5 1827 42.9 73.9 96.1 151.8 171.2 194.8 224 8 265.2 457.5 543 3 41.9 73.3 95.5 150.4 170.0 193 3 221.8 2614 436.0 520.0 Between 18 and 20 experimental points were used to obtain the regression coefficient. These points were collected during -55 min and correspond to digitized samples taken when the frequency of the applied AC waves was between 0.063 and 6.3 rad/sec. Abstracted from Table 4, Appendix 9 As seen in Table 4, both R ,^ and b increase as a function of the slimes thickness (see Eq. 5 and Fig. 34A) indicating that larger concentration gradients across the slimes layer generate larger ohmic drops. Thus, the ohmic drop generated by these concentration gradients can promote the dissolution of the slimes layer only if large concentration gradients are also present. Furthermore, the ohmic drop generated by the slimes electrolyte (IRJ is smaller than the "current independent' term b only up to -5.3 mm slimes (i.e. ^- reaches a value of -1 at 5.3 mm slimes). After this slimes thickness, the IR™ term not only becomes larger than the b term, but it increases at a faster rate. The large variations in the values of these terms above -5.3 mm slimes are related to the precipitation of secondary products. Precipitation of secondary products changes both local ionic concentrations and local electrolyte conductivities. Moreover, the changes in the pm value, (Fig. 34B)1 also indicate increases in its value towards the end of the electrolysis cycle. Dissolution of slimes compounds at slimes thicknesses larger than 8 mm results in non-linear 1 pm is the resistance of the slimes electrolyte per cm of slimes: Rm [Qcm2] pm[Qcm] = SlimesThickness[ cm ] [156] M e h i i I i • I • i I i i I i i I i i I • i I i i I i • I i • I . C M i i i I i i I i i I i i I i i I i i I i i I i i I i i I i i .eaa l.sa s.se s .4a 7.2a 9.ea .aaa l.sa 3.6a 3.4a 7.2s 9.aa mm Slimes mm Slimes Fig. 34 Changes In the value of the resistance of the slimes electrolyte as a function of the slimes thickness (Exp. CA2, Table 4) (A) R,,, (Qcm2) changes (B) pm (Qcm) variations . e e e I . S B 3 . 6 a s . 4 e 7 . 2 a 9 . 0 0 mm Slimes Fig. 35 Changes in the parameters b and IR™ with relationship to the experimental variations of the anodic overpotential (Exp. CA2, Table 4). [157] Data analysis relationships between overpotential and current \ Under these conditions, DC current enters the slimes electrolyte from both the anode/slimes electrolyte interface and the slimes/slimes electrolyte interface and this produces non-uniformities in the distribution of current across the slimes layer. The relationship between r|a, b, and IRm is graphically presented in Fig. 35. The jump in the value of b at slimes thicknesses larger than 8 mm indicates that noble compounds have reached the potential at which they can react Faradaically. By adding the value of IRn, to the b value, the experimental r|A is obtained 2 . This is a very important relat ionship: It links the slimes solution properties to the changes taking place in the lead anode and in the slimes layer. Thus, for different electrolysis conditions and anode compositions, optimum parameters for lead electrorefining can be obtained by studying the variations in the b and IRm values at different slimes thickness. Moreover, it appears as if by merely applying a sinusoidal galvanodynamic scan (i.e. one scan whose amplitude is -20 Amp/m 2 at co~0.1 rad/sec) at preset slimes thickness, the same information obtained using the FRA can be derived 3 . Table 5 .A Analysis of the spikes produced during the application of the AC waveform. in the presence of a net DC current (Exp. CA6) Parameters Derived from Regression From Eq. 4 Experimental Analysis Computations Slimes Slope Intercept, r 2 |yr|2, b pm, Qcm » » , mV Thickness Rn.. b, (mV) mV2 mV mV mm Qcm2 il? m m m 0.17 0.14 3.56 1.96 5.14 4.75 32.0 57.8 m 3.06 5.37 1.52 189 m 0.99 0.85 0.40 15.64 1.59 2.55 4.98 3.52 m 76.6 130.5 78.3 1341 6.64 7.49 2.70 3.13 113.6 140.9 0 88 0.97 10 16 4.09 216 2.31 4.06 4.18 52.5 60.9 166.1 201.9 168.2, 205.2 4 experimental points were used to obtain the regression coefficient These points were collected during -12 min and correspond to digitized samples taken when the frequency of the applied AC waves was between 0.63 and 6.3 rad/sec. Abstracted from Table 5.a, Appendix 9 1 Non-linearities are identified when |y| increases and r2 decreases. 2 e.g. compare columns (IRm+6) and TIa in Table 4. 