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Towards development of optimal sequential injection analysis methods Kester, Michael Dean 1994

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TOWARDS DEVELOPMENT OF OPTIMALSEQUENTIAL INJECTION ANALYSIS METHODSbyMICHAEL DEAN KEsTERB.Sc. (Hons.), University of British Columbia, 1990A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIESIndividual Interdisciplinary Programme[Analytical Chemistry / Pulp and Paper]We accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAOctober 1995© Michael Dean Kester, 1995In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of t,’PLi/JPa€Y 7fl3/The University of British ColumbiaVancouver, CanadaDate /A /9csDE-6 (2/88)IIABSTRACTCurrently, several research groups in the pulp and paper industry areactively pursuing the development of improved detection strategies for prioritypollutants. A new technique in analytical chemistry called sequential injectionanalysis, may be able to provide a robust, inexpensive, automated method fordetection of resin acids (known fish toxins) with appropriate use ofimmunochemical sensing. Most new analytical techniques, however, requirefundamental studies in order to understand and optimize the physical processesthat occur during the analysis. Towards this end, a dual-channel sequentialinjection analyzer has been designed and used for fundamental studies ofdispersion. In an attempt to simplify the development of sequential injectionmethods, a unique graphical user interface with a virtual manifold has beenproposed and implemented for control of the analyzer. The software is able toautomatically and systematically manipulate over 20 instrumental parameters insearch of optimal operating conditions; all information is recorded in acomprehensive database for rapid recall and display.The first dataset to be collected on the analyzer includes over 6,800experimental dispersion profiles that were created by injection of a tracer dye.The effects of injection volume, flow rate, and manifold geometry were examinedand quantified using peak moments. The random-walk model was shown to holdIIIfor sequential injection peak profiles which undergo multiple flow reversals ofvarying length. Optimization of the mutual penetration between two sequentiallyinjected zones was investigated using several new descriptors for zonepenetration, sensitivity, throughput and reagent economy. When the combinedconditions of maximum zone penetration and sensitivity were considered, theoptimal sample and reagent injection volumes were shown to be independent ofmanifold length and flow rate.To gain further insight into the sequential injection technique, a computersimulation based on the random-walk model was proposed and implemented. Aunique injection procedure was demonstrated, which simulates the sequentialloading of multiple zones, in addition to the flow reversal process. Simulateddispersion profiles agree well with experimental dispersion profiles createdunder laminar flow conditions. Visualization of the theoretical concentrationprofiles which occur during injection and flow reversal allowed prediction ofimproved sensitivity at the point of zero net fluid movement.ivTABLE OF CONTENTSABSTRACT iiTABLE OF CONTENTS___________________________________ivLIST OF TABLES viiiLIST OF FIGURES ixGLOSSARY xviACKNOWLEDGMENTS____ _____xxiCHAPTER 1: INTRODUCTION___________I1.1 OVERVIEW I1.1.1 Detection Strategies 31.1.2 Resin Acid Detection 41.1.3 Immunochemical Sensing 61.2 PRINCIPLES OF FLOW INJECTION ANALYSIS 71.3 PRINCIPLES OF SEQUENTIAL INJECTION ANALYSIS 101.4 REVIEW OF SEQUENTIAL INJECTION ANALYSIS LITERATURE 161.5 SCOPE OF THE THESIS 201.6 REFERENCES 25CHAPTER 2: SEQUENTIAL INJECTION ANALYSIS SYSTEM 302.1 INTRODUCTION 302.1.1 Brief History of Computer-Controlled FIA Systems 312.1.2 Computer Control Over Sequential Injection Systems 332.2 SEQUENTIAL INJECTION ANALYSIS HARDWARE 352.2.1 Computers and Interfaces 352.2.2 Valves 412.2.3 Pumps 452.2.4 Detectors 522.3 SEQUENTIAL INJECTION ANALYSIS SOFTWARE 532.3.1 Programming Graphical User Interfaces 532.3.2 Flow Injection Development and Optimization System 55V2.4 GRAPHICAL USER INTERFACE (GUI) FOR SIA 562.4.1 Program Overview 572.4.2 Parent Multiple Document Interface 592.4.3 The Virtual Manifold 602.4.4 Viewing, Editing, and Using Icons 622.4.5 Designing a Manifold 632.4.6 Recording a Method 652.4.7 Manifold Priming and Pump Calibration 692.4.8 Summary Form 722.4.9 Automated Optimization 732.4.10 Data Analysis and Representation 762.5 CONCLUSIONS 772.6 REFERENCES 79CHAPTER 3: EXPERIMENTAL DESIGN AND SYSTEMCHARACTERIZATION____________________823.1 INTRODUCTION 823.1 .1 Peak Descriptors 833.1.2 Multiple Flow Reversals 903.2 EXPERIMENTAL 913.2.1 Reagents 913.2.2 Sequential Injection Manifold 923.2.3 Flow Cell 943.2.4 Peristaltic Pump Tubing 953.2.5 Experimental Basis Set 963.2.6 Analytical Procedure 993.3 RESULTS AND DISCUSSION 1023.3.1 Absorbance of Dye 1033.3.2 Reproducibility of the Injection Volume 1053.3.3 Calculation of S, Value 1093.3.4 Zeroth Moment 1133.3.5 First Moment 1153.3.6 Second Moment 1163.3.7 Skew 1183.3.8 Excess 1193.3.9 Multiple Flow Reversals 1213.4 CONCLUSIONS 126vi3.5 REFERENCES 128CHAPTER 4: OPTIMIZATION OF ZONE OVERLAP IN SEQUENTIALINJECTION ANALYSIS 1304.1 INTRODUCTION 1304.1 .1 Zone Overlap Descriptors 1354.2 EXPERIMENTAL 1434.3 RESULTS AND DISCUSSION 1434.3.1 Zone Overlap Descriptors 1494.3.2 Analysis of Response Surface Maps 1494.4 CONCLUSIONS 1694.5 REFERENCES 171CHAPTER 5: RANDOM-WALK MODEL FOR SEQUENTIAL INJECTIONANALYSIS 1725.1 INTRODUCTION 1725.2 THEORY 1755.3 INJECTION PROCEDURE 1815.3.1 Theoretical Considerations of the Injection Procedure 1865.4 EXPERIMENTAL PEAKS 1895.5 INTERFACE 1915.5.1 Multiple Document Interface Form 1925.5.2 Simulation Profile Form 1935.5.3 Physical Settings Form 1955.5.4 Flow Settings Form 1965.5.5 Time Settings Form 1985.5.6 Model Settings Form 1995.6 RESULTS AND DISCUSSION 2005.6.1 Investigation of Random-Walk Model Parameters 2005.6.2 General Agreement of the Random-Walk Model for SIA 2145.6.3 Laminar Flow Factor 2215.6.4 Cross-Sectional Molecular Distribution 2325.6.5 Cross-Sectional Zone Penetration 2415.7 CONCLUSIONS 2485.8 REFERENCES 251VIICHAPTER 6: CONCLUSIONS AND FURTHER WORK 2536.1 SEQUENTIAL INJECTION ANALYSIS SYSTEM 2536.2 EXPERIMENTAL DESIGN AND SYSTEM CHARACTERIZATION 2546.3 OPTIMIZATION OF DISPERSION IN SEQUENTIAL INJECTIONANALYSIS 2556.4 RANDOM-WALK MODEL FOR SEQUENTIAL INJECTION ANALYSIS256VIIILIST OF TABLESTable 2-1. Pin-out used for IBM Digital Acquisition and Control Adapter(DACA) board #1. 39Table 2-2. Pin-out used for IBM Digital Acquisition and Control Adapter(DACA) board #2. 40Table 2-3. Peristaltic pump calibration data indicating a lower standarddeviation when longer calibration times are used. 51Table 2-4. Software programs or files used to implement sequential injectionanalysis software. 58Table 3-1. Experimental parameters (each run in triplicate) for the flow rate,sample zone volume, reagent zone volume, manifold length or volume (fromvalve to detector), and manifold configuration (coiled or straight). 99ixLIST OF FIGURESFigure 1-1. A general flow injection manifold showing flow lines, peristalticpump(s), injection valve, reaction coil, and detector. 9Figure 1-2. The concentration profile formed after dispersion of an initiallysquare injection plug. 10Figure 1-3. A simple sequential injection analyzer showing the bi-directionalsyringe or peristaltic pump, reaction coil, and the multiport selection valve. _1 IFigure 1-4. Sequential loading of sample and reagent zones; productformation occurs as sample and reagent mutually penetrate each other. 14Figure 1-5. After the flow is reversed sample and reagent continue to mix andreact as the product zone approaches the flow-through detector. 15Figure 2-1. Schematic of the computers, interlaces, and devices used in thesequential injection analysis system. 38Figure 2-2. Valve circuitry constructed to control each of the six-positionvalves at addresses 6 (this diagram) and 7 (without inverter on BO 8 line)with valve position feedback loop; taken after reference 10 withseveral modifications. 42Figure 2-3. Additional components and circuitry designed to achievebi-directional control over a Rheodyne model 5703 six-positionvalve mechanism. 43Figure 2-4. Electrical schematic for optically isolated solenoid mini-valves. 44Figure 2-5. Plot of voltage sent to the control unit versus voltage received atthe pump motor as a function of time. 48Figure 2-6. Overview of SIA software showing the most significant forms andhow the data are stored and retrieved from disk. 59Figure 2-7. Multiple document interlace (MDI) parent form which acts as acontainer for all other forms. 60Figure 2-8. Sequential injection manifold form showing controls for twopumps, graphics for two syringes, two six-position valves, a three-position minivalve (on top of left syringe), a two-position mini-valve (on top of right syringe),and controls for acquisition, delays, and a stir cell. 61xFigure 2-9. Icon viewer form which is used to scroll through various tubes andaccessories which are used to build a virtual manifold on the screen. 62Figure 2-10. A virtual manifold for the determination of phosphate. 64Figure 2-11. Method editor form showing settings for two pumps, two miniaturesolenoid valves (mini-valve one and two), two six-position valves (multi-valveone and two), one ten-position valve (multi-valve three), as well as time settingsfor stirring, acquisition, and delay. 66Figure 2-12. A method for the determination of phosphate is shown as anexample. In (a), the syringe draws in water from the bottle to its left for thirtyseconds. Then, the syringe is connected to the reaction coil through the mini-valve and a sequence of (b) ammonium helptamolybdate, (c) phosphate sample,and (d) ascorbic acid are sequentially aspirated for three seconds each into thereaction coil. Finally, in (e), the six position valve is connected to the detectorchannel and the solution is expelled through the flow cell to waste whileacquiring the detector signal for sixty seconds. 68Figure 2-13. Priming and calibration form showing controls for specific valveand pump to prime and calibrate. 70Figure 2-14. Experimental summary form which displays all of the importantexperimental data for each run. 72Figure 2-15. Variable record form showing record number 31 whichinvolves two variables. 74Figure 3-1. Half Gaussian peak profiles (shaded area) bisected (a) verticallyand (b) horizontally. 86Figure 3-2. Sequential injection manifold used for dispersion studies(dimensions not to scale). 94Figure 3-3. Absorbance spectrum of a 1.5 mM solution ofK3Fe(CN)6made upinl.OMKCI. 104Figure 3-4. Absorbance of 11 standard solutions of 0.0 to1.5mM Fe(CN)6.______________ 105Figure 3-5. Relative standard deviation of 40, 80, and 120 pL injectionvolume (n = 5) as function of flow rate. 107Figure 3-6. Injection volume as measured by mass difference for a 40 pLinjection at 1.0 mL min1. 108xiFigure 3-7. Injection volume as measured by mass difference for a 120 i.iLinjection at 1.0 mL min1. 109Figure 3-8. Peak profile as a function of injection volume at 2.0 mL min1 and15 cm valve-to-detector distance; profiles from injections of 40, 80, 120, 160,200, and 240 pL are shown (smallest to largest, respectively). 110Figure 3-9. Effect of flow rate, valve-to-detector (LD) distance, and manifoldgeometry on maximum peak height as a function of injection volume. 112Figure 3-10. The effect of the injection volume on the peak height for the 100cm coiled manifold.____________113Figure 3-11. Effect of flow rate on the zeroth moment (peak area) as a functionof injection volume for different manifold geometries. 114Figure 3-12. Effect of flow rate on the first moment (peak centroid) as afunction of injection volume for different manifold geometries. 116Figure 3-13.. Effect of flow rate on the second moment (peak variance) as afunction of injection volume for different manifold geometries. 117Figure 3-14. Effect of injection volume and flow rate on skew of peak profile atdifferent manifold geometries. 119Figure 3-15. Effect of injection volume and flow rate on excess of peak profileat different manifold geometries. 120Figure 3-16. Effect of the number of flow reversals (n) and the flow reversallength (I) on the variance of a 120 pL injection at 2.0 mL min1. 123Figure 3-17. Effect of the reversal length (normalized) on the square root ofthe variance for 2 through 8 reversals. 124Figure 3-18. Effect of the number of reversals and the reversal lengthonpeakexcess. 126Figure 4-1. Overlap of sample and reagent zones are shown by overlayingprofiles which were created on separate injections (each 240 pL). 133Figure 4-2. Overlap of sample and reagent zone showing the degree ofreagent excess (WRE) relative to the reagent width (WR). The isodispersion point(ID) represents the point of mutual zone penetration. 140Xl’Figure 4-3. Overlapped sample and reagent zones created by injecting eitherlow volumes (40 pL) or high volumes (240 pL) of the dye, at 2.0 mL min1 with avalve-to-detector distance of 15 cm. In (a) VR = V = 40 pL, (b) VR = V =240 pL, (c) VR=4OPL, V3240 pL,and(d) VR=240pL, V3=4OpL. 146Figure 4-4. Overlapped sample and reagent zones created by injecting eitherlow volumes (40 i.iL) or high volumes (240 pL) of the dye, at 0.5 mL min’1 with avalve-to-detector distance of 15 cm. In (a) VR = V = 40 pL, (b) VR V =240 pL, (c) VR=4OpL, V3=240 l.IL, and (d) VR=240pL, V8=4OpL. 146Figure 4-5. Overlapped sample and reagent zones created by injecting eitherlow volumes (40 pL) or high volumes (240 pL) of the dye, at 2.0 mL min1 with avalve-to-detector distance of 100 cm. In (a) VR = V = 40 pL, (b) VR = V240pL,(c)VR=4OpL, V=240pL, and(d) VR=240pL, V3=4OpL. 148Figure 4-6. Overlapped sample and reagent zones created by injecting eitherlow volumes (40 liL) or high volumes (240 pL) of the dye, at 0.5 mL mm1 with avalve-to-detector distance of 100 cm. In (a) VR = Vs = 40 pL, (b) VR V5240 pL, (C) VR = 40 l.iL, V = 240 pL, and (d) VR = 240 iiL, Vs = 40 iJL. 148Figure 4-7. Response surface maps of sample zone penetration (Rp) asdefined by Equation 4-2. 152Figure 4-8. Response surface maps of sensitivity (Rs) as definedby Equation 4-4. 155Figure 4-9. Response surface maps of reagent economy (RE) as definedby Equation 4-5. 157Figure 4-10. Response surface maps of throughput (RT) as definedby Equation 4-6. 159Figure 4-11. Response surface maps for the composite function, Rop, wherek1 = k2 = 1, and k3 = k4 = 0 according to Equation 4-6. 163Figure 4-12. Response surface maps for the composite function, RQpT, wherek1 = k3 = 1, and k2 = k4 = 0 according to Equation 4-6. 164Figure 4-13. Response surface maps for the composite function, wherek1 = k2 = k4 = 1, and k3 = 0 according to Equation 4-6. 167Figure 4-14. Response surface maps for the composite function, ROpT, wherek1 = k2 = k3 = k4 = I according to Equation 4-6. 168XIIIFigure 5-1. Tube variables used in the sequential injection simulation; thetube is described by x, y, and z Cartesian coordinates, with the multi-positionvalve interface defined at z = 0. 183Figure 5-2. Simulation parameters for the detection line, and thedetection zone. 185Figure 5-3. The Flow Simulation form (shown) serves as a container (multipledocument interface, MDI) for all other forms. 193Figure 5-4. The Simulation Profile form shows the manifold tube with fourcentral injection zones and the simulated peak profiles. 194Figure 5-5. The Physical Settings form includes simulation data for manifolddimensions (tube diameter, valve-to-detector distance, injection length, anddetector volume), physical parameters (number of molecules injected andtemperature), as well as a time and date stamp. 195Figure 5-6. The Flow Settings form shows flow pattern settings andsinusoidal flow parameters. 197Figure 5-7. The Time Settings form is used to specify the length of time topause for one valve movement, the length of time for each iteration, and thelength of time for each reversal. 198Figure 5-8. The Model Settings form is used to enter up to five additionalnumerical parameters in the model calculations. 199Figure 5-9. Effect of the molecular diffusion coefficient (Dm) on simulatedpeaks (thick lines) relative to experimental peaks (thin lines); the multiplicationfactor used relative to 7.6 x 10 cm2 s is shown for each profile. 204Figure 5-10. Effect of molecular diffusion coefficient multiplication factor on(i) the sum of the squares of the errors (SSE) between experimental andsimulated peaks, and (ii) the simulated peak area relative to theexperimental peak area. 205Figure 5-11. Effect of varying the simulated flow-cell volume on the sum of thesquares of the errors (SSE). 206Figure 5-12. Effect of modifying the internal diameter of the simulation tube onthe sum of the squares of the errors (SSE) between the simulated andexperimental profiles and the simulated peak area relative to theexperimental peak area. 207xivFigure 5-13. Effect of injection volume on simulated peak areas relative to an80 pL experimental peak. 208Figure 5-14. Relative flow rate as a function of distance to the center of thetube and the power factor, P, in Equation 5-12. 210Figure 5-15. Comparison of simulated and experimental profiles for an 80 pLinjection at 2.0 mL mm1 with a valve-to-detector distance of 100 cm. 211Figure 5-16. Effect of power factor on simulated peak profiles (thick line)relative to experimental profile (thin line). 213Figure 5-17. Effect of power factor, P, on (i) the sum of the squares of theerrors (SSE) between simulated and experimental peak profiles, and (ii) thesimulated peak area relative to the experimental peak area. 214Figure 5-18. Comparison of simulated and experimental peak profiles (thicklines and thin lines, respectively) for valve-to-detector distances of (a) 15 cm,(b) 50 cm, and (c) 100 cm. 216Figure 5-19. Peak height and peak area as a function of valve-to-detectordistance for simulated and experimental peak profiles. 217Figure 5-20. Comparison of simulated and experimental peak profiles (thicklines and thin lines respectively) for an 80 pL injection at (a) 0.5, (b) 1.0, (c) 2.0,and (d) 4.0 mL min. 218Figure 5-21. Peak height and peak area as a function of flow rate for simulatedand experimental peak profiles. 219Figure 5-22. Comparison of simulated and experimental peak profiles (thicklines and thin lines respectively) as a function of injection volume; the flow ratewas 2.0 mL min1 and the valve-to-detector distance was 15 cm. 220Figure 5-23. Peak height and peak area as a function of injection volume forsimulated and experimental peak profiles; the flow rate was 2.0 mL min1 and thevalve-to-detector distance was 15 cm. 221Figure 5-24. Effect of laminar flow factor, on simulated peak profile (thickline) relative to experimental peak profile (thin line) for 0.00 ( 1.00. 223Figure 5-25. Effect of (on (i) the sum of the squares of the errors (SSE)between the simulated and experimental peaks, and (ii) the simulated peak arearelative to the experimental peak as shown in Figure 5-24. 224xvFigure 5-26. Effect of laminar flow parameter, on simulated peak profile for0.80C 1.00. 225Figure 5-27. Effect of on (i) the sum of the squares of the errors (SSE)between the simulated and experimental peaks, and (ii) the simulated peak arearelative to the experimental peak as shown in Figure 5-26. 226Figure 5-28. Effect of on the simulated peak profiles (thick line) relative tothe experimental peak profile (thin line). 227Figure 5-29. Effect of on (i) the sum of the squares of the errors (SSE)between the simulated and experimental peaks, and (ii) the simulated peak arearelative to the experimental peak as shown in Figure 5-28. 228Figure 5-30. Simulated and experimental peak profiles (thick lines and thinlines respectively) for 160 and 240 pL injection volumes at 2.0 mL min1 with avalve-to-detector distance of 15 cm. 229Figure 5-31. Effect of €on simulated peak profiles (thick line) at 0.5 mL mm’1and 4.0 mL mm’1 relative to experimental profiles (thin line) with an injectionvolume of 80 pL and a valve-to-detector distance of 15 cm. 231Figure 5-32. Molecules found within the shaded “slab” are used for in thecross-sectional molecular distribution plots. 234Figure 5-33. Cross-sectional molecular distribution during injection of an 80 pLsample zone through the valve (central vertical line). 238Figure 5-34. Cross-sectional molecular distribution during injection of an 80 pLsample zone through the valve (central vertical line). 239Figure 5-35. Cross-sectional molecular distribution during injection of an 80 pLsample zone through the valve (central vertical line). 240Figure 5-36. Axial cross-section of zone-penetration between two 80 pL zonesinjected sequentially at 2.0 mL mm”. 244Figure 5-37. Axial cross-section of zone-penetration between two 80 pL zonesinjected sequentially at 2.0 mL min’”. 245Figure 5-38. Axial cross-section of zone-penetration between two 80 pL zonesinjected sequentially at 2.0 mL mm”'. 246Figure 5-39. Relative peak maximum for zone penetration as a function oftime, as predicted by the simulation. 248xviGLOSSARY12-bit 212 =40962D Two dimensions3D Three dimensionsA AmperageADC Analog to digital converterADC units Digital values from 0 to 4095 produced by analog to digitalconversion of 0 to 10 voltsA0 Area of the zone overlap (ADC units • s)A Area of the sample zone (ADC units ‘ s)BI Binary InputBO Binary OutputC Concentration (Molar)C0 Initial concentration (Molar)n7ax Maximum concentration (Molar)C Initial concentration of reagent (Molar)C Initial concentration of sample (Molar)C Maximum height of the overlap (Molar)CPU Central Processing UnitD Dispersion number (dimensionless); D = C°/Cd Distance from the valve to the detector (cm) used in thesimulationd Tube diameter (m)4d Equivalent length of the detection zone (cm) used in thesimulationDAC Digital to analog converterDACA Data Acquisition and Control Adapter, manufactured by IBMDaxiai Axial diffusion coefficient (cm2 &1)DIP Switch Dual In-line Pole switchxviiDLL Dynamic Link Library; a collection or library of computercode used for programming in the Windows environmentDm Molecular diffusion coefficient (cm2 &1)DR Dispersion number of reagent zone (dimensionless);DR R/CRDradial Radial diffusion coefficient (2 s1)D Dispersion number of sample zone (dimensionless);D=C/CE Peak excess (dimensionless)FIDO Flow Injection Development and Optimization systemFIA Flow Injection AnalysisForm A window or frame on the computer screen (or display)GUI Graphical User InterlaceHP Hewlett-PackardH P1 B Hewlett-Packard Interface Buszii Length of the injection zone (cm) used in the simulationi.d. Internal diameter of a tube (cm)IBM International Business Machines, Inc.ID Isodispersion point (s); the point in time when an adjacentsample and reagent zone have mutually penetrated eachother to the same degreeIEEE-488 A general purpose interlace bus; a standard for transmittingdata and control commands between electronic equipmentk1,234 Weighting coefficients for the composite optimizationparameterkT Sum of k1 to k4I Length of one step or flow reversalLD Length of tube from the valve to the detector (cm)L Length of tube from the valve to the pump (cm)M Molar (moles L1)M0 Zeroth peak moment (ADC units s)M1 First peak moment or centroid (s)M2 Second central peak moment or variance (2)M Higher-order central peak moments, where n > 2xviiiMB MegabyteMDI Multiple document interface; serves as a “container” form forall other subordinate forms of a Windows applicationn Number of steps or flow reversalsODBC Open database connectivity (a standard database protocolintroduced by Microsoft to allow sharing of data recorded indifferent formats)P Zone penetration parameter (dimensionless)or exponent used in laminar flow convection equationPC Personal ComputerpH The negative log of the hydronium ion activityppm Parts per million; I mgppb Parts per billion; I pgPTFE Polytetrafluoroethylene (chemically inert fluoropolymer usedfor manifold tubing)PVC Polyvinylchloride (used for peristaltic pump tubing)iiq Length of a molecular step in the axial direction due toconvective flow (cm)Q Flow rate (mL min1)Qmin Minimum flow rate (mL min1)Qmax Maximum flow rate (mL min1)r Radius (cm)Tube radius (cm)rad RadiansRAM Random Access MemoryRe Reynolds number (dimensionless)RE Optimization parameter for reagent economy(dimensionless)md A random number uniformly distributed between 0 and IROM Read Only MemoryRopT Composite optimization parameter (dimensionless)Optimization parameter for sample zone penetration(dimensionless)xixR3 Optimization parameter for sensitivity (dimensionless)RS—232 The standard asynchronous communications adapter (serialport, COMI — COM4) on most personal computersRSD Relative standard deviation (%)RT Optimization parameter for system throughput(dimensionless)S Peak skew (dimensionless)SIA Sequential Injection AnalysisSSE Sum of the squares of the errorsT Temperature (degrees Celsius)t Time (s)tB Time for the detector to return to baseline (s)Maximum time for the detector to return to baseline (s)t1 Time of the ith signal (s)U Linear flow velocity (cm &1)U Average linear flow velocity (cm &1)UV-visible Ultraviolet-visible range of the electromagnetic spectrum(Ca. 200 to 800 nm)V VoltageVD Volume of the tube from the valve to the detector (pL)VGA Video Graphics Association (which standardizes videoelectronics)VR Reagent volume (pL)V3 Sample volume (lJL)W0 Baseline width of sample and reagent zone overlap (s)WR Baseline width of reagent zone (s)WRE Baseline width of reagent excess (s)W Baseline width of sample zone (s)x x-dimension (cm)y y-dimension (cm)y, The ith signal (ADC units)z z-dimension (cm)a Radius of the pump head (cm)Delta or difference2max Wavelength of maximum absorption (nm)p Fluid dynamic viscosity (kg m1 1)p Fluid density (kg m3)Population standard deviation (s)2 Variance or second central moment of the peak (s2)Pump head frequency (radians &1)Laminar flow factor (dimensionless)Indicates proportionalityGo InfinityxxxxiACKNOWLEDGMENTSThere are a number of individuals who have in some way been involvedin this work and have my sincere appreciation. First and foremost, Dr. AdrianWade, who has not only taught me excellent analytical research skills, but alsodetermination and perseverance in spite of incredible opposition. I would like tothank Dr. Colette Breuil for her effort and assistance through a difficult situation,and her encouragement to pursue the Ph. D. degree. Dr. Denys Leclerc, whohad to pick up where others left off offered insight, guidance, motivation, labspace and support. Dr. Richard Kerekes offered educational guidance and thecontinual reminder that everything would work out in the end, with the security offinancial support whenever it was required. Finally, I would like to express mydeepest appreciation to my fiancée, Lise Lafond. She has instilled in me a highdegree of self-confidence and has given the unconditional emotional supportneeded to complete this work under often adverse conditions. For this, I remainforever in her debt.I would also like to express my gratitude for funding support from aPaprican Merit Award, two MacMillan Bloedel Graduate Fellowships, and threescholarships from the Science Council of British Columbia in the form of aGraduate Research in Engineering and Applied Technology (G.R.E.A.T.) award.I would also like to thank my industrial sponsor, Paprican, for financialcontributions and support of the project.I1. Introduction“If, therefore, anyone wishes tosearch out the truth of thingsin serious earnest,he ought not toselect one special science;for all the sciences are conjoinedwith each other and interdependent.”René Descartes1.1 OvERvIEwRecent years have brought considerable change to the pulp and paper industry.Increased social pressures for better environmental protection have created novelopportunities for the development of analytical methods that are capable of detectingpriority pollutants [1]. The need to detect these chemicals at low concentrations in acomplex sample matrix created the impetus for development of new techniques whichprovide both selective and sensitive determination of individual analytes. As a result,information gathered by these new chemical sensing methods can be used to improveprocess efficiency by providing greater control over manufacturing processes.2An ideal instrument would operate in both at-line and on-line modes [2, 3]. At-line operation involves a human technician presenting samples to the analyzer as theyarrive from various sample points in the plant. The technician is thus in a position toregularly check on the operation of the analyzer and can rapidly change from oneanalytical chemistry to another as needs arise. On-line use can be as a permanentinstallation for routine process analytical measurements, or for short-term in-situanalysis for process optimization and diagnostics. In the on-line mode, an analyzerwould be dedicated to running particular predetermined analyses on samples which aretransported directly to it from the main plant reaction vessels, pipes, or effluentstreams.A successful form of continuous flow analyzer, flow injection analysis [4, 5], hasfound its way into routine industrial monitoring applications in the petrochemical,nuclear, water quality, pharmaceutical, biotechnology, agricultural, and (to a limitedextent) pulp and paper industries. However, there are a few recognized drawbacks thatlimit the robustness of flow injection commercial analyzers in the industrialenvironment. These include the long-term reproducibility of flow rates using peristalticpumps, and the need for a different manifold for each chemistry. By far the mostsignificant factor is the rubber or PVC pump tubing used for fluid propulsion. Peristalticpumps operate on the principle of a series of moving rollers that pinch a flexible pumptube against an adjustable tension device. As the rollers move in one direction theytrap and move small segments of fluid in the tube much like the peristaltic action ofswallowing. The tubing eventually wears out (over a period of 2-3 weeks of continuous3use) which leads to flow-rate drift and poor flow-rate calibration, necessitatingreplacement and recalibration of the tubes on a regular basis. As well, the ability tovary the chemical conditions within the analyzer (e.g., volume of injection, degree ofmixing, selection of reagent) to allow detection of different analytes is somewhatrestricted; usually, an entirely new manifold needs to be designed and optimized.Recently, however, a new technique has been described [6], which overcomes many ofthese inherent difficulties. This new technique is called sequential injection analysis,and will form the focus of this thesis.1.1.1 Detection StrategiesMost “real” chemical sensing involves detection of specific analytes or analyteclasses in a complex (natural) matrix. Selective determination of the large number ofknown organic compounds is, without doubt, the new and most challenging analyticalfrontier. Characterization of relatively pure individual organic compounds is achievedby infrared spectrometry, mass spectrometry, and magnetic resonance techniques [7,8]. Commonly, analysis of mixtures of organics (or selected organics present inmixtures) can require complicated, expensive, “hyphenated techniques” such as gaschromatography - mass spectrometry (GC-MS), and can only be done by highly trainedpersonnel in better equipped analytical laboratories. However, specially designedselective molecular sensing technologies based on methods of spectrophotometricanalysis [9, 10] can often fulfill appropriate fully quantitative and semiquantitative4screening functions at a fraction of the cost and in a form that far more analyticalchemists can use.1.1.2 Resin Acid DetectionResin acids are liberated during the pulping process of coniferous wood and aretoxic to fish at the 1-2mg L1 level [11]. On-site detection of resin acids in pulp millprocess streams and effluent is difficult to achieve. Methods of analysis for theirdetection have relied on sophisticated instruments such as gas chromatography [12-201, high-performance liquid chromatography [21-24], or gas chromatography — massspectrometry [25-27]. These techniques require extensive analytical proceduresincluding preliminary isolation of the resin acids by either liquid or solid-phaseextraction and I or derivatization. Often, laboratory results aren’t available for days —which may be long after a toxicity breakthrough occurs at the mill. Therefore, severalresearch groups in Canada have focused on development of simple, rapid, quantitative,and inexpensive methods for determining concentrations of resin acids in pulp millprocess streams and effluent discharge.UV-visible colorimetric absorption techniques using chemically selectivereagents are widely used and accepted in analytical laboratories. They requireinexpensive equipment, and analyses of this nature can usually be performed by nonspecialists. Recently, two simpler methods for detection of resin acids have beendeveloped using spectrophotometric techniques [28-29]. In the work by Kester et al.5[29], a conventional flow injection regime proved to be a somewhat satisfactory meansof providing an automated, quantitative, safer method of analysis that requires aminimal volume (less than two millilitres per sample) of the corrosive and possiblycarcinogenic reagents that are currently used for resin acid detection in some BritishColumbia pulp mills. In order to improve the analysis further still, a glass flow-cellwhich incorporates extraction, reaction, and detection was conceived, constructed, andimplemented with success. Unfortunately the detection level reached by this system isat the 20 ppm level in the concentrated extract, therefore necessitating a 10- to 100-fold preconcentration step before analysis. This work, however, illustrated the potentialfor automation of complex chemical assays in the pulp and paper industry using muchsimpler instruments and less expensive methods of detection.It was obvious at this stage, that reagents or chemistries which provided muchgreater sensitivity and selectivity were needed in order to provide the industry with amethod capable of detecting resin acids in their real sample matrix at the sub-ppmlevel. Immunochemical sensing [30-31] was thus considered as a potentially powerfulway to meet these criteria, while still working within the realm of simplespectrophotometric detection. The reaction conditions for such methods arenecessarily milder and easier to use. As well, immunochemical analysis is easilyadaptable to continuous-flow methods such as flow injection analysis [32-35], or betterstill, the new technique of sequential injection analysis.61.1.3 Immunochemical SensingIn the most general sense, an immunoassay is a technique for measuring thepresence of a substance using an immunological reaction [36-37]. Although theindividual methods used for such measurements vary considerably, all involve reactionof a specific antibody (reagent) with a specific antigen (analyte). Detection can bemade by colorimetry, fluorescence, chemiluminescence, radiology, or byelectrochemical sensor. Advantage of the inherently high degree of specificity can betaken when it is necessary to analyze a single