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The electrochemical oxidation and combustion of carbon. Turnbull, John Douglas Shand 1957

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THE ELECTROCHEMICAL OXIDATION AND COMBUSTION OF CARBON  by  JOHN DOUGLAS SHAND TURNBULL  A THESIS SUBMITTED IN PARTIAL FULFILMENT QF THE REQUIREMENTS FOR THE DEGREE OF MASTER QF APPLIED in Department  SCIENCE  the  of Mining and M e t a l l u r g y  We accept t h i s t h e s i s as the standard r e q u i r e d  conforming  to  from candidates  f o r the degree o f MASTER OF APPLIED  SCIENCE  Members of the Department and M e t a l l u r g y .  of  Mining  THE UNIVERSITY OF BRITISH. COLUMBIA October, 1 ° 5 7  ii ABSTRACT  The  o x i d a t i o n and c o m b u s t i o n o f g r a p h i t e i n a l e a d -  b o r o s i l i c a t e s l a g of the composition s t u d i e d w i t h and w i t h o u t  PbO„Si02.0.1Na2B407 w e r e  an a p p l i e d p o t e n t i a l .  The r e a c t i o n was  f o l l o w e d by t h e a n a l y s i s o f t h e d e s o r b e d anode g a s . The  CO/CO2 r a t i o  o f t h e a n o d e g a s i n a n y one e x p e r i m e n t  was f o u n d t o i n c r e a s e l i n e a r l y w i t h t i m e i n a l l c a s e s . i n c r e a s e was t h o u g h t t o be r e l a t e d t o t h e d e c r e a s i n g concentration.  The  ±  6 kilocalories.  A theoretical i n chemical  2  density. f o r the  a n a p p l i e d p o t e n t i a l was f o u n d  This i sconsiderably higher  (8 t o 17 k i l o c a l o r i e s ) r e p o r t e d  values  of C 0  increasing current  with  apparent d i f f e r e n c e i n a c t i v a t i o n energies  d e s o r p t i o n o f CO a n d CO2 w i t h o u t t o be 32  oxygen-ion  The CO/CO2 r a t i o was f o u n d t o i n c r e a s e  temperature and t o decrease w i t h  This  than the  f o r t h e gaseous r e a c t i o n ,  explanation f o r the increased  production  and e l e c t r o c h e m i c a l c o m b u s t i o n o v e r  o b s e r v e d i n g a s e o u s c o m b u s t i o n was a d v a n c e d .  This  that  explanation  e x t e n d e d t h e d e s o r p t i o n model o f Long and Sykes t o t h e s l a g graphite reaction. ratio  increases w i t h time i n chemical  predict  chemical  c o m b u s t i o n , b u t does n o t  t h i s observed e f f e c t f o rt h e electrochemical r e a c t i o n . The  the  T h i s e x t e n d e d m o d e l e x p l a i n s why t h e CO/CO2  r a t e o f oxygen removal from t h e s l a g d u r i n g t h e  r e a c t i o n was c a l c u l a t e d f r o m t h e r a t e o f e v o l u t i o n a n d  composition  of t h e desorbed gas.  The a c t i v a t i o n  energy  is  2 6 - 5 kilocalories.  Absolute r e a c t i o n r a t e  calculations  were made f o r r a t e - c o n t r o l l i n g s t e p s o f immobile a d s o r p t i o n , mobile a d s o r p t i o n ,  chemical r e a c t i o n , and d e s o r p t i o n .  c u l a t e d r a t e s were at observed  rate.  least a factor  of 10  different  The c a l from the  In presenting  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  the requirements f o r an advanced degree at the  University  of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. agree that permission f o r extensive for s c h o l a r l y purposes may  I further  copying of t h i s t h e s i s  be granted by the Head of  Department or by h i s r e p r e s e n t a t i v e .  my  I t i s understood  that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission.  »»j  Department of  9- Mc-fa //<-•/-  The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. Date  /"7c*.y  /S  A  ACKNOWLEDGEMENT  The  a u t h o r would  like  a s s i s t a n c e , and e n c o u r a g e m e n t of t h e s t a f f o f t h e Department especially  t o acknowledge  freely  the advice,  g i v e n b y t h e members  o f M i n i n g and M e t a l l u r g y , ,  t h a t o f D r . C.S„ Samis,. who d i r e c t e d  this  investigation. The  author i s also indebted  Research Council  t o the N a t i o n a l  and t h e D e f e n s e R e s e a r c h B o a r d f o r t h e  f i n a n c i a l assistance  necessary t o carry out t h i s  project.  V  TABLE OP CONTENTS Page 1.  INTRODUCTION  1  G A S I F I C A T I O N OF CARBON . . . Oxidation Process  2  . . . .  Combustion Process  3  .  7  IONIC OXIDATION AND COMBUSTION OF CARBON  11  E n t r o p y Change OBJECT AND SCOPE OF THE PRESENT INVESTIGATION EXPERIMENTAL PROCEDURE OVERVOLTAGE  MEASUREMENTS I N F A Y A L I T E SLAGS  REACTION OF GRAPHITE I N L E A D - S I L I C A T E SLAGS Materials  .  Apparatus  .  Slag Composition  , . .  l£  . . . . . .  1$  . . . . .  .  16  16 .19  . „  Procedure  ...  21  . .  Analysis . . . . .  20 20  ,  C u r r e n t D e n s i t y Measurement  RESULTS  Hj.  16  Slag Preparation . .  Gas  . . . .  .. . . . . . . . . . . .  CHEMICAL OXIDATION . ABSOLUTE REACTION RATE CALCULATIONS  22 2$ 2$  . . . . . . . . .  2$  CHEMICAL COMBUSTION  27  ELECTROCHEMICAL COMBUSTION  32  DISCUSSION DESORPTION MECHANISM  . ' lj.2 h,2  vi Page P r o p e r t i e s of Graphite and Carbon . . . . . . . . . . 1. Formation 2.  i}3 .  l\.3  . . . . . . . . . . . . . . . . . . .  IL$  .Slag-Graphite I n t e r f a c e . . . . . . . . . . . . . . .  l\S  1. Semi-Conductor Band Theory . . . . . . . . . . .  l±9  2 . Slag-Graphite  $2  Structure  Interface  . . . . .  Mechanism f o r the Combustion of Graphite  . . . . . . .  COMPARISON OF EXPERIMENTAL RESULTS WITH THEORY CONCLUSIONS  . .  . . . . . . . . . . . . . . . .  RECOMMENDATIONS FOR FURTHER WORK BIBLIOGRAPHY  .  . . .  . . . . . . . . . . . . . . . . . . .  .  6£ 67 68 69 72  APPENDIX A APPENDIX B  60  . . . . . . . . . .  . . . . . .  79  vii LIST OF FIGURES F i g u r e No. 1.  Page  Apparent A c t i v a t i o n Energy D i f f e r e n c e Combustion .  .  .  .  .  .  Energy Diagram  .  .  .  .  .  i n Gaseous  .  .  .  .  .  .  .  5  . . . . . . . . . . . .  9  2.  Potential  3.  Experimental  Apparatus f o r F a y a l i t e S l a g s  4.  Experimental  Apparatus f o r P b O . S i 0 2 . l  5.  Photograph  6.  A r r h e n i u s P l o t f o r Chemical. O x i d a t i o n . . . . . .  7.  V a r i a t i o n o f CO/C0 2 R a t i o w i t h Time f o r  of E l e c t r o c h e m i c a l l y  Chemical Combustion  B  .  9.  Apparent A c t i v a t i o n Energy D i f f e r e n c e  23 26  . . . . . . . . . . . . .  A c t i v i t y of PbO i n P b O - S i 0 2 M e l t s  16  Na2 4°7  O x i d i z e d Anodes  8.  Chemical Combustion  . . . .  29  . . . . . . . .  31  for  . . . . . . . . . . . . .  33  10.  V a r i a t i o n of CQ/C0 2 R a t i o w i t h Time at  900°C  .  .  35  11.  V a r i a t i o n of CQ/C0 2 R a t i o w i t h Time at  Q25°C  .  .  36  12.  V a r i a t i o n of C 0 / C 0 2 R a t i o w i t h Time at  950°C  .  .  37  13.  V a r i a t i o n of CQ/C0 2 R a t i o w i t h Current D e n s i t y  .  38  14.  Apparent A c t i v a t i o n Energy D i f f e r e n c e s Electrochemical  15.  Combustion  for  . . . . . . . . .  40  V a r i a t i o n of Apparent A c t i v a t i o n Energy Difference  w i t h Current D e n s i t y  . . . . . . .  41  . . . . . . . . .  44  16.  Aromatic Hydrocarbon S e r i e s  17.  T T - E l e c t r o n Molecular Orbitals  18.  E l e c t r o n D i s t r i b u t i o n i n Graphite  . . . . . . . .  47  19.  E l e c t r o n Band S t r u c t u r e of Carbon . . . . . . . .  48  i n Benzene  . . . .  47  viii  F i g u r e No. 20.  Page  V a r i a t i o n of Energy Gap w i t h Heat  Treatment  Temperature 21.  Hall  50..  Coefficient  as  a F u n c t i o n of  Temperature  of Heat Treatment 22.  Band S t r u c t u r e  23.  Postulated  53  of S l a g - G r a p h i t e  Structure  of  Contact  55  Slag-Graphite  Boundary Layer 24.  Influence  57  of A p p l i e d P o t e n t i a l on Slag--Graphite  Band S t r u c t u r e  59  25.  Oxygen Bonding on G r a p h i t e  26.  tT-Bond Orders i n Phenpxyl R a d i c a l  27.  TP-Bond Orders f or oC-Naphthoxyl and A-Naphthoxyl  6l  . . . . . . . .  6l  Radicals 28.  Ketene S t r u c t u r e  63 .  .  63  THE ELECTROCHEMICAL OXIDATION AND COMBUSTION OF CARBON  INTRODUCTION  One of the chemical r e a c t i o n s  most u s e f u l  has been the r e a c t i o n of c a r b o n - c o n t a i n i n g m a t e r i a l s T h i s heterogeneous r e a c t i o n i s o f c o n s i d e r a b l e industrial for  interest  some y e a r s .  and has been the s u b j e c t of  to mankind w i t h oxygen.  theoretical  and  extensive  research  However, a m o d i f i c a t i o n of t h i s p r o c e s s i n v o l v i n g  the r e a c t i o n of carbon w i t h the oxygen i o n s i n a m e l t , as  typified  by the anodic r e a c t i o n o c c u r r i n g i n the a l u m i n a - r e d u c t i o n  cell,  has  r e c e n t l y been accorded much This i n v e s t i g a t i o n  is  interest. concerned w i t h the consumption of  carbon u s i n g a molten l e a d - b o r o s i l i c a t e oxygen. it  Before d i s c u s s i n g  i s advantageous f i r s t  the procedure and r e s u l t s of t h i s  study,  to c o n s i d e r the present knowledge of  gaseous consumption of carbon. comparison,  s l a g as a source of i o n i c  the  Using these data as a b a s i s of  the changes i n v o l v e d i n u t i l i z i n g oxygen i o n s i n p l a c e  of m o l e c u l a r oxygen w i l l  be d i s c u s s e d .  GASIFICATION OF CARBON The consumption of carbon may be c o n s i d e r e d to of  two general  s t a g e s : an o x i d a t i o n step i n v o l v i n g a d s o r p t i o n and  chemical r e a c t i o n , d e s o r p t i o n of  consist  and a combustion step c o n s i s t i n g  carbon o x i d e s .  of  the  The o x i d a t i o n stage normally c o n t r o l s  - •2 the  rate  actual both  of  reaction,  amount o f  and t h e  combustion stage determines  c a r b o n consumed p e r m o l e c u l e  CO and CO2 a r e  desorbed  studied  extensively  ment t h a t thus  the  rate-controlling  tion  Furthermore, and does not  (J),  first  studies,  (5)»  t h e mechanism o f  definitely  established.  reaction rate theory,  step.  approximate  and t h e r e  oxygen remains The  activa-  (8(• comprehensive  (Q),  not  that  either  calculations  no e x p e r i m e n t a l  kinetic  been  by u s i n g t h e  absolute  immobile  or mobile adsorption  However, these is  an  and  between 20 and 50 k i l o -  numerous  calculated  agree-  t o 02,  sites  c a r b o n o x i d a t i o n has  adsorption with dissociation determining  lie  Gulbransen  has  respect  involves  been  general  reaction order.  (6)> (7)>  i n s p i t e of  has  There i s  c o n c e n t r a t i o n of  i n f l u e n c e the  p e r gram mole However,  (4).  order with  e n e r g i e s have b e e n f o u n d t o  calories  o x y g e n gas  step probably  the  since  Process  carbon with  (2),  the r e a c t i o n i s  molecule. constant  (1),  oxygen  simultaneously.  Oxidation The o x i d a t i o n o f  of  the  are  is  the  rate-  only  v e r i f i c a t i o n of  either  mechanism. Therefore, 1.  may be c o n c l u d e d  The o x i d a t i o n o f with respect  2.  it  The r a t e sites.  is  carbon i s  to m o l e c u l a r not  that:  a first-order  reaction  oxygen.  i n f l u e n c e d by the c o n c e n t r a t i o n of  3.  The c a l c u l a t i o n s  3 -  of Gulbransen i n d i c a t e t h a t  adsorption with d i s s o c i a t i o n may be the r a t e - c o n t r o l l i n g  o r mobile  either  adsorption  step.  Combustion Process One  of the most s i g n i f i c a n t  the combustion of carbon i s reacted  charcoal,  reactor.  coke,  that  of G i l l i l a n d  did  et a l  s t u d i e s on ' (10).  Upon r e p l a c i n g the n i t r o g e n c a r r i e r gas w i t h  pure d i l u t i o n . not back-react  conditions.  They  and g r a p h i t e w i t h a i r i n a f l u i d i z e d - b e d  change was found i n the r e s u l t a n t of  experimental  ratio  C0/C02  T h i s would i n d i c a t e  that  C02>.no  over and above  the CO2 in- the  g  a  that s  w i t h the carbon to form CO under these  I t may be concluded from t h i s work, t h e r e f o r e ,  that  the CO and CO2 desorbed from a carbon s u r f a c e are primary products  of  combustion.  Much work has desorbed gas.  Arthur  been done on the CO/CO2  ( 1 1 ) , who s t u d i e d  C02 i n the temperature  ratio  i n the  the d e s o r p t i o n of CO and o  range from 470 to 900 C . , found t h a t  CO/CO2 r a t i o was u n i q u e l y determined by the temperature t o the e q u a t i o n C0/C0  Long and Sykes the desorption^ of CO as 1 1  .  