3 Use of linear polarization techniques such as SACV (small amplitude cyclic voltammetry) should provide the same results [10-13]. [158] Data analysis Table 5.B Analysis of the spikes produced during the application of the AC waveform, under current interruption conditions (Exp. CA6) Parameters Derived from Regression Analysis Computations From Eq.4 Experimental Tune, hrs Slope Rm, Qcm2 Intercept, b, (mV) r 2 |yr \mv2 pm, Qcm TR^+b, mV mV 0.63 2.44 3.83 43.07 112.8 2.23 3.62 3.83 1.64 0.99 60.8 i i i i^i i i i ; : 44.5 lllliiliillli 0.2 0.89 0.91 0.95 88 21.95 41.19 62.43 22.09 21.63 2.82 4.57 4.84 m 60.8 48.4 44.5 5.3 0.2 82.1 WmmMi 44.0 9 experimental points were used to obtain the regression coefficient These points were collected during -27 min and correspond to digitized samples taken when the frequency of the applied AC waves was between 0.63 and 6.3 rad/sec. Abstracted from Table 5.b, Appendix 9 The TJa spikes observed in Exps. CA6 and CC1 were also analyzed according to Eq. 5. The results obtained from such an analysis are shown in Tables 5A and 6. A linear relationship between overpotential and current was only found in the region where the potential excursions were absent. Furthermore, a quasi-linear relationship between overpotential and current was also found under current interruption conditions (Table 5B, Exp. CA6) *. Table 6 Analysis of the spikes produced during the application of the AC waveform, in the presence of a net DC current (Exp. CC1) Parameters Derived from Regression Analysis Computations From Eq. 4 Experimental Slimes Thickness mm Slope R „ Qcm2 Intercept, b, (mV) r 2 |yrl2, mV 2 b lRm pm, Qcm IRm.mV IR.,+6, mV mV 1.37 1.79 2.22 2.65 3.07 3.50 0.52 0.63 0.74 0.81 0.92 0.96 32.4 38.0 42.8 48.0 52.4 58.4 0.98 0.97 0.98 0.95 0.93 0.93 0.1 0.3 0.4 1.1 1.7 2.3 3.21 3.11 2.97 3.06 2.94 3.12 3.80 3.51 3.34 3.05 2.99 2.74 10.1 12.2 14.4 15.7 17.8 18.7 42.6 50.2 57.2 §Mmm 70.3 i l 7 ! l l l : 42.8 50.6 57.8 64.4 70.9 78.1 5 experimental points were used to obtain the regression coefficient These points were collected during -12 min and correspond to digitized samples taken when the frequency of the applied AC waves was between 0.63 and 6.3 rad/sec. By comparing the data presented in Tables 4, 5A, and 6 it can be seen that: 1 In Table 5B, r2 and |y| vary widely yet the predicted (IRm+o) and experimental (T|a) overpotentials are nearly equal. [159] Data analysis i) The anodic overpotential values observed at slimes thicknesses lower than 3.5 mm (before potential excursions appeared in Exps. CA6 and CC1) are different in the three analyzed experiments: T| A (Exp CA2) > rjA (Exp CA6) > r|A (Exp CC1). This results in differences among the computed RQ, and b values ii) The smallest and b values obtained at a fixed slimes thickness are observed in Exp. CC1. The fact that in this experiment pm decreases as the slimes layer thickens is significant. iii) A relationship that relates the slope b to the average slimes electrolyte resistance. Rn, , and to the local electrolyte concentrations cannot be inferred yet \ The observed differences in the values of the r|A components (IRn, and b) at a fixed slimes thickness are related to the bulk electrolyte composition, to the presence of addition agents, and to the changes in the slimes physico-chemical properties (i.e. porosity, tortuosity). Addition agents appear to play an important role in the anodic overpotential increases . This was also observed in the sulphamic acid system 1251a. Thus, in Exp. CC1 the distinct R^, and b values indicate that the addition agents increase n A mainly by restricting the flow of ions 3 . In the presence of a Faradaic current, I, this restriction can be related to the ratio: The larger m this ratio, the smaller the restriction for the movement of electrolyte across the slimes layer and the lower the observed overpotential. In Exp. CC1 the ^- ratio is ~3 and remains nearly constant. On the other hand, at similar slimes thickness, for the other experiments this ratio shows marked decreases (from 2.5 to 1.3 for Exp. CA2 and from 3.4 to 1.6 for Exp. CA6). 1 i.e. b values cannot be derived from Rm values and vice versa : Average electrical conductivities may be equal yet local concentrations may be different. 2 The amount and nature of addition agents incorporated during the refining of Pb using a sulphamic acid electrolyte has also been shown to have a strong impact on the permeability of the anode slimes [25]. 