analyte “lost” in a complex naturalmatrix. This is especially important for organic compounds which are difficult to detectusing conventional methodologies. When developing an immunochemical assay, thelargest obstacle to overcome is finding an antibody that specifically and selectivelybinds to the antigen of interest. Fortunately, activity in this area of research hasincreased greatly over the past ten years and development and determination ofpolyclonal and monoclonal antibodies has become more common in modernbiotechnology laboratories. A limited quantity of polyclonal antibodies for resin acids isnow available at the Forest Products Biotechnology group in the Faculty of Forestry,Department of Wood Science, at the University of British Columbia. Attempts to obtaina monoclonal antibody cell line for resin acids continues to be one of their researchgoals. The original scope of this thesis included combining the new technique ofsequential injection analysis with antibodies which are specific for one particular resinacid, or at least one class of resin acids. However, as anticipated, the length of timenecessary for collaborating researchers to obtain and prepare quantities of suitable7monoclonal antibodies was such that a monoclonal cell line was not available at thetime when decisions concerning the direction of this work had to be made. As well, theamount of work which proved necessary to design, build, characterize, and optimize asuitable analyzer was more than could be imagined at the time. Therefore, this projectwas narrowed to include only the development, characterization, and optimization ofthe sequential injection system, including a computer model for studying the sequentialinjection technique. Application of monoclonal antibodies for resin acids to thesequential injection analysis system (described in this thesis) must be left to futureresearchers when the antibodies become available.1.2 PRINcIPLEs OF FLOW INJECTION ANALYSISFlow injection analysis is a versatile, continuous flow, sample preparation anddelivery methodology, which was first introduced in 1975 [38]. Since then, it has seenrapid and extensive development [4-5] with over 5000 research papers published todate. The rapid growth of flow injection techniques is due to its very wide range ofapplications as a means for sample transport and sample preparation for analytedetermination. Flow injection can automatically and reproducibly mix samples andreagents, and then deliver the reacted and dispersed species to a wide range ofdetectors which accept a microlitre-scale flowing stream, such as atomic absorptionspectrophotometers, inductively coupled plasmas, UV-visible spectrophotometers, ionselective electrodes, and so on. The performance of a flow injection system is greatlyenhanced by addition of a microcomputer for control, data acquisition, and near real-8time data processing. Indeed, there are types of experiments that would not befeasible without computer control. The automated nature of and reproducible timing offlow injection analysis often increases sample throughput and precision, allows fastkinetic chemistries to be examined, and provides an ideal analyzer for continuousmonitoring of process streams, effluent discharge, and both natural and potablewaters [2-3].A simple flow injection manifold is shown in Figure 1-1. The sample stream ischanneled through a sample loop (typically 25 to 200 pL) mounted on the injectionvalve. Injection is performed by turning this valve causing the carrier! reagent streamto flow through the sample loop, flushing the sample towards the reaction coil. Theflow lines are usually inert polytetrafluoroethylene (PTFE) or stainless steel tubing(typically 0.5 - 1.5 mm i.d.). Low pressure peristaltic pumps with rubber or poly(vinylchloride) (PVC) pump tubing are most often used for stream propulsion, and usuallyflow rates for the carrier and I or reagents range from 0.1 to 5.0 mL min1. If necessary,additional reagents can be merged into the carrier I reagent stream before thecontinuously dispersing sample zone passes through the reaction I dispersion coiltowards the flow-through detector.9Waste WasteFigure 1-1. A general flow injection manifold showing flow lines, peristaltic pump(s),injection valve, reaction coil, and detector.Use of coiled reaction tubes, single-bead string reactors, and knotted reactorsenhance mixing of the sample with the reagent(s). This phenomenon has beenattributed to the increased radial mixing caused by secondary flow [4-5]. Finally, thesample reaches a detector where the signal is measured as a transient response.Since the originally homogeneous sample zone has dispersed into the carrier I reagentstream, a concentration profile is formed as shown in Figure 1-2. This is the peakshape that is recorded at the detector. Analyte concentration is proportional to peakheight, area, or width. The concentration, C, can be measured at any point along theconcentration profile. The dispersion number, D, is measured as C° / C, and thus takeson a value of greater than 1.Dispersion within the manifold occurs by two principle processes, diffusion andconvection. Variables such as reaction coil length, tube diameter, flow rate,temperature, and sample size affect the degree of dispersion. These parameters canReagentPump(s)Injection Dispersion IValve Reaction Coil10be effectively optimized to produce the most desirable result (e.g., maximum sensitivity,maximum reproducibility, maximum sample throughput, etc.).CoInitial DispersedConcentration ConcentrationProfile ProfileFigure 1-2. The concentration profile formed after dispersion of an initially squareinjection plug.1.3 PRINCIPLES OF SEQUENTIAL INJECTION ANALYSISSequential injection analysis [6] is a very recent analytical development which ishighly suited for process control and remote environmental monitoring. It provides aconvenient way to develop, test and implement chemistries which allow sensitive,selective detection of chosen analytes. The total hardware required for a simple single-channel sequential injection instrument shown in Figure 1-3 is typically only a singleselector valve, a single high-precision pump (of either syringe or peristaltic design), adetector which is able to accept a flowing stream, and (usually) a computer to controlthe timing and synchronization of all units to the necessary high precision. Despite thiscrnCCID = C° / CC24CC11simplicity, sequential injection systems can fulfill many of the liquid handling functionsthat could otherwise be done only by a laboratory robot or by a human technician.Reagent IMulti-PositionSelector ValveSampleBi-directional WastePeristaltic PumpFigure 1-3. A simple sequential injection analyzer showing the bi-directional syringe orperistaltic pump, reaction coil, and the multiport selection valve.Sequential injection analysis offers significant advantages for on-processanalytical chemistry, laboratory-based analysis and automated research studies. Theadvantages of such systems over conventional flow injection analysis include:• a simpler manifold; usually only one pump and one valve are necessary• the ability to incorporate diverse chemical analyses in the same manifoldwithout reconfiguration• long-term stability of flow rates when syringe pumps are being used; no needfor recalibration of flow ratesStandardReagent 2WashReaction I DispersionCoil /12• the ability to vary the injected volume of sample and reagent(s) dynamicallyvia computer• the ability to obtain optimal mixing conditions while minimizing sample andreagent useTwo major disadvantages already noted by others are:• the requirement for relatively sophisticated operating software• the reduction in throughput (relative to flow injection analysis) due to anaspiration cycle necessary to load the sample or reagent(s), and to fill thesyringe with wash (if a syringe pump is used)In sequential injection analysis, the computer-controlled valve and pump areprogrammed to select appropriate volumes of various reagents, samples, standardsand buffers, mix them for a well defined time in a highly reproducible manner, detectthe product(s) formed (using the same forms of sensors as available for flow injectionanalysis), and automatically clean out the instrument in preparation for the next sample.Spectrophotometric, electrochemical, thermal, chemiluminescence, fluorescence,atomic emission, photoacoustic, mass spectrometric and other forms of detection arepossible. Typical method precision is as for flow injection systems, and relativestandard deviation of I % or less for replicate analyses is usually achievable.13The simplest analytical method for mixing a sample with a reagent zone to forma detectable product using the sequential injection technique is as follows:The multiposition valve is turned to the line containing wash or carrier solution(position I in Figure 1-4) and a volume sufficient to flush out the entirereaction I dispersion tube and the detector flow line is aspirated into the manifoldtowards the pump. The volume aspirated should be at least 4-5 times thevolume of the manifold which needs to be flushed with wash. If a bi-directionalperistaltic pump is used, this step is usually not necessary.2. The pump is paused briefly (usually I s) to prevent an undesired pressure surgewhile the multiposition valve turns to the sample line (2). The desired samplevolume is aspirated for the length of time necessary at the current flow rate (e.g.,2.4 s at 2.0 mL min1 will inject a 40 pL volume).3. The pump is again paused briefly while the multiposition valve turns to thereagent line (3). A sufficient volume of reagent is aspirated and mutualdispersion of the sample and reagent zones begins immediately, allowingchemical reaction to occur. This step is not necessary if a chemical reaction isnot required to effectively detect the analyte of interest (e.g., detection ofchloride using a chloride-specific electrode).14I StandardFigure 1-4. Sequential loading of sample and reagent zones; product formation occursas sample and reagent mutually penetrate each other.4. The flow is then stopped, the multiposition valve is switched to the detection line(position 4 in Figure 1-5) and the flow is reversed to propel thesample I product I reagent zone towards the detector for measurement.5. If increased mixing is necessary, the flow can be periodically reversed back andforth to enhance the dispersion process occurring between the sample andreagent zones, and therefore, increase the amount of sample reacted. If longerreaction time is necessary, the flow can be stopped while the sample I reagentinterface is either in the reaction / dispersion tube or in the flow-throughdetector. Stopping the flow while the sample I reagent interface is in thedetector allows kinetic measurements to be made on the reaction rate.6. A sufficient volume of wash effectively rinses the manifold flow lines includingthe detector cell in preparation for the next analysis.Multiposition ValveWash‘WashProductSampleTo PumpSampleReaction I Dispersion TubeReagent157. If necessary, the detector can be calibrated using a standard solution (shown atposition 5) by the single-standard calibration technique for sequential injectionanalysis recently reported in the literature [39].Reaction / Dispersion TubeStandardFigure 1-5. After the flow is reversed sample and reagent continue to mix and react asthe product zone approaches the flow-through detector.It should be noted that the above procedure assumes that the sample line isclimatized to the current sample solution. If this is not the case (e.g., the sample line isplaced in a new sample solution), then sufficient volume of the sample solution shouldbe aspirated and expelled to waste in order to ensure that sample carryover does notoccur.It is easy to see why this technique approximates manual wet-chemical methodsof analysis. It also provides improved protection for the analyst from noxious reagentsand prevents contamination of samples by the analyst. A large number of conceivablereaction chemistries can be handled in this way. The simple yet robust design of theMultiposition ValveWashWashProduct‘iFSampleTo Pump / Sample Reagent16instrument allows the analytical measurements to be made (I) in the place where theanalytical need exists, (ii) by the person who needs the analytical data, (iii) within areasonable amount of time, and (iv) with minimal maintenance I down time. Thebi-directional syringe pump is far better suited to remote, long-term unattendedoperation than the peristaltic pumps commonly found in flow injection analysis. Thus,there is a growing interest in this technology from researchers who need to dounattended, automated process control and environmental monitoring.1.4 REvIEw OF SEQUENTIAL INJECTION ANALYSIS LITERATuREWhen this project was started in January of 1992, only three papers onsequential injection analysis had appeared in the literature. Since then, at least 17additional research papers which discuss the principles of or the application of thesequential injection technique have been published. What follows is a brief review ofthe majority of the known publications as they appeared in the literature since 1990 inchronological order.The paper entitled “Sequential injection: a new concept for chemical sensors,process analysis and laboratory assays” by Ruzicka and Marshall appeared inAnalytica Chimica Acta in 1990 [6]. This paper introduced the concept of sequentialinjection which they say arose from consideration of the random-walk model (it was thework of Betteridge, Marczewski and Wade that introduced this to flow injection [40]). In1991, Ruzicka and Gubeli reported the application of stopped-flow sequential injection17analysis to an assay of traces of a proteolytic enzyme using fluorescence detection[41]. They obtained highly reproducible results and a detection limit of 7.2 ng mL1 ofthe pure active enzyme. Gubeli et a!. also reported the first fundamental study ofsequential injection analysis using a sinusoidal flow pump [42]. They consideredoptimization of zone penetration between two and three sequentially injected zones,and demonstrated the analysis of chloride and phosphate by this method. Severalguidelines for method development were presented, however, they used a sinusoidalflow pump (discussed in Chapter 2) at one flow rate using one manifold dimension.The work done in this thesis uses their work as a starting point for further investigationof optimal operating conditions for the sequential injection technique.In 1992, Ruzicka published a review of flow-injection, stopped-flow, andsequential injection methodologies [43] where he emphasized the need for a greaterunderstanding of the effect of stopping and reversing the flow in the sequential injectionprocess. Christian and Ruzicka discussed methods of exploiting the stopped-flowinjection method for chemical assays [44] and pointed out the additional degree ofinformation (kinetic) that can be obtained this way. Pollema et a!. [45] reported the firstimmunochemical sensing method with the use of a sequential injection analyzer. Theyused the method to investigate short-time antibody binding by immobilizing theantibodies on 4.5 jim diameter magnetic beads. The magnetic beads could beaspirated by the syringe pump into the 1.0 mm i.d. reaction coil and held in place withan electromagnet under computer control while reagents were passed through them.The spent beads could then be released by the magnet and flushed to waste. They18achieved a detection limit of 155 ng mL1 (ppb) using fluorescence detection with asampling frequency of 30 samples h1. It is a method along these lines that would bemost suitable for detecting low concentrations of resin acids in mill streams and is theultimate goal of this line of research.Baron et a!. [39], published a method which uses the sequential injectiontechnique which enables detector calibration using only one standard as well asdilution of high sample concentrations. Chung et al. [46], outlined a sequential injectionmethodology for fermentation monitoring. Marshall and van Staden [47] investigatedthe parameters affecting zone penetration in sequential injection analysis. Theyconsidered the effect of tube diameter (0.5, 0.8, and 1.5mm i.d.), reaction tubegeometry (knitted, coiled, and straight), and sinusoidal pump speed (maximumamplitude of 3.2 to 6.4 mL min1)on the degree of zone penetration as calculated by thearea of overlap between two adjacent injected zones (this is discussed more in Chapter4). Their results indicated that greater zone penetration occurred when one usessmaller tube diameters, but that this was obtained at the expense of precision. Straighttubes were also shown to give improved zone penetration over coiled or knitted tubes.The work in this thesis will also expand on these results by considering the effect ofstraight and coiled tubes using multiple linear flow velocities.In 1993, Shu et a!. [48], published a method for monitoring D-lactic acid in porkby immobilized D-lactate dehydrogenase, and Lukkari et al. [49], published a methodfor determination of total ammonium-nitrogen and free ammonia in a fermentation19medium, both using sequential injection analysis. Guzman et a!. [50] demonstrated theability of the sequential injection technique to handle a complex chemical analysis(fluorometric assay of factor thirteen) which involved six different solution zones, twodifferent chemical reactions, appropriate dilutions, and the acquisition of conventionalquantitative peak data and kinetic information. Guzman and Compton [51] thencompared the analysis of factor thirteen by the sequential injection method to the sameassay performed by a Zymark Benchmate robot. Ivaska and Ruzicka [52] found that byappropriate selection of pump tube and pump head rotation frequency, sufficientinjection reproducibility could be achieved using a peristaltic pump; it was previouslyassumed that a syringe pump was necessary to achieve a high degree ofreproducibility of injection volume. Pollema and Ruzicka [53] characterized planarconcentration gradients for cell-perfusion studies using a sequential injection system.More recently, a review of sequential injection analysis and its future possibilitieshas been published [54] as well as a review of sequential injection analysis forelectrochemical measurements and process analysis [55]. Shu et a!. [56], againreported a method for monitoring D-lactic acid, this time during a fermentation process.Cladera et a!. [57], reported the design of a sequential injection system which uses anordinary automatic titration burette actuated by a stepper motor for stream propulsion.They report that they can achieve similar precision of fluid movement by using thisdevice as can be achieved using a peristaltic pump. Finally, the first known article onthe use of sequential injection analysis for process monitoring in the pulp and paperindustry in Finland was reported [58]. The analysis is based on the formation of a20coloured complex between Ca2 and o-cresolphthalein complexone for thedetermination of calcium in white water of a paper machine. Their working range of5-500 mg L1 of Ca2 was achieved with a sample volume of 30 pL. The method wastested with off-line samples and in an on-line application at a paper mill for periods of 6hours (every 10 minutes) over a period of several days. They found that the methodworked well at monitoring the fluctuation of calcium concentration in real time. Duringthe on-line testing, a continuously flowing side stream of the fiber suspension from thehead box of the paper machine led to a continuously operating (6000 rpm) processcentrifuge (Westfalia). The centrifuge occasionally introduced small air-bubbles intothe sample stream, and therefore improvement in the sampling system was suggested.This recent paper further illustrates the possibility of this line of research in the pulpand paper industry.1.5 ScoPE OF THE THESISAt the start of this thesis, there were no commercially available systems forperforming sequential injection analysis, even though pumps, valves and suitable flow-through detectors had been available for quite some time. It was apparent from theliterature that the major obstacle to overcome when designing sequential injectionmethods was the writing of sophisticated control software for development of analyticalmethods. Therefore, a major portion of this thesis is devoted to the design anddevelopment of a new sequential injection analysis system (Chapter 2) which iscapable of not only performing a sequential injection method, but also automatically21exploring system variables. In addition, programming of new methods is simplified by aunique graphical user interface developed particularly for this purpose.Instrumentation-oriented research requires a significant time investment for thestudent to become familiar with programming and electronics. The advancement inscience obtained through proving some new theory can only be attained once thecomplicated apparatus is available. This impediment comes at a time when the abilityto do research is increasing in momentum exponentially, society’s body of knowledge indifferent disciplines is increasing at the same rate, there are still academic boundarieswhich deter interdisciplinary studies, and researchers grounded in different disciplineswill have very different skill sets. In order to help transfer this new technology(sequential injection analysis) from one discipline to another (from analytical chemistryto pulp and paper, and biotechnology), an extremely simplified interface between theend-user and the instrument was necessary.An analysis performed by the sequential injection method is governed by twofundamental processes. The first, which occurs in almost all flow analyses, is physicaldispersion of the injected sample into a suitable carrier stream due to convective flowand molecular diffusion. The second process is chemical reaction, which may or maynot be necessary in order to detect the analyte. An analysis which relies solely on thefirst process (dispersion) would be the determination of chloride with a flow-throughion-selective electrode. An assay which includes the second process (dispersion andchemical reaction), would be the analysis of chloride by its reaction with a reagent22(such as mercury (II) thiocyanate and iron (III) nitrate) during transport to aspectrophotometric detector. In the first case, the dispersion process is acting alone,while in the second case dispersion and chemical reaction occur simultaneously. Ineither case, it is dispersion which is the primary physical phenomenon which governsthe chemical concentration gradient produced within the tube, and as such, has themost significant influence on the output of the analysis. It is also evident from theliterature that this area of research still needs considerable attention.Chapter 3 will focus on an investigation of dispersion profiles (without chemicalreaction) produced by the sequential injection analysis system described in Chapter 2.The automated optimization software will be used for this comprehensive empiricalinvestigation and its performance evaluated. The dispersion profiles will be subjectedto numerical analysis by moments, in order to investigate the effects of varying thesystem operating conditions. The number of flow reversals, and length of the flowreversal step will be investigated through examination of the peak variance to confirmthe applicability of the random-walk model to sequential injection analysis.Chapter 4 introduces new parameters which aim to quantify the degree of zonepenetration between two adjacent injection zones. The effect of linear flow rate,sample and reagent injection volumes, and manifold dimensions on mutual penetrationof two sequentially injected zones will also be investigated. Study of this area ofsequential injection analysis should form the fundamental focus of research in the nextfew years.23In Chapter 5, the random-walk model is introduced by outlining previous work,and discussing its relevance in the present work. The basic premise of the randomwalk model relies on is the continuous tracking of the three-dimensional position ofindividual molecules as they progress through the manifold under a defined set ofconditions. In each iteration of the model, every molecule is allowed a three-dimensional diffusional step of random length, in addition to an axial movement due toconvective flow according to a laminar flow profile. This model will likely be the onlyfeasible numerical solution for the sequential injection technique for quite some time. Anovel simulation of the injection procedure, developed in this work to accommodate thesequential stacking of zones in the reaction coil will be illustrated. Numericalsimulations done with this model will be compared in detail to experimental dispersionprofiles obtained in Chapter 3. Investigation of several model parameters will be donein an attempt to improve the agreement between experimental and predicted results.Parameters tuned include sample size, degree of laminar flow, effective diffusioncoefficient, and laminar flow profile.In summary, the overall scope of this thesis includes:• development of the hardware, software, and computer interface of a newsequential injection analyzer using a graphical user interface24• characterization of the analyzer using a tracer dye to create dispersionprofiles which are subjected to moment analysis and recorded as retrievablerecords in a comprehensive database• investigation and optimization of the parameters affecting zone penetrationfor reagent-based assays under typical analyzer conditions• development of a model to theoretically explain the dispersion process foundin the sequential injection techniqueUpon completion of this thesis, a sophisticated analyzer will be developed andready for use in investigating automated resin acid detection in the pulp and paperindustry with the use of polyclonal or monoclonal antibodies. 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Acta,302 (1995), 297.[58] J. Hyman and A. Ivaska, Anal. Chim. Acta, 308 (1995), 286.302. Sequential InjectionAnalysis System“The software s the instrument.”National Instruments slogan, Ca. 19922.1 INTRODUCTIONResearch into the development of flow injection methods has been primarilydominated by empirical control over flow rate and experimental timing. This is mainly aresult of the complex, interdependent nature of the system variables. Computerizationof control of this process has been done by several researchers in order to achieveimprovements in precision, reproducibility, automation, and throughput. In a sequentialinjection method, however, an even greater flexibility of solution handling is achieved.Since there is no physically separate injection loop (present in flow injection analysis),both sample and reagent volumes can be manipulated through the control software,This has a profound impact on a researcher’s ability to create variation in theconcentration gradients within the reaction coil. Thus, software-driven, empiricaloptimization techniques will have an even greater overall influence in finding optimalconditions of a sequential injection method than ever before. This chapter will describe31the hardware and software of a dual-channel sequential injection analysis system,designed and constructed to automatically perform empirical optimization experiments.A virtual manifold is proposed and implemented as a Windows-based graphical userinterface for sequential injection analysis.2.1.1 Brief History of Computer-Controlled FIA SystemsIn most cases, an analytical flow system can be conceived as two essentialelements, namely, the physical hardware which manipulates the fluids, and thecomputer software which manipulates the physical hardware. When flow injectionsystems were first being assembled in the mid to late nineteen seventies, the hardwarerequirements were relatively simple. An analytical system comprised of a simpleinjection valve (electrically actuated or manual) which provided injection of a discretesample volume in line with a reaction coil connected to a flow-through sensor. Fluiddrive was usually performed by a peristaltic pump lent from a previous generation ofhardware called air-segmented flow analysis, or by a constant-head flow device.Typically, only a chart recorder was necessary to capture the transient output signal atthe detector. Measurement of peak height from a stable baseline was used to quantifythe analysis. Obviously, simple systems of this nature had their limitations with respectto efficient control and optimization of the analysis at hand.In the early nineteen eighties, researchers and analytical manufacturers beganto realize the benefits of controlling the analytical hardware with personal computers32running specialized software. This step into the next generation of hardware systemswas made possible by the computer revolution which started about this time, resultingin personal computers becoming more viable as a research tool in the laboratory andthe industrial sector. Stewart et a!. [1] gave the first report of computer control over aflow injection system. Subsequent software programs to control flow injection systems[2-7], however, rarely did more than turn the pump(s) on or off, turn an injection valve ata pre-selected time, and digitize the detector response for peak storage. However,replacement of the chart recorder with computerized data acquisition techniquesallowed research into peak shape to become much more accessible. By this time, peakwidth and peak area, as well as a multitude of other peak descriptors based on thedigitization of the response profile could be used for quantitation, and allow scrutiny ofthe analytical method. Much more could be determined from an analysis than justchemical concentration at one point in time (as in a peak height measurement).Instruments of this nature became increasingly common throughout the nineteeneighties with several researchers exploring more complex computer-aided optimizationtechniques [8-9]. For example, optimization techniques which are based on a factorialdesign or simplex optimization [10-12] have been investigated extensively [13-17]. Theultimate goal of this line of research is to get the control software to either (i) map outthe effects (via factorial design) of the most significant parameters on the givenanalysis, or (ii) intelligently search an n - dimensional parameter space for optimaloperating conditions. Self-tuning flow injection systems would be the naturalconsequence of this direction of investigation. Simplex optimization is preferred in33situations where there are too many variables to adequately examine individually. Forexample, to factorially investigate ten values of each of five parameters would requireI 0 = 100,000 experiments to be tried. At a fast pace of 100 experiments per hour, itwould take over 40 days of non-stop experimentation (assuming constancy ofcalibration throughout). Thus, the focus of research had turned towards more efficientmethods of optimization which intelligently explore an n - dimensional space.Optimization-oriented software for flow injection analysis of this nature has thefollowing basic characteristics. The software comprises of an initial set-up routinewhich defines flow rate boundaries for a given number of pumps (perhaps as many as 5to 7). The software then chooses flow rates for each pump so as to effect differentchemical conditions within the manifold (concentration ratios, residence time, etc.) andbegins recording the detector response. Variation in the flow rates is usually done byeither a complete factorial design or by more efficient optimization techniques such asthe composite modified simplex [12-13]. Thus, the majority of the previous work hasbeen on modification of flow rates of several pumps for an individual one-step injectionprocedure (even though the optimization algorithms used are quite capable ofoptimizing procedural situations).21.2 Computer Control Over Sequential Injection SystemsOptimization of a sequential injection method is an order of magnitude morecomplex than its flow injection predecessor since the researcher must deal with a multi-34step or procedural process. This creates an additional dimension of information to beoptimized in the analysis. In the system developed as part of this work, as many astwenty-one instrumental parameters are tunable in any step of the analytical method.Furthermore, these parameters to be optimized not only include flow rate, but alsovalve positions, sample volume, reagent volume(s), flow reversals, delay timing, and soon. Hence, greater overall control over the chemical conditions is only achievablethrough this technique after a substantial investment in more sophisticated controlsoftware has been made [20, 27].A unique approach, with the use of a Graphical User Interface (GUI) to create avirtual manifold on the computer screen is proposed and implemented in this work inorder to simplify the complexity of (i) designing the analytical procedure, and (ii)mapping of the effects of the tunable parameters. In this first step towardscomputerized optimization of SIA techniques, more efficient mathematical tools such assimplex optimization will not be considered. Instead, what is desired is a system withthe ability to independently map out the effects of all system parameters completely,thereby providing a more comprehensive, informative dataset. A general overview ofthe interfaced hardware, and the most significant capabilities of the software interfacethat is proposed and implemented in this work will now be the focus of discussion.352.2 SEQuENTIAL INJECTION ANALYSIS HARDWAREThe underlying concept behind the principle of sequential injection analysis ishardware simplicity. For industrial monitoring and process control, the undesirablecharacteristics of flow injection systems (such as multiple pumps, multiple valves, andmultiple hardware configurations) need to be eliminated if robust, low-maintenanceanalyzers are to gain widespread industrial acceptance.Although only one pump, one multi-position valve, and one detector arenecessary to perform a given analysis, the system developed here, for automated SIAresponse-surface mapping is, in actuality, a dual-channel system. This increase ininterfaced hardware enhances the flexibility and “open-endedness” of the instrument asa research tool. More elaborate experimentation can be performed on this instrumentthan on one which is limited to one pump and one valve. The final methods developedon this instrument would likely be implemented on much simpler hardware systemsconsisting of little more than one pump, one valve, and one detector.2.2.1 Computers and InterfacesThe SIA control computer is a 33 MHz, 80486 DX Intel-based, IBM-compatible,personal computer. It has a 1 MB super VGA video card, 128k cache, and 8 MB ofRAM. There are two physical hard drives on the system totaling 235 MB of storagespace. By today’s standards, this system is now limited by the video card, the CPU,36and the cache. Upgrading any of these would improve the speed at which the systemis able to redraw its graphical interface and interact with the user. However, this wasconsidered an advanced system at the time it was bought (1991).The SIA control computer uses two multi-purpose IBM Data