according  ., „ , _ _ -12,400  3.4  term of 1 0  the  2  =10  (4)  e  R  T  have measured the a c t i v a t i o n energy  53 k i l o c a l o r i e s per gram mole w i t h an entropy  Their.measured v a l u e f o r the a c t i v a t i o n energy f o r  d e s o r p t i o n o f CO2 i s  for  the  38 k i l o c a l o r i e s w i t h an entropy term of 1 0 7 , Thus  -  k-  the C O / C O 2 r a t i o from t h e i r data Is g i v e n b y the  T h i s i s In good  agreement w i t h t h a t of A r t h u r .  From the equations of A r t h u r , it  equation  and  Long and  Sykes,  i s seen that t h e i r a c t i v a t i o n energy d i f f e r e n c e s f o r  the d e s o r p t i o n of 0 0  and  CO2  are 12. IL k i l o c a l o r i e s  and  17 k i l o c a l o r i e s r e s p e c t i v e l y . Rhead and Wheeler ( 1 2 )  Combusted  carbon at  temperatures f r o m l j . 0 0 to 6 f ? 0 ° C . by b o t h a s t a t i c dynamic method.  The  and  r e s u l t i n g CO/COg r a t i o s are shown In  F i g u r e 1 w i t h the data of Long and  Sykes, and  Arthur.  f i g u r e i s a graph of l o g C O / C O 2 " r a t i o a g a i n s t the of the absolute  temperature.  The  and  of C 0 . 2  slope of t h i s l i n e  The  gives f o r the  T h i s energy d i f f e r e n c e i s only  apparent because the C O / C O 2 rat;Lo i s not specific reaction rates.  This  reciprocal  an "apparent" d i f f e r e n c e i n the a c t i v a t i o n energies d e s o r p t i o n of CO  a  the r a t i o of  d a t a of Rhead and  the  Wheeler  y i e l d s an apparent a c t i v a t i o n energy d i f f e r e n c e of 8  kilo-  c a l o r i e s per gram mole, as compared w i t h the v a l u e s of 1 2 . i | and  17 k i l o c a l o r i e s found by A r t h u r , and  Long and  Sykes,  respectively. The  c a t a l y t i c e f f e c t s of v a r i o u s substances  the d e s o r p t i on of C O 2 Bridger  (111),  and  (if?).  to a c c e l e r a t e the r e a c t i o n , w h i l e halogens, and  Fe(C0)£  (13),  have been s t u d i e d by A r t h u r  Mertsns  a l l inhibit  on  Hydrogen i n any form seems P0C1 , 2  F C l ^ CCl^,  the p r o d u c t i o n  of  NO, CQ2.  - £ -  Figure  1,  Apparent A c t i v a t i o n Energy D i f f e r e n c e s f o r the D e s o r p t i o n o f CO and CO2 i n Gaseous Combustion  - 6The e f f e c t large  of the  amounts  i n h i b i t o r s c a n be d e s t r o y e d  o f Hg o r H g O .  t r a n s i t i o n metals  i n the  graphite  t h e CO d e s o r p t i o n r e a c t i o n . effected  lattice  CO i s  and c h a n g i n g t h e  preferentially  that  temperatures  -many c o n f l i c t i n g found  data  independent  of  of  result  is  TT - e l e c t r o n s  TT-bond orders  i n s u c h a way  o  i n the l i t e r a t u r e . that  temperature and p r e s s u r e . is,that  are  Strickland-Constable o n l y CO was p r o d u c e d .  (18) o b s e r v e d a CO/COg r a t i o  o f about  (17) On  one,  The o n l y c o n c l u s i o n t h a t  t h e d e s o r b e d gas  will  probably  i n CO. From t h e f o r e g o i n g d i s c u s s i o n ,  1.  rate  b e t w e e n 900 C and 1200 C , t h e r e  may be drawn f r o m t h e s e d a t a be r i c h  that  desorbed.  In the combustion of graphite  the o t h e r hand, Meyer  the  this  absorbing  o At  a d d i t i o n of  (16) h a v e f o u n d  increase  They p o s t u l a t e  by t h e t r a n s i t i o n m e t a l atoms  from the g r a p h i t e that  L o n g and S y k e s  by t h e  CO and C 0 2 a r e  primary products  it  may be c o n c l u d e d  of the  that:  combustion of  carbon. 2.  At r e l a t i v e l y low t e m p e r a t u r e s , u n i q u e l y d e t e r m i n e d by  3.  At high temperatures,  the C0/C02 r a t i o  is  the.temperature. the desorbed  gas  i s predominantly  CO. 4.  The a p p a r e n t d e s o r p t i o n of calories .  a c t i v a t i o n energy d i f f e r e n c e s CO and C 0 2 a r e  for  between 8 and 17  the kilo-  -  5„  Adsorbed C0  2  hydrogen  7  -  o r water vapour  d e s o r p t i o n r e a c t i o n , w h i l e P0C1 , P C I 3 , 2  NO, h a l o g e n s , and F e ( C O ) ^ 6.  accelerate the  Inhibit  CCl^,  it.  T r a n s i t i o n m e t a l s i n t h e l a t t i c e promote' t h e d e s o r p t i o n o r CO.  IONIC OXIDATION AND COMBUSTION OF CARBON In  a h e t e r g e n e o u s r e a c t i o n , a n y one o f a number o f  p r o c e s s e s may b e r a t e c o n t r o l l i n g . considered here;  Three  s t e p s w i l l be  namely,  1. A d s o r p t i o n 2.  Chemical Reaction  3-  Desorption  In  the i o n i c  o x i d a t i o n of carbon, the adsorption  p r o c e s s c o n s i s t s p r i m a r i l y o f t h e d i s c h a r g e o f oxygen onto the carbon s u r f a c e .  The e x t r a e l e c t r o n s i n t h e  v a l e n c e s h e l l o f t h e oxygen  ion w i l l  flow, i n t o t h e c o n d u c t a n c e  band o f t h e c a r b o n a t t h e a d s o r p t i o n s i t e s . atoms c r e a t e d  i n t h i s manner w i l l  The  CxOy  activated  as p o s t u l a t e d b y S i h v o n e n ( 1 9 ) ,  T h i s complex,  w i l l b e f r e e t o move a b o u t t h e C a r b o n  surface.  "Oxygen atoms w h i c h a r e combined along the s u r f a c e toward  the boundary  He  weakly  states: ... move  c a r b o n atom c h a i n s .  T h e y may t h e n a t t a c h t h e m s e l v e s t o f r e e b o u n d a r y the  oxygen  form c h e m i s o r p t i v e bonds  w i t h the carbon surface i n a l o o s e l y - h e l d complex.  ions  atoms a t  rupture points." T h i s complex  g r a d u a l l y forms a d e f i n i t e  w i t h the p e r i p h e r a l carbon i n the r e a c t i o n  bond  stage. Subsequently,  - 8 the c a r t o n - c a r b o n bond i s Strickland-Constable  ruptured and CO or C O 2 i s  desorbed.  ( 2 0 ) d e s c r i b e s t h i s d e s o r p t i o n step  as  follows: w  As the carbon molecule i s p r o g r e s s i v e l y  the process must  eaten away  i n v o l v e the c o n t i n u a l breaking of the hexagon  rings.  The approaching oxygen atoms w i l l meet w i t h carbon i n d i f f e r e n t various  s t a t e s of chemical combination and i t  is  possible  that  whether CO or C 0 2 i s desorbed w i l l depend p r e c i s e l y on what state i s .  this  However, the p r o g r e s s i v e d e m o l i t i o n of the hexagon  can be assumed t o take p l a c e i n a f a i r l y r e g u l a r manner as a f i x e d p r o p o r t i o n of t h e carbon w i l l i n g p r o p o r t i o n w i l l form It  after of  as  2  T h i s diagram,  t h a t of Gulbransen ( 9 ) .  the oxygen as i t  a schematic it  diagram showing  goes from the i o n i c  through the "discharge" proces's, and i s  CO o r C O 2 .  certain  C0 ."  the change i n f r e e energy of the oxygen as  desorbed  rings  r e a c t t o form CO and the remain-  i s advantageous to c o n s t r u c t  s t a t e i n the b a t h ,  and  finally  shown i n F i g u r e 2 , i s  patterned  The o r d i n a t e r e p r e s e n t s the f r e e  passes from one step to the next.  energy  The a b s c i s s a  r e p r e s e n t s d i s t a n c e i n Xngstrom u n i t s as the oxygen t r a v e l s from the bath onto the i n t e r f a c e , tation,  and thence i s desorbed.  For true  represen-  a t h r e e - d i m e n s i o n a l model shoud be u s e d .  However,  for  convenience the d i s t a n c e has been represented plane as going from bath to d i s c h a r g e  schematically  on a  on c h e m i s o r p t i o n s i t e s ,  c h e m i s o r p t i o n s i t e s through a s e r i e s of s t a t e s i n t e r m e d i a t e  from the  between  - 9-  C-Surface  I Adsorption 1  Desorbed CO  I I I  O x i d a t i o n Stage  i  Distance  I  Figure  ^ 2«  Combustion Stage ^  Distance  F r e e Energy Diagram  - 10 c h e m i s o r p t i o n and b o n d i n g and  chemical combination to s t a t e s of pure  thence t o t h e gas  There are four diagram  The  i n which  o f minimum f r e e  energy  As  oxygen ions  i n the bath,  2.  As  chemisorbed  CxOy c o m p l e x e s  3.  As  c h e m i c a l l y bonded r e a c t i o n p r o d u c t s o f CO  4.  As  desorbed  CO  and  The  lower  free  t o bonded CO  is F ,  a  n  d  2  i s produced,  surface. and  CO2  on t h i s  reaction  diagram;  includes  the  combustion  states.  energy  bath t o the chemisorbed  COg  f o r t h e gaseous  h i g h e r minimum-energy s t a t e s t h e two  on t h e anode  CO2.  o x i d a t i o n p r o c e s s as d e f i n e d  reaction,  on t h e  be f o u n d , namely, .  1.  t h e two  If  phase„  states  o x y g e n may  chemical  required  to activate  t h e oxygen from  complex i s Fi^, from the chemisorbed f r o m bonded CO t o d e s o r b e d  the r e a c t i o n curve w i l l  be  CO  gas  the  complex  i s F^„  s i m i l a r to the dotted U  line  i n Figure  T h i s diagram The  1, w i t h t h e c o r r e s p o n d i n g a c t i v a t i o n  i s qualitative  rate-controlling  energy. reaction,  However,  free  there  since  have t h e h i g h e s t  i t i s n o t known w h i c h  necessary a c t i v a t i o n  barrier  case of g r a p h i t e the  step w i l l  energy  F^ . T  t h e e n e r g i e s a r e not known.  a l l t h r e e a c t i v a t i o n b a r r i e r s have The  potential  only because  free  activation  free  step i s l i m i t i n g  the  been drawn e q u a l .  f r e e . e n e r g y t o overcome t h e  comes f r o m t h e t h e r m a l e n e r g y i n a lead-borosilicate  energy change f o r the o v e r a l l  of t h e b a t h .  s l a g , as found  In  in this  the  study,  p r o c e s s i s n e g a t i v e , but  i s not enough t h e r m a l e n e r g y p r e s e n t t o overcome t h e  potential  - 11 barrier  until  potential  is  the  temperature  applied  oxygen i o n i s  across  increased  the a c t i v a t i o n  energy  graphite  measurable  at  rate The  potential  energy o f  is  is  the  Since  a potential  The a n o d i c  the voltage  the  free  If  the  energy  of  activation will and t h e is  the  energy  large,  is  is  energy  tipped  will  is  s l a g and t h a t  so  the  that  lowered,  to  barrier.  a  for  the  be  poten-  oxygen overvoltage  rate-determining  small,  energy.  the  oxygen  when a  Thus the  same v a l u e  energies w i l l  the  help the  relatively  activation  between  of  created  needed  is  of  proceed at  the d i f f e r e n c e  have n e a r l y the  these  electrical  applied.  of a c t i v a t i o n  experimental  an  barrier  overvoltage  e n t r o p y of; a c t i v a t i o n  e n t r o p y change  is  excess  energy  step.  activation,  energy diagram  in lead-borosilicate  rate-controlling  a measure of  if  the p o t e n t i a l  the oxygen i n the  tial  applied  9500C0  bath,  decomposition voltage  gas.  surmount  over  lowered.  850°G i f  i n the desorbed is  the  and t h e  is  the r e a c t i o n of  is  as  this  free  the heat  If,  however,  of the  significantly  different.  Entropy Probably consumption o f difference of  reaction,  t h e most; s i g n i f i c a n t  c a r b o n by o x y g e n gas  i n the as  e n t r o p y change  described rate  Where ^ , S + respectively,  Change  of the  by t h e  = J^T  and activated  difference  between, t h e  and by o x y g e n i o n s  for  the  overall  transition-state  is  the  reaction. theory,  The r a t e is  e are  the  e n t r o p y and  complex.  enthalpy,  T h u s a n y change  in  the  entropy of a c t i v a t i o n w i l l term e ' ^  g r e a t l y a f f e c t t h e rate„  The e n t r o p y  'can c o n v e n i e n t l y be r e p r e s e n t e d a s t h e c h a n g e i n t h e  p a r t i t i o n functions of the reacting species during reaction.  The  p a r t i t i o n f u n c t i o n i s made up o f t h r e e t e r m s : t h e t r a n s i t i o n a l , r o t a t i o n a l , and v i b r a t i o n a l  partition functions.  Each term i s  c a l c u l a t e d f o r t h e c h a n g e i n t h e number o f d e g r e e s o f f r e e d o m o f that type ( i . e .  translational,  rotational,  o r v i b r a t i o n a l ) which  occurs i n the r e a c t i o n . In  t h e gaseous r e a c t i o n t h e r e a c t a n t oxygen m o l e c u l e has  t h r e e t r a n s l a t i o n a l , two r o t a t i o n a l , a n d one v i b r a t i o n a l d e g r e e o f freedom.  The p r o d u c t m o l e c u l e CO^ h a s t h e same number o f t r a n s -  l a t i o n a l a n d r o t a t i o n a l d e g r e e s o f f r e e d o m and t h r e e degrees o f v i b r a t i o n a l freedom.  additional  However, t h e change i n t h e  p a r t i t i o n f u n c t i o n , and t h u s t h e r a t e , caused by t h e i n c r e a s e o f t h r e e v i b r a t i o n a l d e g r e e s o f f r e e d o m i s v e r y s m a l l , p o s s i b l y no more t h a n 1 0 . The e n t r o p y c h a n g e i n t h e o x i d a t i o n o f c a r b o n by ions i s r a d i c a l l y d i f f e r e n t .  