3 Notice that whereas Exps. CA2 and CA6 were carried out using the lead anode "mould" cooled face, Exp. CC1 was performed using the "air" cooled face. The microstructures of these electrodes were found to be similar. Thus, the anodic overpotential variations can hardly be related to microstructural differences between the different electrodes. [160] Proposed analogue representation of a lead bullion electrode covered with a layer ol slimes. Analysis of the TJa spikes obtained upon current interruption also indicated a linear relationship between rjA and current (Table 5B). Under current interruption conditions 1=0 and rjA does not have an ohmic component, yet, by slowly displacing the dynamic pseudo-equilibrium observed during the relaxation of the concentration gradients, it was possible to obtain the integral value of the resistivity of the slimes electrolyte, R n , \ As seen in Table 5B this value decreases as the concentration gradients relax. Furthermore, at the end of the current interruption cycle, T]A~0, yet, as indicated by the finite R n , value, the electrolyte present within the slimes was found to have a different conductivity than the bulk electrolyte. (b) Proposed analogue representation of a lead bullion electrode covered with a layer of slimes. So far in this thesis it has been shown that the response of electrochemical systems to AC waveforms can be used to obtain kinetic and diffusional parameters. Resistors, capacitors, and CPE's have been used to link changes in the AC spectra to associated physico-chemical parameters. A general model is to be proposed to analyze the observed AC impedance spectra. This model is based on a set of assumptions. From this model and from the experimental data, several electrical analogues are developed to examine the AC impedance data and to find the link between these analogues and the physical phenomena they may represent. Fig. 36 shows a general analogue model of a lead bullion electrode covered with a layer of slimes. Six interfaces can be identified in this figure. Each one of these interfaces has an associated impedance 2 : 1 i.e. the pseudo-steady state observed during the relaxation of the concentration gradients in the entrained electrolyte was slowly displaced by applying a sinusoidal current waveform. 2 The impedance of the reference electrode is neglected in this analogue. [161] Proposed analogue representation of a lead bullion electrode covered with a layer of slimes. za/se = Faradaic impedance at the lead anode/slimes electrolyte interface. = Faradaic impedance at the sltaes/slimes electrolyte interface. Zgi/be = Faradaic impedance at the slimes/bulk electrolyte interface. Z a / 8 , = Electronic impedance at the lead anode/slimes interface. Zw = Warburg ionic diffusional impedance throughout the slimes electrolyte. Zyj„ = Warburg ionic diffusional impedance in the slimes electrolyte/bulk electrolyte interface. The value and mathematical expressions that each of these impedances can adopt is a function of the current density, the slimes electrolyte composition, the slimes layer microstructure and composition, and the electrode's thermal history and composition. Thus, a single mathematical representation of the overall impedance may be too difficult to determine unambiguously. Moreover, some of these impedances are distributed (i.e. their value changes as a function of the position) and coupled (i.e. they change only if other impedances change). Despite the complex interrelationships existing among the different impedances, their individual contribution to the total impedance can be assessed by analyzing each of them separately. From this analysis and from experimental data, the relative magnitude of each of these impedances with respect to the total impedance can be inferred. The individual analysis of the components of the impedance has to start from the simplest scenario. This will be the case when only a DC current is applied to the electrode. In this case the total impedance of the system has only a real component [ZDC = Z(j(a)(O=0]. Thus, while the impedance is not an explicit function of time, if measured in a system where changes are taking place, its value at a fixed frequency will be a time dependent quantity. Thus at (0=0 the changes in impedance as a function of time, Z^f), can be defined as follows: where: TJ (t) = overpotential (compensated for rid observed upon passage of current as a function of the electrolysis time. By using a reference electrode reversible to Pb + 2 no corrections for liquid junction at the reference electrode/electrolyte interface have to be incorporated in the T\(t) values. [162] Proposed analogue representation of a lead bullion electrode covered with a layer ol slimes. During the galvanostatic dissolution of a lead bullion electrode, rj increases as the slimes layer forms. Thus, all the information on the impedance comes from knowledge of the changes in rj as a function of time. By subtracting T|Q 1 from the r\(t) values one of the most obvious contributions to the impedance has been identified and subtracted from the overall