Acquisition andControl Adapter (DACA) boards (obtained from Mendelson Electronics; Dayton, OH,USA) as shown in Figure 2-1. These each feature sixteen binary inputs, sixteen binaryoutputs, four channels of 12-bit analog to digital conversion (ADC), and two channels of12-bit digital to analog conversion (DAC). The pin assignments for each of theseboards are shown in Table 2-1 and Table 2-2. Board #1 is used to control the two six-position valves, the six mini-valves (only five were used), two accessories (e.g., stirmotors), and send a reference or acquisition request to the diode arrayspectrophotometer control computer. It is also used for monitoring the uni-directionalvalve position, the bi-directional valve position, and up to four analog detectors. Board#2 is used for control over the ten-position valve, and the two pumps (speed anddirection). It is also used for monitoring the syringe microswitches (indicating full orempty syringes), the current position of the ten-position valve, and for tracking theposition of the two syringes through their linear potentiometers connected to analoginput channels I and 2. The input and output position codes for the ten-position valvesare created by the appropriate combination of the numbers 1, 2, 4, 8, and 10,corresponding to BO 1,2, 3,4, and 5, and BI 8, 9, 10, 11, and 12, respectively.37One additional IBM DACA board was interfaced to a Hewlett-Packard DiodeArray Spectrophotometer (HP8452) control computer (an Intel 80286 CPU, with 1 MB ofRAM). This DACA board allows the SIA control computer to send a reference requestsignal (via B014 on DACA #1 and B14 on DACA #3) and an acquisition request signal(via BOl 5 on DACA #1 and B15 on DACA #3) to the diode array control computer whichruns a DOS-based program written in-house in Microsoft Professional BASIC version7.00 by Ivan H. Brock. This software continuously polls DACA board #3 for a referencerequest or an acquisition request and sends the appropriate instruction to the diodearray detector through an IEEE-488 interface. The detected signals for up to twowavelengths are sent back to the SIA control computer through BNC cables connectinganalog output 0 and I on DACA #3 and analog input 0 and I on DACA #1,respectively.38This hardware configuration allows the diode array computer to be easilyinterfaced to the SIA control computer as a detector through the existing interfaceboards, without specialized Windows drivers and minimal software overhead on thecontrol computer. In addition, other detection sources can be quickly connected tothese same channel inputs (analog input 0 and I on DACA #1) when the diode arraydetector is not in use. This also allows the diode array and the SIA system to be usedat the same time for separate analytical purposes with minimal hardware manipulation.Computers and Interface Boards InterfacedDevicesFigure 2-1. Schematic of the computers, interfaces, and devices used in the sequentialinjection analysis system.39Table 2-1. Pin-out used for IBM Digital Acquisition and Control Adapter (DACA)board #1.IBM DACA Board #1Binary_____ __________________BinaryOutput_______InputLow LowByte ByteBinary BinaryOutput InputHigh HighByte Byte00 Valve Toggle 00 Valve StatusForward/Reverse forU I Bi-directional Valve02 Mini-Valve 103 Mini-Valve 204 Mini-Valve 305 Mini-Valve 406 Mini-Valve 501 Bi-directional Valve Position #102 Bi-directional Valve Position #203 Bi-directional Valve Position #304 Bi-directional Valve Position #405 Bi-directional Valve Position #506 Bi-directional Valve Position #607 Mini-Valve 608091007Valve Address:Address of 6 is theUni-directional ValveAddress of 7 is theBi-directional ValveDACA Board Clock Status08 UnusedUnused12 Accessory I1 3 Accessory 21 4 HP Reference Request Line09 Uni-directional Valve Position #11 0 Uni-directional Valve Position #2I I Uni-directional Valve Position #312 Uni-directional Valve Position #41 3 Uni-directional Valve Position #514 Uni-directional Valve Position #615 HP Acquisition Request Line 5 UnusedDigital 0 Unused Analog 0 DetectorChannellto Unused to j Detector Channel 2Analog Digital 2 Detector Channel 3Output Input 3 Detector Channel 440Table 2-2. Pin-out used for IBM Digital Acquisition and Control Adapter (DACA)board #2.IBM DACA Board #2Binary Binary____ _______________________Output Input________Low LowByte_____ _________________ByteInput PositionCode forBinary Binary Ten-PositionOutput Input ValveHigh HighByte Byte00 Ten-Position Valve OutputEnable 00 Syringe 1 Microswitch - Emptied01 1 Output Position02 2 Code for03 4 Ten-Position04 8 Valve05 1006 Go To Home Position01 Syringe 2 Microswitch - Filled02 Syringe I Microswitch - Emptied03 Syringe 2 Microswitch - FilledUnused07 Step One Position04050607Unused080910080910111224810I I Pump I Direction121 3 Pump 2 Direction1415UnusedUnused131415Digital 0 Pump 1 Speed Output Analog 0 Unusedto i Pump 2 Speed Output to I syringe i Position InputAnalog Digital 2 Syringe 2 Position InputOutput Input 4 Unused412.2.2 Valves2.2.2.1 Valve TypesThree multi-position valves have been interfaced through the software. Two aresix-position, pneumatically-actuated rotary valves (Rheodyne, Inc.) and the third is aten-position, electronically-actuated valve (Valco Instruments Co. Inc., Houston, TX,USA). Both of the six-position valves were constructed after an original design byWentzell et a! [10]. The controller circuit boards were modified for this work in order toinclude feedback of valve position to the computer. The circuit diagram for thecontrollers used for the six-position valves is shown in Figure 2-2.The second six-position valve was modified still further to enhance itsfunctionality. An additional pneumatically-actuated directional switch was added toallow switching of the rotational direction of the valve. The software was modified toincorporate this feature and includes a routine to choose the direction of rotation“intelligently,” taking the shortest route to the next position. The schematic for theadditional circuitry for the second, more advanced six-position valve is shown in Figure2-3. The bi-directional, pneumatic ratchet mechanism throws a directional lever (lowerright) which toggles between clockwise and counter-clockwise positions. This valve istypically used preferentially over the non-reversing valve due to its advancedfunctionality.42BI 1BI 2El 3BI 4BI 5816-v24 VREEDRELAYGordos831C-4DISPLAYSTATUSLED SII4700 RESISTORSFigure 2-2. Valve circuitry constructed toaddresses 6 (this diagram) and 7 (withoutfeedback loop; taken after reference 10 withcontrol each of the six-position valves atinverter on BO 8 line) with valve positionseveral modifications.BO 01FORWARD43. COUNTER\ CLOCKWISEVALVEGNDROTAflONFigure 2-3. Additional components and circuitry designed to achieve bi-directionalcontrol over a Rheodyne model 5703 six-position valve mechanism.A third multi-position valve was interfaced through the DACA board as well.Manufactured by Valco Inc., this ten-position valve is self-contained and is electricallyactuated (versus pneumatically), thus requiring no compressed air line. Its greaterreliability offsets the greater speed of the pneumatically actuated six-position valves;speed is now less important since the system pauses for 1.0 s at each position in itsrotation in order to maintain consistent timing.In addition, up to six, small 12 V solenoid valves can be interfaced through thesoftware. In this case, two combination “mini-valves” were used, one with two outlets,and the other with three outlets, for a total of five solenoid valves (i.e., future addition of15 VVARISTORCOMPUTERMANUALREVERSE5 PSI AIR IN24 VREEDRELAYGordos831C-4 GNDCLOCKWISEVALVEROTATIONDPSTSWITCH44one more solenoid valve is possible). Six binary outputs on the DACA board controlthe six valves (high = open, low = closed), through a reed-relay control interface whichprovides the valve with either 0 or 12 V at approximately 800 mA. The circuits wereoptically isolated as shown in Figure 2-4 in order to minimize electrical noise betweenthe solenoid valves and the rest of the interfaced circuitry. Although this circuit isrepeated six times in an interface box, only five of these valves (one two-way and onethree-way) are interfaced to the DACA board through binary outputs 2 through 7 onboard # Feedback ControlAfter extended periods of continuous operation, the potential exists for asolenoid valve to misfire. Overheating of the solenoids might cause the valve to stickand miss a valve movement. If this is done only once in a long-term optimization, thereagent or sample could potentially be diluted with a large quantity of wash, forexample, thus diminishing the validity of all future runs. This problem is not asBO 2-7BOARD 15V12 V15V VARISTOR24 VREEDRELAYGORDOSSIEMENS ILQ-74 831C-4 GNDFigure 2-4. Electrical schematic for optically isolated solenoid mini-valves.45apparent in flow injection systems in which contamination of the sample or reagentscould only occur if a pump flow reverses inappropriately. Safety checks are built intothe software for the multi-position valves which are hard-wired with a feed-back loopallowing the computer to check if the valve has arrived in the correct position beforeexecuting a pump movement. At this point the software can stop further execution ofthe experimental runs, and signal the user to provide maintenance for themalfunctioning valve. However, while this solution works well for all three multi-positionvalves, it is difficult to implement on the small solenoid mini-valves since it is difficult(but perhaps not impossible) to physically determine whether or not they have openedafter application of the appropriate voltage. Appropriate inclusion of either aninductance coil on the solenoid of the mini-valve, or a miniature flow meter near themini-valve would potentially enable the software to sense whether or not the valve hasfired at the appropriate time.2.2.3 Pumps2.2.3.1 Syringe PumpsIt has been argued [26, 28] that the important characteristic of a liquid propulsionsystem is repeatability, and not necessarily linearity. Reproducibility of flow rate isespecially critical for sequential injection analysis where it is the reproducibility of theflow rate which determines the reproducibility of the sample and reagent injectionvolume. To this end, a sinusoidal syringe pump was manufactured and distributed by46Alitea for these systems in an attempt to obtain the most repeatable flow rate possible.The reciprocating cam-mechanism of one of these pumps is such that the syringemoves with the y-component of a circular motion. This produces a flow rate that followsa sine function with a frequency equal to the frequency of the rotating pump headaccording toEquation 2-1 y = asin(czt)where y is the syringe position, a is the radius of the pump head (cm), o is the pumphead frequency (rad and t is the time (s) since the syringe was empty.These sinusoidal pumps were the first devices on the market to address theneeds of the new sequential injection analysis technique. Several other pumps whichachieve the necessary precision offering linear flow are now being manufactured. Thenewer pumps operate with stepper motors and screw drives, which were initiallyavoided due to their presumed imprecision.A great deal of work was done in this project in an attempt to improve thegeneral characteristics of the Alitea sinusoidal flow syringe pumps. Initially, thepossibility of (1) linearizing the sinusoidal flow, and (2) operating the pump by trackingits absolute movement instead of by timing was investigated. It was thought that thiscould be done with a continuous loop feedback control. A 10 cm linear potentiometerwas mounted on the side of the syringe pump so that the potentiometer could track the47position of the syringe head. This method of measuring the syringe position wasaccurate to Ca. 10 1iL for the following reasons. The linear potentiometer returned apotential difference from 0 to 10 volts depending on the position of the syringe. Thiswas converted by the DACA board into a signal with 12-bit precision, but since thepotentiometer was approximately twice as long as one full syringe stroke of 5.0 mL, theprecision of measurement was reduced by one half:Equation 2-2 1 stroke 5000 1tL. = 24 ,uLx 212 ADC units I stroke ADC UnitStill greater imprecision is created since the software loop cycled only fastenough to read the potentiometer ADC value at a resolution of about 3 to 4 unitscorresponding to about 7.2 to 9.6 j.iL. This is not precise enough for accuratelydispensing solutions which are sometimes as low as 10 to 20 tL. This uncertainty canbe reduced by changing the size of the syringe to I mL (a factor of 5) and by changingthe size of the linear potentiometer (a factor of 2), but a smaller syringe size limits theflexibility for optimization purposes (less volume can be pumped per stroke).Electronically scaling the output of the linear potentiometer to provide a better matchfor the analog input channel would also conceivably improve the precision by a factorof two.The pump control unit sends a voltage signal to the pump motor which has beendamped by capacitors. This creates a significant hysterisis effect in the pump circuitry,thereby causing a delay in the change of pump motor speed. Figure 2-5 shows the48voltage sent to the control unit as a step function over time (OV to by to OV) and thevoltage received by the pump motor (after signal processing in the control unit). Asshown, the hysterisis effect is significant, indicating recharge times as high as 10seconds. This eliminates the possibility of instantaneous flow rate change during orbetween sequential injection steps. The same effect will occur for the peristaltic drivenpumps manufactured by Alitea, since the same pump motor and electronics are used.1086Voltage420Figure 2-5. Plot of voltage sent to the control unit versus voltage received at the pumpmotor as a function of time.From the foregoing, it was concluded that the control software must allow thepumps sufficient time to power up. An instantaneous request for a change of flow ratebetween SIA method steps would produce inaccuracies in fluid movement as the pumpadjusted to the new speed over a finite length of time. Additionally, the pumps were4Voltage receivedat pump motorTime (s)0 5 10 15 20 2549subsequently operated based on time and not absolute displacement (although thelatter would still be possible with the inclusion of a more sophisticated tracking device).No physical changes were made to the Alitea pumps other than mounting a linearpotentiostat on the outside of the housing to track the absolute position of the syringe. Peristaltic PumpsThe peristaltic pump is by far the most common pump used for continuous flowmethods of analysis. While this type of pump dominated flow injection systemsworldwide, it was initially thought that it would be unable to provide the necessary flowrate precision required for hydrodynamic injection by SIA. Today, however, theperistaltic pump is commonly used in sequential injection systems too; they are capableof producing the necessary precision if the pump head frequency is reasonablecompared to the aspirated volume [28]. On this system, the minimum pump speedallowed is one-quarter of the maximum speed for the pump, at which the relativestandard deviation of replicate peaks is generally not compromised.Peristaltic pumps require periodic recalibration in order to minimize the effects offlow rate drift due to tube wear; this is especially true if long-term optimization programsare to be run. The software automatically recalibrates the pump after a user-specifiednumber of runs have been made (see the “Priming and Calibration” section later in thischapter). The length of pumping time necessary to achieve a precise calibration wasinvestigated. Table 2-3 shows data from the automated calibration of the peristaltic50pump (at a relatively low flow rate) with the use of 0.76 mm i.d. pump tubing. The pumpwas calibrated by pumping carrier solution (e.g., 1.0 M KCI) through the reaction coil,through a six-position or ten-position valve, and then into a plastic bottle resting on adigital balance (accurate to less than a milligram). The software determines the massof the container on the balance (through an RS-232 interface port) before and afterrunning the pump at a user-specified rate for a user-specified length of time.Correction is made for the specific gravity of the solution used for calibration. In thecase of this calibration experiment, the pump was operated at 50% of full speed, whichcorresponds to sending it a 12-bit digital signal of (50% x 212 - 1) = 2047. Thecalculated minimum flow rate, Q (mL min1) is the projected flow rate at 25% of themaximum pump speed. This lower limit was chosen in order to ensure a relatively highpump head frequency is obtained for the desired flow rate (i.e., less pulsation andgreater precision) and will be discussed in more detail in Chapter 3.51Table 2-3. Peristaltic pump calibration data indicating a lower standard deviation whenlonger calibration times are used..Relative StandardCalibration Rep I Rep 2 Rep 3 Rep 4 Rep 5 Average DeviationTime_(s)DACIQ 2719 2548 2621 2735 2752 2675 3.26%DAC-unitsmL mino,1 30 0.37 0.39 0.38 0.37 0.36 0.37mL miff1Qmax 1.51 1.61 1.56 1.50 1.49 1.53mL miff1DACIQ 2733 2758 2781 2752 2812 2767 1.10%DAC-unitsmL miff160 0.37 0.36 0.36 0.36 0.36 0.36mL rran4Qmax 1.50 1.48 1.47 1.49 1.46 1.48mL miff1DACIQ 2800 2792 2782 2796 2796 2793 0.25%DAC-unitsmL mm4Qmin 120 0.36 0.36 0.36 0.36 0.36 0.36mL miff1Qmax 1.46 1.47 1.47 1.47 1.46 1.47mL miff1DACIQ 2809 2800 2821 2808 2810 2810 0.27%DAC-unitsmL miff’Qmin 300 0.36 0.36 0.36 0.36 0.36 0.36mLmin4Qmax 1.46 1.46 1.45 1.46 1.47 1.46mL miff152The results in Table 2-3 indicate that little improvement in flow rate calibrationprecision is achieved after 120 seconds. Improved relative standard deviation wouldbe expected at lower calibration times for tubing with higher flow rates due to therelative increase in mass difference. For the majority of this work, 120 seconds is thedefault setting for calibration time.2.2.4 DetectorsVirtually any type of detector which outputs an analog signal can be interfaced tothe SIA software provided that a sampling frequency of 10 Hz is sufficient. The softwareis able to acquire input from two analog channels of either 0 to 10 V or -5 to +5 V (setby DIP switches on the acquisition card).For some studies, a simple log-amp photometric detector incorporating a quartzhalogen light source with interference filters and axial geometry flow cell was used andis described elsewhere [24]. The majority of the studies made use of a diode arrayspectrophotometer (HP8452, Hewlett-Packard, Palo Alto, CA, USA) capable of 2 nmresolution from 190 to 820 nm, with a single wavelength acquisition rate of 10 Hz.Simultaneous monitoring of up to six wavelengths on the spectrophotometer ispossible, however, only two wavelengths were transferred to the SIA control computerthrough the DACA interface (see Figure 2-1). All data were acquired by the SIA controlcomputer at 10 Hz.532.3 SEQuENTIAL INJECTION ANALYSIS SoFTwAREIt was realized from the outset that there is an inherent need for moresophisticated software in order to perform sequential injection analysis with any degreeof competence [20]. It was hoped that this would not be a significant deterrent in thedevelopment and widespread acceptance of this technique. The issue of sophisticationadvances further if we desire the software to be able to empirically optimize a givensequential injection procedure. This portion of the project addresses the issue ofsoftware sophistication while making the human-instrument interface easier to use andmore easily understandable than any of its predecessors.2.3.1 Programming Graphical User InterfacesIn the late nineteen eighties and early nineteen nineties a major softwarerevolution occurred for IBM-compatible personal computers (IBM-PC). This transitionfrom DOS-based software to more graphically oriented Windows-based softwareoccurred relatively quickly and with it came the necessary tools to programsophisticated graphical user interfaces. Microsoft Visual Basic and Microsoft VisualC++ or QuickC have been the most popular programming software packages available,While Microsoft Visual Basic (using standard Basic language conventions) is faster andeasier to program [21, 23], the software written in the C-language is lower level, thusmaking the final application ultimately run faster. The Microsoft Visual Basic languagewas chosen in order to speed up application development, and any deficiencies in54operating speed of the finished product can be compensated for by use of high-endcomputer hardware which very recently became inexpensive.In traditional BASIC programming, it is the program which controls execution ofthe subroutines; this is known as procedural programming. In Visual Basic, thesoftware is considered to be event-driven, in that the user decides on the events whichoccur. The software presents a list of choices to the user through a graphicalrepresentation of text-boxes, buttons, graphics, and so-on, and waits for the user input.The user then decides which event is necessary to run now and activates it by eitherkeystrokes or mouse clicks. When an event occurs (such as a mouse click) thesoftware then executes an event procedure, a list of instructions to carry out uponacknowledgment of a specific event. It is for this reason that the user has more controlover the application which leads to greater control over the hardware which isinterfaced to the computer.By moving to an event-driven programming language such as Microsoft VisualBasic, programming of the instrument by the end-user is simplified considerably. Witha Graphical User Interface (GUI), virtual instruments [22] can be created andmanipulated on a computer screen with mouse movements. As well, the operator isable to see the status of the hardware from a concise diagram of it on the computerscreen, and the operator is able to choose and change physical settings on theinstrument simply by pointing to the appropriate pump, valve, detector, or accessory onthe computer screen. This is the most significant step towards simplification of a55complex programming situation, and through this substantial simplification of theinterface, it is hoped that the ultimate user will be able to better focus their attentionand intellect on the chemical analysis method they are trying to develop, rather thanprogramming of the software.2.3.2 Flow Injection Development and Optimization SystemRegardless of how open-ended and flexible a hardware I software system isdesigned to be from the outset, it inevitably has its experimental limitations. Advancedflow injection systems used for laboratory research purposes such as the Flow InjectionDevelopment and Optimization (FIDO) system [10, 18] are no exception. The FIDOsystem consisted of up to nine pumps, four valves, photometric and electrochemicaldetectors, and sophisticated software routines for control. The software (written inMicrosoft QuickBASlC version 4.0) was designed to automatically develop and optimizeFIA methods by either or both of simplex optimization techniques and response-surfacemapping.The FIDO software is a cornerstone to optimization software for flow injectionsystems and is therefore, the starting point for development of the current sequentialinjection software primarily due to the similarity in hardware and interfacing circuitry.Some of the lower level FIDO control routines have been copied and then modified forcurrent use. The objective was to develop a finished software product which removed56the complexity of the programming environment from the user, but allowed extremeflexibility in flow programming for a very wide range of chemical analyses.2.4 GPHlcAL USER INTERFACE (GUI) FOR SIAThe objective of this portion of the project was to create a software environmentwhich overcame many of the limitations of previous flow optimization software and metthe following requirements:• Flexible: the user should be able to instruct the software to perform a varietyof different functions, experiments, optimizations, pertaining to research intoSIA methods development. As such, the software is well suited to a researchand development environment.• Graphical: the set-up of complex methods, and optimization of systemparameters should be simplified with a comprehensive graphical userinterface.• Modular: portions of the code should be able to be added or removedquickly and easily to modify the functionality of the instrument (e.g., addingnew types of pumps or valves).57• Efficient: experiments, manifolds, and optimizations should be easy to modifyor reuse.• Database access: the large amount of data created should be stored in anexpandable, comprehensive database for future reference.2.4.1 Program OverviewThe software programs and files with their respective versions and authors ormanufacturers used for this system are listed in Table 2-4. All of the interface waswritten in Microsoft Visual Basic Professional Version 3.0. A dynamic link library (DLL)file, “VBIO.DLL”, written in-house in Microsoft QuickC for Windows, facilitated input andoutput functions for the IBM DACA boards. Microsoft Visual Basic provides customcontrols that are used to access the database which is administered by MicrosoftAccess. However, a program (available from Microsoft Bulletin Board) called“COMLAYER.EXE” must be run which installs a “Compatibility Layer” between version3.0 of Microsoft Visual Basic and version 2.0 of Microsoft Access. Without thisprogram, Microsoft Visual Basic is only compatible with version 1.1 of Microsoft Access.Microsoft Query is used to search for and transfer data from Microsoft Access toMicrosoft Excel for further processing. Microsoft Excel is used for plotting twodimensional graphs and three-dimensional response-surface maps for visualization ofthe data.58Table 2-4. Software programs or files used to implement sequential injection analysissoftware.Program I File Latest Manufacturer I AuthorVersion UsedMicrosoft Visual Basic for 3.0 Microsoft CorporationWindows, Professional Redmond, WA, USAMicrosoft Access 2.0 Microsoft CorporationRedmond, WA, USAMicrosoft Excel 5.Oa Microsoft CorporationRedmond, WA, USAMicrosoft Query 1.0 Microsoft CorporationRedmond, WA, USACentral Point Icon Editor 2.0 Central Point SoftwareBeaverton, OR, USAVBIO.DLL 1.0 Ivan Brock, Graduate StudentUBC, Vancouver, BC, CanadaCOMLAYER.EXE 1.0 Microsoft CorporationRedmond, WA, USAFigure 2-6 shows an outline of the sequential injection analysis software system.There is a parent Multiple Document Interface (MDI) form (top box in diagram) whichserves as a container for all other forms. The other boxes in the diagram which areconnected with plain lines are the other most significant forms of the system. The lineswith double-headed arrows indicate storage and retrieval of data from the indicatedfiles or tables in the database. Manifold, calibration, bottle content and peak data filesare stored as ASCII text files where the extension “xxx” represents a number from 001to 999. Method and icon files are stored as binary files.The term “form” refers to a window or frame on the computer screen (or display) that iscustomized as the interface of the application. Input boxes, graphics, and pictures are included on aform to give the form a specific functionality.59Manifold j Method I Variables Summary Peripheralj Ediltor L Database FormsManifolds MethodsStored as “*.man” Stored as “*.met” Calibration L. ]Priming andStored as “*.cal”_E 7_CalibrationIcons Icon• .Stored as “*.jco”_fl 1 Viewer“Expermnt.dbf” (Microsoft Access 2 0 Database). Variable Records stored in “Variables” Table Bottle Contents L 7 Bottle. Experimental Run Information stored in Stored as “*.set”_r j Contents“Experimental Summary” Table. Statistical Data (Peak Moments) stored in “Moments” Peak Data I Detectora Stored as “*xxx” 7 DisplayFigure 2-6. Overview of SIA software showing the most significant forms and how thedata are stored and retrieved from disk.2.4.2 Parent Multiple Document InterfaceFigure 2-7 shows the main Multiple Document Interlace (MDI) form. This servesas the outermost shell within which all other forms are contained. The only menu forthe system appears at the top with a buttonbar for all of the primary forms. Any formswhich are active but minimized appear as icons at the bottom of this main form. Scrollcontrols are available for the method step number and the number of replicates can beset. The form can be sized appropriately, as well as minimized to the desktop to allowthe user to perform other functions on the computer such as file management, datamanagement, or report writing while the SIA system is not in use.SIA System ShellParent Multiple Document Interface (MDI) Form60Sequential_Injection_Analysis_____________2.4.3 The Virtual ManifoldThe most significant form of the SIA software system is the “Manifold” form. Inaddition to allowing the user to program all of the devices interfaced to the computer, itshows a real-time graphical status of the entire system. On this form, shown in Figure2-8, the syringe positions and the valve positions change in concert with the actualdevice (as a result of feedback loops at the interface level). Since “a picture is worth athousand words”, the user is better able to visualize the status of the system (e.g., theposition of the pumps, the connections made with the multi-position valves, etc.) from aform of this nature rather than a form full of words and numbers. This is especiallyimportant when the possible combinations of valve positions increases substantially.For example, while a mere 216 combinations of valve positions are possible with theFigure 2-7. Multiple document interface (MDI) parent form which acts as a container forall other forms.61manifold shown in Figure 2-8, the entire system is capable of 2160 unique valveposition combinations. This would be difficult to comprehend if it were not for agraphical user interface of this nature which allows the user to trace out the tubingconnections made by the valves at any given time. As well, the user can change theseconnections and instrumental settings by simply pointing to a new valve position, forinstance, and clicking the mouse. If necessary, this form can be sized to only includeone pump and one valve, or other valve types (e.g., the ten-position valve) can beadded. Tubes, detectors, and accessories can be dropped into place from the iconform to build the virtual instrument on the screen.Figure 2-8. Sequential injection manifold form showing controls for two pumps,graphics for two syringes, two six-position valves, a three-position mini-valve (on top ofleft syringe), a two-position mini-valve (on top of right syringe), and controls foracquisition, delays, and a stir cell.622.4.4 Viewing, Editing, and Using IconsThe icon viewer form presents the “building blocks” of a manifold. The virtualmanifold is constructed from icons placed on a grid. The user can scroll throughdirectories of different tube shapes (elbows, T-pieces, etc.) and accessories beforeselecting the appropriate fitting to be picked up and dropped into place on the manifoldform. If a piece is required that does not yet exist, the user can double-click on asimilar icon (if there is one), which activates an icon editor program (Central Point IconEditor, Central Point Software, Beaverton, OR, USA). The user can then edit theexisting icon (or start with a blank screen) into the desired piece, name the new icon,and save it to disk for future use. The new icon will be displayed in the icon viewerform and can be used in any subsequent virtual manifold.Figure 2-9. Icon viewer form which is used to scroll through various tubes andaccessories which are used to build a virtual manifold on the screen.6324.5 Designing a ManifoldDesigning a manifold is a relatively straight-forward process. However, the usermust decide on the most efficient use of the manifold form for two reasons. First, dueto limitations in system resources inherent to Microsoft Windows, the grid has amaximum size of 17 icons across and 8 icons down (136 in total). Second, at this time,the pump and valve positions are fixed, thus limiting the number of connections oraccessories that can be shown around these devices. Future versions of this softwarewill likely include more flexibility in their positioning.Once the physical hardware on the bench is in place, the user then constructsthe virtual manifold on the screen, keeping in mind the above limitations. Figure 2-10shows an example of a completed manifold used in the determination of phosphate.Labels with arrows have been added for explanation purposes only and do not appearon the manifold normally. Reagent I (R1) is ammonium heptamolybdate, Sample (S) isa phosphate sample, and Reagent 2 (R2) is ascorbic acid. A syringe pump isrepresented by the tall black rectangle which slowly fills with blue as the syringe fillswith solution. The syringe is currently in its fill mode (arrow below syringe box ispointing down), and connected through the three-position mini-valve to the reactioncoil, which is connected to an H2O bottle connected to the six-position valve. In theexample shown, the pump has been instructed to aspirate (draw solution into itself) at 2mL min1 for 30 seconds. This is illustrated by the arrow below the syringe windowwhich is pointing down. The detector is represented by a light source and light sensor,64the waste container is represented by a jerry can, and the sample and reagentcontainers are represented by brown glass bottles.Figure 2-10. A virtual manifold for the determination of phosphate.When bottle icons are dropped onto the manifold, the software prompts the userfor a bottle number which is used to keep track of the bottle contents. On a separateform called bottle contents, the reagent and sample names can be recorded for eachnumbered bottle. Thus, when the user clicks on a bottle on the virtual manifold, thecontents of the bottle are displayed in the title bar.The pump, detector, stir cell, and delay time settings can all be adjusted bymeans of their horizontal scroll bars. The valve positions can be adjusted by clickingon the line that the user would like the valve to move to. For instance, by clicking on65the line to the right of the detector, the virtual manifold will immediately redraw itselfshowing the new connection of the reaction coil connected through to the detector. Atthe same instant, the real valve on the bench moves to the position which connects it tothe detector.Thus, all of the pumps, valves, and accessories which comprise the analyzercan be quickly and easily manipulated from the virtual manifold. Once drawn, themanifold can be recorded to disk as an ASCII “*.man” manifold file for future retrieval.2.4.6 Recording a MethodFor method recording purposes, the method editor form (Figure 2-11) is used.When a given step of the method is set up on the virtual manifold, the numerical valuesfor all of the settings can be transferred onto the method editor form by pushing the“Get” button on the lower right corner. A comment which describes the current step(e.g., “Aspirate reagent one for 10 seconds at 2 mL min’1”) can be recorded in the textbox appearing above the control buttons. If desired, the current method step can nowbe manipulated numerically through this form, instead of graphically through the virtualmanifold.As many steps as necessary can be added to a given method simply by pressingthe “Insert” and “Delete” buttons. The “Get” and “Send” buttons transfer the settingsfrom and to the virtual manifold. The resulting multi-step method can be stepped66through by pressing the up or down step number arrow on the parent MDI form (Figure2-7, top left corner). After the user has ensured that the method will execute as desired(by watching the instrument step through the procedure), the method can be saved todisk for future retrieval as a binary “*.met” method file.. .rnirnnrnnum9ii ‘Pump & I faweOnejv&ve Twotv&VeT&1044’Pump two J‘ 4°!JA2j t/L?J;, t.