oxygen  Partition functions f o r liquids,  a l t h o u g h n o t a c c u r a t e l y known, a r e much l e s s t h a n t h o s e f o r g a s e s b e c a u s e o f t h e r e s t r i c t i o n o f movement i n l i q u i d s .  The t r a n s -  l a t i o n a l p a r t i t i o n f u n c t i o n f o r t h e oxygen i o n s i n t h e s l a g may be i n t h e n e i g h b o r h o o d o f 10 t o 1 0 0 0 , w h i c h may be  used  artificially  r e p r e s e n t e d a s l e s s t h a n one d e g r e e o f t r a n s l a t i o n a l f r e e d o m .  The  p r o d u c t g a s , on t h e o t h e r hand, has t h r e e d e g r e e s o f t r a n s l a t i o n a l freedom.  Thus, p e r m o l e c u l e o f oxygen, t h e change i n t h e t r a n s -  l a t i o n a l d e g r e e s o f f r e e d o m d u r i n g r e a c t i o n i s f r o m l e s s t h a n one  -  to  three  For  the  13  -  s i x , depending upon whether CO2  or  production  of  COg  at  one  or  CO  is  desorbed.  atmosphere pressure  and  1000°C,  •50 this  c h a n g e may  vibrational (which the  he  e  could  However, by  this  reaction  step  and  the  rate.  chemical a  the  oxidation  mobile  o x i d a t i o n of  times.as mobile  f a s t as  adsorption  justified  of  f o r the  be  therefore, be  by  an  electrochemical gaseous  step  the  reaction.  the  rate  by  that  the  actual  than the  be  slowest  step  will  affect  electro-  gaseous  rate  If  i t i s assumed  is  electrochemically (9)  f o r the  rate The  will  be  reaction.  about  by  that  gaseous  oxygen i o n pressure  of 10  assumption.that  i s r a t e - c o n t r o l l i n g i s not  electrochemical  the  rate w i l l  for this  Gulbransen  assuming  change  2  f i x e d by  greater  and  and  10^ .  oxygen molecules  and  rotational  function  t h a n 10-^.  suggested  the the  to  mean t h a t  It will  smaller  graphite,  atmospheres,  i0^°  change i n entropy  adsorption  small  entropy change  about  rate w i l l  as  the  does not  I t i s probable,  rate-controlling,  -6  be  amount.  factor considerably  the  10  this  Assuming  overall partition  r e l a t e d to  —)  increased  .  y  changes, the  i s i n turn  term  10  about  13 the  necessarily  -  14  OBJECT AND SCOPE OF THE PRESENT The o b j e c t the  electrochemical  slags. in  this  investigation  P r e l i m i n a r y t e s t s were  the  INVESTIGATION  consumption of  iron crucibles.  melt  of  -  has  graphite  conducted u s i n g  impossible  to  a p p a r a t u s and c o l l e c t  samples of  the desorbed  the  rate of  however, above all  reduce  that  950°C.  the  this  the  influence  ratio  of  of  duction of  crude anode  a  slag  of  temperature,  kinetic gas  required  to  gas-tight  It  was  thought  graphite was  A that  would  found,  therefore  used  only for  experiments. the  d a t a were  without  c o m p o s i t i o n P b O . S i 0 2 . 0 . lNa2B40r/,  current  CO and COg i n t h e anode  addition,  slags  a measurable r a t e  s l a g was  in  carbon oxides.  the  slag.  proceeds at  a  It  rapid that  from the  A lead-borosilicate  Utilizing the  lead  reaction  subsequent  construct  then considered.  r e a c t i o n w o u l d be so  immediately  fayalite  However, the h i g h temperatures  s l a g was  study  by o x y g e n i o n s  s l a g made i t  lead-borosilicate  been t o  the  gas  density was  and t i m e  investigated.  obtained  for  application  of  the a  on t h e In  rate of  pro-  potential.  - 15 EXPERIMENTAL PROCEDURE  OVERVOLTAGE MEASUREMENT I N F A Y A L I T E SLAGS. An a t t e m p t v o l t a g e measurements of  was made t o  simultaneously obtain over-  and CO/CO2 gas  ratios  slag  the c o m p o s i t i o n : FeO  48%  Si0  33%  2  17%  CaO FeS2 This  Si0  using a fayalite  2  point  phase  slag  diagram.  2%  has t h e l o w e s t m e l t i n g p o i n t o n t h e  CaO-FeO-  The F e S 2 was added t o l o w e r t h e m e l t i n g  further. The  densities  overvoltages  on a g r a p h i t e  generated with various current  anode r e l a t i v e t o  a platinum  reference  e l e c t r o d e were m e a s u r e d on a Beckman m o d e l H-2 pH m e t e r u s i n g apparatus  shown i n F i g u r e 3.  Although the anode-platinum e l e c t r o d e  d i s t a n c e was o n l y 0.1 i n c h e s ,  a significant  by t h e r e s i s t a n c e  was n o t e d i n t h e  of the  slag  the  voltage  drop  created  overvoltages  measured. It with  was  not p o s s i b l e  t o o b t a i n gas  t h e s e o v e r v o l t a g e measurements  involved prohibited system. melting  It  because the h i g h  coincident temperatures  t h e c o n s t r u c t i o n o f a l e a k - p r o o f gas  Was t h e r e f o r e d e c i d e d t o  points.  samples  investigate  collection  slags with lower  -  F i g u r e 3.  16  -  Experimental Apparatus f o r Fayalite Slags  - 17 REACTION OF GRAPHITE I N LEAD-BOROSILICATE SLAGS. The m a j o r p o r t i o n o f  this  concerned w i t h l e a d - b o r o s i l i c a t e showed t h a t above  graphite  950°C.  ance o f  the  It slag  slags.  was a l s o f o u n d t h a t created  the large  a considerable  overvoltage  been  P r e l i m i n a r y examination  c h e m i c a l l y reduced the l e a d  anode t o t h e p l a t i n u m r e f e r e n c e to obtain useful  i n v e s t i g a t i o n has  i n the  electrical  IR v o l t a g e  electrode.  slag  Thus i t  only  resist-  drop from the was n o t  possible  measurements. Materials  The a n o d e s  were c o m m e r c i a l e l e c t r o d e  by t h e N a t i o n a l C a r b o n Company. assay grade.  The l i t h a r g e  T h e b o r a x and s i l i c a  f l o u r were  graphite and t e s t  supplied lead  were  technical-grade  reagents. Apparatus The e x p e r i m e n t a l a p p a r a t u s , consisted  basically  of  as  shown i n F i g u r e  4,  crucible held  by a  a 30-gram f i r e c l a y  plumbago pot and a g r a p h i t e  anode w i t h a g a s - c o l l e c t i n g  cup and  tube. The s l a g - c o n t a i n i n g drilled placed  i n the  bottom,  fireclay  hole  and t h e c h r o m e l c a t h o d e - l e a d w i r e were  i n t h e plumbago p o t w h i c h h e l d 1320  The c r u c i b l e was h e l d  i n place  The o n e - i n c h d i a m e t e r to f i t  crucible, with a  grams  of molten l e a d .  by a c h r o m e l c l a m p . graphite  electrode  a 3 / 4 - i n c h h o l e i n a 15-gram f i r e c l a y  was  crucible.  t u r n e d down  -18-  «  To Gas  Analyzer  Graphite Anod e Vitreosil Tube  Gas-Collecting  Fireclay  Crucibles  Chrome1 Cathode Lead-Wire Slag  M o l t e n Lead Cathode Plumbago  Figure  I4...  Experimental Apparatus  f o r PbO'SiO  p  Crucible  Slags  -  19  -  which had the top cut o f f two inches from the base.  This cup  also had a separate •f-.inch hole f o r the g a s - c o l l e c t i n g tube. V i t r e o s i l tubing of ^ - i n c h i n s i d e diameter was used to convey the anode gas outside the furnace. The whole anode assembly was cemented w i t h a mixture of s i l i c a and water glass.  A f t e r curing at about 1 2 0 ° C , t h i s cement was very  s a t i s f a c t o r y up to about 1 0 f ) 0 ° C t h e highest temperature used i n t h i s study. The anode gas was transported to the gas-analysis apparatus by f?/l6-inch tygon tubing.  The v i t r e o s i l - t y g o n  j o i n t on top of the furnace was cooled by a small f a n . The furnace used was equipped w i t h s i x h o r i z o n t a l jg~inch-diameter globars arranged i n two p a r a l l e l sets of three.  The temperature was measured by a  chrome1-alumel  +  thermocouple, and c o n t r o l l e d to w i t h i n -^.Centigrade degrees at the thermocouple t i p by a Leeds & Northrup Micromax model tt  C  n  c o n t r o l l e r w i t h ah M.E.C. automatic p r o p o r t i o n i n g c o n t r o l  unit. The e l e c t r o l y z i n g d i r e c t current was supplied by an u n f i l t e r e d full-wave copper-oxide t r a n s f o r m e r - r e c t i f i e r . S l a g Composition The s l a g used was of the composition: 72%  FbO Si0  Na B^0 2  20.3$  2  7  7-7$  - 20  -  T h i s c o r r e s p o n d s t o an a p p r o x i m a t e m o l a r of P b O . S i Q 2 . O o l N a 2 B 4 . O 7 . fluidity  of the s l a g .  The  b o r a x was  composition  added t o i n c r e a s e t h e  T h i s p a r t i c u l a r . c o m p o s i t i o n was  selected  a r b i t r a r i l y at the b e g i n n i n g of t h e i n v e s t i g a t i o n o n l y because of i t s r e l a t i v e l y  l o w m e l t i n g p o i n t ( l e s s t h a n 770°C„) and  intermediate lead-oxide content.  Subsequent work has  a p p a r e n t l y t h e s l a g c o m p o s i t i o n has a d e f i n i t e e f f e c t composition of the desorbed a discontinuity i n this outset, a different  gas.  region.  shown t h a t on  the  Also conductivity data Had  this  (21) show  b e e n known a t t h e  s l a g composition would  have been  selected.  Slag Preparation Four hundred a fireclay  grams o f t h e s l a g c o m p o n e n t s w e r e f u s e d i n  c r u c i b l e and h e l d a t 950°G  grams o f t e s t  Then  100  l e a d were added and t h e s l a g a l l o w e d t o r e a c h  equilibrium w i t h the lead. and u t i l i z e d  f o r two h o u r s .  The  c r u c i b l e and  s l a g were then c o o l e d  i n the apparatus described. Procedure  The  a p p a r a t u s , w i t h o u t t h e a n o d e , was  d e s i r e d temperature  h e a t e d up t o t h e  and h e l d f o r a t l e a s t o n e - h a l f h o u r  a s t e a d y t e m p e r a t u r e . Then t h e anode, w i t h an a p p l i e d p o t e n t i a l o f a p p r o x i m a t e l y 10 v o l t s , was g a s - s a m p l i n g tube a t t a c h e d . A f t e r about a g a i n up t o t e m p e r a t u r e  and  gas  to  attain  open-circuit  p l a c e d i n t h e s l a g and ten minutes,  s a m p l i n g b e g u n . The  the s l a g times  th> was  required  -  21  c o l l e c t the 100-cubic c e n t i m e t e r Each sample was and  analyzed  -  gas  samples were r e c o r d e d .  as soon as i t had  been c o l l e c t e d  the anode gas produced i n the meantime was  the atmosphere.  •  I n any constant.  one  vented  '  r u n , the t o t a l c u r r e n t f l o w i n g was  As each run p r o g r e s s e d , the r e s i s t a n c e of  slag increased.  to  the  n e c e s s a r y to i n c r e a s e  gradually  the a p p l i e d p o t e n t i a l i n o r d e r to keep the c u r r e n t  constant.  The  Thus i t was  held  runs were of v a r y i n g l e n g t h depending upon  the t e m p e r a t u r e , r a t e of oxygen removal f r o m the s l a g , and how  w e l l the apparatus was  constructed.  The  experiments  were u s u a l l y h a l t e d e i t h e r by anode f a i l u r e due  t o gaseous  o x i d a t i o n of the p o r t i o n exposed i n the f u r n a c e or by  the  s l a g foaming up i n t o the g a s - c o l l e c t i n g t u b e , thus c u t t i n g o f f the gas f l o w .  As any  one  run p r o g r e s s e d , the  increas-  i n g s i l i c a c o n t e n t of the s l a g caused i t t o become more v i s c o u s and,  t h e r e f o r e , more prone t o foam. Current Density  Measurements  D u r i n g p r e l i m i n a r y t e s t s , i t was anode s u r f a c e was  o x i d i z e d very unevenly.  found t h a t the", Since  thought t h a t changes i n b o t h the temperature and  i t was the  amperage would a l t e r the o x i d i z e d s u r f a c e a r e a , a l l subsequent runs were c a r r i e d out at a c o n s t a n t temperature.  The  c u r r e n t d e n s i t y was  amperage  then c a l c u l a t e d  u s i n g the measured o x i d i z e d a r e a of the anode. t h i s s e l e c t i v e o x i d a t i o n made the measurement of  Since the  and by  -  22-  e f f e c t i v e anode areas very d i f f i c u l t , d e n s i t i e s may  the c a l c u l a t e d c u r r e n t  be i n c o n s i d e r a b l e e r r o r .  be as high as 50  the probable e r r o r but i t may There was  no way  to assess  percent.  of p r e d i c t i n g the area of the anode t h a t  would be a t t a c k e d under any one shown i n F i g u r e 5«  It is difficult  set of c o n d i t i o n s .  This i s c l e a r l y  Anodes A and B were o x i d i z e d under i d e n t i c a l  c o n d i t i o n s of amperage, temperature However, i t i s apparent  and  initial  composition.  from the p i c t u r e that the areas  i n r e a c t i o n are very d i f f e r e n t  f o r the two anodes.  