impedance. However, other contributions to the overall impedance cannot be as easily identified and/or quantified. By analyzing the path of the DC current on its way from the anode to the bulk electrolyte a deeper insight in the Z^. components can be obtained. Thus, as shown in Fig. 36 there are two main paths for the DC current: One through the anode/slimes electrolyte interface and the second through the anode/slimes interface. If current enters the slimes filaments it can either leave them through the bulk electrolyte (path A) or through the slimes electrolyte (path C). On the other hand if any current crosses the anode/slimes interface it can either go across the slimes electrolyte (path B) or return to the anode via a ground loop (path D). For current to go through the slimes filaments it will first have to overcome a resistance associated with Z a / S l . As the slimes filaments were found to be grounded to the anode 2 such resistance must be negligible. Any current entering the slimes filaments can only produce Faradaic work at the slimes/slimes electrolyte interface if and only if the activation energy barrier of such process is overcome. This requires large overpotentials and ionic gradients across the slimes layer. If any current diverts towards the slimes filaments it can either go across the slimes/slimes electrolyte interface (path A) or across the slimes/bulk electrolyte interface (path C). The experimental evidence is that Faradaic reactions of the slimes compounds are insignificant at overpotentials less than 200 mV. For example, the amount of bismuth corroded is less than 30 ppm, too small to account for significant Bi corrosion currents crossing the slimes filaments. Thus, during most of the electrorefining cycle, any current going through the anode/slimes interface can only result in charging of the 1 T j a is equal to the current density, I, times the uncompensated ohmic resistance, R, (nn=IR9). 2 See Chapter 4 section II.A. 1 [163] Proposed analogue representation ola lead bullion electrode covered with a layer of slimes. Anode/S l imes Interface i i S l i m e s •: f i l a m e n t z Sl imes/Elect ro ly te Interface i i f Zsl/be sl/se W 5 * a/se L e a d A n o d e S l i m e s E l e c t r o l y t e llllllllllillllllllllllllll .-^  >• ;:?.;:?/:S;1 irnne"•• ^H&ihneshii Bulk E l e c t r o l y t e S l i m e s L a y e r Fig. 36 Proposed analogue model representation of a lead bullion electrode covered with a layer of slimes. [164] Proposed analogue representation of a had bullion electrode covered with a layer ol slimes. electrical double layer of the slimes filaments *and are insignificant. Thus, from this analysis it can be assumed that for the DC case, up to r\(t) values equal to 200 mV: Za /ai->0, Z ^ - ^ , and Z a l / b e - * > ° . From the previous description it can be assumed that almost all of the applied DC current flows across the anode/slimes electrolyte interface and continues in its way towards the bulk electrolyte by overcoming the diffusional impedance Z^r (path B). All this current is transferred to the electrolyte mainly as a result of the Faradaic transfer of Pb + 2 to the slimes electrolyte. For such a transfer to take place, an energy barrier associated with Z a / s e has to be overcome. Such impedance is small (lead dissolves almost reversibly), yet it can increase if conditions at the interface change (i.e. as a result of the presence of secondary products blocking the interface). Once Pb + 2 ions are transferred to the slimes electrolyte, an ionic current is established. The resistance that the ions find in their movement across the slimes is a function of Zw which is an intensive and position dependent quantity. The larger the effective distance the ions have to travel before reaching the bulk electrolyte the larger this impedance. The complex migraUonal/diffusional processes taking place across the slimes electrolyte can be described by Z ^ . Furthermore, if as a result of the movement of ions across the slimes electrolyte/bulk electrolyte interface a diffusion layer is established, a semi-infinite Warburg impedance has to be included as well, although for well mixed bulk electrolytes its presence can be neglected. Once the Pb + 2 ions reach the bulk electrolyte they are transferred to the cathode by convection, migration and diffusion. Thus, the analysis of the DC experimental data presented in Section III.2 of this chapter can now be related to the analogue model shown in Fig. 36. In the DC analysis of the anodic overpotential changes, the lead dissolution processes were assumed to proceed unhindered whereas the slimes layer was assumed to remain unreacted. This is equivalent to assuming that Z a / s e - » 0 and that Zsj/ae-^ oo , and Z s ] / b e — w h i c h is in agreement with the statements on the characteristics of the electrical analogue here presented. Thus, the Rm value obtained from the analysis of the changes in overpotential as a function of 1 Notice that under DC conditions a capacitor will act as an open circuit and will have an infinite impedance. The impedance of a capacitor, Zc, is given by: zc=^, thus at co=0, Z,.