‘LS’9 3k1i &A*fld10 1 4Ioo Fa 4* v4 0 00 F —__IW —ofas’ - s ,.I!7-’’_ ___ ___i;‘11tiWfl’1i; z4k ;k” /L!J d?cl / :Figure 2-11. Method editor form showing settings for two pumps, two miniaturesolenoid valves (mini-valve one and two), two six-position valves (multi-valve one andtwo), one ten-position valve (multi-valve three), as well as time settings for stirring,acquisition, and delay.A method for the colorimetric determination of phosphate is shown in Figure 2-12 as an example. Each manifold configuration for each of the five steps of the methodare shown in sequence. The user would see only one manifold which wouldautomatically change as the user executed the method. The syringe initially loads alarge volume of distilled water (30.0 seconds at 2.000 mL min1) from the bottleconnected directly to the mini-valve at the end of the syringe (Figure 2-12a). The minivalve is then switched to the reaction coil which is connected to the six-position valve67(Figure 2-12b). The six-position valve is simultaneously connected to the ammoniumheptamolybdate bottle. A small quantity of this solution is aspirated (3.0 seconds at2.000 mL min1), before the six-position valve is switched to the phosphate sample.The same volume of phosphate is aspirated (Figure 2-1 2c), as is the second reagent,ascorbic acid (Figure 2-12d). Finally (Figure 2-12e), the pump direction is reversed(arrow below the syringe), and the six-position valve is connected to the flow-throughdetector. The syringe is operated for a maximum of 60.0 seconds (although it willautomatically stop when empty), and the detector is monitored for the same length oftime. The solution in the reaction coil passes through the detector and into the wastecontainer (Jerry can).In this example, the sinusoidal syringe pump is used, and therefore the flow rateis non-uniform. The 2.000 mL min1 reading on the manifold refers to the flow rateencountered at maximum amplitude. The flow rate decreases at each end of thesyringe stroke but since only 60 degrees of pump rotation are used (versus 180), theflow rate only decreases by Ca. 14% from this value. For this reason, the top scroll barin the pump one frame (indicating volume) is not used. If a linear flow pump was used(i.e., peristaltic) the scroll bar would indicate the volume corresponding to 30.0 secondsat 2.000 mL min1 (i.e., 0.500 mL).68Figure 2-12a-e. A method for the determination of phosphate is shown as anexample.In (a), the syringe draws in water from the bottleto its left for thirty seconds. Then, thesyringe is connected to the reaction coil through the mini-valve and a sequence of (b)ammonium helptamolybdate, (c) phosphatesample, and (d) ascorbic acid aresequentially aspirated for three seconds each into the reaction coil. Finally, in (e), thesix position valve is connected to thedetector channel and the solution is expelledthrough the flow cell to waste while acquiring the detector signal for sixty seconds.692.4.7 Manifold Priming and Pump Calibration•In FIA, the pump(s) generally need to be run uni-directionally for a length of timelong enough to flush any air bubbles out of the manifold. In SIA, however, the primingprocedure is more intricate. To prime a multi-position valve such as the ten-position, orone of the six-position valves, the priming and calibration form is used as shown inFigure 2-13. The valve number (1, 2, or 3) is selected and the user decides whether toeither (i) load on one line and empty on many, or (ii) load many lines and empty on one.The first case would be desirable if the user wanted to take wash or air into the reactioncoil through one line and use it to flush out several other lines when shutting down thesystem. The second case would be desirable if the user wanted to prime severaldifferent lines with several different solutions by loading them each individually into thereaction coil and then expelling them to a waste line.The selection of valve lines to use for loading and emptying can beaccommodated by the form in the following way. The line numbers contained within the“Load” frame on the form allow only one line to be marked at a given time. If the userclicks on line four for example, line one would be deactivated and line four would bemarked for loading. In the “Empty” frame, any number of valve lines can be marked (or“checked”) for emptying on, and the pump will aspirate on the load line and empty oneach empty line sequentially. If the user wishes to perform option (ii) above, clicking onthe “Switch” button, will reverse the load and empty frames allowing loading on manylines and emptying on only one. The volume aspirated in each priming cycle is70determined by the “Prime Time” box which indicates the length of time in seconds thatthe pump should aspirate at the maximum priming speed available (set elsewhere).Multiple priming cycles on the same line can be done (by setting the number ofreplicates) if the line to be primed is long relative to the reaction coil line; this ensuresthat the line being primed is completely flushed with its respective solution without fearof contamination of the pump.Figure 2-13. Priming and calibration form showing controls for specific valve and pumpto prime and calibrate.If a syringe pump is used, then in addition to priming the valve, the entire syringemust be flushed and climatized to the wash solution with all air bubbles removed. Thisis often difficult to do when the syringe is directly connected to a reaction coil that is ofcomparable volume to the syringe itself. It was decided, therefore, to connect the mini-71valves (with two or three exit ports) directly to the end of the syringes for mostapplications. This allows faster priming of wash solution which can be aspirated from ashort line going directly into a wash bottle, thereby bypassing the reaction coilcompletely.The calibration portion of the form is used for calibrating the peristaltic pumps.The calibration speed is chosen at half of full speed ((% x 212) - I = 2047) for at least120 seconds as shown earlier (Table 2-3). The valve line box indicates the line whichis connected to a digital scale such that the pump expels fluid into a container sitting onthe scale platform. The software reads the digital scale to obtain an initial weight, thepump operates for the specified length of time, and the software then calculates theflow rate (at half speed) by mass difference. Different densities in wash solutions canbe accommodated by the value in the specific gravity box. The minimum flow rate boxis calculated based on one-quarter of full pump speed in order to minimize pulsing andto avoid any non-linearities and non-zero intercepts in the pump speed calibrationwhich occur at low frequencies. The user can then specify the number of runs betweencalibrations, as appropriate, in order to adjust for any flow rate drift occurring overextended lengths of operation; this is particularly useful for long-term optimizationswhich are sensitive to flow rate.722.4.8 Summary FormAn example record is shown with the experimental summary form in Figure 2-14.All of the displayed data are stored in an expandable database. The current recordnumber, 7275, is the 68th peak of an optimization. This is the second replicate of anoptimization using the method “Fe_P2_1O.met” combined with variable record number31, in which variable I is 9.6 seconds and variable 2 is 2.4 seconds. The peak data,stored as an ASCII file under the name shown, is displayed in the bottom right windowwhich can toggle as a text comment editor (for the file “Fe_DI .txt”) for the experiment.Figure 2-14. Experimental summary form which displays all of the importantexperimental data for each run.732.4.9 Automated OptimizationAnother objective of this work was to simplify the setup procedure forinvestigation of any of the sequential injection variables for optimization and methoddevelopment. To set up an optimization, the following procedure is used:1. Load or design the manifold and the method to be optimized.2. Scroll to the instruction step of the method which is to be optimized.3. Switch to the method editor form.4. Double-click on the parameter in the current step which is to optimized (e.g.,pump one time, valve two position, etc.)5. The variables form, Figure 2-15, will appear which lists all of the relatedinformation about the parameter to be optimized (top box).6. The user can then enter the boundaries for that parameter in the currentinstruction step.74Figure 2-15. Variable record form showing record number 31 which involves twovariables.The form in Figure 2-15 shows the parameters for a two variable optimization.The two variables shown are the length of time for pump one to operate wheninstruction number one and two (out of three) are executed. In successive runs, duringinstruction number one, pump one will operate for 2.4 to 14.4 seconds in 2.4 secondincrements (six levels total), while during instruction number two, pump one will operatefor 0 to 14.4 seconds in 2.4 second increments (seven levels). This amounts to 42individual experiments to be mapped. This form can expand to the right toaccommodate as many as five variables, or variables can be individually deleted.75Once the variable is set up, it is recorded in the experimental database as arecord (variable record number 31 in the example shown) which can be later retrievedwith either the same method or used on a different method. This eliminatesredundancy in record keeping if the same parameters need to be optimized in severaldifferent methods. A realistic maximum of five variables has been set in order tosimplify programming.After the variables have been defined, the user must set the number ofreplicates of each method to run (on the MDI parent form, Figure 2-7), and switch to theexperimental summary form (Figure 2-14). By pressing “New” on the experimentalsummary form, the system moves to the end of the experimental database and createsa new blank record. The user then optionally enters the common data that will appearin each record, such as number of variables, concentration units, acquisition frequency,data units, operator, C° value, variable record number, and all of the path and fileinformation for recording results. Then, by pressing the “Fill” button, new records arecreated, one for each experimental run, which contain the relevant information forperforming all of the experiments. For example, if variable one had six steps, variabletwo had seven steps, and three replicates of each method were desired, the totalnumber of new records created would be 6 x 7 x 3 = 126. In this way, three replicatesof each of the seven levels of variable two would be recorded for each of the six levelsof variable one. As the records increase, the variable values are incremented, thepeak number is incremented, the replicate number is incremented, and the extension ofthe peak data file name is incremented numerically to match the peak number of the76database (peak number 68 is shown in Figure 2-14). At this point, the database hasbeen primed with the relevant information to run each experiment and record theresults, such as the date, time, peak height, peak area, baseline, time to peakmaximum, peak moments, and the entire peak data file which contains the digitizeddetector response.To run the experimental records, the user must simply point the system to thestarting record number, specify which record to stop on, and request that the systembegin experiments. The system then reads each experimental instruction from thedatabase, performs the method, records the results, and moves on to the next recordmuch like a ticker-tape machine. By taking this organizational approach to recordkeeping, individual runs of an optimization experiment can be re-run at a later time, ifnecessary, to correct problems that are encountered such as air-bubbles or running outof reagent. This was impossible in the previous FIDO software for example, where theentire optimization had to be restarted from the beginning.2.4.10 Data Analysis and RepresentationThere are several efficient Windows-based software programs now available formanipulation of data which are recorded in database format. These highly integratedsoftware packages simplify processing of the data in the native database (e.g.,Microsoft Access Version 2.0) or after transferring to a spreadsheet (eg., MicrosoftExcel Version 5.Oa). Transferring the data to the spreadsheet is done via a “Query”77which can be performed on the database files (using Microsoft Query Version 1.0) inorder to efficiently extract only the necessary data for further numeric processing or forgraphical representation (including three dimensional surfaces). With all of theseintegrated tools commercially available, it was deemed unnecessary to incorporate anyadvanced data analysis or graphical analysis subroutines into the sequential injectionsoftware.2.5 CoNcLusioNsA new design for a sequential injection analysis optimization system has beenproposed and implemented with a Windows-based graphical user interface. Theunique virtual manifold used for system control and programming makes a significantstep towards improved control over these new systems. This development of virtualinstrument control was deemed necessary from the outset due to the complexity ofoptimizing a sequential injection method. As anticipated, the interface has performedwell, and over 10,000 experimental runs have been recorded to date, with no notableproblems.The design and implementation of this hardware I software system is the firststep in the body of this work. The advantages of such a system will now be exploited inthe rest of this thesis. In Chapter 3, the results obtained by using this analysis systemto map out the effects of the most significant parameters affecting dispersion will bediscussed. In Chapter 4, the dispersion profiles described in Chapter 3 will be used to78explore the concept of zone penetration in a sequential injection analysis. The datareported in Chapter 3 will also be used for comparison with the random-walk model forsequential injection analysis proposed in Chapter 5.792.6 REFERENcEs[1] K. F. Stewart, J. F. Brown, and B. M. Golden, Anal. Chim. Acta, 114 (1980), 119.[2] L. T. M. Prop, P. C. Thijssen and L. G. G. Van Dongen, Talanta, 32 (1985), 230.[3] M. A. Koupparis, P. Anagnostopoulou and H. V. Malmstadt, Talanta, 32 (1985),411.[4] W. Wasberg and A. Ivaska, Anal. Chim. Acta, 179 (1986), 433.[5] K. Wolf and P. J. Worsfold, Anal. Proc., 23 (1986), 365.[6] G. D. Clark, G. 0. Christian, J. Ruzicka, G. F. Anderson and J. A. Van Zee, Anal.lnstr., 18(1989), 1.[7] G. 0. Marshall and J. F. Van Staden, Anal. Instr., 20 (1992), 79.[8] A. C. Ariza, P. Linares, M. D. Luque de Castro and M. Valcarcel, J. Auto. Chem.,16(2) (1994), 59.[9] D. Betteridge, T. J. Sly, A. P. Wade and D. G. Porter, Anal. Chem., 58 (1986),2258.[10] P. D. Wentzell, M. J. Hatton, P. M. Shiundu, R. M. Ree, A. P. Wade,D. Betteridge and T. J. Sly, J. Autom. Chem., 11(1989), 227.[11] D. Betteridge, T. J. Sly, A. P. Wade and J. E. W. Tiliman, Anal. Chem., 55(1983), 1292.[12] D. Betteridge, A. P. Wade and A. G. Howard, Talanta, 32(8B) (1985), 709.[13] D. Betteridge, A. P. Wade and A. G. Howard, Talanta, 32(8B) (1985), 723.80[14] P. M. Shiundu, P. 0. Wentzell and A. P. Wade, Talanta, 37 (1990), 329.[15] A. P. Wade, P. M. Shiundu and P. D. Wentzell, Anal. Chim. Acta, 237 (1990),361.[16] P. M. Shiundu, A. P. Wade and S. B. Jonnalagadda, Can. J. Chem., 68 (1990),1750.[17] P. M. Shiundu,and A. P. Wade, Anal. Chem., 63(1991), 692.[18] P. M. Shiundu, Automated Methods Development in Flow Injection Analysis,Ph.D. Thesis, University of British Columbia, 1991.[19] N. G. Sundin, Automated Mapping of Response Surfaces for Continuous FlowMethods of Analysis, M.Sc. Thesis, Daihousie University, 1992.[20] T. Gubeli, G. D. Christian, and J. Ruzicka, Anal. Chem., 63 (1991), 2407.[21] H. R. Keller, P. Fernandes de Aguiar and D. L. Massart, Trends in Anal. Chem.,11(4) (1992), 131.[22] F. J. Sáez de Viteri and D. Diamond, Anal. Proc., 31(1994), 229.[23] F. A. Settle, 0. Y. Pharr, C Lagerhoim, L. Lasida, C. Myers, E. Knick, andR. Williams, Implementation of graphical user interfaces and file structures forintelligent automation using Microsoft Visual Basic, Abstract of paper presentedat the International Symposium on Laboratory Automation and Robotics(October 1993), J. Auto. Chem., 16(1) (1994), 21.[24] C. J. Patton and S. R. Crouch, Anal. Chim. Acta, 179 (1986), 189.[25] P. M. Shiundu and A. P. Wade, J. Autom. Chem., 13(1991), 83.[26] J. Ruzicka, G. D. Marshall and G. D. Christian, Anal. Chem., 62 (1990), 1861.[27] J. Ruzicka, Anal. Chim. Acta, 261 (1992), 3.[28] A. Ivaska and J. Ruzicka, Analyst, 118 (1993), 885.81823. Experimental Design andSystem Characterization“When the only tool you have is a hammer,every problem begins to resemble a nail.”Abraham Maslow3.1 INTRODUCTIONThe first comprehensive set of experimental data produced on the sequentialinjection analysis system that is described in Chapter 2 encompasses an empiricalinvestigation of the instrumental parameters thought to be most influential on peakshape [1-10]. These parameters include the injection volume, flow rate (i.e., linearflow), valve-to-detector distance, and manifold configuration (straight or coiled). Theinfluence of the flow reversal [3-8] is also investigated by considering its effect on peakshape for several reversal lengths (I) and for multiple reversals (n). Typical values ofthe above parameters for sequential injection analysis are investigated with the use ofthe automated optimization routines of the analyzer by injection of a tracer dye. In thisway, the influence of dispersion (without chemical reaction) and the effect of the systemparameters on the peak shape are investigated and stored in a database. Information83from this dataset is used to (i) ensure the analyzer is operating as anticipated,(ii) demonstrate the ability of the analyzer to automatically and independentlyinvestigate several operational parameters, (ii) characterize the system response,(iii) understand the factors influencing peak shape to a greater degree, (iv) optimizezone penetration (Chapter 4), and (v) provide a comparison with peak profilesproduced with the random-walk model (Chapter 5).3.1.1 Peak DescriptorsPeak descriptors can be used to numerically evaluate the differences in peakshape caused by variation of the instrumental parameters. Besides the usual peakshape descriptors of peak height, peak area, and time to maximum peak height,statistical moments can be used to evaluate a digitized peak profile [13-20]. Momentshave been used for peak shape evaluation in non-segmented flow systems on severaloccasions, and have been used to an even greater extent for chromatographic peakshape analysis [13-14]. The zeroth and first statistical moments can be calculated asEquation 3-1 M0= I,:oy,tdtf10(t)y,(t)dtEquation 3-2 M =M084where M0 and M1 are the zeroth and first ordinary moment, respectively, and y1(t) is thevalue of the function at time t. The second and all higher central moments can becalculated once the zeroth and first ordinary moments are known according toCO (t, — M1 )y,(t)dtEquation 3-3 M = 1=0M0, n 2.In general, all odd higher moments characterize peak asymmetry while even highermoments characterize peak broadness. It should be noted that moments higher thanM3 and tv!4 become increasingly sensitive to both noise and inaccuracies indetermination of the peak truncation points.In this work, the summation method [15] is used for determining the statisticalmoments by adding small vertical slices of the peak over the pre-determined integrationlimits according toEquation 3-4 M0 =all It1y,Equation 3-5 M1 = all.’- MJ’y,Equation 3-6 M = all! , n 2M085where At is the data acquisition period (0.1 s in this work), y, is the detector response inthe ith interval, and t1 is the time in seconds of the ith interval. The value of i includesall data points between the beginning and the end of the peak profile. The methodused for calculation of peak start and stop points is discussed below.The derived functions of skew (measure of asymmetry relative to a Gaussiancurve) and excess (measure of “flatness” relative to a Gaussian curve) can becalculated according toEquation 3-7 S =M”2andEquation 3-8 E=—where M2, M3, and M4 are the second, third, and fourth moments respectively. A fullGaussian curve has skew and excess values of 0. For reference, one half of aGaussian curve, bisected vertically, has a skew of 0.995 (Figure 3-1) while that of aright triangle has a value of 0.566 [181. Similarly, one half of a Gaussian curve,bisected horizontally based on equal area (lower half) has an excess of 1.377 whilethat of a square profile has an excess of -1.200.86Figure 3-1. Half Gaussian peak profiles (shaded area) bisected (a) vertically and (b)horizontally.It is imperative that the zeroth and first ordinary moments be calculatedaccurately because of the dependence of the higher moments on these values. Thezeroth and first moments express the peak area and peak centroid respectively. Thesemoments are calculated using the data points which fall within the peak truncationlimits, where the peak starting point is taken as time zero. Others have considered theeffects of peak truncation on moment calculations [18-20], and have stressed theimportance of obtaining reliable integration limits, especially for the higher ordermoments which puts a disproportionately higher weight on data which is furthest fromthe first statistical moment. In a digitized strip of data, peak start and stop points canbe determined either from the change in slope of the data set or from when the signalexceeds some threshold value such as 10%, 1%, or 0.1% of the peak height ormaximum scale reading. In this work, it was found from manual inspection that themost reliable results were obtained from peaks which were considered by using acombination of these two techniques. In other words, the software most accuratelypredicted the start and stop position of the peak profile (in all cases which were visually(b)87examined) by using the following method. The time t, in the dataset was taken as thepeak starting point if it satisfied the following criteria:1. The value t, must occur before peak maximum.2. The slope of the signal calculated by subtracting [(y + y,) /2] from[(yi+i + Yi+2) /2] and dividing by 0.2 s, must be more than 0.7 ADC units persecond. The value y, is the 12-bit analog-to-digital signal at time t,, and 0.7 ADCunits is the standard deviation of the baseline signal for the current system usingthe diode-array spectrophotometer, expressed in analog-to-digital conversionunits.3. The difference between [(yi+i + yi+2) /2] and the average baseline signal (n = 40)must be greater than 0.2% of the full-scale reading.Similarly, the time t1 in the dataset was taken as the peak ending point if it satisfied thefollowing criteria:1. The value t, must occur after peak maximum.2. The slope of the signal calculated by subtracting [(yi + y’) I 2] from[(y,+1 + Yi+2) I 2] and dividing by 0.2 s, must be less than 0.7 ADC units persecond. The value y, is the 12-bit analog-to-digital signal at time t,, and 0.7 ADC88units is the standard deviation for the current system using the diode-arrayspectrophotometer, expressed in analog-to-digital conversion units.3. The difference between [(Yi + y,) /2] and the average baseline signal (n = 40)must be less than 0.1 % of the full-scale reading.In this way, the steeper slope found at the beginning of the peak and the more gradualreturn to baseline at the end of the peak are more readily determined since they areconsidered under asymmetrical conditions. Several hundred peaks created undervarious conditions were manually inspected to ensure the accuracy of the peaktruncation points as calculated by the above criteria. Excellent agreement was found inall cases although the recording of an air bubble passing through the flow cell producesunpredictable results. In addition, each of three replicate peaks created under identicalconditions had computer-determined peak starting points which agreed within ±0.1 s ofthe average value and peak ending points within ±1.0 s.It is expected for this system, that the zeroth moment (peak area) will be stable(i.e., replicate injection volumes should be precise), linearly proportional to injectionvolume (i.e., the zeroth moment is a measure of the number of injected molecules),inversely proportional to flow rate (i.e., the average length of time an individualmolecule spends in the detector and contributes to the peak area decreases as the flowrate increases), and independent of manifold geometry (i.e., the total number ofmolecules passing through the detector is independent of the path traveled to get89there). As well, it is expected that the first moment (peak centroid) will be stable (i.e.,the flow rate will consistantly cause the centroid of the peak to arrive at the detector atthe same time for replicate analyses), linearly proportional to injection volume (i.e., thelength of time necessary for the centroid to arrive at the detector increases with thelength of time necessary to inject the sample), linearly proportional to manifold length(i.e., increasing the manifold length requires that all of the molecules, on average,travel a further distance which takes a greater amount of time), and inverselyproportional to flow rate (i.e., the velocity at which the peak centroid travels from theinjection valve to the detector increases with flow rate and therefore the arrival time isproportionally decreased). Finally, it is expected that the second moment (variance)will increase exponentially with injection volume (i.e., the variance of a disperseddistribution profile increases exponentially as the width of the original distributionprofile is increased), increase proportionally with manifold length (i.e., according to therandom-walk model), and be inversely proportional to the flow rate (i.e., the peak areaand, therefore, the width or variance of a dispersion profile decreases as the flow rateincrease since the molecules are passing through the detection zone at a faster rate).Confirmation of these assumptions will be investigated in this chapter in order tovalidate the utility of statistical moments as peak descriptors for quantifying dispersionprofiles created by sequential injection analysis. This will also aid in quantifying themost significant parameters effecting peak shape created by this system. Thepossibility of using the higher order moments in representations such as skew and90excess for studying the effect of the flow reversal process on the dispersion profile willalso be investigated.3.1.2 Multiple Flow ReversalsThe concept of multiple flow reversals for increasing dispersion withoutincreasing the manifold dimensions has been introduced recently [4-5]. Using a flowinjection manifold and methodology, it has been shown that the degree of dispersion,as measured by the dispersion coefficient, is linearly related to the length of the flowreversal, and by a factor of a square root with respect to the number of reversals [3].This supports the applicability of the random-walk model (originally used by Giddings toexplain the separation process in chromatography [21]) to “flow pulsing” in flowinjection analysis [3]. The model (in its simplest form) is given by the equationEquation 3-9 =orEquation 3-10 = nIwhere I is the length of a given step, n is the number of steps taken, and a is populationstandard deviation, which represents a relative spread or dispersion of the objects. Inchromatography the objects are the molecules being separated, while in flow injectionanalysis the objects are the molecules dispersing within the manifold. Assuming that91the concentration gradient produced during the sequential injection process isnegligible, it is expected that a similar relationship should hold between the variance(M2 or u2) of a peak profile produced by the sequential injection method, the number ofreversals (n) and length of the reversals (I). This will also be investigated in thischapter.3.2 ExPERIMENTAL3.2.1 ReagentsDispersion experiments were done using a carrier stream of 1.0 M KCI. Thenon-reactive dye used to study the dispersion process was 1.5 mMK3Fe(CN)6made upin 1.0 M KCI. All solutions were made up in MilliQ de-ionized water and sonicated forapproximately 5 minutes to remove as much dissolved gases as possible (to reducebubble formation during the reduced-pressure aspiration cycle). Any loss in volumeduring the sonication process was made up with the addition of more water. It wasfound that bubble formation within the manifold (caused by the reduced pressure duringaspiration of solutions) could be eliminated to a large extent by raising all solutioncontainers above the analyzer by ca. 100 cm. The constant head produced in this waywas sufficient to minimize the deleterious effect of air bubbles on the dispersion profile.A maximum absorbance of this dye in the visible range was found at2max = 416 nm. The molecular diffusion coefficient is taken as 7.6 x 10.6 cm2 s [22-23].92The linearity of the detector response within the range of concentrations investigatedon the system was determined by preparing 11 solutions ranging from 0.0 to 1.5 mMK3Fe(CN)6and measuring their absorbance by using the same flow cell as that used forthe dispersion studies. In order to determine the stability of the reagent for long-termunattended optimization experiments, these same solutions (stored in screw-top glassvials) were re-measured after a period of 1, 5, and 12 days.3.2.2 Sequential Injection ManifoldA diagram of the sequential injection manifold employed for the dispersionexperiments is shown in Figure 3-2. The peristaltic pump was used instead of thesyringe pumps in order to obtain linear flow throughout the region of study. All manifoldtubing (except pump tubing) is flexible 0.84 mm internal diameterpolytetrafluoroethylene (PTFE) tubing (Cole Parmer, Chicago, Illinois, P/N 6417-31).The distance from the valve to the pump tubing (Lp) is large enough (200 cm) toprevent any dye solution from reaching the pump tubing during any injection cycle. Thetube which connects the pump to the valve (Lp) is connected to the central connectoron the 10-position valve (by flanging at the valve head). The flow cell is connected tothe valve through one of the ten selectable valve lines (position 4). Tubes connectedat valve position I and 3 (by flanging at the valve head) were 1.0 m long and lead tothe wash solution (1.0 M KCI), while position 2 leads to the dye solution (1.5 mMK3Fe(CN)6). The tubing between the pump and the valve (Lp) and the tubing between93the valve and the detector (LD) was kept as straight as possible or coiled in around a1.0 cm or 6.5 cm cylinder to produce different degrees of secondary flow.A previously reported system [5] employed a larger diameter “holding coil”(50 cm x 1.32 mm i.d. = 684 pL) nearest the pump which is connected to a seconddiameter coil (100 cmx 1.02mm i.d. = 817 pL) nearest the 10-position valve. The tubeconnecting the valve and the detector had yet another dimension (115 cm x 0.5 mm i.d.