effective  By measure-^  ment, anode A has f o u r times the e f f e c t i v e area of anode B,  and,  thus, one-quarter the c u r r e n t d e n s i t y of t h a t on anode B. Anode C, o x i d i z e d i n a l e a d - b o r a t e s l a g , desorbed r a t i o s very s i m i l a r t o those obtained w i t h l e a d - s i l i c a t e  CO/CO2  slags.  This s u r f a c e i s much more evenly o x i d i z e d than those of anodes A and Bo  T h i s s l a g may  g i v e more r e l i a b l e c u r r e n t - d e n s i t y r e s u l t s  than those obtained i n l e a d - b o r o s i l i c a t e s l a g s .  However, because  some of the anode carbon dropped i n t o the bath d u r i n g t h i s p a r t i c u l a r run and was t i o n may  be  not e l e c t r o c h e m i c a l l y consumed, the o x i d a -  preferential. Gas A n a l y s i s  A l l the gas tus.  samples were analyzed i n a Hays o r s a t appara-  Carbon d i o x i d e was  absorbed  i n a potassium hydroxide  solution,  oxygen i n Hays-brand "Seez C>2 and carbon monoxide i n ammoniacal W  cuprous.  -  Figure  23  -  Photograph of E l e c t r o c h e m i c a l l y O x i d i z e d Anodes  - 2k chloride.  P o r most o f t h e r u n s t h e a p p a r a t u s was  by the a d d i t i o n accelerate  of a second  analysis.  The  s o l u t i o n of s u l p h u r i c sulphate  c a r b o n monoxide p i p e t t e  measuring  a c i d w i t h about  100  c c . gas  samples  a n a l y z e r under p r e s s u r e ; t h a t water  i n the b u r e t t e by  i n s i d e t h e b u r e t t e was about  1 mm.  was  a five  sodium  were c o l l e c t e d  i n the  i t s own  never  pressure.  allowed to b u i l d  t o t a l volume o f gas a n a l y z e d was  p e r c e n t , r a n g i n g f r o m 80  analyzed gases.  displaced The  up more t h a n  T h i s would  suggest  However, a  a p p r e c i a b l e d e c r e a s e i n the "dead" gas volume.  gas  series  t o 1000°F. f o r t e n h o u r s  showed The  fact  were c o l l e c t e d by p r e s s u r e d i s p l a c e m e n t  seem t o i n d i c a t e  f a c t t h a t no gas  volume  t h a t some i n e r t  no  by a i r o c c u r r e d .  less  The  the lower the f i n a l  a n o d e s w h i c h was  t h a t the samples  heated  always  of  t h a t no  This b e l i e f samples  c o n t a m i n a t i o n of the i s further  c o n t a i n e d any  first  h a l f hour,although i t i s possible  would  be  consumed b y  CO  the  +  sample  s u p p l a n t e d by  oxygen a f t e r t h a t the  the  the  oxygen  reaction  *  Co  w h i c h i s f a v o u r a b l e t h e r m o d y n a m i c a l l y a t the used.  pressure  t o 93> p e r c e n t .  b e i n g d r i v e n o f f f r o m t h e anode.  would  percent  ten percent  I s , t h e anode g a s  l o n g e r a sample t o o k t o c o l l e c t , of  was  Hg g r e a t e r t h a n a t m o s p h e r i c p r e s s u r e . The  t h a n 100  fluid  to  added. The  the  modified  temperatures  -  -  2£  RESULTS  Throughout t h i s paper the terms " c h e m i c a l and  "chemical combustion" w i l l  combustion of graphite the  tial  r e f e r t o the oxidation  by oxygen ions  i n the slag  a p p l i c a t i o n o f an e l e c t r i c a l p o t e n t i a l .  trasted  with  oxidation"  the electrochemical  reactions  and  without  T h i s i s coni n which a potent  i s applied.  CHEMICAL OXIDATION The  initial  were c a l c u l a t e d  rates  o f oxygen r e m o v a l f r o m t h e s l a g  by u s i n g the r a t e  composition of the desorbed gas.  of e v o l u t i o n  These r a t e s , w h i c h may be  i n e r r o r b e c a u s e t h e a p p a r a t u s was n o t a l w a y s are this  shown i n an A r r h e n i u s p l o t line  and t h e  i n Figure  6.  gas-tight, The s l o p e o f  c o r r e s p o n d s t o an a c t i v a t i o n e n e r g y o f 26 ^ 5  k i l o c a l o r i e s p e r gram m o l e . ABSOLUTE REACTION RATE CALCULATIONS By  use o f t h e determined r a t e s  energy, i t i s p o s s i b l e reaction  to calculate  and a c t i v a t i o n  theoretical rates  f o r various rate-determining steps by applying  e q u a t i o n s o f G l a s s t o n e , L a i d l e r , and E y r i n g limiting  of  steps which they considered a r e :  1.  Immobile A d s o r p t i o n  2.  Mobile  3.  Chemical Reaction  Adsorption  a. F i r s t - o r d e r K i n e t i c s b. Z e r o - o r d e r K i n e t i c s  (22) .  the  The r a t e ^ -  -  26  -  o X •H  CD  bO  3  RECIPROCAL TEMPERATURE x 10  6 . Arrhenius Plot for Oxidation  Chemical  4„  Desorption Although  rate-controlling, be  evaluated  other  steps  Appendix  they have a l s o d e r i v e d ah e q u a t i o n the  q u a n t i t i e s i n v o l v e d i n the  or even e s t i m a t e d  w i t h our  h a v e b e e n e x a m i n e d and  present  for diffusion  expression  cannot  knowledge.  The  the r a t e s c a l c u l a t e d i n  A. At  1000°C, the  experimentally observed r a t e i s 2 x  atoms o f oxygen r e a c t i n g p e r  square centimeter  r a t e i s compared w i t h t h e c a l c u l a t e d v a l u e s calculated  rates are very  observed.  The  different  every  i n Table  from that  \\  k i n e t i c s r a t e - c o n t r o l l i n g a r e a f a c t o r of 5 x 10 zero-order  kinetics,  and  second. 1.  This  A l l the  experimentally  r a t e s a s s u m i n g i m m o b i l e a d s o r p t i o n and  mobile adsorption,  10^^  7  first-order  faster.  The  desorption values  are  i n e r r o r by a b o u t 105.  Thus, the r a t e s c a l c u l a t e d , assuming  these  steps r a t e - c o n t r o l l i n g ,  are at l e a s t  slower  than  that observed.  c a l c u l a t i o n s are mines the o v e r a l l  100,000 times  I f the v a r i o u s assumptions i n v o l v e d i n  c o r r e c t , none o f t h e p r o c e s s e s rate.  considered  evidence  these deter-  T h i s f a c t makes t h e p o s t u l a t i o n t h a t  d i f f u s i o n i s ' r a t e - c o n t r o l l i n g appear a t t r a c t i v e , experimental  f a s t e r or  but  there  i s no  to i n d i c a t e that t h i s i s so.  CHEMICAL COMBUSTION The t u r e and ratios  time  v a r i a t i o n of the desorbed i s shown i n F i g u r e  C0/C0^  ratio with  tempera-  7. T h i s f i g u r e shows t h a t t h e  CO/CO2  i n c r e a s e w i t h t e m p e r a t u r e , as f o u n d i n g a s e o u s c o m b u s t i o n  of  TABLE I  Rate E q u a t i o n  Immobile A d s o r p t i o n (0=)  + [C]  iio.gr  Gr  Co]  f. e. h  Theory 1x10  Z  • Rate Observed  26  2x10  18  Discrepancy 5x10  1  Mobile A d s o r p t i o n 2xl0  Col  ,2x10  1 3  18  10'  Desorption  Cc - o]=3  t °  lxlO24  2xlO  l 8  5x10-  lxlO26  2xlO  l 8  5x10  First-Order Kinetics  Zero Order K i n e t i c s  Ix 1 0  2 4  2x10 18  5x10^  -  29  -  TIME IN MINUTES  F i g u r e 7. V a r i a t i o n of C 0 / C 0 Combustion  2  R a t i o w i t h Time f o r  Chemical  - 30 carbon,  and, unexpectedly,  t i o n was begun assuming gas is  increases with time.  investiga-  that t h e r e should be no v a r i a t i o n i n the  composition w i t h time of combustion at any one temperature. very s u r p r i s i n g to f i n d t h a t ,  i n these experiments',  r a t i o d e f i n i t e l y increases with time. at  This  a l l s i m i l a r to t h i s  the CO/CO2  The o n l y s i t u a t i o n  reported  i s the slow i n c r e a s e i n the CO/CO2 r a t i o  noted i n a l u m i n a - r e d u c t i o n c e l l s  as the alumina  decreases.  concentration  '. In these runs, without an a p p l i e d p o t e n t i a l ,  the  lead  oxide composition of the s l a g decreased as much as 17 p e r c e n t ; is,  from 72 percent  to 55 p e r c e n t .  activity in a lead-silicate calculated  i n Appendix B.  shown i n F i g u r e 8. oxygen i s this  Olsen  The v a r i a t i o n of the  s l a g w i t h c o m p o s i t i o n has The r e s u l t s  of t h i s  T h i s graph shows t h a t  that  oxygen  been  calculation  the a c t i v i t y of  are the  changing r e l a t i v e l y s l o w l y i n the composition range of  study.  9 x 10"  It  F o r example,  to 5 . 5 x -10"  (21)  at  1000°C  atmospheres.  the a c t i v i t y decreases from However, S c h e l l i n g e r and  found a d i s c o n t i n u i t y i n the c o n d u c t i v i t y of  lead-silicate  s l a g s In t h i s  i n d i c a t e that  there i s  t h i s area. tetrahedron.  c o m p o s i t i o n range.  a structural  The normal s i l i c a t e With the i n i t i a l  similar  T h i s may  rearrangement  structure  occurring i n 4_ i n a s l a g i s a SiO^  c o m p o s i t i o n used i n t h i s  study,  2there  is  only enough oxygen to form SiO^  the t e t r a h e d r a l  character  groups,  of the s i l i c o n bonds,  As the oxygen i o n c o n c e n t r a t i o n d e c r e a s e s ,  or,  preserving  Si^O-^g^ - i o n s .  these Si40;L2^~  : MOLE FRACTION PbO Figure  8.  Activity  of  PbO i n P b O - S i O p  Melts  -  units w i l l  32 -  b e g i n a s s o c i a t i n g w i t h one a n o t h e r and t h e m o b i l i t y  of t h e oxygen i s decreased.possibly affect It  This decrease  i nm o b i l i t y might .  t h e desorbed gas r a t i o .  i sapparent  f r o m t h e c h a n g e i n t h e CO/CO2 r a t i o  w i t h t i m e t h a t t h e s e r a t i o s c a n o n l y be c o m p a r e d a t t h e same oxygen c o n c e n t r a t i o n o f t h e s l a g . removal,  i t h a s b e e n p o s s i b l e t o e v a l u a t e t h e CO/CO2 r a t i o s f o r  different  t e m p e r a t u r e s a t t h e same s l a g  values, plotted ture  U s i n g t h e r a t e s o f oxygen  logarithmically  composition.  These  against the reciprocal  i n F i g u r e 9> g i v e a n a p p a r e n t  activation  energy  difference  f o r t h e d e s o r p t i o n o f CO a n d CO2 o f 3216 k i l o c a l o r i e s mole.  W i t h i n the experimental e r r o r , t h i s apparent  d i f f e r e n c e appears  tempera-  p e r gram energy  t o be c o n s t a n t w i t h v a r y i n g c o m p o s i t i o n .  T h i s v a l u e i s somewhat h i g h e r t h a n t h o s e found i n t h e gaseous  (8 t o 17 k i l o c a l o r i e s )  reaction.  ELECTROCHEMICAL COMBUSTION Experiments w i t h varying at  900°C, 925°C, a n d 950°C.  s i n c e below because  c u r r e n t d e n s i t i e s w e r e done  The t e m p e r a t u r e  r a n g e was l i m i t e d  900°C t h e s l a g foamed i n t o t h e g a s - c o l l e c t i n g  tube  o f i t s i n c r e a s i n g v i s c o s i t y , a n d a b o v e 950°C t h e r a t e . o f  the chemical reaction.was s u f f i c i e n t CO/COg r a t i o .  to materially affect the  S e v e r a l runs were c a r r i e d  o u t a t 975°C.  Because  o f t h e c h e m i c a l o x i d a t i o n , h o w e v e r , no u s e f u l d a t a w e r e o b t a i n e d .  - 33 -  1.5  0.1+1  0.3 U  7.5  ,Y r  i  .  7-6  '  • •,  7-7  ,- ;< i  7.8  i  7-9  i _  ' 8.0  RECIPROCAL TEMPERATURE x 1 0 ^  Figure 9 -  Apparent A c t i v a t i o n Energy D i f f e r e n c e Chemical Combustion  for  -  34 -  The v a r i a t i o n of the CO/CO 2 d e n s i t y at and  12.  each temperature  These graphs  r a t i o w i t h time and c u r r e n t  studied i s  shown i n F i g u r e s 10, 11,  show t h a t the CO/COg r a t i o  increases  l i n e a r l y w i t h time as found i n chemical combustion, but the of  increase  of t h i s r a t i o g e n e r a l l y decreases w i t h  current d e n s i t y . the CO/COg  r a  "ti°  Also, a  t  rate  increasing  i n c r e a s i n g the c u r r e n t d e n s i t y decreases  any one t i m e .  The l o g a r i t h m i c v a r i a t i o n of the CO/COg r a t i o w i t h the log  o f the c u r r e n t d e n s i t y i s  temperatures  investigated.  10, 11, and 12 at  shown i n F i g u r e 13 f o r the t h r e e  These data were obtained from F i g u r e s  a c o n c e n t r a t i o n of 4.77 percent  a s s o c i a t e d with the PbO i n the s l a g , the i n i t i a l lysis  concentration.  a change of 0.3 percent from  T h i s change i s  at one ampere f o r 30 minutes.  the l o g - l o g r e l a t i o n s h i p i s not  of the oxygen  e q u i v a l e n t to  F o r l o n g e r times of  this ratio, not  The temperature  however, i s not c o n s i s t e n t ,  was much g r e a t e r  than u s u a l .  In. the  950°C 9J>0°C  from the anode o t h e r than CO and COg T h i s a b n o r m a l i t y may have  the CO/CO2 r a t i o of the desorbed gas. measuring the c u r r e n t d e n s i t i e s discrepancy.  decreases  v a r i a t i o n of  with the runs at  f o l l o w i n g the t r e n d of the o t h e r two s e r i e s .  s e r i e s the e v o l u t i o n of gas  reaction,  linear.  