-*». [165] Proposed analogue representation ola lead bullion electrode covered with a layer of slimes. current can only be related to changes in the value of Z^. A relationship between the observed b values and Zy, may also exist, yet, impedance values obtained at frequencies other than zero have to be provided (see Eq, 9). The previously introduced DC model also must be consistent with the experimental evidence observed under current interruption conditions. Depending on the extent to which concentration gradients had been established prior to the current interruption, an overpotential decay will always be observed. Eventually, the electrolyte compositions inside and outside the slimes electrolyte equilibrate, ionic movement virtually stops, and the impedance disappears as the overpotential vanishes (i.e. as n . ^ -» 0). On the other hand, as a result of the ionic concentration differences between the slimes electrolyte/bulk electrolyte and the anode/slimes electrolyte interfaces, a series of concentration cells may be established because electronic current can flow across the slimes filaments (path D). This process may consist of (as an example) continued corrosion of the lead anode, accompanied by deposition of noble elements in the electrolyte, as Bi + 3 , SbO+, or Ag* on slimes filaments. These internal currents may be too small or difficult to measure, however, they can affect the characteristics of the overpotential decay and consequently of the impedance. As concentration gradients disappear, the rate of these internal processes declines, up to the point at which they become negligible. The phenomena associated to the current interruption case can also be represented by the analogue circuit shown in Fig. 36. Diffusional processes can be represented by Zy, and Z^^. However, as concentration gradients within the slimes layer relax, Z^ describes diffusional processes that resemble more semi-infinite diffusion than diffusion in a bounded region. As described previously, Z^ is linked to the components of the concentration overpotential, and for a purely diffusional process, Rn, should be equivalent to the diffusion resistance Ro (i.e. to the value of Z^ at co=0). In the analysis of the components of the AC impedance, the same line of thought followed during the DC analysis will be used: First, the different paths that the AC wave can follow will be traced. Then the relative contribution of each of the associated impedances to the overall impedance will be estimated. On the basis of this and from experimental evidence, simplifications of the general [166] Proposed analogue representation ol a toad bullion electrode covered with a layer ol stones. analogue model will be proposed. The validity of the proposed model will be tested by analyzing the changes in impedance in the presence and in the absence of a net Faradaic DC current. In the previous analysis it was found that all the applied DC current can be assumed to flow across the anode/slimes electrolyte interface. On the other hand, a superimposed AC wave can either cross the same interface and/or divert through the slimes filaments. If it diverts to the slimes filaments, it can cross the slimes/slimes electrolyte interface without actually perfonriing any Faradaic work. This will happen if the slimes layer can be considered to have only a capacitative component. For these processes to take place, the AC waveform will have to produce alternating potential fields at the slimes/slimes electrolyte double layer interface. This will result in large capacitative effects being observed in the impedance spectrum. Thus, if any AC current crosses the slimes/slimes electrolyte interface, equivalent impedances related to the capacitative part of the slimes impedance should be observed even in the absence of a net Faradaic current. As the experimental impedance spectra obtained under current interruption conditions did not indicate the presence of large interfacial areas, AC current transfer across the slimes layer in the presence of a net Faradaic current can be neglected. The experimental data indicate that while a net DC current is being applied, formation of Pb + a is the