= 226 pL). Implementation of these three dimensions serves to (I) increase the holdingvolume of the system (so that large volumes can be injected without reaching thepump), (ii) reduce the internal friction during the aspiration cycle (which will reducebubble formation), and (iii) keep tubing as narrow as possible in the most critical areas.Other researchers [7-8] found a deterioration in system precision due to the gasbubbles which form under the reduced pressure when 0.5 mm tubing was used. Theinternal diameter of 0.84 mm for the PTFE tubing used in the current studies is chosenas a compromise between conditions (i) to (iii) above, while satisfying the necessity ofusing the same diameter tube throughout the system for consistency.943.2.3 Flow CellThe standard quartz flow cell (HeIlma, Fisher Scientific, Vancouver, B.C.) usedin all experiments had a 1.0 mm i.d. by 1.0 cm light path, equivalent to 7.85 pL volume.The tube connecting the valve and the detector (L1,) was connected by a flange at thevalve head. The other end of the tube was forcibly inserted into the quartz flow cell allthe way up to the light path where the flow path makes a 90-degree bend, and thensealed in place with epoxy resin. The dimension L of 15, 50 and 100 cm incorporatesthe length of the 0.84 mm PTFE tubing from the light path of the flow cell back to thevalve connection of the tube which connects to the pump (i.e., it includes the dead-volume of the valve head which has an i.d. of Ca. 0.8 mm. A 0.84 mm i.d. PTFE tubeRubber Pump Tubing0.64, 1.30, 1.65mm i.d.0.84 mm i.d.PTFE Tubing10 - PositionValve Head= 200 cmBi-directionalPeristaltic Pump1.0 Molar KCI 7.85 pLFlowCell1.0mm i.d.Light Path1.0cmFigure 3-2. Sequential injection manifold used for dispersion studies (dimensions notto scale).95was also sealed with epoxy in the exiting line of the flow cell and led to a wastecontainer.3.2.4 Peristaltic Pump TubingTwo separate Alitea pumps (either syringe or peristaltic) are controllable by thesoftware system described in Chapter 2. Although the two syringe pumps have theadvantage of pulseless flow, the complications introduced by the sinusoidal flowpattern is undesirable for the current investigation. Thus, peristaltic pumps were usedunder conditions which minimized pulsing (described further in Chapter 5) and a flowrate calibration was performed every 20 injections to correct for drift.Tygon® pump tubing (Cole-Parmer, Chicago, Illinois) was used in all studies.Flow rates of 0.5 and 1.0 mL min1 were achieved by using 0.64 mm i.d. tubing, 1.0 and2.0 mL mm1 by using 1.30 mm i.d. tubing, and 4.0 and 6.0 mL min1 by using 1.65 mmi.d. tubing. The appropriate selection of pump tubing diameter maintained sufficientprecision in most cases for the injection volumes of 40 through 240 pL created by theperistaltic pump. A series of experiments were performed to determine thereproducibility of the injection volume when using the peristaltic pump. The pump wasoperated for the length of time necessary to inject the desired volume at the currentflow rate while the manifold tubing was suspended in a waste container seated on adigital balance. By mass difference, the actual volume of solution moving through the96tube could be determined and the relative standard deviation of the injected volumewas calculated.3.2.5 Experimental Basis SetThe results of the current study are recorded in a comprehensive database(serving as a future reference) and are used for the zone overlap optimization done inChapter 4, and for comparison with the simulated peaks created by the random-walkmodel discussed in Chapter 5. Any cross-section of experimental data can beimmediately “queried” from the database using search filters and displayed graphicallyfor analysis or comparison with other data. This investigation also serves as an initialexercise for the newly developed automated sequential injection analysis systemdescribed in Chapter 2.The experimental parameters investigated in this study are shown in Table 3-1.Three different manifold lengths (LD) were used, and at each length, threeconfigurations were investigated for the two segments of tube L and LD (straight orcoiled at 1.0 cm or 6.5 cm). In all cases, the tubing from the valve to the pump (Lp) was200 cm. This produced 9 (3 x 3) variations altogether. At each of these ninevariations, a variable amount of dye was injected (40 to 240 pL in 40 pL increments)before injecting a variable amount (0 to 240 pL in 40 pL increments) of “spacer” (washsolution of 1.0 M KCI). This created 42 (6 x 7) additional variations which were eachmeasured at six different flow rates (0.5, 1.0, 2.0, 3.0, 4.0, and 6.0 mL min1) producing97252 (6 x 6 x 7) unique experimental conditions. These 252 experimental conditionswere performed at each of the 9 manifold configurations to produce 2,268 (9 x 252)experimental conditions, each performed in triplicate, thereby resulting in6,804 (3 x 2 268) individual experiments to be logged on the analyzer and recorded inthe database.The choice of injection volumes and flow rates results in a dataset which coversthe majority of conceivable operating conditions for an analysis performed by thesequential injection method. The minimum volume of 40 pL was chosen since injectionvolumes of any less than 40 pL were prone to irreproducibility (see Results andDiscussion). At 1.0 mL min1 the volume of 40 pL corresponds to a valve head rotationof 442 degrees, which is slightly more than one revolution. Ivaska also found thatreproducibility in the injection volume diminishes if less than one pump head revolutionis used [9]. Increments of 40 pL for the injected volume and the spacer volumeproduced regular spacing intervals for response surface mapping and data analysis.The flow rates were chosen such that the injection volumes of 40 pL (which are basedon the time for injection) could be achieved by using even multiples of 0.1 s, therebyreducing any round-off errors which might arise otherwise. The upper limit of 240 pLwas chosen because in the extreme case of two 240 pL volumes being stackedsequentially, the maximum linear distance traveled from the valve towards the pumpwould be Ca. 87 cm under plug flow conditions, or 174 cm under laminar flow conditionsfor which the linear axial velocity at the tube center is twice the average linear velocity.This approaches the total length of tubing between the pump and the valve98(Lp = 200 cm). Further increase in this length (to allow larger injection volumes) wouldonly increase the friction and result in a pressure drop within the manifold during theaspiration cycle (thereby enhancing bubble formation).Previous work in this area [5] specified injection volumes in multiples of S2values. The S,2 value for a system is the injection volume necessary to produce adispersed peak profile which has a height equivalent to one-half of C°. This is aconvenient point of reference since all flow systems will have their own unique value ofS% for reference [1]. However, since S varies with manifold dimension, flow rate, andthe flow reversal distance, there would be a much greater variation in injection volumesnecessary in this study if multiples of S,2 were used in each case, in addition toincreasing the complications of cross-comparison within the multi-dimensional datasetcreated. However, data which indicate the S, value at each flow rate and manifolddimension (without a spacer injection) will be shown for reference.The configuration column in Table 3-1 indicates that the two segments of tube,L and LD, were either straight or coiled around a cylinder of 6.5 cm or 1.0 cm diameter.The manifold tubing was kept as straight as possible in the straight tube configuration.In all cases, unavoidable bends in the tubing occur at the injection valve and thedetector (Figure 3-2), and may contribute to secondary flow. Coiled tubes were used toenhance secondary flow and reduce dispersion. Although this does not represent anexhaustive investigation, several combinations of straight and coiled tubes were usedin order to investigate the effect of secondary flow in sequential injection analysis. The99tube L,, is listed as straight in all configurations with a manifold length of 15 cmbecause the tube is too short to coil.Table 3-1. Experimental parameters (each run in triplicate) for the flow rate, samplezone volume, reagent zone volume, manifold length or volume (from valve to detector),and manifold configuration (coiled or straight).Manifold Length / LpI L0 Flow Rate Injection SpacerVolume (LD, VD) Configuration (mL min1) Volume ( pL) Volume ( pL)15.Ocm/ straight/straight 0.5 40 083 pL 6.5 cm I straight 1.0 80 401.0cm/straight 2.0 120 803.0 160 1204.0 200 1606.0 240 20024050.Ocm/ straight/straight 0.5 40 0Experimental 277 pL straight I 1.0 cm 1.0 80 40Parameters 1.0cm / 1.0cm 2.0 120 80(each injection 3.0 160 120done in 4.0 200 160triplicate) 6.0 240 200240100.Ocm/ straight/straight 0.5 40 0554 pL straight / 1.0 cm 1.0 80 401.Ocm/1.Ocm 2.0 120 803.0 160 1204.0 200 1606.0 240 200240Total Numberof 3 3 6 6 7Combinations3.2.6 Analytical ProcedureThe following analytical procedure was used in all cases except in the multipleflow reversal investigation:1001. The 10 - position valve was set to the first position (thus connecting the valve tothe dye supply tube) and 40, 80, 120, 160, 200, or 240 pL of dye was aspiratedat a flow rate of 0.5, 1.0, 2.0, 3.0, 4.0, or 6.0 mL mm1.2. The flow was stopped for 1.0 s as the valve turned to the next position (thusconnecting the valve to a tube containing wash solution, 1.0 M KCI) and 0, 40,80, 120, 160, 200, or 240 pL were aspirated at the same flow rate as that usedin step 1.3. The flow was stopped for 1.0 s as the valve turned to the next position (thusconnecting the valve to the flow cell tube).4. The flow was then reversed and the solution was driven at the same flow ratethrough the flow cell and into the waste container. The flow would continue for apre-determmned length of time which was sufficient to wash all traces of dyesolution from the system. During this time, the signal from the diode-arrayspectrophotometer was acquired (at 416 nm) by the control software andsubsequently stored to disk as an ASCII file.5. In all experiments the flow rate was automatically calibrated with the digitalbalance after every 20 injections using a 120 s calibration period.The following procedure was used in the multiple flow reversal investigation:101The 10 - position valve was set to the first position (thus connecting the valve tothe dye supply tube) and 120 pL (3.6 s) of dye was aspirated at 2.0 mL min1.2. The flow was stopped for 1.0 s while the 10 - position valve was switched to thesecond position to allow 640 pL (19.2 s) of 1.0 M KCI to be aspirated in order tomove the sample plug further into the manifold away from the valve.3. The flow was again stopped for 1.0 s while the valve moved to the detection lineat the next position. The detection line consists of a 50 cm segment of tubecoiled around a 1.0 cm diameter cylinder which connects the valve to thedetector, and a 100 cm segment of straight tube connecting the detector to thewaste container.4. The flow was then restarted in the forward direction (towards the valve) for atotal displacement of either 80, 160, 240 or 320 pL (2.4, 4.8, 7.2, or 9.6 s,respectively). The same carrier solution (1.0 M KCI) was present in thedetection line.5. The flow was then instantaneously changed to the opposite direction (towardsthe pump) until the same volume of fluid was displaced as in step 4. Thisconstitutes one “flow reversal step” (n = 1), which was performed from I to 8times. Note that the total displacement (160, 320, 480 or 640 pL) of one flowreversal step is twice the volume displaced in one direction of the step.1026. After all reversals had taken place, the flow was stopped for 1.0 5, restartedtowards the detector and the resulting peak profile was recorded. The flowtowards the detector was of sufficient volume (6.0 mL) to ensure all traces of thedye were flushed through the detection line to waste, thereby eliminating anycarryover. An injection profile which did not include the flow reversals in steps 4and 5 was also included in the dataset for reference. Reported results are anaverage of three replicates performed for each combination of flow reversallength (I) and number of reversals (n).3.3 RESULTS AND DISCUSSIONAt the present time, no specific dispersion theories have been suggested toexplain the dispersion profile created by the sequential injection process [11]. In thelimited amount of research done in this field, dispersion theories developed for flowinjection systems (assuming a rectangular block input function and unidirectional flow)have been assumed to be valid for use in sequential injection analysis as a firstapproximation [5-7]. Two major differences between these two injection methods(which are likely to influence the dispersion profile) are (i) the asymmetric concentrationgradient created during injection of the sequential injection zone (shown in Chapter 5)and (ii) the influence of the flow reversal where the concentration profile inverts itselfone or more times. However, flow injection theories on their own are still far fromcomplete and are often limited by boundary conditions and an inability to incorporatenon-uniformity in the experimental apparatus [1-2]. The degree of the discrepancies103created by (i) and (ii) above have not yet been quantified and, as such, any attempt torelate the peak profiles created by a sequential injection system to flow injection theoryshould be done with caution. The work of Reijn et a!. [12] who considered the effects oftimed and delta input functions on the flow injection response curve might be a goodstarting point. However, until further work can be done in the theoretical research areaof sequential injection analysis, researchers are limited to describing the characteristicsof the analyzer by empirical experimentation with limited theory for guidance [11].3.3.1 Absorbance of DyeWhen performing long-term optimization experiments using a tracer dye, it isinitially necessary to (i) determine the most suitable wavelength for detection,(ii) ensure that the detector response is linear within the working range, and (iii)ascertain that the absorbance of the dye solution remains stable over long periods oftime. A sufficient volume of 1.5 mM K3Fe(CN)6was pumped through the flow cell (toensure saturation) before stopping the flow and scanning a full UV-visible spectrum(using 1.0 M KCI as a reference solution). Figure 3-3 indicates an acceptablewavelength of maximum absorption at 2max = 416 nm, which was used in all dispersionexperiments. The highest point of this peak should produce the most stable readingand would correspond to C° for the system under study since it represents theabsorbance of the undiluted dye in the flow cell.Figure 3-3. Absorbance spectrum of a 1.5 mM solution ofK3Fe(CN)6made up in 1.0 MKCI. In all dispersion experiments the dye is monitored at Xmax = 416 nm.The linearity of the response at subsequent dilution from the C° value was nextascertained by preparing 11 solutions ranging in concentration from 0.0 to 1.5 mMK3Fe(CN)6 and measuring them in the same way as C°. The absorbance of thesesolutions at 416 nm was also measured after 1, 5, and 12 days. Figure 3-4 shows thelinearity and stability of the dilutions over the 12 day period. Therefore, theabsorbance of the dye solution produces a linear response from the detector andshows no signs of deterioration with time.104=C)C20. o 0 0 0 0 0 0 0 0 0 0 0 0 0 0o • C4 (0 0 (0 C’1 (0 0 (0 C’J (0 0(‘1 C’1 c) c) LO U) (0 (0 (0 F F- (0WaieIength (nm)1051.61.4__1.2ECcol.00.8C0.6< 0.60 0.90 1.20 1.50[K3Fe(C6] (mMolar)Figure 3-4. Absorbance of 11 standard solutions of 0.0 to 1.5 mMK3Fe(CN) Reproducibility of the Injection VolumeThe injection volume is determined by the flow rate and the length of time thepump is operated. Therefore, the uncertainty in the injection volume is a function of theuncertainty in the starting and stopping position of the rotating pump head [9]. Thisamount of error is negligible in comparison to the variable positioning of the 8 rollerslocated around the pump head. Discrete elements of fluid are pinched between therollers as the pump head rotates, and the volume of one of these elements can becalculated if the pump head frequency is known. For example, for a 40 pL injectionvolume dispensed at a flow rate of 1.0 mL min1 by a pump which has been calibratedusing 0.64 mm i.d. pump tubing, the total rotation of the pump head is 442 degrees. AtAge ofSolution(days)00Alci 120.30Absorbance = 1000 [K3Fe(C6] - 0.005R2= 0.999710645 degrees per roller, this corresponds to 9.82 rollers, each delivering 4.07 pL of fluidon average. The volume of this element of fluid varies with the diameter of the pumptubing, and therefore larger diameter tubing should be avoided since it will generallyhave a larger volume of fluid moved by each roller. Larger diameter tubes cannot beruled out, however, since they are required to effect higher flow rates due to the upperlimit of the rotational frequency of the pump. Because it is difficult to ensure that theroller heads line up from one injection to the next, a small amount of uncertainty wouldbe expected in the actual injected volume (as measured by mass difference), andfurther, the discrepancy in volume would be expected to exhibit periodicity over severalinjections. Figure 3-5 shows the relative standard deviation (RSD) of 5 replicateinjections of 40, 80, and 120 pL at 6 different flow rates. In general, the RSDdecreases with increasing injection volume, although the average magnitude of thestandard deviation for the entire dataset ranged from a low of 0.18 pL to a high of1.30 pL and an average of 0.87 pL. It is clear that, for the pump currently being used,injection volumes of less than 40 pL would have too much relative uncertainty toproduce reliable results. However, since the uncertainty at 40 pL is a little suspect, anaverage of triplicate measurements is made in almost all data presented in this work,thereby reducing the systematic noise of the dataset.1074. 3-5. Relative standard deviation of 40, 80, and 120 pL injection volume (n = 5)as function of flow rate.As previously described, the periodicity of the fluid movement due to thealignment of the pump head rollers was investigated by connecting the pump, throughthe valve, to a digital balance and recording the amount of fluid moved by massdifference. In Figure 3-6 and Figure 3-7 the periodicity of the actual injection volume isshown for the movement of 40 and 120 pL of fluid, respectively. The 40 pL injectionappears to repeat itself after 6 injections while the 120 pL injection repeats after only 3.This is attributed to the alignment of the roller head on sequential injections. Allinjections were performed immediately one after another and no other pump headmovement occurred between each 40 or 120 pL movement. We can conclude that thepump head does indeed affect the reproducibility of the injection volume, andfurthermore, that this reproducibility is periodic, It is interesting to note that if—.-- 40 pL—.— 80 iii.—A—l2OpL1 2 3 4 5 6Flow Rate (mL nin1)-J#1)E0>0a)108reproducible alignment of the peristaltic pump rollers on subsequent injections could beachieved, then the reproducibility of the injection volume could be improved (i.e.,compare every sixth injection in Figure 3-6 starting at injection number 2). It should benoted that when subsequent sequential injection operations are performed, additionalrandomization in the pump position will occur at each step, such that the overalprecision of the analysis is likely to be better than the series of subsequent injectionsas shown here. As well, the irreproducibility of injection volume will not result in anirreproducibility of equal magnitude in the detector response to product concentration,especially if the product is formed at the interface of two adjacent zones of high volume.41.541.040.540.039.539.038.50Figure 3-6. Injection volume as measured by mass difference for a 40 pL injection at1.0 mL mm1.5 10 15 20 25Injection Number109123122-J121E120.‘ 119118117 -0Injection NumberFigure 3-7. Injection volume as measured by mass difference for a 120 pL injection at1.0 mL mm1.3.3.3 Calculation of S. ValueAs the injected volume of dye is increased, its height asymptotically approachesthe value of C° as shown in Figure 3-8. The injection volume necessary to reachC/C0 = 1/2 or D = 2 is referred to as S. It is generally assumed that for flow injectionpeaks the increase in peak height below S,2 is approximately linear [1, 5]. The value ofS,4 is a function of the dimension and geometry of the flow channel [1]. Because of theasymptotic increase above S,4, it is generally believed that any increase in injectionvolume beyond S,4 is done at the expense of sample consumption and decrease inthroughput, with minimal improvement in sensitivity but some improvement in precision.5 10 15110This assumes that this same relation holds true for the sequential injection technique[5, 8]. A discrepancy exists for SIA, however, in that although the volume from theinjection valve to the detector is constant, by increasing the sample volume (Vs), theaverage distance traveled by the sample zone into the flow channel towards the pumpis increased, thereby increasing the overall effective manifold volume. Moreimportantly, the concentration gradient of the injected sample zone cannot beconsidered to be a rectangular block input function as will be demonstrated using therandom-walk model in Chapter 5. However, these simplifying assumptions do notcause too much concern in calculation of S,, which can still be determined in the usualway.0C)C) 3-8. Peak profile as a function of injection volume at 2.0 mL min1 and 15 cmvalve-to-detector distance; profiles from injections of 40, 80, 120, 160, 200, and 240 pLare shown (smallest to largest, respectively).0 5 10 15 20 25 30Time (s)111For reference, the values of peak height (Cm I C°) for the experimentalconditions under consideration are shown in Figure 3-9. For each plot, the value of S2can be found by finding the injection volume which produces a response (peak height)of 0.5. These data demonstrate the dependence of S,2 on the reactor volume(governed by the length of the tube from the valve to the detector), flow rate, andmanifold configuration. In general, the trend is similar for straight and coiledconfigurations at each manifold length. As expected, manifolds with the shortest valveto-detector distance, LD, approach the maximum peak height at the lowest injectionvolumes and therefore have the lowest S-2 values.112Flow Rate(lit nin1)• 0.5•1.0• 6.0Flow Rate(nit nin’).0.511.0• 2.0• 3.0*4.0A 6.0Flow Rate(ntnin)•0.5• Rate(ntnin1)• 6.0Figure 3-9. Effect of flow rate, valve-to-detector (LD) distance, and manifold geometryon maximum peak height as a function of injection volume.(a) 15cm! Straight1.0 —(b) 15 cm! Coiled1.0 —A‘6fO.50.0Flow Rate(nt nin)•0.5• 1.0• 2.0• 3.004.0A 6.0‘600.50.0Flow Rate(ntnn1)•*4.0A 6.0-7A0 40 80 120 160 200 240Injection Volume (ji)(c) 50cm! Straight1.00 40 80 120 160 200 240Injection Volume (pL)(d) 50cm/Coiled1.0— —- —‘6C)0.01.0—-/0 40 80 120 160 200 240Injection Volume (IL)(e) 100 cm!Straight77,,0 40 80 120 160 200 240Injection Volume (pL)‘6C)j3‘6C)0.5I0.0(0 100cm/Coiled‘600)0II..— —-—0 40 80 120 160 200 240 0 40 80 120 160 200 240Injection Volume (ji) Injection Volume (p1)113According to flow injection theory, a plot of - log(1 - crnax, C°) versus injectionvolume should produce a linear response. This has been shown to hold true for thesequential injection technique [5] although the results of the current work show that thisrelationship breaks down at higher flow rates (Figure 3-10). As the flow rate isincreased, it becomes increasingly difficult to achieve a response with a peak height ofone-half C°. This should be borne in mind when optimizing injection volumes whenworking at higher flow rates.0.60.5o 0.4E00.30.100 50 100 150 200 250 0 50 100 150 200 250Injection Volume (pL) Injection Volume (pL)Figure 3-10. The effect of the injection volume on the peak height for the 100 cm coiledmanifold.3.3.4 Zeroth MomentAs predicted by theory, and shown in Figure 3-11, the zeroth moment (peakarea) is independent of the manifold geometry, linearly proportional to injection volume,and inversely proportional to the flow rate. The linearity and stability of these results isimportant since all of the higher order moments use the zeroth moment for114normalization. As well, inspection of the precision of the data indicates that the peaktruncation method employed produces consistent results. The units for the zérothmoment (peak area) are (analog-to-digital-conversion-units x seconds) expressed asADC’s.1 1200000(a) 15cm/Straight FbwF (b) 15cm/Coiledl00 (nt ryin).0.5•O.5A1.0 8 8ooo A 1.0• 2.0•2.0•ao 600000 • 3.0/ Fl(ntnjr1) 10000000 040 ° *4.06.0A6.0 400000400000 2NN 200000 40 80 120 160 200 240 280 0 40 80 120 160 200 240 280Irjection Volume (IlL) Injection Volume (pL)1200000_(c) 100cm / Straight Fbwte (c 100cm/Coiled1000000 (nt nirf1). 88000008 8oo A 1.0SS.2.0.3 600000 • 3.0/ Flte600000 (ntnjrf1) 10000000 *4 04.06.0400000400000 2aN000I.,00 40 80 120 160 200 240 280 0 40 80 120 160 200 240 280Injection Volume (p1) Injection Volume (p1)Figure 3-11. Effect of flow rate on the zeroth moment (peak area) as a function ofinjection volume for different manifold geometries.1153.3.5 First MomentAs expected, the first moment, which signifies the peak centroid or center ofmass, is linearly dependent on injection volume, inversely proportional to flow rate, anddependent on manifold geometry (Figure 3-12). The linearity and stability of this valueis also significant since all higher order moments are calculated relative to this value.Straight tubes produce peaks which have a higher first moment due to the decrease inradial mixing which causes more molecules to lag behind along the walls of the tube.Hence, similar to flow injection analysis, throughput can be increased by increasingradial mixing. This will have to be balanced, however, with the need for greaterdispersion that promotes penetration of adjacent zones (see Chapter 4). It should alsobe noted that choosing a flow rate of less than 2.0 mL min1 with the manifolddimensions shown here increases the first moment substantially, as does increasingthe manifold length.11660 60(a) 15 cml Straight FIte (b) 15cm / Coiled50 (ntnin) 5° (ntnin)4o •O.5 •O.5A1.0 A1.O•2.0 .2.0030 o30: zzZZE [0 40 80 120 160 200 240 280 0 40 80 120 160 200 240 280Irection Vokzne (pL) Injeclion Volume (IlL)60 60(c) 100 cm! Straight Fte (c 100cm / Coiled Fbw te50 (rniri) 5° (yJjpl)40 •0.5 ;4Q •0.53Oo 2010 1:0 40 80 120 160 200 240 280 0 40 80 120 160 200 240 280lrqection Voknie (ii) Injection Volume (p1.)Figure 3-12. Effect of flow rate on the first moment (peak centroid) as a function ofinjection volume for different manifold geometries.3.3.6 Second MomentThe second moment (variance) of the peak profile is expected to be inverselyrelated to the flow rate, exponentially related to injection volume, and dependent onmanifold geometry. Figure 3-13 shows the second moment plotted on a logarithmicscale against injection volume at all six flow rates. These data indicate that the secondmoment does increase with increasing injection volume and decreasing flow rate. This117is to be expected since larger injection volumes will have an increased peak width andreduction of the flow rate increases the length of time the injected zone takes to passthrough the detector. Increasing the manifold length increases the second moment andreduces the influence of injection volume, since the ratio of sample volume to manifoldvolume is decreased. At both manifold lengths, coiling reduces the second moment byincreasing the degree of radial mixing relative to axial dispersion. This is also inagreement with current flow injection theory.icxo woo(a) 15cm/Straight (b) 15cm/CoiledFlow lte Flow lte(ntnrf’) (ntnir),4100—4—0.5-4—0.5 ,100_—A—- 1.0—A--1.O 8a)a)8______________________________________ _ _ _ _ _—‘—2.0_ _ _ _ _—‘—2.010—.— 3.0—e--- 4.0-‘ 6.0 -‘ 6.0—ê---4.00 I I I I _0 I I I I I I0 40 80 120 160 200 240 280 0 40 80 120 160 200 240 280InjecUon Vohiiie (p1..) lnjeclion Volume (pL)1000 1000Flow Ite Flow Fte(ni rrh) (ni j,t)100 ___— i—--—. — 100 A-1—4—0.5 , —4—0.5—A—1.0A I• 2.0a)E A A A—.— 2 10______3 0—O- —‘---3.0CQ —4—4 A- .. . AA A—4-4.0-4-6____ _ _____________-4—6.0(c) 100cm/Straight (cO lOOcmICoiled0 I I I I I I 0 I I I I I I0 40 80 120 160 200 240 280 0 40 80 120 160 200 240 280Injection Volume (IL) lrecUon Volume (p1)Figure 3-13. Effect of flow rate on the second moment (peak variance) as a function ofinjection volume for different manifold geometries.1183.3.7 SkewSkew is a measure of the degree of peak asymmetry. It is useful to quantify thisfor sequential injection peaks since a greater degree of peak asymmetry is anticipateddue to the asymmetrical concentration gradient of the initial injection plug. The data inFigure 3-14 indicate that the peak profiles range in skew from almost symmetrical at0.5 mL min1 with a long coiled manifold, to highly skewed peaks created at 4.0 to6.0 mL min1 with a short straight manifold. The degree of skew appears to beindependent of injection volume except in the case of the 15 cm coiled manifold whereskew decreases with increasing injection volume. Since the distance between thevalve and the detector is so short in this case, the data indicate that the concentrationdistribution found at the detector is influenced to a large degree by the mixing occurringduring the injection process. Thus, an increase in radial mixing relative to axial mixinghas the overall effect of reducing peak skew. The skew is also reduced when thedistance between the valve and the detector is increased, in agreement with the tanksin-series model, which asserts that the peak symmetry approaches a Gaussiandistribution as the number of mixing stages (tanks) increases [1].1193.0 “U(a) 15cm! Straight Flow lte (b) 15cm / Coiled flow te2.5 (ntnin) 2.5 (n1nih•)—1—0.52.0 2.0—A-- 1.0 —A—1.0—‘—2.0 ——- 2.01.5—1—3.0 —1—3.00—0—4.01.0••—.——-—.-———.—---.--—• -1-4.0 1.0—1-6.00.5 0.50.0 I I I I 0.0 I I I I I0 40 80 120 160 200 240 280 0 40 80 120 160 260 240 280Injection Volume (ii) Injection Volume (p1.)3.0 3.0(c) 100cm/Straight (c 100cm/Coiled2.5 (ntnirf’) 2.5 (ntnirf1)—‘—0.5 —1-0.52.0 2.0—A—I —A-- 1.0—‘—2. 1.5 —‘—2.01 1.5.1-3 1- 3.00—0-4 —0—4.01.0 1.0-1-6____________—1-6.0, ..——•-----. I__ __ __ ______0.5 0.5__0.0 I I I I I tI.l I I0 40 80 120 160 200 240 280 0 40 80 120 160 200 240 280Injection Volume (ii) Injection Volume (p1.)Figure 3-14. Effect of injection volume and flow rate on skew of peak profile at differentmanifold geometries.3.3.8 ExcessThe degree of excess is a measure of the “flatness” of a peak profile relative to aGaussian distribution which has an excess of 0. Taller, more peaked profiles will havea negative value for excess while flatter more dispersed profiles will have a positivevalue. The degree of excess follows a trend very similar to skew under all conditions(Figure 3-15). Decreasing the flow rate or increasing the manifold length are both120effective ways of decreasing the excess since both conditions allow more time for radialmixing, thereby creating taller, more “peaked” profiles. In addition, the degree of radialmixing caused by coiled tubes also reduces the excess at both manifold lengths (Figure3-15b and d). It is noteworthy that relatively consistent near-zero values for excess areachieved in the case of the 100 cm coiled manifold, which implies that the distributionprofile has achieved a Gaussian shape and reached a degree of dispersion which isrelatively uninfluenced by flow rate.8.0 8.0(a) 15cm/Straight F (b) 15 cmi Coded Fbw te6.0 (nin1) 6.0 (ntnirf1)4.0 4.0::—--6.0—a--6.0-2.0-2.0I I I—4.0 I I I I I04080120160200240280 04080120160200240280Iredon Vokaiie (IL) Ireclion Vo&ane (IL)o.u ov(c) 100cm/Sfrai ( 100cm/Coded6.0 (ntnin) 6.0 (ntnin1)4.0 4.02—.— 2.02.0___2.0—.— 3.00.0 .*EEE*z4 0.0 i i-2.0 -2.0—.4.0 I I I I .4.0 I I0 4080120160200240280 04080120160200240280IrecfloqiVoaiiie(IL) Injection Volume(IL)Figure 3-15. Effect of injection volume and flow rate on excess of peak profile atdifferent manifold geometries.121It is clear from the foregoing survey of peak descriptors calculated on thesequential injection peak profiles created by the analyzer, that a comprehensive rangeof peak shapes has been created. In all of the above cases, only the dispersionprofiles resulting from the injection of a given sample volume without further flowreversal have been considered. With such a system, however, it is of course possible(and usually necessary for reagent-based analyses) to change the injection valve toanother position and continue to reverse the flow while a second zone is injected. Insuch a situation, the first zone undergoes further dispersion since it must travel fartherinto the manifold towards the pump before the flow is reversed towards the detector.This creates even greater diversity in the dispersion profile since the distance traveledby the first zone towards the pump before reversing introduces yet another variable.Still greater variability can be achieved by reversing the direction of flow several timesat variable amplitudes. Multiple flow reversals will be discussed in the next section.3.3.9 Multiple Flow ReversalsAt the outset, it was important to design and implement a sequential injectionsystem that would be able to map out the effects of several variables of different typeswith equivalent dexterity. Indeed, this has been achieved with the sequential injectionsystem described in Chapter 2 which, unlike its predecessor FIDO, can investigateparameters such as delay time, valve position, volume of fluid moved, pump speed,stop-flow time, number of flow reversals, and amplitude of flow reversals. Although the122investigation of each of these parameters provides insight into the optimal operatingconditions of such an analyzer, it is the last two which are demonstrated now becauseof their significance in the original conception of the sequential injection technique [4,5, 7].The effect of one or more flow reversals was investigated for the injection of120 pL of dye using a flow rate of 2.0 mL min1. For the system under consideration,120 pL of dye produced a peak height which ranged from a maximum detectorresponse of C” I C° = 0.184 (with zero flow reversal steps) to a minimum ofcrnax I C° = 0.132 (with eight flow reversals steps). The two parameters investigatedwere (i) the step length of a flow reversal (I) and (ii) the number of flow reversals (n).The step length of a flow reversal (I) is normalized by subtracting the variance of thepeak profile created with one flow reversal. Figure 3-16 shows that a linearrelationship exists between the change in peak variance relative to that for one flowreversal b4a 2) and the number of flow reversals (n). This is in agreement with thebasic premise of the random-walk model given in Equation 3-9. A linear relationbetween the change in the square root of the variance relative to one reversal length(tsa) and the flow reversal length (I) given in Equation 3-10 is also shown to hold inFigure 3-17. This is in agreement with results by Marshall [3] who found a linearrelationship by performing a similar experiment using a flow injection system (squareplug injection), where peak height was used as a relative measure of dispersion insteadof peak variance. Hence, the general relation u2 n12 is shown to hold for theReversalLength(Normalized).1.2A3.4Figure 3-16. Effect of the number of flow reversals (n) and the flow reversal length (I)on the variance of a 120 liL injection at 2.0 mL min1.123sequential injection technique, and forms the basis of the applicability of the random-walk model for simulation purposes as will be discussed in Chapter 5.7060504030201000 2 4 6 8Number of Reversals124Number ofReersaIs•n=2•n=4Afl6•n8Figure 3-17. Effect of the reversal length (normalized) on the square root of thevariance for 2 through 8 reversals.The implications of the above agreement are significant for sequential injectionanalysis in that it is the length of the flow reversal which is critical in determining thedegree of variance (dispersion) of the peak profile. That is, increasing the length of areversal step is far more effective than increasing the number of reversals between twosequentially stacked zones in the sequential injection system. It must be kept in mind,however, that increasing the flow reversal step length necessitates a longer distancebetween the pump and the valve which can have negative effects on the systemvolume and the measurement precision due to increased pressures.86200 1 2 3 4 5Reversal Length (Normalized)125In addition to the second moment, the skew and excess of the peak profiles wereconsidered under conditions of multiple flow reversals. The skew of the peak profilewould be expected to approach 0 (a symmetrical true Gaussian) in comparison to theprevious results shown due to the increased manifold dimensions. The peak skew inall cases was reduced to 0.5. There is no discernible trend in the data caused bydifferent reversal lengths since the variation in skew at this level is within the noiselevel of the measurement. The peak excess shown in Figure 3-18, however, doesindicate a general increase for longer reversal lengths and at greater numbers ofreversals. As well, one reversal length of 160 IL (2 x 80 pL) actually has the effect ofreducing the excess slightly, thereby creating a narrower profile than one withoutreversal. This effect decreases as the ratio of the reversal length relative to the zonelength increases (i.e., at higher reversal lengths).126U,U,0C.)xLU0. of ReersaIsRersaILength(Normalized).1A2.3.4Figure 3-18. Effect of the number of reversals and the reversal length on peak excess.3.4 CoNcLusioNsSeveral conclusions can be drawn from this work which describes acomprehensive dataset of sequential injection dispersion profiles created on theanalyzer described in Chapter 2. The K3Fe(CN)6 solution used for all experiments islinear within this experimental working range and stable for at least 12 days. Thereproducibility of the injection volume is periodic and dependent on the alignment of thepump roller head. In general, the injection volume delivered by the peristaltic pump iswithin Ca. 2.0 pL of the target value. For this reason, smaller injection volumes than40 pL were not included in the dataset, and all injections were performed in triplicate0 2 4 6 8127thereby allowing averaging of the results. The value of S,4 is shown to be dependenton system flow rate and manifold geometry. As well, the linear relationship between- log(1 - crnax I C°) and injection volume is shown to break down at higher flow rates forthe sequential injection method.The usefulness of peak moments as descriptors for sequential injection peakprofiles is considered for the first time. The peak moments are shown to be an effectivemeans of discriminating between various peak shapes for the sequential injectionmethod. The trends in the moment calculations are as anticipated and the stability ofthese descriptors is only compromised in the third and fourth moments at higher flowrates, as evidenced by noise in the skew and excess data. These descriptors shouldfind much greater use in peak shape analysis of sequential injection peak profiles dueto the increased variability of peak shape produced by this new technique.Finally, an investigation of the influence of multiple flow reversals indicatesagreement between sequential injection analysis and the random-walk model. Thissignifies that the model can be used at the molecular level to predict dispersion profilescreated by the sequential injection technique (assuming a one-phase liquid withhomogeneous flow), and will be discussed further in Chapter 5.1283.5 REFERENcEs[1] J. Ruzicka and E. H. Hansen, Flow Iniection Analysis, Second Edition, 1988,John Wiley & Sons, Toronto, Canada.