F i g u r e 13 shows t h a t g e n e r a l l y the CO/COg r a t i o with i n c r e a s i n g current d e n s i t y .  electro-  The d i f f i c u l t i e s  affected in  a l s o may have some b e a r i n g on t h i s  -  3£ -  TIME IN MINUTES Figure  10. V a r i a t i o n o f C0/C0 R a t i o w i t h Time a t 2  900°C.  -  36 -  0.2k  I 0  I  '  10  '  1  I  I  50  30  1  —I  70  L-  ,—»  '  i  90  J — •  110  TIME IN MINUTES Figure  11.  Variation  of  CO/COg R a t i o w i t h Time  at  92J?°C.  -  37  -  -  38  -  i5 L  Figure  13.  Variation Density  of C 0 / C 0  2  Ratio  with  Current  -  The  data of F i g u r e 13 are  i n F i g u r e 14. consistent  39 -  As expected,  shown i n an A r r h e n i u s p l o t  the r e s u l t s at  w i t h the o t h e r two s e r i e s ,  9 5 0 ° C are not  with a straight  line  o c c u r r i n g o n l y at a c u r r e n t d e n s i t y of f i v e amperes per square inch. C o n s i d e r i n g the two s e r i e s at seen t h a t the apparent for  difference  Q  0 0 ° C and 9 2 5 ° C ,  i n the a c t i v a t i o n  the d e s o r p t i o n of CO and COg (that i s ,  line) infers  is  energies  the slope  decreases with i n c r e a s i n g c u r r e n t d e n s i t y .  it  of  This  the graph  t h a t the a c t i v a t i o n energy f o r the p r o d u c t i o n of COg i s  increasing r e l a t i v e to that density.  f o r CO w i t h i n c r e a s i n g c u r r e n t  T h i s does not seem reasonable  p r o d u c t i o n o f CO2 i n c r e a s e s r e l a t i v e to increasing current density.  because the r a t e of that  f o r CO w i t h  F u r t h e r , an e x t r a p o l a t i o n of  curve to zero c u r r e n t d e n s i t y g i v e s an apparent  activation  energy d i f f e r e n c e  contrasted  of about  100 k i l o c a l o r i e s ,  as  this  with  the value of 3 2 k i l o c a l o r i e s found f o r chemical combustion. S i n c e such h i g h apparent are o b t a i n e d , attached plot  a c t i v a t i o n energy  differences  i n e l e c t r o c h e m i c a l combustion no importance can be  to the energy d i f f e r e n c e s  of the CO/CO2 r a t i o .  o b t a i n e d from an A r r h e n i u s  - kO -  0.2,  0.l£.  8..1  '  '8.2  8.3  8.k  8.5  8.6  RECIPROCAL TEMPERATURE x 10^" Figure  lk.  Apparent A c t i v a t i o n Energy D i f f e r e n c e s f o r E l e c t r o c h e m i c a l Combustion  Figure 15>.  V a r i a t i o n of Apparent A c t i v a t i o n Energy D i f f e r e n c e w i t h Current Density  - 42 DISCUSSION  In the combustion of g r a p h i t e , i n v e s t i g a t i o n show that  the desorbed gas  the r e s u l t s of is  this  r i c h e r i n C0  a l i q u i d oxidant i s used i n p l a c e of oxygen gas  as a  reactant.  The a p p l i c a t i o n of a p o t e n t i a l causes the COg content of gas  produced to i n c r e a s e  F i g u r e 7.  further.  This i s  amount of COg produced.  ted that  the CO/COg r a t i o  i n the desorbed g a s . i n c r e a s e s w i t h  these r e s u l t s i s g i v e n next.  it  has been p o s s i b l e  potential.  mechanism to e x p l a i n at l e a s t  the s l a g - g r a p h i t e contact  the  F u r t h e r , i t has been demonstra-  time of r e a c t i o n both w i t h and wittiout an a p p l i e d A tentative  the  shown c l e a r l y i n  I n c r e a s i n g the c u r r e n t d e n s i t y a l s o i n c r e a s e s  relative  when  2  partially  By c o n s i d e r i n g the i n f l u e n c e of  on the band s t r u c t u r e  to determine the e f f e c t  i o n s on the d e s o r p t i o n r e a c t i o n s  of the  graphite,  of u s i n g oxygen  as d e s c r i b e d by the mechanism  of Long and Sykes. ( 1 6 )  DESORPTION MECHANISM To promote a b e t t e r understanding of the, proposed mechanism, the r e l e v a n t discussed is  properties  i n some d e t a i l .  of carbon and g r a p h i t e  The band theory of  semi-conductors  d e s c r i b e d and a p p l i e d to the s l a g - g r a p h i t e i n t e r f a c e .  electronic structure explain,  of the i n t e r f a c e  thus deduced i s used  through the mechanism of Long and Sykes,  experimental  results.  are  some of  The to the  - k3 Properties 1.  -  o f G r a p h i t e and  Carbon  Formation G r a p h i t e i s the u l t i m a t e product of the t h e r m a l  d e c o m p o s i t i o n o f a l l o r g a n i c s u b s t a n c e s and be  can  c o n s i d e r e d t h e l i m i t i n g member o f a s e r i e s  hydrocarbons  as shown i n F i g u r e 16  i n t e r m e d i a t e s u b s t a n c e s formed than that required  by  (23). less  to form graphite.  logically  of a r o m a t i c  Carbons  are the  severe heat This heat  treatment  treatment  c o n s i s t s merely of h e a t i n g the o r i g i n a l o r g a n i c m a t e r i a l i n the absence  o f a i r or I n a r e d u c i n g atmosphere.  temperature  i s i n c r e a s e d , p o l y m e r i z a t i o n o c c u r s and, r e g a r d -  l e s s whether result  t h e o r i g i n a l o r g a n i c was  Is a system of c r o s s - l i n k e d  molecules.  At the s e t t i n g  As  the  aromatic or not,  the  planar condensed-ring  temperature, a s o l i d  i s formed  i n which the condensed-ring p l a n e s are stacked p a r a l l e l i n g r o u p s . These r i n g systems  or hydrocarbon groups.  of the p e r i p h e r a l hydrogen crystallites (2k)  temperature  t o 7 0 0 ° C , b u t t h e y r e t a i n most o f t h e i r  r a n g e kOO hydrogen  grow g r a d u a l l y i n t h e  o f 20  have c a l l e d  F r o m 700  t o 8 0 0 ° C , much  i s driven o f f , leaving  small  t o 30 £ d i a m e t e r w h i c h B i s c o e and  "turbostratic  crystallites."  " t u r b o s t r a t i c " r e f e r s t o t h o s e mesomorphous w h i c h a r e made up  peripheral  of p a r a l l e l  no d i r e c t i o n a l r e l a t i o n s h i p treatment temperature  The  word  crystallites  and e q u i - s p a c e d p l a n e s b e a r i n g  t o one  another.  i s i n c r e a s e d up  As o  the heat  t o 3000 C ,  the  c r y s t a l l i t e s grow g r a d u a l l y a n d , when t h e i r d i a m e t e r 100A  (23),  they r o t a t e i n t o  Warren  the r e g u l a r g r a p h i t i c  exceeds  structure.  _ 44 -  Structure  Compound  C  c  0  6 6 H  H  14 10  c  i6 io  C  n o  5.48  CO  io 8  C  Entropy i n E.U. Per Carbon Atom at 298°K  3.61  H  $9  H  graphite  H  Figure 1 6 .  Aromatic Hydrocarbon Series  3.21  1.36  - K$ 2. S t r u c t u r e The g r a p h i t e l a t t i c e as proposed by B e r n a l (26) c o n s i s t s o f carbon atoms arranged i n h e x a g o n a l r i n g s i n e q u i d i s t a n t l a y e r s s t a c k e d i n t h i s manner: o n e - h a l f the atoms i n one l a y e r l i e n o r m a l l y above h a l f the atoms i n t h e l a y e r b e n e a t h , w h i l e the o t h e r h a l f a r e n o r m a l l y above t h e c e n t r e s o f t h e hexagons b e n e a t h . i t s e l f i n t h e sequence abab.  Thus t h e s t r u c t u r e r e p e a t s  However, t h i s s t r u c t u r e does  n o t account f o r c e r t a i n f a i n t l i n e s i n the x - r a y powder photographs o f many g r a p h i t e s .  L i p s o n and Stokes (27)  have proposed an a l t e r n a t i v e s t r u c t u r e made up o f about 80 p e r c e n t of the B e r n a l s t r u c t u r e , 6 p e r c e n t o f a d i s ordered s t r u c t u r e  ( t u r b o s t r a t i c ) and l k p e r c e n t o f t h e  o r i g i n a l s t r u c t u r e proposed b y Debye and S c h e r r e r ( 2 8 ) , w i t h a l a y e r sequence  abcabc.  The s t r u c t u r e o f t h e s o - c a l l e d is s t i l l a controversial subject.  amorphous carbons  However, i t appears t h a t  i n g e n e r a l , these carbons c o n t a i n some v e r y s m a l l t u r b o s t r a t i c c r y s t a l l i t e s and a d i s o r d e r e d  three-dimentionally  c r o s s - l i n k e d s t r u c t u r e i n w h i c h c e r t a i n o f t h e hexagons have been r o t a t e d 60 degrees about t h e i r axes. Wo m a t t e r what i t s t h e r m a l h i s t o r y , e v e r y carbon or g r a p h i t e c o n t a i n s many l a y e r s o f condensed r i n g s .  In  t h i s arrangement, each carbon atom has f o u r v a l e n c e e l e c t r o n s : t h r e e tT-type e l e c t r o n s w h i c h f o r m c h e m i c a l bonds s y m m e t r i c a l about each carbon atom i n t h e p l a n e o f the r i n g , and one TT-type m o b i l e e l e c t r o n w h i c h i s a t r i g h t a n g l e s  to  the graphite plate.  single ring  This TT-electron d i s t r i b u t i o n f o r a  ( b e n z e n e ) i s shown i n F i g u r e 1 7 .  These  e l e c t r o n s g i v e c a r b o n and g r a p h i t e t h e i r m e t a l l i c  character..  C.A. C o u l s o n ( 2 9 ) h a s c a l c u l a t e d t h a t f o r a n i n f i n i t e lattice  graphitic  t h e W (E) a g a i n s t E c u r v e i s a s shown i n F i g u r e 1 8 .  However, t h i s c u r v e i s n o t c o n s i s t e n t w i t h curve as i n t e r p r e t e d  by S. M r o z o w s k i  t h i s curve f o rd i f f e r e n t  density-resistivity  (30),  By a n a n a l y s i s o f  c a r b o n s , he h a s come t o t h e c o n c l u s i o n  t h a t t h e r e must be a f i n i t e e n e r g y gap  ^>JE b e t w e e n t h e f i l l e d  e l e c t r o n energy bands and t h e c o n d u c t a n c e band. gap  7T-  This energy  ,.^>.E, w h i c h t e n d s t o z e r o i n g r a p h i t e , means t h a t c a r b o n a n d  graphite w i l l  be i n t r i n s i c  semi-conductors  The g e n e r a l l e v e l s o f e n e r g y d i s t r i b u t i o n f o r c a r b o n are  shown i n F i g u r e 1 9 .  the  g r a p h i t e s t r u c t u r e : t h e tS  There a r e t h r e e m a i n e l e c t r o n bands i n o r l o w e r - l e v e l band w h i c h h a s a  mean e n e r g y l e v e l o f a p p r o x i m a t e l y 1 2 e l e c t r o n v o l t s f r o m t h e escape b a r r i e r ,  t h e TT -band w h i c h h a s a mean e n e r g y l e v e l o f  about f i v e e l e c t r o n v o l t s above t h e  6 " -band  and a work  function  of  a b o u t 4 . 3 e l e c t r o n v o l t s , ,and t h e c o n d u c t a n c e band a d i s t a n c e  ^  E a b o v e t h e t o p o f t h e f T -band.  approaches the  T h i s energy gap, which  zero f o r i n f i n i t e g r a p h i t e p l a n e s , i s a f u n c t i o n o f  h e a t - t r e a t m e n t and i s p l o t t e d a g a i n s t c a l c i n a t i o n  tempera-  ture i n Figure 20. The p e r i p h e r a l atoms i n b a k e d  carbons and  g r a p h i t e s h o u l d be e x t r e m e l y r e a c t i v e b e c a u s e t h e y h a v e one free valence electron.  H o w e v e r , t h i s h a s p r o v e n t o be.  -  Figure 17.  47  -  TT-Electron Molecular O r b i t a l s i n Benzene,  Figure 1 8 ,  Electron Distribution i n Graphiteo  - lid  Figure  19.  -  Electronic Carbon  Band  Structure  of  - 49 incorrect.  I t i s p r o b a b l e , on e n e r g e t i c g r o u n d s , t h a t  f r e e < 5 * - e l e c t r o n and a 77°-electron w i l l some s t a t e  of h y b r i d i z a t i o n .  vacancy  atom  and l e a v e a m o b i l e  i n t h e TT - b a n d . Slag-G-raphite  1. S e m i - C o n d u c t o r  Band  Intrinsic  filled  Interface  Theory  s e m i - c o n d u c t o r s s u c h a s g r a p h i t e and  carbon have a r e l a t i v e l y est  form a s p i n p a i r i n  Thus e a c h p e r i p h e r a l  w i l l have e f f e c t i v e l y f o u r <5*-electrons  s m a l l energy gap between t h e h i g h -  b a n d and t h e empty c o n d u c t i o n b a n d . A l t h o u g h t h e  m a t e r i a l i s an i n s u l a t o r a t a b s o l u t e z e r o , a t f i n i t e a t u r e s enough e l e c t r o n s a r e t h e r m a l l y e x c i t e d to  this  t h e empty band t o p r o d u c e  a limited  from the f i l l e d  amount o f c o n d u c t i o n .  T h i s c o n d u c t i o n i s produced n o t only by the e x c i t e d but also by the holes created In  temper-  i n the n e a r l y f i l l e d  electrons band.  the case o f a few e l e c t r o n s i n t h e n o r m a l l y  empty band,, t h e s e e l e c t r o n s Their velocity  a c t as a f r e e  classical  assembly.  i s z e r o a t t h e b o t t o m o f t h e b a n d and i n c r e a s e s  p r o p o r t i o n a l l y t o the square r o o t f r o m t h e b o t t o m o f t h e band.  o f t h e i r energy measured  T h e i r e f f e c t i v e mass, however,  may b e l a r g e r t h a n t h a t o f a f r e e  electron. Since they are  f e w i n number, t h e y do n o t f o r m a d e g e n e r a t e F e r m i - D i r a c g a s a s do t h e e l e c t r o n s Maxwell-BoItzmann The  i n a m e t a l , b u t obey t h e c l a s s i c a l  statistics.  