preferred reaction. Such a reaction takes place without a significant energy expenditure and is the path of least resistance for the flow of current. If this is the path for least resistance for DC current, it can also be assumed to be the path of least resistance for the AC current. Thus, assurning that all the AC current crosses this interface, the overall impedance will have only three components: Z a / a e , 7^,, Zw„ (notice the similarity between the DC and the AC cases)1. Accordingly, in the absence of a net Faradaic current, the polarity of the double layer can be switched and/or its potential difference changed simultaneously in the slimes/electrolyte and the anode/slimes interface. Only then, the capacitative and resistive process associated with these impedances can be observed as changes in the impedance of the system. Consequently, 1 Notice that in the worst scenario in which in the presence of a DC current the AC current actually crosses the slimes/slimes electrolyte interface and causes Faradaic reactions, a wide non-uniform current distribution can result. If this had taken place the system would had been changed to the extent that steady state concentration gradients during the AC measurements would not have been observed, the system would have oscillated to the extent that the impedance measurement could not have been taken. [167] Proposed analogue representation of a lead bullion electrode covered with a layer ol slimes. other processes overlooked by the anodic overpotential measurements under current interruption conditions may be better analyzed by AC impedance techniques. Basically, the main difference between the DC and the AC experiments is that while DC currents cannot cross the slimes/slimes electrolyte interface at r\ lower than 200 mV, AC waveforms can cross such an interface and by doing so induce changes in the measured AC impedance. However, in the presence of a net Faradaic current such process may be hindered to the extent that such transfer does not take place at all. If this is the case, then all the DC and AC current flow is at the anode/slimes electrolyte interface. Nonetheless, if any AC current flows across the slimes layer it may result in impedance changes only in the high frequency region of the impedance spectrum at which point charge transfer phenomena are isolated from diffusional processes in the slimes electrolyte. The situation changes at overpotentials at which Faradaic reaction of the slimes filaments can take place1 . Under these conditions, both DC and AC currents will cross the slimes/electrolyte interface and in doing so, at that point, abrupt changes in impedance will take place. On the other hand, in the absence of a net Faradaic current (i.e. under current interruption conditions) the hindrance for the current flow across the slimes layer disappears (as the whole electrode can change polarity and/or act as a corrosion or concentration cell) and impedances associated with the slimes filaments will be observed in the total impedance. Summary of assumptions used in the development of the analogue model: 1) A one dimensional representation of the lead bullion electrode covered with a layer of slimes. 2) Electrolysis takes place under isothermal conditions 2 . 3) The Warburg diffusional impedance can be used to describe the ionic mass transfer processes that take place across the slimes electrolyte. 4) The AC impedance measurement is obtained without significantly affecting the quasi-equilibrium conditions witJiin the slimes layer. 1 These abrupt impedance changes upon Faradaic reaction of the slimes filaments can be seen by comparing Figs. 13 and 14. 2 Isothermal temperature of the slimes electrolyte can be assumed on the basis of sufficient thermal conductivity of H2SiF6-PbSiF6 solutions and of the large porosity of the slimes layer, contributing to convection. [168] Data analysis 5) In the presence of a net Faradaic current the lead anode and the slimes layer are equipotential. 6) Changes in the microstructure of the slimes layer as a result of blockage of ionic flow (i.e. by the precipitation of secondary products) can be incorporated within the Warburg diffusional impedance or by additional impedances connected in series with it \ 7) Blockage of the anode/slimes electrolyte interface (i.e. by the precipitation of secondary products) inhibits charge transfer processes and increases the Faradaic impedance, Z a / s e . 