[2] M. Valcarcel and M. D. Luque de Castro, Flow-Iniection Analysis, Principles andApplications, 1987, John Wiley & Sons, Toronto, Canada.[3] G. Marshall, Ph.D. Thesis, University of Pretoria, South Africa, 1994.[4] J. Ruzicka and G. D. Marshall, Anal. Chim. Acta, 237 (1990), 329.[5] T. Gubeli, G. D. Christian and J. Ruzicka, Anal. Chem., 63 (1991), 2407.[6] J. Ruzicka and T. Gubeli, Anal. Chem., 63(1991), 1680.[7] J. Ruzicka, G. D. Marshall, and G. D. Christian, Anal. Chem., 62 (1990), 1861.[8] G. D. Marshall and J. F. van Staden, Process Control and Quality, 3 (1992), 251.[9] A. Ivaska and J. Ruzicka, Analyst, 118 (1993), 885.[10] G. D. Christian and J. Ruzicka, Anal. Chim. Acta., 261 (1992), 11.[11] J. Ruzicka, Anal. Chim. Acta, 261 (1992), 3.[12] J. M. Reijn, W. E. van der Linden and H. Poppe, Anal. Chim. Acta, 114 (1980),105.[13] 0. Grubner, Anal. Chem., 43(14) (1971), 1934.[14] J. P. Foley and J. G. Dorsey, Anal. Chem., 55 (1983), 730.129[15] B. F. Johnson, R. E. Mahck and J. G. Dorsey, Talanta, 39(1) (1992), 35.[16] J. P. Foley and J. G. Dorsey, J. of Chrom. Science, 22 (1984), 40.[17] M. S. Jeansonne and J. P. Foley, J. of Chrom. Science, 29(1991), 258.[18] E. Grushka, M. N. Myers, P. D. Schettler, and J. C. Giddings, Anal. Chem.,41(7) (1969), 889.[19] S. N. Chester and S. P. Cram, Anal. Chem., 43(14) (1971), 1922.[20] K. R. Harris, J. of Soin. Chem., 20(6) (1991), 595.[21] J.C. Giddings, Dynamics of Chromatography, Part 1, Principles and Theory,Dekker, New York, 1965.[22] P. D. Wentzell, M. R. Bowdridge, E. L. Taylor and C. MacDonald, Anal. Chim.Acta, 278 (1993), 293.[23] M. van Stackelberg, M. Pilgram, and V. Toome, Zeitschrift für Electrochemie,57(5) (1953), 342.1304. Optimization of Zone Overlap inSequential Injection Analysis“It is not always easy even for scientiststo tell whether their theories are made validbecause they accord with reality,or because they accord with other scientistsand funding agencies.”Benjamin Woolley4.1 INTRODUCTIONIn order to perform most reagent-based assays, the sequential injectiontechnique relies on the simultaneous merging of two or more zones of sample orreagent(s) stacked in the manifold tubing. Therefore, the study of the mutualpenetration of two adjacent zones should form the focus of fundamental research in thisfield. Only by understanding the factors which influence this zone penetration undertypical sequential injection conditions, can we have any hope of adequately optimizingthe sequential injection process. Obviously, the ability to optimize a process byunderstanding it, has its advantages over an empirical optimization or a “black box”approach. However, there will undoubtedly be a limit to our understanding when basic131assumptions, physical laws, and formulae will no longer be able to explain the complexbehaviour that real sequential injection systems exhibit; all too often, there exists toomany interacting variables and non-uniformities in the system to be adequatelyaddressed simultaneously. When this limit is reached, chemometric techniques suchas simplex optimization will likely be employed in an attempt to “blindly” search foroptimal operating conditions which produce the most desired output from the analyzer.Since the sequential injection technique is such a new method of analysis, abetter fundamental understanding of the underlying factors affecting mutual penetrationof the sample and reagent zones needs to be pursued at this time. Very little work hasbeen done in this field so far [3-9]. Previously, theoreticians working in the field of flowinjection analysis have usually concerned themselves with studying the dispersion ofan entire injected sample volume (which was habitually defined by the physicalgeometry of the manifold) under a continuous, unidirectional flow regime [1-2]. Suchconvenient computer control over the volume of the injected zone(s) was rarelyconsidered before the introduction of sequential injection analysis, and was thereforenot normally within the scope of a theoretical study; neither was the concept ofintermittent pump movement during sample or reagent introduction, especially inconjunction with the flow reversal process. The introduction of these new factors on theanalytical process results in a severe increase in the complication of our understandingof the resultant dispersion profile. All of these new factors (variable injection volumes,intermittent pump movement, and flow reversal) need to be addressed in order to cometo a satisfactory explanation of the system output.132The first paper considered to be a fundamental investigation of the mergingprocess which occurs in sequential injection analysis was written by Gubeli et al. andappeared in Analytical Chemistry in 1991 [3]. They introduced the concept of zoneoverlap as the key parameter which must be controlled in order to produce ameaningful readout for reagent based chemistries. Chemical reactions can only occurwithin elements of fluid in the region of zone overlap between mutually dispersedsample and reagent zones. It is the relative concentration of the sample and reagentwithin this zone (and reaction time) which determine the extent of the chemical reactionand, therefore, the characteristics of the product concentration profile. Gubeli et a!. [3],investigated the concept of zone overlap by overlaying peak profiles created byseparate injection of sample and reagent volumes as shown in Figure 4-1. Note thatthe reagent zone appears first since it is closest to the detector upon flow reversal, andthat the sample zone is more dispersed since it has travelled a further distance than thereagent zone. The isodispersion point (ID) represents the point of mutual zonepenetration. It is generally understood that the most efficient method of penetrating thesample zone with reagent is by aspirating the sample zone first and then the reagentzone. If necessary, the reader can replace any reference to the “sample” and “reagent”zone in this work with the “first-loaded” and “second-loaded” zone, respectively.0.2133Figure 4-1. Overlap of sample and reagent zones are shown by overlaying profileswhich were created on separate injections (each 240 pL).Gubeli et aL [3] used a zone penetration parameter, P, to facilitate comparison ofprofiles produced with different injection volumes of sample and reagent, which wasdefined asEquation 4-1 = 2W0W3 + W,where W0 is the baseline width of the sample and reagent peak overlap, W is thebaseline width of the sample zone, and WR is the baseline width of the reagent peakt.This interpretation assumes a misprint in the original publication (Analytical Chemistry, 63(1991), page 2408, Equation 1) which defines P as P= 2W0 (Ws + WR). In order to obtain a range of[0, 1] for P as the text states, a division sign must be placed after W0. parameter relies on the peak width at the baseline intersection of tangents drawnat the peak inflection points to determine the degree of zone penetration (Figure 4-1).A value of 0 would be expected for no overlap while a value of I would be expected forcomplete (time-domain) overlap. Marshall and van Staden [9] used the overlappingpeak area instead of width for calculating the degree of zone penetration, P. Thisparameter, however, does not discriminate between the sample and reagent zones foroptimization purposes and does not take into account the sensitivity of the analysis.For example, it would be expected that a value of P = 1 (indicating complete overlap) ismore likely to be obtained at (i) lower injection volumes and (ii) greater axial dispersion.Both of these conditions reduce the radial concentration of sample and reagent in thetube at any point in time, thereby reducing the product peak height, and therefore, thesensitivity of the analysis. Moreover, optimization of a sequential injection proceduremay include finding conditions which maximize the throughput, reagent economy orreproducibility. Often, these optimal operating conditions can only be obtained by acompromise of at least one of the other desirable characteristics of the analysis.In light of the foregoing, several additional optimization parameters will beintroduced here in order to consider which operating conditions produce an “optimal”analysis by the sequential injection method. In this chapter, the results from asystematic investigation of factors known to affect dispersion (such as injection volume,flow rate, and manifold geometry) during the sequential injection procedure will bediscussed [3, 9].135In order to study the degree of zone penetration occurring under varyinganalytical conditions, the sample and reagent zones were recorded separately, andthen overlayed one on top of the other. The experimental peak profiles obtained in thedataset described in Chapter 3 will be used. Injection of three or more zones will begoverned (in general) by the same principles outlined for two zones.4.1.1 Zone Overlap DescriptorsOptimal operating conditions for a given sequential injection method will varydepending on several competing factors. Optimal conditions should include acombination of maximum zone penetration, minimum sample and reagent waste,maximum sensitivity, and maximum sample throughput. Maximizing or minimizing anyone of these conditions inevitably results in compromising one or more of the otherconditions. For example, an increase in zone penetration (as defined by P) is expectedat higher dispersion numbers (D = C°/C) thereby lowering the sensitivity by asubstantial decrease in peak height. Increased sensitivity can usually be achieved byincreasing the sample or reagent volume but this improvement is limited as D (thesample zone dispersion) decreases from 2 to 1, and is usually at the expense ofwasted reagent. As well, using greater sample and reagent volumes increases thelength of time for the previous run to be washed out of the system, thereby decreasingsample throughput. Obviously, optimal operating conditions are going to have to beconsidered for each specific application and compromises will have to be made.136Each of the optimized conditions mentioned above is governed primarily by(i) the volume of the injected sample and reagent zones, (ii) the flow rate, and (iii) themanifold geometry (straight tubes versus coiled, with variable valve-to-detectordistances). The tube diameter would also be expected to play a role in optimizationstudies [9]. However, as was mentioned in Chapter 3, only one tube diameter(0.84 mm) is considered here. The purpose of this work is to investigate the effecteach of these factors has on creating various optimized conditions (i.e., maximumpenetration, maximum sensitivity, minimum reagent waste, and maximum throughput).A ratio, which describes each optimization parameter on a scale of 0 to I (from least tomost optimal), has been calculated so as to understand how each is influenced byinjection volumes, flow rate, and manifold geometry. Zone PenetrationIn this work, the degree of sample zone penetration is calculated asEquation 4-2 R 4where A is the area of the sample zone and A0 is the portion of A subjected to zoneoverlap. A value for R near 0 indicates minimal sample overlap by the reagent zonewhile a value near I indicates the most complete sample zone overlap. This ratio,however, does not consider the extent to which the reagent zone is penetrated by thesample zone since it is usually beneficial to have the reagent volume in excess of the137sample volume. A high value for R produces a situation which is much likeconventional flow injection analysis where reagent is present in all regions of thesample zone. It is in this situation that the most reproducible and meaningful detectorresponse will be found. A low reagent to sample ratio, however, would limit Rp to themaximum area of the reagent which would be roughly equivalent the maximum volumeof the overlap. The resulting ratio would be somewhat less than I indicating that thereis a portion of the sample zone which is not penetrated by reagent. It should be kept inmind, however, that high R values would likely be found at high reagent-to-samplevolume ratios, a condition that has the potential to waste reagent. Thus, reagenteconomy must also be considered for optimization purposes. SensitivityIf the height of the product peak is used to quantify the amount of analytepresent in the sample, then the sensitivity of an analysis depends on finding themaximum of this value. The maximum of the product peak will normally occur in theelement of fluid which contains the highest overall concentration of sample and reagent(usually the isodispersion point, Figure 4-2). If the sample zone is saturated withreagent due to a high reagent-to-sample volume ratio or if C >> C, then the maximumproduct peak height will be shifted towards the maximum of the sample zone where theanalyte has the greatest concentration. In either case, a descriptor is calculated by138considering the highest point of the zone overlap (which may be the height of thesample zone) according to2CEquation 4-3 R3 = OLwhich will approach 0 for a very dispersed sample and reagent profile (i.e., high D3 andDR), and approach I for a sample and reagent zone which have undergone minimaldispersion. In practice, the height of the overlap on the C/C° scale is usually less than0.5 (indicating a dispersion value (D) greater than 2 for either ID or the maximum of thesample zone) and therefore, the factor of 2 is included in order to scale the R ratioover the range [0, 1]. This descriptor must be applied with caution since the actualmaximum of the product peak will have a greater dependence on the initial reagent-to-sample concentration ratio. Reagent EconomyWhen reagents are limited or expensive, as is the case in many biotechnologyapplications, it may be necessary to consider conditions which minimize the degree ofreagent waste. Reagent is wasted when there exists periods of time when only reagentis present in the detector, and therefore, no product can be formed or detected. In thisstudy, this effect is estimated by( WREEquation 4-4 RE =11—“ WR139where WRE is the baseline width (measured in seconds) from the start of the reagentpeak profile to the start of the sample peak profile and WR is the baseline width(measured in seconds) of the reagent zone as shown in Figure 4-2. The baseline widthis measured from the baseline intersection of tangents drawn at the peak inflectionpoints (as is often done in chromatography). This method of calculating the peak widthde-emphasizes the effect of the low concentration of sample or reagent that exists inthe leading or tailing edge of the peak profile and improves the reproducibility of themeasurement. The ratio RE is expected to increase from 0 to I as the degree ofreagent excess decreases. Higher values of RE are expected for lower reagent-to-sample volume ratios, however, this condition reduces sensitivity and zone penetration,and therefore, a compromise must be sought. Although this ratio is most applicablewhen the zones are of similar magnitude (i.e., C C), this ratio will still reach a highvalue even when the reagent peak profile is much taller than the sample, and istherefore a more useful optimizing parameter for determining excess reagent than theequivalent peak area ratio. As well, the degree of sample waste is inherently taken intoconsideration when optimizing the zone penetration parameter (Rp) which only reachesa value of I when the sample zone is completely penetrated by the reagent.1401.00.80.6C.) 4-2. Overlap of sample and reagent zone showing the degree of reagent excess(WRE) relative to the reagent width (WR). The isodispersion point (ID) represents thepoint of mutual zone penetration. ThroughputSome applications of sequential injection analysis such as those found in highvolume analytical laboratories, may require a high sample throughput in order tomaximize profit margins. For this dataset, throughput is estimated by considering therelative length of time for the peak to return to baseline at the detector after the sampleand reagent zones have passed. The largest value in the dataset is used fornormalizing the rest of the experiments considered according to141Equation 4-5 R = 1 — _P_Jwhere tB is the time for the detector response to return to baseline and tr is themaximum length of time for the detector response to return to baseline for the series ofexperiments under consideration. In this way, the value for R will range from 0 to I asthe return time to the baseline decreases. In this work, the start time is considered tobe at the onset of detector recording (which occurs after the sample and reagent zonesare loaded), even though the throughput is affected to some degree by the length oftime taken to initially load the zones into the injection line. However, since the timetaken to load the zones is proportional to the length of time for detector recording, andthe descriptor is normalized, the calculated result by inclusion of the zone-loading timewould be approximately the same as the one used here. Composite FunctionThe four conditions of maximum (I) sample zone penetration, (ii) sensitivity,(iii) reagent economy, and (iv) throughput can usually only be optimized at the sacrificeof one or more of the other conditions. For example, sensitivity may be improved at theexpense of reagent economy or sample throughput. For any particular application,however, it may not be necessary to optimize all of the above conditionssimultaneously. That is, if the sensitivity of an analysis is more important than reagenteconomy or throughput, optimal operating conditions might favour higher sample and142reagent volumes without concern for processing time. Or, for long-term unattendedfield-screening purposes where it is known that the monitored analyte has a relativelyhigh concentration, reagent economy might be improved at the expense of sensitivity.In order to investigate optimal conditions in several analytical situations, a weightedcomposite function of the above optimization parameters is investigated. This functionis tunable for the desired influence of each parameter by appropriate weighting of thecoefficients. This function is calculated asEquation 4-6 R0 = R + k2 R3 + k3 RE + k4 R]where the first term is a measure of sample zone penetration (Equation 4-2), thesecond term is a measure of sensitivity (Equation 4-3), the third term is a measure ofreagent economy (Equation 4-4), and the fourth term is a measure of throughput(Equation 4-5). The relative weighting (on a scale of 0 to 1) for each of the coefficients,k1, k2, k3, and k4, is set according to the relative importance of the respective term to theanalytical requirements. The value k is the sum of k1 through k4, thus maintaining ascale of 0 to I for the ROpT value. Investigation of the Rop value with differentweightings for profiles created over the full range of physical parameters (such asinjection volumes, flow rate, and manifold geometry) will provide a better understandingof the influence each parameter has on the analyzer output.1434.2 ExPERIMENTALThe experimental dataset described in Chapter 3, which was obtained using thesequential injection system described in Chapter 2, is evaluated here. The overlap oftwo peaks are considered by overlaying separate injection profiles for the sample andreagent zone. Peaks in the dataset which are considered to be reagent zones areones in which 40, 80, 120, 160, 200, or 240 pL of dye is injected with 0 pL of spacer(1.0 M KCI) following it. Peaks which are considered to be sample zones are ones inwhich 40, 80, 120, 160, 200, or 240 pL of dye in 1.0 M KCI is injected with 40, 80, 120,160, 200, or 240 pL of spacer following it (corresponding to the space taken by thereagent zone). It is assumed that the first injected zone is the sample zone becausethis produces an overlap situation which increases the likelyhood of the sample zonebeing completely penetrated by reagent (as will become evident in the Results andDiscussion).4.3 RESULTS AND DISCUSSIONBefore quantifying optimal operating conditions based on the peak descriptorspreviously discussed, it is first necessary to consider several extreme examples of zoneoverlap which occur in the dataset. The first situation to consider is the shortestpossible distance from the valve to the detector (15 cm) shown in Figure 4-3 at2.0 mL min1 and Figure 4-4 at 0.5 mL min1. The four extreme possiblities for thesample and reagent injection volumes (Vs and VR, respectively) are (a) VR = V = 40 pL,144(b) VR= V=24OpL, (c) VR=40pL, V=240pL, and (d) VR24OjJL, Vs=4OpLwhere VR is the reagent volume, and V is the sample volume. Through inspection ofthese figures, it is possible to create a variety of peak dispersion profiles by changingthe order of injection in addition to the injection volume. For example, injection of a40 pL zone changes shape considerably depending on whether it was injected beforeor after a 240 l.iL zone (Figure 4-3d sample zone and Figure 4-3c reagent zone,respectively). These two figures also illustrate the reason for injecting the sample zoneprior to the reagent zone since the overlap situation in Figure 4-3d will produce themost reproducible, meaningful detector response, similar in nature to flow injectionanalysis. In this situation, the entire sample zone is saturated with reagent and theproduct peak height will occur near the sample zone peak maximum. If the sensitivityof the analysis needs improvement, the sample zone volume can be increased such asin Figure 4-3b, although a limit to the height of the sample zone (or the overlap zone),is quickly reached. In situations of high sample volume (Figure 4-3b and c), the degreeof penetration reaches a limit, and the tailing end of the sample peak becomes starvedfor reagent. In these cases, the product peak maximum is found closer to theisodispersion point between the two zones where reagent and sample concentrationare at a maximum. Finally, in situations of low sample and reagent volume (Figure 4-3a), sample and reagent are conserved, and the throughput is high (Ca. 180samples hr1), but these benefits come at the expense of sensitivity and reproducibility.The peak profiles are quite similar in Figure 4-4 where the flow rate has beenreduced to 0.5 mL min1. The most notable change is the time scale which is three145times larger than that in Figure 4-3, thereby decreasing the throughput by a similarfactor. In this case, decreasing the flow rate has almost no advantage since there isonly a minor improvement in reproducibility and no improvement in the height of theisodispersion point.0.6(a)IIFigure 4-3. Overlapped samplevolumes (40 pL) or high volumesdetector distance of 15 cm. In (a)Vs=240jJL, and(d) VR=240lJL,1 . reagent zones created by injecting either low(240 pL) of the dye, at 2.0 mL min with a valve-toVR=V3=4OpL,(b) VR=V3=240pL, (c) VR=40pL,Vs=4OpL.1 .00.80.6° .00.8oO.60 4-4. Overlapped sample and reagent zones created by injecting either lowvolumes (40 iL) or high volumes (240 pL) of the dye, at 0.5 mL min with a valve-to-detector distance of 15 cm. In (a) VR = V = 40 pL, (b) VR = V3 = 240 pL, (c) VR = 40 pL,V = 240 pL, and (d) VR = 240 pL, V = 40 i.iL. 20 30 40Time (s)00001. R0 102030 40Time (s)(d) R0 1020 30 40Time (s)(c) S0 10 20Time (s)30 4000000(a)II0 30 60 90 120Time (s)1.0(C) S0.80.6D0.4 R0.20.00369120Time (s)(d) R0 306090 120Time (s)0 30 60Time (s)90 120147Increasing the distance from the valve to the detector to 100 cm has a significantinfluence on the peak shape, as shown in Figure 4-5 and Figure 4-6. In all cases, thepeak centroid and dispersion have increased. There is a more notable differencebetween high and low flow rates (Figure 4-5 and Figure 4-6, respectively) at thisgreater manifold length. For example, the same degree of zone penetration is evidentin Figure 4-5a and Figure 4-6a, yet the heights of the zones in Figure 4-6a indicateimproved sensitivity (i.e., they are approximately twice as high) and much greatersymmetry is evident (this of course comes at a cost of a much lower throughput).From the foregoing, it is clear that optimal operating conditions are arrived atthrough a dynamic balance between injection volume, flow rate, and manifolddimension. Further variation in peak shape and zone penetration can be achieved bymodifying the shape of the manifold (i.e., straight tubes versus coiled), however onlymanifolds with the tubes wound around a cylinder of 1.0 cm diameter will be consideredhere since this situation is most commonly performed in practice. In general, it is thesituation shown in (d) in each of these figures that is the most useful, especially whenincorporating maximized sample zone height and throughput, with minimized reagentwaste.1.0 1.00.8 0.80.6 0.6C)0.4 0.40.2 0.20.0 0.01.0 1.00.8 0.80.6 0.60.4 0.40.2 0.20.0 0.0Figure 4-6. Overlapped sample and reagent zones created by injecting either lowvolumes (40 pL) or high volumes (240 pL) of the dye, at 0.5 mL mint’ with a valve-to-detector distance of 100 cm. In (a) VR = V = 40 pL, (b) yR = V = 240 pL,(c) VR = 40 pL, V = 240 iL, and (d) VR = 240 pL, V = 40 pL.148(a)R S10 20 30 40 50 60Time (s) 0.60o° (s)(d)I(c)0 10 20 30 40 50 60 0 10 20Time (s)Figure 4-5. Overlapped sample and reagent zones created by injecting either lowvolumes (40 pL) or high volumes (240 pL) of the dye, at 2.0 mL min with a valve-to-detector distance of 100 cm. In (a) VR = V = 40 pL, (b) VR = V = 240 pL,(C) VR = 40 pL, V = 240 pL, and (d) VR = 240 pL, V = 40 pL.30 40 50 60Time (s)C)C)(a)0 50 100 150 200Time (s)(c)0 50 100 150 200Time (s)(b)0 50 100 150 200Time (s)(d)0 50 100 150 200Time (s)149It is true that efficient zone penetration can also be obtained by “sandwiching”the sample zone between two reagent zones [3]. Although this is not hard to achieve inpractice, the zone overlap dynamics of the second and third zones are going to followsimilar trends as the first and second zones. Therefore, two-zone penetration is thefocus of the current study, while consideration of the mutual penetration of three (ormore) zones using similar descriptors and analytical conditions is left for futureinvestigation.4.3.1 Zone Overlap DescriptorsThe R, R, RE, and RT values will first be considered independently so as toexamine their influence on the system response. Then, combinations of the functionswill be considered for specific applications by appropriate weighting of the compositefunction. Realistically, an adequate understanding of the simultaneous combination ofonly two, or possibly three, of these optimization factors will be possible.4.3.2 Analysis of Response Surface MapsThe data here are presented in the form of response surface maps [10-11]where the volume of the reagent and sample zones form the x and y axes and theoverlap descriptor constitutes the z (or response) axis. Each shade of grey on theresponse surface indicates a 10% change on the response axis. As well, the readershould pay close attention to the x and y axes which may change direction (40 pL to150240 pL or 240 pL to 40 pL) in order to provide the best perspective on the responsesurface. The 3-D view and orientation of the surface will not be varied, and the samplevolume will always appear on the left axis and the reagent volume on the right axis. Zone PenetrationThe first and most important descriptor in sequential injection analysis is zonepentration. This has been noted in the work of Gubeli et a!. [3] who used a slightlydifferent descriptor defined in Equation 4-1. The data shown in Figure 4-7, however,indicate the degree of sample zone penetration as defined by Equation 4-2. Shown areindividual response surface maps for 15, 50, and 100 cm manifolds at 0.5 and4.0 mL min1. In all cases maximum penetration of the sample zone occurs at thelowest volume of sample and highest volume of reagent. This is an obvious result butas the sample volume is decreased, so is the sensitivity of the analysis. If thesensitivity of the analysis is not of concern, then it is recommended that the smallestsample volume that can be reproducibly injected be used, while a minimum of twice asmuch reagent be used (consider the leftmost corner of the response surface mapwhere the increase in response as VR increase from 40 to 80 pL is significant). In thisway, the sample zone will be almost completely penetrated (Rp> 0.9) and as long asC >> C, the product concentration profile will have the characteristics of a flowinjection response profile with the maximum height near the sample zone. Increasing151the reagent volume to greater than twice the sample zone provides no furtherimprovement (consider all points where V = 40 pL).There appears to be no advantage to increasing the manifold length beyond15 cm since the surface maps (a), (C), and (e) all appear similar in shape, as do (b),(d), and (f). The greatest amount of zone penetration occurs in (f) where a plateau isreached at V < 120 pL and VR> 120 pL. This occurs because higher flow rates overlonger distances cause the bolus shape to extend axially and penetrate the next zoneto a greater degree. It is also important to note that increasing the reagent volume isless effective at increasing zone penetration than decreasing the sample volume(i.e., the slope of the map is steeper from right to left than from front to back).It must be remembered that this parameter only considers the area of the samplepeak which is overlapped by reagent and does not take into account the height of theoverlapped zone or the sample peak. Thus, if sensitivity of the analysis is important,then the information provided by this parameter must by considered in conjunction withthe sensitivity parameter which is discussed next.152(c) q = 0.5 mL min1Ld = 50.0 cm1.0 cm coil1. 80Vs(b)(d) q = 4.0 mL min1Ld = 50.0 cm1.0cm coil1.0i0.9+ 80Figure 4-7. Response surface maps of sample zone penetration (Rp) as defined byEquation 4-2.&Vs160 200120.16024040Vs120.16024040(f)&120200240Vs1534.3.2.2 SensitivityWhen optimizing a reagent-based chemistry, it is usually necessary to search forconditions which produce the most sensitive analysis. In flow injection analysis, this istypically done by increasing the sample injection volume and ensuring that the systemdispersion is kept to a minimum. A limit is reached, however, as D3 approaches 1, orwhen the reagent on either side of the sample is unable to completely penetrate thecenter of the sample zone (thereby creating a “double peak” due to a lack of reagent).For sequential injection analysis, it is expected that the sensitivity of the analysiswill increase with increasing injection volumes of sample and reagent (assuming astoichiometric concentration ratio between the sample and reagent). Figure 4-8 showsthe sensitivity of the analysis as measured by the maximum height of the overlap(Equation 4-3) which is initially the isodispersion point, and then shifts to the height ofthe sample or reagent zone as the ratio VR: V or V: VR, respectively, becomes large.These surfaces indicate that lower flow rates (at all manifold dimensions) produce themost sensitive analysis. This is to be expected since the slope of the interface betweenthe two zones (which has a significant influence on the height of the isodispersionpoint) is expected to be much greater due to a decrease in parabolic extension of onezone into the. next. The surfaces also indicate that a maximum (plateau) is reached atlower volumes for shorter manifold lengths, although the same height (degree ofsensitivity) is attainable for all manifold lengths (e.g., a value of about 0.95 is reachedfor R3 in all cases for 0.5 mL min1).154One final important feature is found within these response surface maps. Asmentioned previously, the measure of sensitivity increases first with the isodispersionpoint, and then reaches a maximum defined by the height of the sample or reagentzone (usually whichever is the lesser of the two injected volumes). By considering theinjection of a constant volume of sample with an increasing amount of reagent, it wouldbe expected that the sensitivity would increase with the reagent volume (if the reagentconcentration is limiting). It is also expected that the sensitivity will reach a maximumafter which the sensitivity will decrease with the decreasing peak height of the samplezone. The peak height of the sample zone decreases due to the proportionally longerdistance that the sample zone must travel as the reagent zone is increased. Thisrelationship is evident in the data by considering Figure 4-8a along the line whereV = 80 pL and VR ranges from 40 to 240 pL. The sensitivity first increases withreagent volume and then decreases. By close inspection, the same trend is evident onother surfaces as well, It is also important to note that this same decrease aftermaximum sensitivity does not occur when considering lines of constant (low) reagentvolume (e.g., Figure 4-8a where VR = 80 pL). This leads to an important point that thisparticular measure of sensitivity of the analysis must be used with caution in that sinceC >> C, the upper limit reached at high V with VR = 80 pL is actually somewhatpessimistic. It is for this reason, that for optimization purposes, this parameter shouldbe considered in conjunction with the zone penetration parameter which improves uponsaturation of the sample zone with reagent. This will be done later in this chapter.155(a)&(c) q = 0.5 mL mindL 50.0cm1.0cm coil&Vs(e) q = 0.5 mL min1Ld = 100.0cm240 200 160120800.5- 200 160 120 80 40240 200 160 120 80 40Vs(b) q = 4.0 mL min1Ld15.Ocm(Vs Vs0.20.10.0240 200 160 120 80Y 4040(d) q = 4.0 mL miW1Ld=50.OcmlOll0.20.10.0..