electrons  of a n e a r l y f i l l e d  band,  however,  behave, i n a v e r y d i f f e r e n t manner.  Since almost a l l the  a v a i l a b l e energy l e v e l s  t h e e l e c t r o n gas I s  are f i l l e d ,  - $0 -  TEMPERATURE OP HEAT TREATMENT  F i g u r e 20.  V a r i a t i o n o f E n e r g y Gap w i t h Treatment Temperature  Heat-  - 51 h i g h l y degenerate. the band and  The  group v e l o c i t y i s zero at the top  i n c r e a s e s with d e c r e a s i n g  of  energy i n the band.  T h i s anomaly i s r e l a t e d to the f a c t t h a t the e f f e c t i v e mass of an e l e c t r o n near the top of the band i s n e g a t i v e .  F o r these  reasons, i t i s more convenient to c o n s i d e r the a c t i o n of holes  i n the n e a r l y f i l l e d  These h o l e s , few electrons f i l l  the  band r a t h e r than the e l e c t r o n s .  i n number, move about the l a t t i c e as  them and l e a v e new  h o l e s behind.  the  I t has  been  shown ( 3 1 ) t h a t , g e n e r a l l y , the h o l e s act p r e c i s e l y as though they were p o s i t i v e l y - c h a r g e d e l e c t r o n s w i t h p o s i t i v e mass.  It  i s p o s s i b l e , i n f a c t , . t o ignore the e l e c t r o n s e n t i r e l y ; that i s , to assume the band i s completely  full  and  t r e a t the holes as a  f r e e c l a s s i c a l non-degenerate assembly of p o s i t i v e e l e c t r o n s obeying the Maxwell-Boltzmann d i s t r i b u t i o n . . Thus the full  nearly  band i s s i m i l a r to a n e a r l y empty band with the d i f f e r e n c e  t h a t , i n the n e a r l y f u l l  band, the current" c a r r i e r s  p o s i t i v e l y - c h a r g e d h o l e s with  are  energy i n c r e a s i n g from the top  to  the bottom of the band. Wilson (32) has  d e r i v e d a formula f o r the e q u i l i b r i u m  number of e l e c t r o n s i n the conduction  band by c o n s i d e r i n g  r e a c t i o n as a d i s s o c i a t i v e e q u i l i b r i u m . assuming no energy gap,  Using h i s formula  the and  f o r g r a p h i t e at 1000°C, the number of 14  e l e c t r o n s i n the conduction cubic centimeter.  band i s 7 x 10  electrons  per  T h i s f i g u r e i s much l e s s than the number of  "free * e l e c t r o n s i n a metal which i s of the order o f 1 0 ? 1  cubic  1  centimeter.  per  The p r e d o m i n a n t  type  ^2 of e l e c t r i c a l  a s e m i - c o n d u c t o r may be d e t e r m i n e d coefficient  o f the m a t e r i a l which R  R = Hall When R i s p o s i t i v e ,  duction  treatment.  as  of carbon  Graphite  density  o f the e l e c t r o n i c charge  i s m a i n l y b y h o l e s ; when R i s  i s by e l e c t r o n s .  f o r carbon.  character  i s defined  coefficient.  shows t h e H a l l  heat-treatment  value  conduction  conduction  (33),  by m e a s u r i n g t h e H a l l  e l e c t r o n or hole  e = absolute  Seldin  coefficient This  Figure  2.  Slag-Graphite  g r a p h shows t h a t  from  the con-  changes c o n s i d e r a b l y w i t h  heat-  shows a p r e d o m i n a n c e o f c o n d u c t i o n zero,  by  or  Interface  order  to f u l l y  understand  changes i n the e l e c t r o n i c bands i s necessary  structure  to consider  the p o p u l a t i o n  of graphite  during reaction,  t h e m o d i f i c a t i o n i n t h e band  caused b y the s l a g - s e m i - c o n d u c t o r  s l a g may be c o n s i d e r e d venient  taken  (overlap).  In  it  21,  as a f u n c t i o n o f  e l e c t r o n s b e c a u s e i t s e n e r g y gap i s v i r t u a l l y negative  in  t  =  where n =  negative,  conduction  source The  similar  of r e l a t i v e l y  to a metal;  contact. that  The  i s , a con-  free electrons.  work f u n c t i o n s f o r t h e s l a g and g r a p h i t e  will  determine  the p o t e n t i a l d i f f e r e n c e at t h e s l a g - g r a p h i t e  contact.  As s t a t e d  earlier,  is i|.3 electron volts.  the work f u n c t i o n f o r g r a p h i t e  Although i t i s d i f f i c u l t  to  estimate  the work f u n c t i o n o f t h e s l a g , i t may be assumed t h a t  i t is  -  Figure  21.  S3  -  Hall Coefficient Temperature  as of Heat  a Function Treatment  of  - $k less than that  of g r a p h i t e  c h e m i c a l r e a c t i o n and s l a g t o the  is  thus a t r a n s f e r of e l e c t r o n s f r o m  the  graphite.  The  changes t h a t  in Figure  22.  is higher  than t h a t of the  take place  Before contact,  a t r a n s f e r of e l e c t r o n s Since  b e c a u s e , above 9 5 » 0 ° C , t h e r e  on c o n t a c t  the F e r m i l e v e l  graphite.  f r o m the  On  are  i n the  contact,  s l a g to the  shown slag  there  graphite  is  anode.  the F e r m i energy of a substance i s e q u a l to i t s  c h e m i c a l p o t e n t i a l {3k-), a t e q u i l i b r i u m t h e F e r m i l e v e l s must be  the  same.  However, the F e r m i l e v e l s w i l l  equilibrium in this level  is filled  up  e l e c t r o n s from the  s y s t e m o n l y when t h e to that  of the  oxygen i o n s  graphite  s l a g by  at the  The graphite and  s u b s e q u e n t o x i d a t i o n and  t i o n o f the  complex. T h i s  boundary l a y e r between the n e s s o f t h i s l a y e r may parallel-plate (35)J  f r o m the  that  be  capacitance  s l a g and estimated equation  is C  c  A  £  reality,  reduced  slag to  adsorption  are p r o b a b l y s u p p l i e d by  Si^O-^  of  in  electrons.  t r a n s f e r of e l e c t r o n s  These i o n s  In  lead  i n v o l v e s t h e movement o f o x y g e n i o n s  their  atoms.  absorb these  Fermi  adsorption  surface.  e q u i l i b r i u m i s n e v e r a t t a i n e d because the the p r o c e s s w i l l  reach  t o the as  by  oxygen  c r e a t e 'a  graphite.  The  assuming the  to apply  surface  the d i s s o c i a -  process w i l l the  the  to t h i s  thicknormal layer  a)  Before  Contact  Figure  b)  22.  Band  Just a f t e r Contact  Structure  of Slag-Graphite  c) D u r i n g  Contact  Reaction  - 56 where C = c a p a c i t a n c e i n e l e c t r o s t a t i c E = dielectric A = area of  K h o d a k (36)  cryolite-carbon per  plates.  have found the  square centimeter.  calculated  of  c o n t a c t l a y e r t o be  constant f o r graphite be  constant  plates  d = separation R e m p e l and  to  o f 10,  a b o u t 20  the  a  carbon-oxygen s e p a r a t i o n  and  one  dielectric  b a r r i e r layer thickness  -  , — -  -  the  microfarads  be  The  graphite  c a p a c i t a n c e of  U s i n g t h i s v a l u e and  i °  units  A  z  <-  i n carbon/ionoxide i s about 1 o  hexagon i s about 3 A a c r o s s the  m a t e l y the  o x y g e n atom and  one  same t h i c k n e s s  as  l a y e r i s shown s c h e m a t i c a l l y The graphite level the  that  i n Figure  raised.  number o f h o l e s i n t h e  s i d e r a t i o n of the be  of  approxi-  above.  This  s l a g to  the  23.  from the  barrier layer w i l l  i n t h i s l a y e r t o be  hexagon, i s  calculated  t r a n s f e r of e l e c t r o n s  t h r o u g h the  phenomenon may  graphite  cause the  This w i l l  Fermi  i n turn  77*"-band t o d e c r e a s e .  By  d i s s o c i a t i v e e q u i l i b r i u m below,  cause a  con-  this  explained.  bound e l e c t r o n ^= hole + free electron number o f f r e e e l e c t r o n s x number o f h o l e s K number o f bound e l e c t r o n s where b o t h the 77" - b a n d .  By  h o l e and increasing  t h e bound  electrons  the, number o f f r e e  are  o A,  points.  T h e r e f o r e , a b a r r i e r l a y e r o f a CxOy c o m p l e x , composed a b o u t one  may  in  the  electrons,  a  Bound a r y Layer  *-  0  VjT.  Figure  23.  Postulated Structure Boundary L a y e r  of  Slag-Graphite  - 58 readjustment caused  i n t h e number o f h o l e s  i n order  and bound  electronsi s .  t o keep t h e e q u i l i b r i u m c o n s t a n t  t h e same.  C o n s e q u e n t l y , t h e number o f e l e c t r o n s i n t h e 77"-band i s i n c r e a s e d when t h e g r a p h i t e Since progresses,  comes i n c o n t a c t w i t h t h e s l a g .  t h e r a t e d e c r e a s e s as t h e c h e m i c a l  there  i s a d e c r e a s e i n t h e number o f e l e c t r o n s  possessing  e n e r g y above t h a t o f t h e F e r m i l e v e l  graphite.  Therefore,  decreasing  l a y e r a t a n y one i n s t a n t  and t h e g r a p h i t e p l a n e s  are becoming l e s s  of the  as t h e r e a c t i o n p r o c e e d s , the a c t u a l  number o f e l e c t r o n s i n t h e b a r r i e r is  reaction  of the b a r r i e r  layer  negative.  When t h e s l a g i s made n e g a t i v e w i t h r e s p e c t t o t h e g r a p h i t e by the a p p l i c a t i o n o f a p o t e n t i a l ,  the Fermi  l e v e l o f t h e s l a g i s r a i s e d so t h a t t h e e l e c t r o n f l o w the  slag to the graphite: i s increased.  change i n F e r m i l e v e l s . l e v e l throughout, layer i s increased  I n order  a proportionate  A s s u m i n g 100 p e r c e n t  of o x i d a t i o n .  shows  t o keep a c o n t i n u o u s  this Fermi  t h e number o f e l e c t r o n s i n t h e b a r r i e r  t h e p o p u l a t i o n o f t h e 77"-band w i l l  electrolysis,  F i g u r e 2li  from  amount.  As a r e s u l t ,  i n c r e a s e a s i m i l a r amount.  current e f f i c i e n c y  during  a l l the e l e c t r o n s t r a n s f e r r e d are the r e s u l t Since  t h e number o f e l e c t r o n s w i t h  energies  above t h e F e r m i l e v e l o f t h e g r a p h i t e d e c r e a s e s a s t h e reaction progresses, must be i n c r e a s e d constant.  the e x t e r n a l p o t e n t i a l of the c i r c u i t  i f t h e c u r r e n t d e n s i t y i s t o be k e p t  This w i l l  raise  the energy l e v e l s  so t h a t t h e e l e c t r o n f l o w i s c o n s t a n t .  of the s l a g  Correspondingly,  the  Figure  Zli.  I n f l u e n c e o f A p p l i e d P o t e n t i a l on Structure  Slag-Graphit  -  60  -  e l e c t r o n d e n s i t y of t h e 77*-band w i l l be  constant.  I n summary, when t h e s l a g and g r a p h i t e  come i n  c o n t a c t , t h e number o f e l e c t r o n s i n t h e g r a p h i t e 77*-band increases  over t h a t of the i s o l a t e d g r a p h i t e .  of chemical  o x i d a t i o n decreases,  vT"-rband w i l l  correspondingly  s l a g i s made n e g a t i v e  relative  As t h e r a t e  the p o p u l a t i o n o f the  decrease.  H o w e v e r , when t h e  to the g r a p h i t e , the Fermi  l e v e l s r e a d j u s t i n s u c h a manner t h a t t h e e l e c t r o n d e n s i t y o f t h e 77" -band w i l l at a constant ation  increase.  Furthermore,  c u r r e n t d e n s i t y w i l l k e e p t h e 77"-band  I t h a s b e e n shown i n t h e p r e v i o u s  Graphite section that  c o n t a c t b e t w e e n t h e g r a p h i t e and t h e s l a g i n c r e a s e s t h e  population  of the g r a p h i t e  t h i s 77"-band p o p u l a t i o n  77*-band.  The e f f e c t o f c h a n g i n g  on t h e d e s o r p t i o n r a t e s o f CO and  C O 2 h a s b e e n shown b y L o n g and S y k e s ( 1 6 ) i n a  treatment  of the e f f e c t o f t r a n s i t i o n metals i n the g r a p h i t e on t h e d e s o r p t i o n  desorption  that the a c t i v e  When an o x y g e n  atom i s a d s o r b e d on s u c h a p e r i p h e r a l c a r b o n s i t e , e l e c t r o n d i s t r i b u t i o n may be o f two t y p e s 25>.  sites  a r e t h e l e s s - f i r m l y bound p e r i p h e r a l c a r b o n  atoms a t t h e e d g e s o f t h e g r a p h i t e p l a n e s .  Figure  lattice  mechanism.  They h a v e a d v a n c e d t h e t h e o r y for  popul-  constant. Mechanism f o r the Combustion o f  the  electrolysis  Type  the  as shown i n  (a) i s a s t r u c t u r e i n w h i c h o n l y one o f t h e  o x y g e n e l e c t r o n s i s p a i r e d w i t h a c a r b o n e l e c t r o n . Type ( b ) ,  -  61 -  a)  b)  Figure 2 5 .  Oxygen Bonding i n Graphite  0.732 0 . 3 8 2 0 . 3 8 2 0.71+8  0 . 2 3 2 / x o . 232  0.748  a)  0 > 8 o  b  b)  Neutral  Figure  Jo.59k  0.872  26.  