8) Dissolution of noble impurities present within the slimes layer takes place only at overpotentials larger than 200 mV. 9) In the presence of a net Faradaic current and at overpotentials values smaller than 200 mV, 100% of the current transfer occurs across the anode/slimes electrolyte interface and: Z a / s e -»0 , Z9l/se-**>, and Z 8 l / b e-»oo. 1 0 ) In the presence of a net Faradaic current capacitance effects associated with the slimes layer are prone to be observed only in the high frequency region of the impedance spectrum a . 1 1 ) The impedance changes attributed to the presence of addition agents can be incorporated within the proposed Faradaic and diffusional impedances. 1 2 ) Impedances associated with the reference electrode can be neglected. (I) Data analysis In this section, several electrical circuits derived from the proposed analogue model are introduced. These electrical circuits were formulated so as to follow the assumptions used in the development of the general analogue model. Among all the analyzed circuits, only those that actually matched the experimental data are presented and discussed. The characteristics of these circuits are established by comparing their parameter values with physico-chemical processes taking place across the slimes layer. 1 Non-uniform porosity across the slimes layer can be expected when secondary products precipitate or re-dissolve. 2 Capacitance effects associated with the noble compounds present in the slimes layer are more significant as the TIa approaches values larger than 200 mV (i.e. in the region where their Faradaic reaction can occur). [169] (i) Case I: impedance spectra obtained in the presence of a net Faradaic current The impedance spectra obtained in Exps. C A 2 . C A 5 . C A 6 , and C C 1 were found to be described accurately 1 by two different yet related electrical circuits (see Fig. 37). The values of the parameters associated with the proposed electrical circuits were obtained by curve fitting 3 the experimental data to the theoretical impedance functions. The Jirst of these circuits is a ZzARd-ZzARea-CPEo analogue (circuit A . 1, Fig. 37) 3 . The impedance of each of the components of this circuit is given by the following equations : ZCPEL = b,m^' ZCPE, = Wmf*1 ZCPEO = Kijnf™ From which the total impedance, Z A , can be obtained as follows: with Rj W zA= -ir+  2—-+B0U^' ...io Rl /?2 D1=— and D2 = — The overall impedance of the circuit A . 1 was re-arranged as described in Eq. 10, so that the relaxation times can be obtained from the D; and D 2 parameters. The relaxation time associated with each one of the ZARC circuits can be obtained as follows: • i x, and \ = D!^ 1 As presented in the various Tables shown in Appendix 9 "described accurately" means that from a statistical regression analysis perspective, good correlation existed between the experimental and the curve-fitted data. The number of parameters involved in the curve fitting routine was never in excess to that required to obtain significant fits according to statistical rules (i.e. as derived from ANOVA statistical tables). 2 This process required the use of complex non-linear square fitting routines . The Zj component of the total impedance was used to obtain the values of individual parameters in the different electrical circuits. Once an initial set of values was obtained, they were used to compute the Z„ component of the impedance and improve the accuracy of the fitting process. 3 For an in-depth review of the characteristics of the ZARC circuits see ref. [is]. [170] Data analysis Circuit A . l "ZARCl CPE,—, —Wv— "ZARC2 Z CPE n W Ffgwrey tewree I I ^  F r W 7 "PP™ | | Bthaon CPE,-, Wr— -CPE. Circuit A . 2 •ZARCl ZARC2 Fig. 37 Electrical circuits used to analyze the impedance spectra  The electrical parameters associated with circuit A . 1 were correlatec with the individual impedances shown in Fig. 36 1 . Thus, the first ZARC circuit was used to represent high frequency phenomena 2 associated with the Faradaic impedances Z a / s e and Z s l / s e . The second ZARC circuit was used 1 R1 was chosen to represent charge transfer resistances associated with the lead dissolution processes, while R2 was related to the DC conductivity of the slimes electrolyte. CPE, represents the distributed nature of the anode/slimes and the slimes/slimes electrolyte interface while CPEa represents the presence of a distributed capacitance generated by the concentration gradients present in the slimes electrolyte. 2 The high frequency term refers to the part of the impedance that was observed at co> 100 rad/sec. [171] Data analysis to represent the low frequency response associated with ionic diifusion across the slimes layer (i.e. with Zy,). The third component of this circuit, a CPE element was introduced to represent diffusional processes (i.e. Zw,.). The second analogue circuit was indirectly assembled