---240 200 160 120 80 4040Figure 4-8. Response surface maps of sensitivity (Rs) as defined by Equation 4-3.1564.3.2.3 Reagent EconomyOne of the significant advantages of performing a reagent-based chemistry bythe sequential injection method is the ability to control the volume of reagent used inthe analysis and, therefore, significantly reduce the amount of reagent waste. Althoughincreasing the reagent volume increases the degree of sample zone penetration, thistoo will reach a maximum after which reagent will begin to be wasted. The degree ofreagent economy is quantified here by the parameter RE as defined in Equation 4-4 andshown in Figure 4-9. Higher values of RE indicate a reduction in time where thedetector contains reagent but no sample. The response is generally flat in nature,indicating little dependence on sample and reagent volumes. The largest difference inRE (i.e., 0.65 <RE < 0.95) is present in (e) and thus reagent economy should be takeninto greater consideration when developing methods with low flow rates and longmanifolds. This again indicates that zone penetration is less effective at low flow rates,thereby decreasing the degree to which the reagent zone is penetrated by the samplezone. In general, this data show the greatest dependence on the volume of the reagentzone with the least reagent wasted when the least amount is used. This obvious resultneeds to be balanced with the degree of zone penetration and sensitivity which arelowest at low reagent zone volumes. Therefore a combination of these parameters willbe considered later in this chapter.(e)Ld= 100.0 cm40 80 120 160 200 240Vs(b) q - -_____120 160 200 2401(a)40 80 120 160200 240240Vs(0)°8T ::0.7 —0.6& 0.5 :. .• •:0.0 . _. 24040 80 120 160 200 240VsVs(d) q = 4.0 mL min4Ld 50.0cm1.Ocmcoil ...... c,.. . .100120 160 200 240Vs(f) q 4.0mLmifl1 . __________=_z. — -Ld 100.0 cm1.0cmcoil______________&80 120 160 200 240VsFigure 4-9. Response surfacemaps of reagent economy (RE)as defined by4-4.1584.3.2.4 ThroughputIn high-volume analytical laboratories, one of the most important criteria uponwhich one judges an analytical system is its sample throughput rate. The throughput ofa system will determine the number of samples that can be processed per unit time,thereby decreasing the cost per analysis. In this work, the throughput of the system ismeasured by the length of time for the detector signal to return to baseline after bothsample and reagent zones have passed. The value of RT as defined by Equation 4-5 isnormalized by the longest time for the signal to return to baseline for the entire dataset.Figure 4-10 shows the influence of sample and reagent volume on this parameter,however, data for 2.0 mL mm1 have replaced the 4.0 mL min1 data since thisparameter is effectively higher than 0.9 for all flow rates higher than 2.0 mL mind. Asexpected, RT decreases slightly with increasing manifold length and significantlydecreasing with flow rate. However, it is at lower flow rates and longer manifoldlengths that the greatest zone penetration and most sensitive analyses are found.Thus, any zone penetration or sensitivity advantage that a lower flow rate or longermanifold length presents is diminished when this function is taken into consideration.(a) —10cmE0.0•-.... ••••• -24040 80 120 160 200 240c) q = 0.5 mL min1L50.0cm1.0 cm cod— ---— ---—1.0-0.9- —0.6 -& 0.5 -. - •-..24040 80 120 160 200 240Vs(e)Ld 100.0 cm10Z;& 0.5 -0.40.3-:0.2 -0.1 -.0.0— 24040 80 120 160 200 240VsVs15940VRVsb q=2.OmLmin1Ld = 15.0cm0.0•-..24040 80 120 160 200 240(d)q2OmLmrnl0.0 ,...• -‘ 24040 80 120 160 200 2400.70.60.5-.‘-----— -— -40 80 120 160 200 240VRVs&VsFigure 4-10. Response surface maps of throughput (RT) as defined by Equation 4-5.1604.3.2.5 Composite FunctionSeveral combinations of these four optimization parameters will now beconsidered and the trade-offs between various optimal conditions will be contemplated.With appropriate weighting of k1, k2, k3, and k4, the composite function defined inEquation 4-6 will allow visualization of optimum operating conditions which exist ascompromises between two or more factors. Maximum Sample Zone Penetration and SensitivityThe first, and most significant combination to consider is conditions whichproduce the greatest sample zone penetration (Rp) with the greatest sensitivity (Re).This is equivalent to combining the surface maps in Figure 4-7 and Figure 4-8, andessentially illustrates the trade-off between increasing the sample volume to obtainbetter sensitivity with a reduction in zone penetration as a consequence. These mapsare shown in Figure 4-11 where k1 = k2 = 1, and k3 = k4 = 0. The shape of thesesurfaces is similar in all cases. As anticipated, the maximum response “plateau” isfound where VR is greater than V, and is triangular in shape. Surprisingly, the lowestvalue of sample and reagent which creates optimum zone penetration and sensitivity isthe same for every manifold length and (volumetric) flow rate. In every case, a value ofV = 80 pL and VR = 120 pL reaches the highest plateau, and injection of volumeslarger than this do not improve the composite function by a significant amount. Thesevolumes, which do not seem to be related to the S2 value for each system (comparewith S2 graphs in Chapter 3), are more likely a function of tube diameter which effects161the length to area ratio of the injected zones. These optimal values would likely beproportionally lower (with VR = 1.5 V) at a smaller tube diameter, however, additionaldata would be needed to confirm this. Marshall and van Staden [9] showed thatreduction in tube diameter results in greater zone penetration (as measured byEquation 4-1 using area instead of baseline width). For reference, the S% value for theconditions shown in each surface map is approximately (a) 60 pL, (b) 60 pL,(c) 120 pL, (d) 140 pL, (e) 150 pL, and (f) > 240 pL.It is evident that any decrease in sensitivity is counter-balanced with a nearlyequal increase in zone penetration, thereby maintaining the level of optimum R0p.Taking this into consideration, there is little advantage to increasing the distancebetween the valve and the detector more than the minimum necessary (usually about15 cm) unless the degree of zone penetration is ultimately more important thansensitivity. Even if this is true, an increase in zone penetration can be effected byaspirating the two zones further (towards the pump) before reversing the flow towardsthe detector, or by multiple flow reversals [3]. The extreme situation to consider here isto have the detector right at the valve (e.g., by using a fiber-optic cable). It will beshown theoretically in Chapter 5 that the greatest sensitivity is achieved by monitoringthe product concentration at the valve.1624. Maximum Sample Zone Penetration and Reagent EconomyIf the sensitivity of the analysis is sufficient for the samples requiringmeasurement, then it would be necessary to consider conditions which producemaximum zone penetration with minimum reagent consumption. This is shown inFigure 4-12, again by using the composite function with appropriate weighting of thecoefficients. In general, reducing the sample volume as much as possible (whilemaintaining reproducible injection volume) and ensuring that the reagent volume is atleast twice the sample volume produces the most optimal analysis for this application.Only slight improvement is found by lowering the flow rate or increasing the manifoldlength. This composite function is dominated by the zone penetration surface which ismore dramatic than the reagent economy surface, and is primarily influenced by thechoice in sample volume.Figure 4-11. Response surface maps for the composite function, ROpT, wherek1 = = 1, and k3 = k4 = 0 according to Equation 4-6.163(a)240 200 160 ;;—•; ;(c) q = 0.5 mL mm1Ld=jmVs240 200VR160 120 . 40OIL200 160120 80 40Vs240200160Vs(d) q 4.0 mL mm’= 50.0 cmLi1.0 cmco_____::::: — 200 160 120 80 40Vsf’ q = 4.0 ml. min’L 100.0cm1.0 cm1.00902240 200 160 120 80Vs(a)cm coil1.00.9—0.80.7240 200 160 120 80 40240200Vs40&0.10.0•4040 80 120 160 200 240164Figure 4-12. Response surface maps for the composite function, R0pT, wherek1 = k3 = 1, and k2 = k4 = 0 according to Equation 4-6.(a) q = 0.5 mL min’1.4=15.0cm(b) q = 4.0 mL min’Ld=15.Ocm1.Ocmco4l0. 80 120 160 200 240Vs(c) q0.5 ml Iin1Li = 50.0cm1.0 cm coilVs120150 200240(d) q=4.0 mlmm1Li = 50.0 cm1.0 cm coil&120 io 200 240Vs0.40.1-0.0 --_4040 80 120 160 200 240Vs Vs1654. Maximum Sample Zone Penetration, Sensitivity, and ThroughputAfter having considered conditions which produce optimal zone penetration withthe greatest sensitivity, it is now interesting to combine these results with conditionswhich produce the highest throughput. Optimization of this situation would produce themost reliable, sensitive, and fastest analysis possible. Figure 4-13 indicates that thesame optimal volumes of V = 80 pL and VR = 120 pL are still maintained, however thecomposite function (which now includes througput) is significantly increased by anincrease in flow rate. Increasing the flow rate to 6.0 mL min1 only serves to increasethe irreproducibility in the analysis owing to an increased likelihood of creating airbubbles, decreased precision of injection volume, and a shortened length of time duringwhich a reliable measurement can be made. Maximum Sample Zone Penetration, Sensitivity, Reagent Economy, andThroughputFinally, if reagent economy is included in the composite function, the responsesurfaces shown in Figure 4-14 are generally the same as those in Figure 4-13.Although the surfaces become less sensitive to local variations because of thecombination of all four optimization parameters, the general relationship of high reagentto sample volume ratio is still apparent. As well, improvement due to increased flowrate at all manifold lengths is evident at 4.0 mL min1 due to a substantial improvementin throughput. The influence of reagent excess (RE) is noticeable at low flow rates(0.5 mL min1) and high VR where the optimal response begins to decrease slightly. As166well, there is a slight shift in optimum at 0.5 mL min1 to a slightly lower reagent injectionvolume, although the same general shape to the “plateau” applies.240 200 160 120 80 40Vs&Figure 4-13. Response surface maps for the composite function, ROpT, wherek1 = k2 = k4 = 1, and k3 = 0 according to Equation 4-6.167(b) q 4.0 mL mi&1 VLd15.Ocm V V VVVV: : V V1.OcmcoilV V VV VVVV(a) q=0.5mLnin1 VLd15.Ocm ::::VVV:V V V1.Ocmcoil V .: :: V240 200 160 120 8040(c) q 0.5 mL min1Ld = 50.0cm1.0cm coil1.00.9 V :. V0.80.7 V‘ I -0.3V0.2 V:V0.10.0V.:240 200160 120 8040VRVs(d) q = 4.0 mL mm1Ld=5icrEz240 200 160120 4r00.10.0200 io10 80 r 40VRVs0.20.10.0200160;;804Vs(a) q = 0.5 mL mm’Ld= 15.0 cm1.Ocmcoil ..•:• .......:1.0..0.9 ..0.8 . . .•.0.7240 200 16040I2OVR120 80Vs(c) q = 0.5 mL mint240 200 160 12080 40&(b) q = 4.0 mL min1Ld = 15.0 cm1.Ocmcoil.. .:1.0(d) q = 4.0 mL min1Ld50.Ocm0.7 A240 200 120 80VsVs168Figure 4-14. Response surface maps for the composite function, ROpT, wherek1 = k2 = k3 = k4 = I according to Equation 4-6.Vs(e) q = 0.5 mL min . . .Ld = 100.0cm.•1.Ocmcod ::..40(f) q 4.OmLmi&1 ...Ld = 100.0cm . :.240 2001608040240 200.16080401694.4 CoNcLusioNsThe optimization of the zone overlap of a single sample and reagent zone isconsidered under conditions of variable injection volume, linear flow rate, and manifolddimension. Initially, several extreme sets of conditions are shown and their relevanceto optimal sequential injection operating conditions are discussed. Several newdescriptors are presented for optimizing the zone overlap under various analyticalrequirements. These descriptors are evaluated in terms of the information andguidance that they can provide when designing a new method. All four optimizationparameters are shown as response surface maps on their own, and several arecombined using a composite function. in general, the combination of optimizationparameters for sample zone penetration (Rp) and sensitivity (R8) are the mostsignificant when deciding upon optimal conditions. In almost all cases, the minimuminjection volumes for V and VR which provide maximum penetration and sensitivity, areindependent of the flow rate and the manifold length.The results here can also be used to gain a better understanding of conditionswhich will produce optimal overlap of more than two zones. Optimal conditions for thefirst and second injected zone should be similar for the second and third zone, and soon. It has already been shown [3] that by increasing the number of zones stacked inthe manifold, multiple-reagent chemistries can be employed by sandwiching the samplezone between two different reagent zones. Consideration of this situation using these170new descriptors should constitute a separate study, in addition to validating the resultsof this chapter with real chemistries.1714.5 REFERENcEs[1] M. Valcarcel and M. D. Luque de Castro, Flow-Iniection Analysis, Principles andApplications, 1987, John Wiley & Sons, Toronto, Canada.[2] J. Ruzicka, and E. H. Hansen, Flow-Iniection Analysis, Second Edition, 1988,John Wiley & Sons, Toronto, Canada.[3] T. Gubeli, G. D. Christian, and J. Ruzicka, Anal. Chem., 63(1991), 2407.[4] J. Ruzicka and T. Gubeli, Anal. Chem., 63(1991), 1680.[5] G. D. Christian and J. Ruzicka, Anal. Chim. Acta, 261 (1992), 11.[6] J. Ruzicka, Anal. Chim. Acta, 261 (1992), 3.[7] M. Guzman, C. Pollema, J. Ruzicka and C. D. Christian, Talanta, 40(10) (1993),81.[8] J. Ruzicka and G. D. Marshall, Anal. Chim. Acta, 237 (1990), 329.[9] C. D. Marshall and J. F. van Staden, Process Control and Quality, 3 (1992), 251.[10] G. E. P. Box and N. R. Draper, Empirical Model-Building and ResponseSurfaces, 1987, John Wiley & Sons, New York, USA.[11] C. K. Bayne and I. B. Rubin, Practical Experimental Designs and OptimizationMethods for Chemists, 1986, VCH Publishers, Deerfield Beach, USA.1725. Random-Walk Model forSequential Injection Analysis“A good simulation,be it a religious myth or scientific theory,gives us a sense of mastery over experience.To represent something symbolically,as we do when we speak or write,is somehow to capture it,thus making it one’s own.But with this appropriation comes the realizationthat we have denied the immediacy of realityand that in creating a substitutewe have but spun another threadin the web of our grand illusion.”Heinz R. Pagels5.1 INTRODUCTIONThe random-walk model of Betteridge et a!. [1] gave practitioners a powerfulconceptual basis for understanding flow injection analysis. The model involvedsimulation of multiple discrete “molecules” within the flow manifold. In each 4t, eachmolecule took a diffusion step and then was moved a distance along the tube due toflow rate and laminar flow. Users could simulate ten parameters including sample size,reaction rate, molecular diffusion coefficient, temperature and flow rate; as such, it wasthe first realistic attempt at modeling the complex interactions of molecular diffusion,173convection and reaction kinetics. The speed of laboratory microcomputers at that timelimited the number of molecules simulated to Ca. 1500, and so only semiquantitativepredictions of peak height versus time were possible. Despite this, simulationscompared against experimental results were found to be of practical use [2]. It wasrecognized at the time that a 100-fold increase in computational speed was necessaryif complex problems (e.g., pH gradients, solvent extraction) were to be adequatelyaddressed. Recently, Wentzell and co-workers revisited the random-walk model [3] forflow injection analysis. By lifting some earlier limitations on computational speed theyobtained accurate predictions of peak shape and duration using up to 1,000,000molecules (piece-wise) per simulated run.The advent of sequential injection analysis in 1990 brought with it anexperimental requirement for far more stringent control of flow and timing. In early FIAsystems flow was continuous and unidirectional, and a microcomputer (if present at all)served solely as a recording device - now the microcomputer has become an essentialpart of the analyzer. The sequential injection analyzer built for this work has as manyas 21 parameters under computer control, any of which can change in each of the 3 toperhaps as many as 15 sequential steps that comprise a method. Designs for futuresequential injection analyses can be expected to produce more complex peak shapesthan FIA because of the mutual partial overlap of multiple zones (reagents, sample andspacers) occurring in conjunction with at least one flow reversal operation. It would beextremely difficult to create a continuous model that dealt with this complex injection174and dispersion procedure. This leaves discrete-time simulation as the only real viablesolution to modeling these interactions.Keeping in mind the recent further advances in computational speed of thedesktop computer, it is proposed in this work that the sequential steps of SIA operationshould be amenable to random-walk modeling. Towards this end, this chapter willreport a novel simulation technique which is able to simulate the physical sequentialinjection procedure, as well as incorporate the flow reversal and dispersion throughoutthe entire manifold. This model can thus be used to gain a better understanding ofphysical dispersion within the manifold and to predict optimum zone penetration andtiming for real sequential injection methods.Definable parameters in this model include flow rate (sinusoidal or linear flow),number of zones injected, internal tube diameter, temperature, valve-to-detectordistance, detector volume, number of flow reversals, and length of each flow reversal.In sinusoidal flow, the pump period, pump start angle, valve switching time, and thesyringe and cam radius are all user-specified. The model can track up to foursequentially stacked zones of reagent or sample. The diffusion constant, relativeconcentration, and zone length (specified by time) can be specified for each injectedzone. Dispersion profiles produced with this model will be shown in comparison withexperimental peaks under similar operating conditions.1755.2 THEoRYThe random-walk model, originally proposed in 1905 by Einstein [4] to explainBrownian motion, has been used to simulate many physical systems which incorporatestochastic events [5-7]. Two similar areas of study which have made use of this modelfor simulating manifold conditions are chromatography [8-9] and flow injection analysis[1-2]. In both cases, the model was shown to correspond well with experimentalresults.The basic premise that the flow injection simulations relied on is the tracking ofthe three-dimensional position of individual molecules as they progress through themanifold under a defined set of conditions. Each molecule tracked is allowed a threedimensional diffusional step of random length, in addition to an axial movement due toconvective flow according to a laminar flow profile. The justification for the diffusionalstep is as follows. The relative spread of the sample (originally injected as a square“plug”) is given by the probability (y2) of finding a molecule at a distance y from theorigin [6] according toEquation 5-1 (y2)ZJ2rDmtJy2exp’tJdy176where Dm is the molecular diffusion constant for the process and t is the length of timeper step. If a large number of molecules take a large number of steps, n, of averagelength, I, at v steps per unit time, then the relative spread is given [6] byEquation 5-2 (y2) = 2Dmt = n! = vt!2.In Chapter 3, it was shown that this relationship holds for the sequential injectiontechnique by considering the second moment of the peak profile as a relative measureof dispersion. With appropriate statistical treatment, it can be shown [6] that theaverage movement of a given step of At in any one dimension is EI .J2DmAt.Correcting for viscosity z (mPas) of an aqueous solution (and therefore temperature,°C) via the relation [15]‘ [i.7o2r — 20)+ 8.36 xl04(T — 20)2Equation 5-3 log I I =‘\hl} (109+T)leads to the corrected step length ofEquation 5-4 Al =(1T /12o)in any one dimension. The actual distance moved in At seconds for a given dimensionis given by Ax = ±rnd(2A1) since Al is the average step length and md is a randomnumber uniformly distributed in the range [0, 1], where the sign of the movement is177taken as random with equal likelihood of either outcome. This distance is more easilycomputed in the simulation by the equivalent expressionEquation5-5 tXx=Ay=&=4tJrnd—2tY.A new coordinate for each dimension is calculated from the old coordinate for the ithmolecule in this way, viaEquation 5-6 Xi(new) = XI(old) + AXEquation 5-7 Yi(new) Yi(old) + A)’Equation 5-8 Zi(new) = ZJ(oId) + & + Aqwhere ziq is due to the axial convective movement due to laminar flow at the tuberadius, which is determined byEquation 5-9 = iJXflew) + Ynew)If r > i then the new radius would lie outside of the tube boundaries. In thissimulation, as in the original flow injection simulation [1], this is corrected by assuminga bounce boundary, where the new coordinate (Xj(flew),Yi(flew)) is set equal to the oldcoordinate (X,(o,d),Y,(o,d)) and the new axial velocity is set equal to half of the old axialvelocity (i.e., Aq(uSed) = O.5Aq).178More recently, Wentzell et aL [3] made several modifications to the model inorder to determine the effect of step size and wall approximations on the model. Themean molecular step size, (Ai = .J2DmAt) will influence the validity of the algorithmbecause of approximations made in calculating axial flow rate and in wall interactions.The easiest method of reducing the step size (ill), and therefore improve the simulationresults, would be to decrease the time interval between iterations, tt = 1/N, byincreasing N, the number of iterations per second. This modification, however, comesat the cost of increased computation. The original work by Betteridge et al. [1] usedN = 1, throughout, while Wentzell et a!. [3] show peak profiles for N = 1, 5, 10, and 100,which asymptotically approach the limiting profile as N gets larger, and ut gets smaller.The conclusion reached by Wentzell was that the mean step size should be no morethat 5 to 10% of the tube radius. In the work presented here, the value of N can becalculated by first solving the mean molecular step size for 4tAl2Equation 5-10 At =2DmBy using Al = 0.002 cm, corresponding to 5% of the tube radius, andDm = 7.6 xl 06 cm2s’ for the experimental dye used, a result of 0.26 s for 4t,corresponding to N = 3.8 is obtained. In this work, N = 10 was used (unless otherwisenoted) which provides a sufficiently small step size according to Wentzell’srecommendations.179Two other compensating factors were also attempted by Wentzell. The firstmodification was to add the average axial velocity between points (x,(, YI(old)) and(XI(,W), yI(,,W)) instead of the axial velocity at point (xI(,,,W), YI(new)) only. The secondwas to calculate the actual position of the molecule after the “wall bounce” experienced.However, they found it computationally simpler to reflect the molecule back along itsoriginal trajectory, rather than correctly bounce it off the wall. This is a validapproximation as long as the flow profile is radially symmetrical. Their results showedthat inclusion of these two compensating factors produced the same results as whenthe step size was sufficiently small. Thus, these compensating factors are generallyonly necessary for small N, and have not been considered here.Assuming parabolic laminar flow conditions hold, the flow velocity (cm s1) at anygiven radius, i from the center of the tube can be expressed as( 2Equation 5-11 U,. = Um1‘0where Um = 2U (according to Taylor [10]), U is the average flow velocity (cm s1) andij, is the radius of the tube (cm). Thus, Aq can be calculated by( rEquation 5-12 Aq = AtU 1—180where P = 2 for regular laminar flow according to Taylor [10]. Modification of the flowprofile has been done [3] by adjusting the power factor used in Equation 5-12, and bymodifying the asymmetry of the flow profile. In the former case, improved fit betweensimulated and experimental dispersion profiles was realized in some situations when Pwas adjusted to values other than 2 (i.e., 1, 3 and 4 were also tried by Wentzell). Theeffect of this factor will be investigated in this work as well, using a corrected value ofu = U(P + 2)/P. Wentzell found that modification of the flow profile asymmetry wasnot able to compensate for the experimental profiles obtained with secondary flow (i.e.,when tubes were coiled) as anticipated [3], and thus, is not considered in this model.A typical sequential injection procedure requires that the flow be started,stopped, and paused, several times, in addition to changing direction, and that thedispersing sample must pass through non-ideal valve and detector geometry. Ideallaminar flow requires a finite amount of time to set up and is reduced by suchimperfections in the manifold geometry. This is sometimes referred to as “developingflow’ and it typically takes 60 to 70 pipe diameters before laminar flow is fullydeveloped. This corresponds to 6 to 7 centimeters of tube length or 47 - 55 pL ofinjection volume before we can expect stable laminar flow (assuming an approximatetube diameter of 0.1 cm). Consequently, the likelihood of the experimental flow profileexhibiting ideal laminar characteristics is reduced, especially for injection volumes orfluid movements less than 40 pL.181Hence, in order to approximate this non-ideal behaviour, a new parameter,which adds an average-flow term to the flow profile, was proposed in this work. Thisparameter is used to adjust the axial flow equation according to(Equation 5-13 U,. = t1maxI 1—--- +(1—)U‘. r,.jwhere 0 1, U = 2U, U is the average flow velocity (cm 1) and i is the radiusof the tube (cm). In this way, the non-ideal flow conditions are approximated by addingthe average flow velocity term on the right. In the limiting cases when (= I the flow ispurely laminar, and when = 0 the flow is purely plug flow.5.3 INJECTION PROCEDUREPreviously, flow injection systems were simulated with the use of the random-walk by randomly placing a large number of molecules within a defined hypothetical“sample loop” with the center of the sample zone taken as the origin of the coordinates.Then, for each molecule, a random diffusion step was added, as well as the convectivestep due to a parabolic flow rate for each iteration of the simulation. The simulationproceeded as the molecules were propelled and diffused towards the detector. Peakprofiles were then created by either (i) integration of the molecules in each of severalzones that the manifold tube had been divided into, or (ii) integration of the moleculespassing through a discrete detector zone as time passes. The former technique allows182visualization of the dispersion process as it occurs, while the latter creates peakprofiles which are comparable with those formed with an experimental detector.The injection procedure for the sequential injection technique is much morecomplex, and thus, the difficulty in using this type of model lies in devising anappropriate injection procedure that conforms as closely as possible to reality. It wasthought that instantaneous injection of a square plug in the same manner as thesimulated flow injection process would be gravely over-simplifying the situation,especially for long injection times. A simulated injection procedure which incorporatesconnection of a multi-position valve to several positions with sequential stacking ofsample and reagent zones into the manifold was needed. To this end, the followinginjection procedure is proposed and has been implemented in this model:1. The model begins by simulating the valve movement to the first position for thelength of time specified by the user (usually 1.0 s, corresponding to 10 iterationswhen At = 0.1 s). Since there are no molecules injected at this point, this steponly serves to increment the model timer from the “start” of the analysis.2. A predetermined number of molecules are positioned randomly in the tube ofradius, ,, with axial boundaries of 0 z Al according to Figure 5-1. Thenumber of molecules (typically 2500) and the length (cm) of 41 (typically 2.0 cm)are both user-defined.183Figure 5-1. Tube variables used in the sequential injection simulation; the tube isdescribed by x, y, and z Cartesian coordinates, with the multi-position valve interfacedefined at z = 0.3. The flow is reversed (towards the negative z-direction) for one iteration of At(typically 0.1 s). A random diffusional step of length according to Equation 5-5 isadded to each dimension. Then, the new x- and y-coordinates are used todetermine the convective step size which is added in the (axial) z-direction. Ifsinusoidal flow is requested, the current flow rate is determined from the currentpump head angle, which is subsequently updated for each zlt.4. A fraction of the (2500) molecules will have stepped far enough in thez-dimension such that their new z-coordinate is negative (i.e., they have movedfrom the supply line, through the valve and into the injection line). Thesemolecules are transferred to a new array in memory and are considered to be“injected.” The molecules that did not step far enough in the negative z-direction(i.e., they are still in the supply line) are discarded.Valve1845. Steps 2, 3, and 4 are repeated for the length of time of injection of this zone. Forexample, to inject 3.0 s of this sample or reagent, with tXt =0.1 s would require30 iterations of steps 2 through 4.6. After the first zone is injected into the injection line, the valve movement mustagain be simulated. This is done by setting the flow rate to zero (as it is inreality while the valve moves), for the length of time of the valve movement.During this time, random diffusional movement of the injected molecules is stillallowed to occur as it would in reality.7. If there are further zones to inject (up to four sequentially stacked zones arepossible in this model), then the above process (steps 2 through 6) is repeatedwith the molecules of the four (maximum) injected zones being “tagged” asmolecule type I through 4 in their respective array in memory.8. If multiple flow reversals are requested, then the molecules are tracked while theflow rate is alternated from positive to negative for the user-specified length oftime.9. Finally, the flow is set to positive (towards the detector) and the molecules aremoved back through the valve and into the line connecting the valve and thedetector. Each of the four molecule types with coordinates such thatd z, d + Ad according to Figure 5-2 are integrated separately, and displayed185graphically in real time as overlapping peaks on the simulation detector. Thedistance d, is determined by the length of tubing from the valve to the detector,and 4d is calculated such that the volume of the detection zone is equivalent tothe volume of the experimental detector assuming a constant tube radius. Thesimulation is stopped after the user-defined detection time has expired or afterfive seconds of post-peak baseline have been tabulated, whichever comes first.Detection-z +z [ZonedtAdc______ValvezFigure 5-2. Simulation parameters for the detection line, and the detection zone.10. The total number of molecules simulated in each zone is recorded in thedatabase (where all of the other simulation information for each run is stored asindividual records), and the peak profile is recorded as a text file to disk forfuture retrieval. If replicate runs are desired (in order to increase the number ofsimulated molecules and thus reduce stochastic noise), the simulator repeatssteps I through 9. The new number of simulated molecules in each zone isadded to the previous values, and the new peak profiles are overlaid on top ofthe old ones.1865.3.1 Theoretical Considerations of the Injection Procedure5.3.1.1 Molecular ConcentrationThere are several issues to consider regarding this injection procedure. Theconcentration of molecules placed in the region zli (determined by the number ofmolecules placed in the zone and the length of the injection zone, ui) should be greatenough to provide a smooth simulation, without overfilling the maximum array size of32,767 molecules for a given injected zone. For example, if 5000 molecules are placedin the injection zone, and of these, approximately 2000 molecules move through thevalve on each iteration of 0.1 s, then any more than 16 iterations (equivalent to 1.6 s ofinjection time) would exceed the maximum array size. If it is overfilled on the firstinjection, the simulation automatically cuts the number of injected molecules in half(thereby reducing the molecular concentration by a factor of 2) and doubles the numberof replicates to run. In this way, the same total number of molecules are simulated,over twice as many runs. Axial StepThe distance Ai should be great enough such that, at the prescribed flow rateand iteration time, no molecules are able to make an axial step greater than thisdistance. This prevents the situation where gaps might occur in the molecular spacingwithin the manifold, especially nearest the center of the tube where the molecules are187making the largest axial steps due to laminar flow. If these molecular gaps occurred,“sawtooth” peak profiles might be produced at the detector as the concentration ofmolecules fluctuates. This situation was prevented by ensuring that zli exceeds thedistance moved by a molecule in one iteration at twice the average linear flow velocity,including the maximum axial diffusional step possible. Supply LineThe purpose of step 4 in the injection procedure is to simulate the supply offresh sample or reagent at full concentration at the beginning of each iteration. If thesupply line was not recharged after each step, the concentration of molecules within itwould soon become parabolically distorted with the center of the tube (nearest the +zend of the injection zone) depleting of molecules first. More importantly, by onlysimulating say 2 cm of supply line instead of the full length of 20 to 100 cm, a largenumber of calculations are eliminated since less molecules need to be simulated. Thismakes the approximation, however, that the flow rate step is sufficiently great tominimize the effect of molecules drifting “backwards” from the injection tube into thesupply line. This unlikely situation would only occur near the wall boundaries where Uapproaches zero but the diffusional step in the z-direction can still be large enough foran “injected” molecule to move back into the supply line.1885.3.1.4 Detection ZoneThe length of the detection zone is determined from the user-specified volume ofthe detector, using the same internal diameter tubing as the manifold. Since thephysical flow-cell and manifold tubing used in the sequential injection analysis systemhave an internal diameter of 1.0 mm and 0.84 mm respectively, zld (in Figure 5-2) canbe extended to maintain constant detection volume as an approximation. This meansthat although the length of the integration zone for the experimental flow-cell and thesimulation are not the same, their total volumes are. Determination of Simulated C°The question arises as to what value to use for C° so that the simulated peakprofiles can be compared on the same vertical scale as experimental peaks. Having anaccurate simulated value for C° would easily facilitate comparison without the need fornormalizing peak profiles by peak area as had been done in previous work [3]. As well,knowing C° would allow the simulation to predict actual peak height instead of justrelative peak height. In order to determine C°, the concentration of molecules for anundispersed sample must be known, that is, the number of molecules found within thedetection zone if the pure sample was flowing through it. Intuitively one would like touse the molecular concentration found in