b.802  Positive  0.53X\0.533 0.695  0.695  c)  Negative  -rBond Orders i n Phenoxyl Radical  -  i n which a stable c a r b o n and of  d o u b l e bond  the oxygen,  CO b e c a u s e  62  -  i s formed  between the  i s more f a v o u r a b l e f o r t h e  peripheral  evolution  t h e c a r b o n - c a r b o n b o n d s a r e w e a k e r and  carbon-oxygen  bond more c l o s e l y a p p r o x i m a t e s t h e CO  However, t h i s  treatment i s not  the bond.  c o n s i s t e n t w i t h the  now  accepted procedures o f m o l e c u l a r o r b i t a l s . T h i s c o n c e p t assumes t h a t e a c h c a r b o n a t o m <5"-type b o n d s w i t h i t s n e i g h b o u r s  three h y b r i d i z e d fourth  77"-type bond  i s delocalized  as shown p r e v i o u s l y i n F i g u r e TT-electrons  c a n be  random p o i n t s calculated positive  17•  i n the carbon l a t t i c e .  the e f f e c t  on  phenoxyl r a d i c a l .  creation  26.  and  delocalized  L o n g and S y k e s  7T-bond o r d e r s o f c r e a t i n g  The  at have  a  to carbon or v i c e v e r s a f o r  results  of t h i s  calculation  I t i s evident from t h i s  of a p o s i t i v e  e v o l u t i o n o f CO ened  structure  or n e g a t i v e carbon hexagon by the p r o c e s s of  shown i n F i g u r e the  Thus, these  and  i n f l u e n c e d by i m p u r i t y c a t a l y s t s  e l e c t r o n t r a n s f e r from catalyst the  over the whole  forms  since  ion w i l l  figure  are  that  favour considerable  the carbon-oxygen  bond  i s strength-  the c o r r e s p o n d i n g c a r b o n - c a r b o n bonds a r e weakened.  Conversely the a d d i t i o n desorption  of e l e c t r o n s w i l l  reduce the  CO  rate. Similar  c a l c u l a t i o n s f o r «< - and /3 - n a p h t h o x y l  r a d i c a l s made b y t h e same w r i t e r s  a r e shown i n F i g u r e  T h i s c a l c u l a t i o n shows t h e same e f f e c t phenoxyl r a d i c a l . p h e n o x y l group  27.  as t h a t f o u n d f o r t h e  Thus t h e c o n c l u s i o n s o b t a i n e d f r o m t h e  are q u i t e g e n e r a l ; namely, i f by  some p r o c e s s  -  63 -  Neutral  - 0.427  -0.373  Positive  0.606  Negative  k 0.477  7f -Bond O r d e r s f o r <* - N a p h t h o x y l and ^-Naphthoxyl Radicals  C =— 0  Figure  28.  —*r  Ketene  0 — C—O  Structure  - 6k a 7 7 * - e l e c t r o n i s removed f r o m t h e c a r b o n l a t t i c e , rate the  o f e v o l u t i o n o f CO w i l l c a r b o n - c a r b o n b o n d s and  oxygen bonds.  result  controlling),  the  of d e s o r p t i o n of The  the  evolution  this  2  by Sihvonen  rings,  this  structure w i l l  second  c a r b o n atom i f t h e s u r f a c e  e x c e s s o f 77?-electrons  cular  and  this  would  to favour  consumption  o f the  carbon  i s completely regular.  strengthen the  single  tend t o p r e v e n t the e v o l u t i o n of  is still  c o u l d b r e a k t h i s bond and  the weakest that  form C0  2  point  as shown i n t h i s  t h e m e c h a n i s m o f L o n g and  f a v o u r t h e d e s o r p t i o n o f CO^  and  favour the p r o d u c t i o n of  i n the  a m o b i l e oxygen  Sykes  t h e n , an e x c e s s o f e l e c t r o n s i n t h e g r a p h i t e  will  (20)  be p r o d u c e d b y t h e l o s s o f e v e r y  structure, i t i s possible  If  increase  i s o f a k e t e n e f o r m s u c h as shown i n  D u r i n g the p r o g r e s s i v e  However, s i n c e  of  CO2.  28.  c a r b o n - c a r b o n bond  of t r a n s f e r  excess of e l e c t r o n s w i l l  Figure  An  will  i f the d e s o r p t i o n s t e p i s  s t r u c t u r e proposed of C0  of  carbon-  of e l e c t r o n s  I f the r a t e  i s c o n s t a n t ( f o r example,  rate  from the weakening  C o n v e r s e l y , the a d d i t i o n  not rate  increased  the s t r e n g t h e n i n g of the  h i n d e r t h e p r o d u c t i o n o f CO. oxygen  an  CO.  partiatom  figure.  i s correct, 77"-band  a deficiency of  will  7T-electrons  CO.  Summary o f D e s o r p t i o n M e c h a n i s m D i s c u s s i o n From the band of  Long and 1.  t h e o r y d i s c u s s i o n and  S y k e s , i t may  The  combustion  produce  a gas  be  concluded  that:  of g r a p h i t e by richer  i n C0  2  the mechanism  ionic  oxygen  should  than t h a t desorbed  in  - 65 The  g a s e o u s r e a c t i o n b e c a u s e t h e "TP-band  e l e c t r o n density of the graphite  i s increased  upon c o n t a c t w i t h t h e s l a g . 2.  As t h e r a t e o f c h e m i c a l decreases,  reaction with the slag  t h e desorbed gas should  become  r i c h e r i n CO b e c a u s e t h e TP-electron t i o n i s decreasing  popula-  proportionally with the  reaction rate. 3.  The a p p l i c a t i o n o f a p o t e n t i a l t o t h e s l a g should  c a u s e t h e g a s t o become r i c h e r i n CO2  because t h i s p o t e n t i a l r a i s e s t h e energy l e v e l s o f t h e s l a g and thus i n c r e a s e s t h e TT-band p o p u l a t i o n . desorbed should current density. constant,  Therefore  increase with  t h e percent  CO2  increasing  I f the current density i s  t h e CO/CO2 r a t i o s h o u l d  remain  constant.  COMPARISON OF EXPERIMENTAL RESULTS WITH-THEORY The  observed f a c t t h a t t h e desorbed gas i s r i c h e r i n .  CO2 when o x y g e n i o n s a r e u s e d i n p l a c e  o f oxygen m o l e c u l e s i s i n  agreement w i t h t h e d e s o r p t i o n mechanism d e v e l o p e d .  The f a c t t h a t  the a p p l i c a t i o n of a p o t e n t i a l causes a f u r t h e r i n c r e a s e i n t h e CO^ c o n t e n t theory  o f t h e gas i s c o n s i s t e n t w i t h t h e mechanism.  also predicts an increase  i n the chemical  reaction.  This  i n t h e CO/CO2 r a t i o w i t h  The time  surprising prediction i s verified  - 66 -  by the experimental data.  However, t h i s increase i n the  CO/COg  r a t i o with time i s a l s o noted during the e l e c t r o l y t i c r e a c t i o n , w h i l e the mechanism requires that the r a t i o remain constant. There appears to be no immediate explanation f o r t h i s  discrepancy.  - 67 -  CONCLUSIONS  It  has  been shown t h a t  a COg r i c h g a s  is  i n t h e c h e m i c a l and e l e c t r o c h e m i c a l c o m b u s t i o n o f a lead-borosilicate  slag.  This  fact  has  e l e c t r o n population of the  TT-band.  between t h e p r e d i c t i o n s  and most that  this  of the  it  adsorption, kinetics, of  the  assumption  used  mobile a d s o r p t i o n ,  and d e s o r p t i o n  i n the the  rate  by  by a  graphite  of  this  that  it  combustion  mechanism is  possible  process.  calculations  are  processes^immobile  first-order  do not  ions.  indicates  the a c t u a l  may be c o n c l u d e d t h a t  c a r b o n w i t h oxygen  i  results  mechanism d e s c r i b e s If  correct,  experimental  graphite  been e x p l a i n e d  mechanism i n v o l v i n g t h e The agreement  produced  kinetics,  c o n t r o l the  chemical  zero-order reaction  -  68  RECOMMENDATIONS FOR  1. varies  Because i t has considerably  with  -  FURTHER WORK  been found  that  shown t o be  parameter; f o r example, whether or not oxygen-ion concentration  done by u s i n g  a large  CO/CO2 r a t i o  t i m e , e x p e r i m e n t s s h o u l d be  i n which t h i s i s d e f i n i t e l y  the  the  of t h e  s l a g b a t h and  a function  done  of  some  i t i s governed  slag.  This  varying  by  could  initial  be  con-  centrations. 2.  This  i n v e s t i g a t i o n has  also pointed  s e l e c t i v e o x i d i z i n g n a t u r e of l e a d - s i l i c a t e lead-borate  s l a g suggested  s h o u l d be  manner.  3.  rates  tial  The  s h o u l d be  of r e a c t i o n w i t h o u t  measured by  the  slags.  The  i n v e s t i g a t e d more  f u l l y because i t appears to o x i d i z e the more r e g u l a r  up  graphite  an  i n a much  applied  poten-  a more s u i t a b l e method i n  t o d e t e r m i n e more a c c u r a t e l y  the  a c t i v a t i o n energy  order  for  oxidation. It. the  The  p o s s i b i l i t y that  slag-graphite  investigated. 5.  The  oxygen  to  i n t e r f a c e i s r a t e - c o n t r o l l i n g should  be  This gas  may  be  d i f f u s i o n of the  d e t e r m i n e d by  s t i r r i n g the  s a m p l i n g a r r a n g e m e n t s h o u l d be  slag.  changed  f a c i l i t a t e more r a p i d a n a l y s i s . A c o n t i n u o u s s e t u p m i g h t prove  useful. 6.  V a r i o u s carbons s i m i l a r t o those used i n  aluminum i n d u s t r y interpreted  i n the  b e t w e e n c a r b o n and  s h o u l d be light  of  graphite.  investigated the  and  electronic  the  the  results  differences  to  -  69 -  •BIBLIOGRAPHY  1. G a d s b y , J . , . H i n s h e l w o o d , C.N., and S y k e s , K.W., P r o c . R o y .  1 8 7 A , 129 (1946) .  Soc, 2.  G o r i n g , G.E., C u r r a n , G . P . ,  T a r b o x , R.P., and G o r i n , E . ,  I n d . E n g . Chem., kjj., 1057 (1952). 3. L a n g m u i r ,  I . , J . Amer. Chem. S o c , J2»  k. L o n g , P . 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J . , " P r o c e e d i n g s o f t h e F i r s t and S e c o n d Conf e r e n c e s on C a r b o n , " U n i v e r s i t y o f B u f f a l o , B u f f a l o , 1956, p. 118. K i t t e l , C , "Introduction to Solid State Physics," W i l e y , New Y o r k , 1 9 5 3 -  32. 333l+.  S., P h y s .  R e v . , 85^1+. 609 ( 1 9 5 2 ) .  35.  T o r r e y , H.C., and W h i t m e r , C.A., " C r y s t a l M c G r a w - H i l l , 191+8, p p . 7 5 ~ 7 6 .  36.  R e m p e l , S . I . , and K h o d a k , L . P . , J . A p p l . Chem., U.S.S.R., 2 6 , 857 ( 1 9 5 3 ) .  37-  R i c h a r d s o n , F.D., and Webb, E . , T r a n s . M e t . , 6 4 , 529-561+ (1955) •  Rectifiers,"  I n s t . M i n i n g and  - 71 C o u g h l i n , J . P . , B u l l e t i n £1+2,  U.S.  B u r e a u o f M i n e s , p.  27.  K u b a s c h e w s k i , 0., and E v a n s , E . L . , " M e t a l l u r g i c a l Thermoc h e m i s t r y , " Pergamen P r e s s , L o n d o n , 195>3>, p . 298. R o s s i n i , , F.D., Wagman, D.D., E v a n s , W.H., L e v i n , S., J a f f e , I . , C i r c u l a r £00, N a t . B u r . S t d s . , 1 9 ^ 2 .  and  -  72  -  APPENDIX A ABSOLUTE REACTION RATE CALCULATIONS  - 73 Immobile Immobile  Adsorption  a d s o r p t i o n may  r e a c t i o n i n v o l v i n g an o x y g e n  be  considered  i o n f r o m t h e s l a g and an a c t i v e  c e n t e r i n a f i x e d p o s i t i o n on t h e g r a p h i t e activated the  surface.  c o m p l e x i s assumed t o f o r m b e t w e e n  active site.  The r a t e o f a d s o r p t i o n  of passage of t h i s  a bimolecular  An  t h e i o n and  i s g i v e n by the r a t e  complex o v e r the p o t e n t i a l energy b a r r i e r .  A c c o r d i n g t o the p o s t u l a t e s o f the a b s o l u t e t h e o r y , e q u i l i b r i u m e x i s t s between a c t i v e c e n t e r s , and  reaction rate  the oxygen  the a c t i v a t e d complexes.  whereC+= concentration  C =  concentration  s  Thus-  of a c t i v a t e d  C . = c o n c e n t r a t i o n of oxygen of  i o n s , the  complexes  ions  sites.  The -f t e r m s a r e t h e c o m p l e t e p a r t i t i o n f u n c t i o n s f o r t h e indicated adsorption  species.  Therefore, according  of i o n s onto s i t e s  centimeter i s given  v  t  of the  the  ( i ) t h kind per square  by  •  c,  £_ L t.  a  h  where ^  to the theory,  differs  from  by the removal of  one  t r a n s l a t i o n a l degree of freedom i n the d i r e c t i o n of the reaction coordinate. g i v e s V " C-^i h  represents  f»  E x t r a c t i o n o f the z e r o - p o i n t e. *  •  the e n t r o p y change  A c t u a l l y the term e  R  •  The  £  energy f  V U equation f o r  - 74 t h i s r e a c t i o n may be w r i t t e n  * [ c ] —>  [o] +  s  where 0 = oxygen i o n i n the  e  z  slag  [CJ]= a c t i v e c e n t e r on the g r a p h i t e [ . 0 ] = oxygen atom adsorbed Since the s t r u c t u r e s o l i d than a gas,  surface.  onto the f i x e d  of a l i q u i d i s  c l o s e r to t h a t of a  we can assume t h a t the t r a n s l a t i o n a l  f u n c t i o n of the oxygen i o n i s v e r y s i m i l a r to that adsorbed  atom.  of  partition the  A l s o the r o t a t i o n a l and v i b r a t i o n a l p a r t i t i o n  functions w i l l  change very l i t t l e  assume t h a t the entropy change i s standard  site.  i n t h i s process.. negligible.  Thus we may  To change  the  s t a t e o f the p a r t i t i o n . f u n c t i o n , however, we must  i n c l u d e the entropy of d i l u t i o n The v a r i o u s v a l u e s equation are as  -"Kl^C.  which i s  to be s u b s t i t u t e d  3.7 x  i n the r a t e  follows:  V = r a t e = 2 x 10^8 atoms of oxygen r e a c t i n g square centimeter every at  0  2.5 x 10  ions per cubic c e n t i m e t e r , assuming the oxygen complexed as S i 4 0 i 2 ^ _  E = approximately  seconds.  26,000 c a l o r i e s  per gram mole  4 x 10-^'  C^= 10-*-^ s i t e s ,  assuming a l l the p e r i p h e r a l carbon atoms are  V=  second  100°C.  reciprocal  e^j-=  per  21  r  C* =  10~20.  active.  2.7 x 10 4 ^ x 3.7 x 1 0 ~ 2 0 = 1 x 1 0 2 6 a t o m s oxygen crn^ s e c .  - 13 T h i s value i s much d i f f e r e n t Thus i t appears that controlling  , from t h a t  immobile a d s o r p t i o n i s  observed.  not the  rate-  step. Mobile A d s o r p t i o n  The f o r m a t i o n of an adsorbed mobile l a y e r an entropy change very d i f f e r e n t adsorption.  i n immobile  Because the l a y e r i s m o b i l e , the c o n c e n t r a t i o n of  a c t i v e centers all  from that  involves  does not appear i n the r a t e e q u a t i o n .  equation f o r t h i s process  The o v e r -  is  where£0]= oxygen atom at the anode s u r f a c e which has been n e u t r a l i s e d by -the r e l e a s e of to the (oJ=  electrons  graphite.  the mobile adsorbed l a y e r , which may be regarded as a two-dimensional  gas.  E n e r g e t i c s favour the f o r m a t i o n of a m o l e c u l a r r a t h e r t h a n an atomic gas.  The oxygen atom has  effectively  degrees of freedom, w h i l e the adsorbed gas  no t r a n s l a t i o n a l  has two t r a n s l a t i o n a l  degrees of freedom.  A l s o the adsorbed molecule w i l l have one  degree of r o t a t i o n a l  freedom which the oxygen atom d i d not have.  Thus the t o t a l  c  entropy term w i l l  '  L  Using the arguments  h  be  -  *  put forward i n the development of  the r a t e equation f o r immobile a d s o r p t i o n ,  we get  f o r mobile  - 76 adsorption  that  - AS where tf  entropy term, which may be r e p l a c e d by  L°]=  c  o  n  c  e  n  t  r  a  t  l °  n  o r  " oxygen atoms at the  anode  surface. x IO- - atoms oxygen per square c e n t i m e t e r  = 1,2  1  4  Using the same c o n d i t i o n s as before t  0  b  the r a t e may be  v = 1.2 x 1 0 . 2 . 6 5 x 1 0 ^ . 5  x 1 0 1 0 . 4 x 10"*  14  e  = 6 x IO-  52  x 3.7  x IO"  2 0  calculated  = 2 x l O ^ atoms oxygen 1  2 cm  sec,  A comparison o f t h i s t o the experimental v a l u e of  18 2 x 10  would i n c i d a t e that the f o r m a t i o n o f a two-dimensional  oxygen gas  i s not r a t e c o n t r o l l i n g . Chemical R e a c t i o n The  and  r e a c t i o n i s assumed to i n v o l v e one atom of  one a c t i v e  s i t e on which r e a c t i o n o c c u r s .  oxygen  The a c t i v a t e d  complex c o n s i s t s of an adsorbed molecule which has a c q u i r e d  the  approximate  The  amount of energy and the. proper c o n f i g u r a t i o n .  r e a c t i o n may be p i c t u r e d as  £QJ  where C = r e a c t i v e equation i s  v - C  Q  carbon at CJ C C  rate  ^  Ceo s r  First-Order Kinetics. If  the s u r f a c e i s  s p a r s e l y covered w i t h adsorbed  atoms, the c o n c e n t r a t i o n of s i t e s , virtually  ' C)^^ £ Q  the s i t e . Thus the  J T  i)  ^ (0 "  C$, i s n e a r l y constant  i d e n t i c a l w i t h the number of s i t e s f o r a bare  oxygen and  surface.  - 77 Under these tion  conditions,  the  o f atoms on t h e anode  rate i s surface  proportional and t h e  to the  reaction  concentra-  is  first  order. The r a t e  This  assumes t h a t  negligible. ted rate  is  the  is  the  1 x 10  is  V  values  ^s.~^~' ~f~  during reaction  previously determined,  atoms o x y g e n . cm^ sec. as  *~£0j  =  e n t r o p y change  Using the  same r e s u l t  ii)  equation  It  that- o b t a i n e d  is the  caleula-  s h o u l d be n o t e d t h a t  for  immobile  this  adsorption,  Zero-Order K i n e t i c s . It  is  o x y g e n atoms t o  assumed t h a t  the  surface  an a p p r e c i a b l e  extent.  c o m p l e t e l y covered w i t h atoms,  ^-QJJ i -  reaction is  independent  of  C5.  This  equation  If s  yields  h  the s u r f a c e  rate *  e  2  cm  adsorbed is  equation  nearly and  the  is  r  a calculated  1 x l O ^ 4 - atoms  c o v e r e d by  v i r t u a l l y constant  Thus t h e  Co]  is  result  of  oxygen  sec.  Desorption D e s o r p t i o n f r o m a n i m m o b i l e l a y e r may be r e g a r d e d i n v o l v i n g an a c t i v a t e d active  site  •^energy t o  acquires  permit  the theory of  i n which a molecule  the n e c e s s a r y  configuration  to  escape from the  anode  absolute  reaction rates,  the  e q u a t i o n may be  it  state  derived:  attached  to  as an  and  activation  surface.  Applying  following  rate  -  s C  V  ll  J«J  78  e ^  where C c  ..  -  T  c o n c e n t r a t i o n p e r square  = 0  centimeter CO and C0  o f t h e adsorbed 2  f * = p a r t i t i o n f u n c t i o n f o r the activated £  c o m p l e x ( n o t CxOy)  = p a r t i t i o n f u n c t i o n f o r adsorbed  o  products ' ° J —=»  The r e a c t i o n may b e g i v e n a s I t thus  involves the desorption of both I f b o t h t h e adsorbed  CO and  molecules  co,  C0 . 2  and a c t i v a t e d c o m p l e x  are c o n s i d e r e d , i m m o b i l e ,  the r a t i o of the p a r t i t i o n  is  I t s h o u l d be n o t e d  approximately unity.  process  as d e f i n e d i s a l m o s t  kinetics. are  Therefore,  f o r both  processes  similar.  E y r i n g (22)  n e a r l y covered  o f 10^  quoted by G l a s s t o n e ,  Laidler,  atoms p e r s q u a r e c e n t i m e t e r f o r a  s u r f a c e as t h e c o n c e n t r a t i o n o f t h e  CO and COo,. t h e r a t e i s 1 * l O * * is  that the desorption  t o t h a t o f zero-rorder  the rate equations  Assuming t h e value and  identical  functions  t h e same as t h a t o b t a i n e d  <**°>~*  f o r zero-order  T  h  l  adsorbed s  value  kinetics.  -  79 -  APPENDIX B ACTIVITY OP OXYGEN IN LEAD-SILICATE SLAGS  - 80 R e c e n t l y , R i c h a r d s o n and Webb activity  o f PbO I n l e a d  silicate  (37)  have s t u d i e d t h e  s l a g s b y means of t h e  equilibrium PbO where PbO i s l e a d  oxide,  the m o l t e n l e a d .  e i t h e r pure o r d i s s o l v e d  E q u i l i b r i u m was a t t a i n e d  i n separate  and a s m a l l  crucibles.  t o come t o t h e e q u i l i b r i u m .  over t h e metal.  Also  o f t h e PbO i n b o t h p h a s e s m u s t be e q u a l .  and  that Sievert's  l a w ( i . e . N -j <* ^Po^ [o  o f oxygen i n m o l t e n l e a d  R i c h a r d s o n and Webb c a l c u l a t e d relation By  cx using  i n molten lead, of  Coughlin of  P  b  o  =  lead  (38).  )  Assuming  a r e known.  that:  t o the  up t o s a t u r a t i o n ,  k •^  o f PbO f r o m  • A ' t ' l . Col .  t h e i r data f o r the s o l u b i l i t y  i t i spossible  the a c t i v -  applies  the a c t i v i t y  o f oxygen  t o c a l c u l a t e the a c t i v i t y  oxygen i n t h e s l a g i f the f r e e  of the l i q u i d  inside a larger  t o prevent the  ity  the  crucibles f o r  t h e p a r t i a l p r e s s u r e o f t h e oxygen over t h e  s l a g must b e e q u a l t o t h a t  solubility  and t h e  T h i s a s s e m b l y was h e a t e d u p t o t h e  r e a c t i o n t e m p e r a t u r e and a l l o w e d equilibrium,  slags  Two s m a l l  i r i d i u m c r u c i b l e covered w i t h double l i d s  At  b y vapor phase  c r u c i b l e f o r s l a g were h e l d  e s c a p e o f PbO v a p o r .  i n the  i s oxygen d i s s o l v e d i n  b e t w e e n t h e m o l t e n PbO o r s i l i c a t e  molten lead lead  Pb + [O]  Pb i s m o l t e n l e a d ; - and (0]  silicate;  contact  —>-  energies of formation  T h i s has been e s t i m a t e d b y  These d a t a , c o r r e c t e d  f o r the heat of f u s i o n  o x i d e as g i v e n b y K u b a s c h e w s k i and E v a n s (39)  t o be  - 81 6,300  c a l o r i e s p e r gram m o l e , a r e shown i n T a b l e  1.  In his  c a l c u l a t i o n s , C o u g h l i n u s e d t h e v a l u e o f 2,800 c a l o r i e s p e r gram m o l e a s g i v e n b y R o s s i n i  (kO).  T h i s value has been  shown t o b e i n e r r o r b y t h e w o r k o f R i c h a r d s o n The  p a r t i a l pressure  and Webb.  o f o x y g e n may be c a l c u l a t e d b y t h e  equation of formation P L  and  '  +  the r e l a t i o n  „  where  P ^ O ,  —  . .  ^  T h i s c a l c u l a t i o n i s shown i n T a b l e be  assumed t o a p p l y h e r e  ^to]  where  =  -  (i.e.N  a c  t  tivity  molten ^AtWefo] = a t o m i c  1.  ^ i?( \  Sievert's  l a w may  )  o f oxygen d i s s o l v e d i n lead percent  In the molten  oxygen  dissolved  lead.  H o w e v e r , when t h e s l a g and m e t a l a r e i n v a p o r - p h a s e  equi-  librium  w h e r e o. ^ i s t h e a c t i v i t y (  Thus,  o f oxygen i n t h e g l a g  o,,„v = fe' A t / C o 3 Co) c  6  When p u r e PbO i s i n e q u i l i b r i u m w i t h t h e m e t a l , , t h e a c t i v ity  o f t h e o x y g e n i n t h e p u r e PbO and i n t h e m e t a l  to the p a r t i a l p r e s s u r e o f t h e oxygen. i n Table  1 w i t h a standard  i s equal  This i s calculated  s t a t e o f one a t m o s p h e r e p f o x y g e n  TABLE 1 . OXYGEN PARTIAL PRESSURE CALCULATED PROM EQUATION Pb T°K  K  cal.  § 0  — * PbO  I =  K  Log K  2  po2  1  K  X  5.25  X  10"  X  3.39  X  i.i5  X  10"  1.995  X  5.02  X  2.52  X  10" •9  1+.13  1.35  X  10^  7-1+1  X  5.5  X  10" :9  -23.15  3.97  9.33  X  103  1.07  X  10^  i.i5  X  1298  -22.7  3.82  6.61  X  io3  1.51  X  lO" *  2.28  X  1323  -22.27  3.68  1+.79  X  io3  2.09  X  lo"^  1+.37  X  1373  -21.39  3.1+0  2.51  X  103  3.98  X  10^  1.58  X  -21+.91  1+.61+  4.37  X  1198  -21).. [+7  h-kl  2.95  1223  -21+. 0^  121+8  -23-58  1273  10^  •10  2.29  1173  10"S  1  10"  •9  •8  10" •8 10" •8 10"  •7  -  83  -  gas. Thus  ,  _  _ I  yfS^  Richardson's data f o r the s o l u b i l i t y l e a d , as shown i n T a b l e 2 , w e r e p l o t t e d  o f oxygen  i n liquid  w e r e t a k e n f r o m t h i s g r a p h and culated  as shown I n T a b l e 3 .  i n the  text.  1.  lead at v a r i o u s  the a c t i v i t i e s  The temperatures  of oxygen  These d a t a are p l o t t e d  f u n c t i o n o f c o n c e n t r a t i o n o f PbO  in  logarithmically  against the r e c i p r o c a l temperature i n F i g u r e solubilities  of oxygen  as  cala  i n Figure 2 , which i s Figure  8  TABLE 2. S O L U B I L I T Y OP OXYGEN I N MOLTEN LEAD IN  VAPOR- PHASE E Q U I L I B R I U M WITH VARIOUS LEAD-•SILICATE SLAGS  M o l e % PbO in Slag  At %  CO] i n l e a d  M o l e % PbO  %  Lol  M o l e % PbO  At  % [ol k.09  2.k5  90  349  85  2.18  85  3.11  83  2.07  83  2.95  100  89.8  1.52  90  85  1.36  83  1.25  2.81  80  1.16  80  1.87  80  2.71  75  0.93  75  1.5k  75  2.25  65  0.532  65  0.02  65  147  50  0.188  5o  0.347  -5o  0.579  kO  0.105  ko.  0.193  ko  0.325  sat'd.  0.16k  sat»d.  0.266  »  Si0  At  C  100  1.76  IOO  119ko  1100°C.  1000°C.  2  sat'd.  0.09k  Si0  2  Si0  2  CO  4=-  TABLE 3. OXYGEN A C T I V I T I E S .29xl0"^ .22x10"^ 1.03  900 C • 900 U  =2  k  M o l e !% A t % PbO 0 100 90 85 83 80 75 65 5o 1+0  i  o  a  1.03 0.9 0.78 0.735 0.66 0.518 0.283 0.091 0.05l  5  o  °  M o l e % At % PbO 0 100 90 85 83 80 75 65 5o 1+0  2.26 1.97 1.74 1.63 1.1+9 1.21 0.715 0.26 0.H+5  .  2.26 a  n  £  1  >  3  •  25x10-5  (0)  20.9x10 18.2 x io-5 16.1 x _ 15.1 x 10-5 13.8 x 10-5 11.2 x 10-5 6.61 x 10"5 2.1+ x 10-5 1.31+ x 10-5  100 90 85 83 80 75 65 5o l+o  1..37 1.18 1.030.98 0.88 0.7 0.393 0.132 0.07I+  f 6 6 x l Q  -5  7  Mole % A t % PbO 0  (o)  -5 2.29 x 10 2 x lO"? . 1.735 x 10-5 1.635 x 10-5 1.1+7 x 10-5 1.152 x 10-5 0.629 x 10-5 0.202 x 10-5 0.113 x 10-5  c  950°C.k' J'62x10-^ 95o 950  a (0) 5.02 x 10"^ 4.33 x x 10-5 3.77 X 10-5 3.59 X i o - 5 3.22 X i o - 5 2.56 X i o - 5  l.l+k x io-5 0.1+81+ x 10-5 0.271 x 10-5  Mole % A t 5 PbO 0 100 90 85 83 80 75 65 5o 1+0  K  Mole % A t % 0 PbO 100 89. 9 85 83 80 75 65 5o 1+0  =^4§g2l^=i• 4i7xio-^  iioooc. » 100 k  1000 ° - i o o o ~ -  2.81 2.1+5 2.18 2.07 1.87' 1.51+ 0.92 0.347 0.193  a (0) x 10"5 x 10-5 x 10-5 x 10-5 26.5 x 10-5 21.8 x i o " 5 13.01+ x i o ~ 5 I+.81+ x 10-5 2.73 x 10"5 39.8 31+. 7 30.9 29.3  1.76 1.52 1.36 1.25 1.16 0.93 0.0532 0.188 0.105  07xio-4  = 6 - 0 f l y 1 0  1776 a (0) -5 10.7 x 10 J 9.25 x 10-5 8.27 x i o - 5 7.6 x 10-5 7.06 x i o - 5 5 . 6 6 x 10-5 3.21+ x 10-5 1.1I+ x 10-5 0.61+ x 10-5  -  86 -  10  Figure  1.  Solubility Reciprocal  o f Oxygen i n Lead Temperature'  vs.  - 37-  MOLE FRACTION PbO  

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