the sample line injection region 41, althoughthis would not be truly representative of the actual injected sample since thesemolecules are replaced at every iteration, Instead, C° was calculated by dividing the189total number of molecules that actually become part of the simulated sample plug (andare not discarded in step 4 of the injection procedure) by the injection volume. Thisgives the molecular concentration at the point of injection even though by the end of theinjection period, molecules have dispersed throughout a volume greater than theinjection volume. Filling the detection zone with this molecular concentration andintegrating the molecules provides a value for C° which can be used to normalize theentire simulated peak profile for comparison with experimental profiles. It will be shownthat peak areas calculated on this basis are in excellent agreement with experimentalpeak areas under all conditions.5.4 ExPERIMENTAL PEAKSIn flow injection analysis, others have successfully developed specializedapparatus which creates conditions which are very close to perfect laminar flow [14].Physically, this is not difficult to do when working with a sample zone of specificvolume, and unidirectional, continuous flow. The sequential injection technique,however, involves repeatedly starting and stopping the flow, in addition to flow reversalof the injected zone(s) back through a possibly imperfect valve channel before reachingthe detector. Therefore, it is thought that construction of an apparatus capable ofproducing perfectly laminar flow under these conditions would be extremely difficult, ifnot impossible. However, it is possible to minimize any physical perturbations in themanifold which would reduce the laminar flow characteristics of the experimental flow190profile. Towards this end, the following steps have been taken to minimize suchperturbations:1. The manifold tubing was kept as straight as possible in order to minimizesecondary flow.2. The pulsing from the peristaltic pump was reduced as much as possible byappropriately adjusting the tube tension, coating the pump tube with silicone oil,and keeping the distance between the pump and the supply lines or waste linesas long as possible (since friction in the tube can dampen the pulsing).3. There is a 180° bend at the injection valve which is unavoidable due to thenature of the mechanism. The flow channel in the valve plate has similardimensions to the manifold tubing and does not have any dead volume.4. An axial flow-cell with a very small total volume (7.85 i.iL) was used which has aninternal diameter similar to the manifold tubing (1.00mm and 0.84 mm,respectively). The manifold tubing from the valve was inserted into the flow-cellall the way up to the detection zone (at a 90° angle) where the flow enters thelight path. Thus, there are no unions in the manifold tubing between the valveand the detection zone.191Experimental peak profiles from the tracer dye, 1.5 mM K3Fe(CN)6,made up in1.0 M KCI, dispersing in a stream of 1.0 M KCI, are used for comparison to the model.An injection volume of 80 pL, injected at a flow rate of 2.0 mL m1n1, with a valve todetector distance of 15.0 cm is used as a standard peak profile for the majority of thecomparisons. These particular conditions produce convection-dominated peaks. Thus,peaks which are influenced to a larger extent by diffusion (e.g., low flow rates andlonger valve-to-detector distances) were also compared to ensure the validity of themodel. Although a valve-to-detector distance of 15 cm may seem relatively short, itmust be remembered that due to the flow reversal, the first injected molecules of an80 pL zone will travel over 30 cm into the manifold, and then back 30 cm to the valve,before traversing the 15 cm distance to the detector, thus traveling a total of 75 cm.5.5 INTERFACEThe simulation software is written in Microsoft Visual Basic Version 3.0 in orderto speed up development time and provide a graphical user interface. As well, data foreach simulation are stored in a database written in Microsoft Access Version 2.0. Thisapproach allows ease of access and provides compatibility with Microsoft Excel Version5.Oa spreadsheets and graphing functions for comparison with experimental data.Microsoft Query 1.00 was used to search and extract data from the database, for importinto Microsoft Excel. Bitmaps of the screen were captured using Central Point ScreenCapture 2.0. A maximum of four simulated profiles for each simulation are stored as acommas delimited text file.1925.5.1 Multiple Document Interface FormThe Flow Simulation form (Figure 5-3) is the multiple document interface (MDI)form which serves as a container for all other subordinate forms. The simulation statusbox on this form is continuously updated and indicates the current part of the analysisbeing simulated. Also shown are the database scroll arrows and current record number(bottom left corner), record start and stop numbers, the current replicate, completedreplicates and total replicates. The update button records any changes the user makeson any of the forms in the database, the run button starts the simulation, and the pausebutton stops the calculations until it is pushed again.Since each simulation constitutes one record, the record start and record stopboxes indicate which records should be run after pushing the run button. The user canspecify the number of replicates to run in the bottom right box which are shown ascurrent replicate, completed replicates, and total number of replicates. Simulating witha greater number of molecules increases the smoothness of the calculated profile. Byperforming the simulation in multiple replicates, the number of molecules held inmemory at any one time is greatly reduced, thereby freeing memory for otherapplications. As well, a given replicate will take less time to calculate, which reducesthe probability of interrupting the simulation in the middle of a run if the user wants toshut down the simulator (an action which would otherwise result in data loss).193I low it,Iul1ir)rFigure 5-3. The Flow Simulation form (shown) serves as a container (multipledocument interface, MDI) for all other forms.55.2 Simulation Profile FormIn the example simulation shown in Figure 5-4 of the Simulation Profile form,Dye A and Dye B are stacked sequentially for 1.2 seconds each into the manifold whilethe flow is to the left. Then, the flow direction is reversed and fluid is pushed towardsthe detector (to the right) for 15 seconds as indicated in the time row under “Detector.”The “Total Time” shows the simulation to be currently at 16.60 seconds from the start ofthe injection process (i.e., including the loading time). The total number of moleculesthat constitute each zone are listed for each of Dye A and Dye B, as well as the totalnumber of molecules expected at the detector. The diffusion constant is listed for eachdye as 0.000005 cm2 s. The left peak profile shown corresponds to Dye B while theright peak profile corresponds to Dye A due to the fact that the Dye B molecules wereloaded into the injection tube last and, upon flow reversal, would reach the detectorfirst. As expected, even though both zones are of the same size, the peak profile for194Dye A is lower than Dye B since it has traveled a greater distance into the injectiontube before flow reversal.Figure 5-4. The Simulation Profile form shows the manifold tube with four centralinjection zones and the simulated peak profiles.1955.5.3 Physical Settings FormThe tube diameter and distance to the detector are included on the physicalsettings form, shown in Figure 5-5. The injection length corresponds to ill and thedetector volume is used to calculate zid according to the given tube diameter. Thevalue for the number of molecules injected corresponds to the number of moleculesrandomly placed in the zone 4i in step 2 of the simulation. The date and time stampsare set upon completion of the last replicate for a given simulation.Figure 5-5. The Physical Settings form includes simulation data for manifolddimensions (tube diameter, valve-to-detector distance, injection length, and detectorvolume), physical parameters (number of molecules injected and temperature), as wellas a time and date stamp.1965.5.4 Flow Settings FormThe Flow Settings form (Figure 5-6) indicates the flow pattern and the sinusoidalflow parameters. Either linear or sinusoidal flow can be selected. If a linear flow isselected, then the flow rate is based on the value entered in the flow rate box (in thiscase 2 mL min’1). If a sinusoidal flow is selected, the value in the flow rate box is notused, and the flow rate during any 4t is calculated based on the entries in thesinusoidal flow parameters section. If the pump is only operated over a certain angularrange (so as to minimize the flow rate difference) then the starting and stopping anglescan be entered. In the example shown in Figure 5-6, with the start and stop angles at60 and 120 degrees respectively, the flow rate varies only by 14% of the maximum rate.As well, if a sinusoidal flow rate is used, it is important to specify the length of time thepump has reversed on the wash line before stacking the sample or reagent zones.That is, if the pump head starts at 60 degrees and the flow is reversed for 20 secondsto load wash solution into the manifold before stacking the first zone, the pump headwill be at a new angle when it starts the injection sequence. Since the flow rate duringany zit varies with the pump head angle, a different volume of sample or reagent wouldbe injected in the same specified length of loading time. The initial length of time forloading of the wash solution is specified in the very leftmost segment of the injectiontube (labeled “Wash”) shown in Figure 5-4.197I 4//,-.>!”/< UnOflrI%w//“. 4thwJ4ate(mtJm1t “ J2 ISp./) &9/ / // // /-.>Nqq4tfro4flpw ‘%V I 1?[*1j?s/ My ?#pW/J/t,’_F In______/- ‘jizo1fjmp Stan Angle5isej’joPumpStopAnglI(dey) j120 [4’,/,flQy /‘M4’”. ‘“‘‘“/ SyriIgaftad%,as4cqLl 1605 V/a%rc()4.a.4fr”4/ —“/Figure 5-6. The Flow Settings form shows flow pattern settings and sinusoidal flowparameters.1985.5.5 Time Settings FormThe Time Settings form shown in Figure 5-7 is used to specify the timing of thesimulation. The valve move time is the length of time the flow stops between valvepositions while diffusion is still allowed to occur. The time per iteration corresponds tout which equals 1/n. The time per reversal is the length of time to reverse the flow inone direction before reversing it again to its original direction.Figure 5-7. The Time Settings form is used to specify the length of time to pause forone valve movement, the length of time for each iteration, and the length of time foreach reversal.1995.5.6 Model Settings FormThe Model Settings form is used to specify the power factor P used indetermining the axial flow profile as discussed previously. The laminar factorcorresponds to which determines the fraction of the z-dimensional step that isinfluenced by laminar flow versus plug flow. Alpha factors 1, 2 and 3 are additionalparameters that can be accessed by the simulation calculations for testing purposes.Figure 5-8. The Model Settings form is used to enter up to five additional numericalparameters in the model calculations.2005.6 RESULTS AND DISCUSSIONThe design and construction of this model which simulates the physicalprocesses occurring within the manifold as realistically as possible was accomplishedwithout any noteworthy difficulties. In the following discussion, the ability of the modelto accurately predict peak profiles that are generated on the analyzer understraight-tube conditions will be examined. It should be understood that theexperimental peak profiles, although not ideal due to hardware limitations, representflow conditions which are primarily laminar, and where secondary flow and turbulenceare minimized. The influence of the molecular diffusion coefficient, detector volume,injection volume, valve-to-detector distance, flow rate, and laminar flow profile on themodel will be considered for comparison to the experimental peak profiles. Validationof the simulation results with data from other researchers is not yet possible since thesequential injection technique is so new. Other fundamental studies showingdispersion profiles created under primarily laminar flow conditions for the sequentialinjection technique have not been published.5.6.1 Investigation of Random-Walk Model ParametersThe ability of the model to accurately predict dispersion profiles produced on anactual sequential injection analyzer lies, in part, in the accuracy of the parameters usedin the simulation. The effect that each parameter produces on the generated profile are201examined here. A procedure of injecting 80 pL of tracer dye into a stream flowing at2.0 mL mm1 through a 0.84 mm internal diameter tube with a valve-to-detector distanceof 15 cm will be assumed as the standard profile unless otherwise noted. For allexperiments, the tracer dye, 1.5 mMK3Fe(CN)6,made up in 1.0 M KCI, is injected into astream of 1.0 M KCI. Effect of Diffusion CoefficientThe molecular diffusion coefficient directly affects the average random steplength and should therefore have a significant influence on the simulation output. Theliterature [3, 11] suggests that under the current experimental conditions the moleculardiffusion coefficient for the tracer dye should be 7.6 x iO cm2 s’. This nominal valueis used as a basis for the majority of the simulations in this work although multiplicationfactors of this number have been used to calculate simulations for comparison toensure its validity. The significant effect which the diffusion coefficient has on the peakprofile is demonstrated in Figure 5-9, where the diffusion coefficient has been modifiedover a range of three orders of magnitude. However, it should be noted that typicalvalues of the diffusion coefficient for similar aqueous solutions are within one to twoorders of magnitude of the nominal value for the dye used here. Increasing themolecular diffusion increases radial mass transfer, thereby reducing the effect that theconvective movement has on any given molecule. That is, on average, moleculesmoving slowly along the walls of the tube will have a greater ability to step into the202faster moving laminae nearer the tube center. This reduces the tailing and produces amore symmetric, less dispersed profile (e.g., Figure 5-9f).It should be noted that for the dimensions being considered, the effect ofincreasing the diffusion coefficient has a much more significant effect on the peakprofiles shown in Figure 5-9 due to increased radial mass transfer relative to axial masstransfer. This is to say, an increase in the diffusion coefficient by two orders ofmagnitude actually reduces the overall peak dispersion in the axial dimension due to amore significant reduction in the effect of the laminar flow profile. Modification of thisfactor selectively (e.g., Dradjal versus Daxiai) may provide improved agreement betweenthe model and more symmetric experimental profiles which have been influenced by (i)secondary flow conditions (such as with coiled tubes) or (ii) greater manifold lengths.To facilitate a simple comparison between the simulated and experimental peakprofiles, (i) the sum of the squares of the errors (SSE) between the simulated andexperimental peak profiles, and (ii) the area of the simulated profile relative to theexperimental profile, will be considered. Figure 5-10 shows these two parameters as afunction of the diffusion coefficient multiplication factor, and both indicate the bestgeneral agreement occurs near 1.0 Dm. In Figure 5-10, the peak area reaches amaximum and then reduces again towards I at high values of Dm due to an overallreduction of slower molecules which linger near the walls of the tube causing anincrease in the overall peak area by spending more time in the detector. The SSEincreases dramatically at this point (i.e., 100 Dm) because of the disagreement in203vertical height at every point in the dispersion profile and not because of adisagreement in peak area (cf. Figure 5-9f).Figure 5-9. Effect of the molecular diffusion coefficient (Dm) on simulated peaks (thicklines) relative to experimental peaks (thin lines); the multiplication factor used relativeto 7.6x10 cm2 s1 is shown for each profile.204(b) 0.2Dm0 5 10 15Time (s)0.0(d) 1.0Dm1.0 1.00.8 (a) 0.1 Dm 0.80.6-.004004 - 5 10 15Time (s)1.0 1.00.8 (c) 0.5 Dm 0.80.6o 0.6 - 00—00.4° 5 10 15Time (s)1.0 1.00.8 (e) 2.0Dm 0.8c0.6 cO.6—0040. 5 10 15Time (s)1.0 1.0. (g) 10.0Dm 0.8o 0.60—004I 0.20.00 5 10Time (s)15(f) 5.0Dm0.8o 0.6004150.20.00 5 10Time (s)J\NZ°°Em0 5 10 15Time (s)0 5 10 15Time (s)2053.00—— SSE —s— Relative Peak Area2.502.00wCl)C) 1.501.000.500.001.0 10.0Diffusion Coefficient Multiplication Factor1. od)>095 Ca)0.900.850.800.1 100.0Figure 5-10. Effect of molecular diffusion coefficient multiplication factor on (i) the sumof the squares of the errors (SSE) between experimental and simulated peaks, and(ii) the simulated peak area relative to the experimental peak area. Effect of Simulated Flow-cell Volume and Tube DiameterObviously the detector volume will have a significant influence on the resultingpeak profile since it affects the axial range of molecules to be integrated. A largervolume would be expected to produce peaks which rise more slowly and take longer toreturn to baseline. The experimental flow-cell has an optical path length of 1.0 cm andan internal diameter of 1.0 mm, giving a calculated cell volume of 7.85 i.iL. Figure 5-11shows the sum of the squares of the errors between the experimental and simulated206peak profiles using different simulated detector volumes. Adjustment of the simulateddetector volume near this value indicates that this volume is indeed optimal.0.600.200.100.00 I I I I I6.75 7.00 7.25 7.50 7.75 8.00 8.25 8.50Simulated Flow Cell Volume (pL)Figure 5-11. Effect of varying the simulated flow-cell volume on the sum of the squaresof the errors (SSE).The internal diameter of the experimental manifold tubing was nominally 0.8 mm.However, the average diameter was determined empirically to be 0.840 mm by massdifference using distilled, de-ionized water and a 6.00 m length of tube. Modification ofthe internal diameter of the simulated tube near the nominal and experimental valuesgenerated profiles which were compared to the experimental peak. The SSE betweenthe experimental peak and the simulated peaks at different internal diameters, shown inFigure 5-12 indicates an optimal internal diameter which is closer to the measuredvalue of 0.84 mm.2071.601.401.201.00Ui(1) 0.80(I)0.600.400.200.000.60 1.10Figure 5-12. Effect of modifying the internal diameter of the simulation tube on the sumof the squares of the errors (SSE) between the simulated and experimental profiles andthe simulated peak area relative to the experimental peak area. Effect of Simulated Injection TimeAnother factor which may influence the fit between the simulated andexperimental peak profiles is the accuracy of the injection volume. If a volume slightlygreater than or slightly less than 80 pL was injected into the experimental manifold (dueto instrumental error) the recorded peak would be larger than or smaller than theexpected profile. Since the volumetric flow rate of the pump is calibrated periodicallyby mass difference, any discrepancy between the specified and the actual flow rate ofthe system is not expected to be of much concern. However, slight inaccuracy in theexperimental injection volume may arise from an inertial lag in flow rate as the flow rate0.70 0.80 0.90 1.00Simulated Internal Tube Diameter (mm)208changes from 0 to 2 mL min1 at the start of the injection period, and from 2 to0 mL min1 at the end of the injection period.Figure 5-13 shows the SSE and relative peak area by varying the simulatedvolume from 60 to 100 pL in comparison to the 80 pL experimental peak. As expected,the simulated peak area increases linearly with the injection volume and indicates anoptimum very near 80 pL, as does the SSE. Since there is relatively good agreementbetween peak areas, adjustment of the simulated or experimental injection volume isdeemed unnecessary. This may not be the case, however, at shorter injection timesand higher flow rates where the inertial lag may have a greater effect.—s--- SSE • Relative Peak AreaFigure 5-13.experimental1.21.00.800.6 .0.40.2Effect of injection volume on simulated peak areas relative to an 80 pLpeak.wC,)Cl) 65 70 75 80 85Simulated Volume (pL)90 95 1000.02095.6.1.4 Effect of Laminar Flow ProfileThe effect of the laminar flow profile on the simulated peak shape was alsoinvestigated. Through comparison of the simulated and experimental peak profiles, itwas clear that better agreement could be made if the tailing portion of the simulatedprofiles (due to laminar flow) could be reduced, thereby shifting the molecules towardsthe peak centroid. Two methods of modifying the flow pattern have been attempted inthis work. The first involves modifying the power of the exponent in Equation 5-12,which produces a change in the axial cross-section of the laminar flow profile accordingto Figure 5-14. As the power, P, increases, the profile becomes broader and themolecular velocity along the tube walls increases while the molecular velocity in thecenter of the tube decreases. A second flow pattern modification was proposed byintroducing a new factor, into the convective movement terms of the simulation. Thisfactor reduces the degree of the laminar flow profile by replacing it with an averageflow component and will be discussed in section 0.4Figure 5-14. Relative flow rate as a function of distance to the center of the tube andthe power factor, P, in Equation 5-12.First, in order to be convinced that the flow regime was primarily laminar for theexperimental profiles obtained, and that a significant amount of secondary flow (orturbulence) was not created, a comparison between three peaks was made. Twopeaks are from an 80 pL injection volume flowing at 2.0 mL min1, with a valve-to-detector distance of 100 cm. The longer manifold length was used here so as toincrease the influence of laminar flow and diffusion. One peak profile was obtainedwith the tubing (before and after the injection valve) wound in a 1 cm diameter coil (toenhance secondary flow) while the other was kept as straight as possible. The thirdpeak was simulated with the model which assumes a perfectly laminar flow throughout.It is clear from Figure 5-15 that the simulated peak is significantly more similar to the-0.3 -0.2 -0.1 0 0.1 0.2 0.3Distance Relative to Centre of Tube (mm)211experimental profile obtained with straight tubing than the one with coiled tubing. Thus,we can be reasonably certain that the peak profiles obtained with the experimentalapparatus using straight tubing are primarily influenced by laminar flow, and that thelaminar flow simulated is more perfect than that experienced by the experimental plug.It is likely the assumptions made by the model (such as zero developing flow time, andperfectly cylindrical manifold geometry) that are limiting the fit between theexperimental and simulated peak.0.300.250.20c0. 5-15. Comparison of simulated and experimental profiles for an 80 pL injectionat 2.0 mL min1 with a valve-to-detector distance of 100 cm.Furthermore, the Reynolds number, Re, can also be used to predict whether theflow will be laminar or turbulent in the experimental system [16]. The Reynolds number0 10 20 30 40 50Time (s)212is simply a ratio of the inertia forces to viscous forces, and, flow is laminar when theviscous forces dominate. The Reynolds number is defined byUdEquation 5-14 Re =/1where p is the fluid density, U is the linear fluid velocity, d is the tube diameter, and p isthe dynamic viscosity of the fluid. Since the Reynolds number is unitless, anyconsistent system of units can be used. The flow is consider laminar for Re <2000,unstable due to the onset of turbulence for .2000 < Re <4000, and turbulent forRe > 4000. By considering an “order of magnitude” calculation, we can take the fluiddensity to be 1000 kg m3, the linear velocity to be 0.1 m s (which corresponds to Ca.3 mL min1), the diameter of the pipe to be 0.001 m, and the dynamic viscosity of thefluid to be 0.001 kg m1 & (which is the value for water at Ca. 21° C). The resultingReynolds number from this calculation is 100, which is well below the upper boundaryof 2000 for laminar flow.The shape of the laminar flow profile can now be investigated by modifying thepower, P, in Equation 5-12. Wentzell et a!. [3] found for their flow injection work, thatalthough there was no change in the peak position, the peaks became significantlynarrower and taller as P increased. They indicated that modification of P improvedagreement between experimental and theoretical results in some instances, which (theysuggest) means that the nature of the flow profile changes with experimentalconditions. Figure 5-16 shows the effect of the power factor on the simulations created213with the SIA model. The general shape change is in agreement with Wentzell et a!.,with the best overall fit occurring for P = 2. These data suggest that an increase in thepower factor does have the ability to shift the tailing molecules towards the peakcentroid, which improves agreement in the peak tail. However, this is at the expense ofa significant lack of agreement near the peak maximum. The SSE between thesimulated peaks (using different values of P) and the experimental peak is shown inFigure 5-17, as well as the relative peak areas. These data also indicate that the bestagreement occurs for P near 2. However, the possibility of the optimal value for Pchanging with experimental conditions still exists.(b) P = 20 5 10Time (s)1.0 1.00.8 0.8O.6 b06—OQ•4°O40.2 0.20.0 0.01.0 1.0(c) P = 30.6 0.6—0.4°0.408 080.2 0.20.0 0.015 0 5Time (s)10 150 5Time (s)10 15 0 5 10Time (s)Figure 5-16. Effect of power factor on simulated peak profiles (thick line) relative toexperimental profile (thin line).152140 SSE • Relative Peak Area0.80 1.080.70 1.0600.60 0 1.04a)0.50 V 1020.40 - V 1.000.30 V 0.9800.20 V 0.9600.10 V 0.940.00 I I 0920 1 2 3 4 5Power FactorFigure 5-17. Effect of power factor, P, on (i) the sum of the squares of the errors (SSE)between simulated and experimental peak profiles, and (ii) the simulated peak arearelative to the experimental peak area.5.6.2 General Agreement of the Random-Walk Model for SIAThe ability of the model to generate accurate peak profiles under typicalanalytical conditions will now be considered. If the model is able to provide us with areasonably accurate peak profile for the dispersion of a dye in a carrier stream, it willultimately be useful for studying and optimizing the various parameters affecting peakprofiles in general. The general premise of the model (cr2 x n 12) was shown to hold foran experimental peak produced by the sequential injection technique in Chapter 3.Peak profiles created with different manifold lengths, at different flow rates, usingdifferent injection volumes will now be compared to experimental profiles created under215similar conditions. For all simulation profiles shown in this section, the detector volumeis 7.85 l.iL, the manifold tube internal diameter is 0.84 mm, the power factor (P) is 2, thediffusion coefficient is 7.6 x 10.6 cm2 s, and the number of iterations per second is 10.Unless otherwise specified, the injection volume is 80 pL, the flow rate is 2.0 mL min1,and the valve-to-detector distance is 15 cm. Valve-to-Detector DistanceFigure 5-18 shows the predicted peak profiles by the random-walk model inrelation to the experimental profiles. The flow rate was 2.0 mL min1 and the injectionvolume was 80 pL. Favourable agreement is found in all three cases. The simulationpeaks start and stop at approximately the same time as the experimental peaks. Ingeneral, similar discrepancies in shape are found at each length; the simulated peakdrops too quickly after peak maximum before crossing over the experimental peak inthe tail section. Since peak height and peak area are the most commonly quoted peakdescriptors in flow analysis they are shown here for reference (Figure 5-19). There isgood agreement between the peak height and area for the simulated and experimentalprofiles. In general, however, the simulated peak profiles have heights and area whichare slightly lower than the experimental ones (except at 100 cm where the simulatedpeak height exceeds the experimental slightly, possible due to noise).216000Figure 5-18. Comparison of simulated and experimental peak profilesthin lines, respectively) for valve-to-detector distances of (a) 15 cm,(c) 100 cm.(thick lines and(b) 50 cm, and0 20 30(a) 15 cm60Time (s)(b) 50 cm0 102030 40 50 60Time (s) 100cmI0 10 20 30 40 50 60Time (s)217. Peak Area (Expt) . Peak Area (Sim) A Peak Height (Expt) . Peak Height (Sim)3.0 :Fi.5 0.50 20 40 60 80 100 120Valve-to-Detector Distance (cm)Figure 5-19. Peak height and peak area as a function of valve-to-detector distance forsimulated and experimental peak profiles. Flow RateThe effect of the simulated flow rate, shown in Figure 5-20, again indicates goodgeneral agreement between simulated and experimental peak shape. The injectionvolume was 80 pL and the valve-to-detector distance was 15 cm. It is interesting tonote the improved agreement for 0.5 and 1.0 mL mm1 during the last one-third of thepeak profile. This would indicate that laminar flow conditions near the tube walls aremaintained to a greater extent for the experimental profiles at lower flow rates. Thiseffect may be due partly to a lesser degree of hysteresis when starting and stoppingthe flow. Disagreement in the tailing (Figure 5-20) and the peak height (Figure 5-21)increases with flow rate. This is thought to be due primarily to a difference in laminar218flow profile. In general, the model is less sensitive to peak height than are theexperimental profiles. The model accurately predicts the inverse dependence of thepeak area on flow rate; there is excellent agreement at 1.0, 2.0, and 4.0 mL min1,although the cause of the discrepancy at 0.5 mL mm1 is unclear.0.7 0.7(a) 0.5 mL min1 (b) 1.0 mL min1___O.i(0 5 60Time (s) Time (s)0.7 0.7(c) 2.0 mL min1 (d) 4.0 mL min10.6 0.60.5 0.5o0.4 o0.40 10 20 30 40 50 60 0 10 20 30 40 50 60Time (s) Time (s)Figure 5-20. Comparison of simulated and experimental peak profiles (thick lines andthin lines respectively) for an 80 lJL injection at (a) 0.5, (b) 1.0, (c) 2.0, and(d) 4.0 mL mind.219—— Peak Area (Sim) —— Peak Area (Expt) —s-- Peak Height (Sim)—*— Peak Height (Expt) 2.0 3.0Flow Rate (mL min1)0()E()0)U)I(UU,00 0.00.0 4.0Figure 5-21. Peak height and peak area as a function of flow rate for simulated andexperimental peak profiles. Injection VolumeBy far the largest discrepancy between the simulated and experimental peakprofiles arises from variation of the injection volume. The predicted peak height issignificantly lower than the experimental, as shown in Figure 5-22 and Figure 5-23.However, the peak areas agree relatively well, with only a modest decrease in thesimulated value at higher injection volumes. This indicates a lack of agreementbetween the distribution of molecules within the manifold tube and not in the totalnumber injected. Again, improved agreement would be achieved if the tailingmolecules were shifted towards peak maximum as is clearly evident in Figure 5-22d.2201.0 (a) 40 pL 1.0 (b) 80 i0.8 0.8c0.60510 15 20 25 051015 20 25Time (s) Time (s)1.0 (c) l6OpL 1.0 (d) 240 ji0510152025 0510152025Time (s) Time (s)Figure 5-22. Comparison of simulated and experimental peak profiles (thick lines andthin lines respectively) as a function of injection volume; the flow rate was 2.0 mL min1and the valve-to-detector distance was 15 cm.22165Co21Figure 5-23. Peak height and peak area as a function of injection volume for simulatedand experimental peak profiles; the flow rate was 2.0 mL min1 and the valve-to-detectordistance was 15 cm.7—+— Peak Area (Sim) —a— Peak Area (Expt) —— Peak Height (Sim) —-- Peak Height (Expt) 40 80 120 160 200 240Injection Volume (pL)5.6.3 Laminar Flow FactorIt became evident that improved agreement between the simulated andexperimental flow profiles would be attained if the tailing molecules of the simulation(near the tube walls) could be brought forward to nearer the peak maximum. Anattempt to achieve this through modification of the convective movement terms of thesimulation is presented here. The addition of Cand the average-flow term to Equation5-13 was thought to produce an overall reduction in the laminar flow characteristic ofthe generated profile.222As expected, the anticipated transformation of the simulated peak profile fromone that is almost a square plug (Figure 5-24a, (= 0.00) with minimal dispersion, to theasymmetric peak profile created by a purely laminar flow profile (Figure 5-24f, (= 1.00)occurs for 0.00 ( 1.00. In order to maintain consistency with previousinvestigations, the peaks shown were created using an injection volume of 80 pL, a flowrate of 2.0 mL min1, and a valve-to-detector distance of 15 cm. However, furtherinvestigation of the laminar flow factor using 40, 160, or 240 pL (where the agreementbetween simulated and experimental peaks is less apparent), would be warranted toinvestigate any possible improvement at these injection volumes. By close examinationof the tailing between 5 and 10 seconds in Figure 5-24e and Figure 5-24f, it is clearthat an optimal value for (lies between these two values. As predicted, the tailingmolecules shown in Figure 5-24f have indeed been moved off of the walls and towardsthe peak maximum. Further reduction of (below 0.80 causes too much of a shift,decreasing the agreement substantially. In Figure 5-25, the SSE and relative peakarea are considered as a function of ( Both indicate an optimum value between 0.80and 1.00. In Figure 5-26, the simulated peak profiles for 0.80 ( 100 are shown(relative to the experimental profile). Close examination of Figure 5-26a and Figure 5-26f reveals that improvement in the tailing portion of the peak profile can indeed bemade by fine-tuning this factor. Figure 5-27 indicates the optimal value for (to be near0.88 according to the SSE, and 0.94 according to the relative peak areas (although if0.88 were used, the simulated peak would be no more than 1% larger than theexperimental peak).223Figure 5-24. Effect of laminar flow factor, on simulated peak profile (thick line)relative to experimental peak profile (thin line) for 0.00 1.00. The injection volumewas 80 pL, the flow rate was 2.0 mL min1, and the valve-to detector distance was15cm.0.2015 0 5 10Time (s)151.00.8(a) ç=,0 5 10Time (s) 5 10Time(s)151.00.8(e) = 0.800Q40.20.0•Time (s)1,.00.8o 0.600. =0.600 510 15Time (s)(f) =1.000 5 10 15 0 5 10Time (s)15Figure 5-25. Effect of on (i) the sum of the squares of the errors (SSE) between thesimulated and experimental peaks, and (ii) the simulated peak area relative to theexperimental peak as shown in Figure 5-24.—a— SSE —— Relative Peak AreawU)U)224a)a)0a)>4-a)a)10 1.2098 1.1576 1.1054 1.0532 1.00I0 0.950.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00225Figure 5-26. Effect of laminar flow parameter, on simulated peak profile for0.80 1.00. The injection volume was 80 pL, the flow rate was 2.0 mL min1, andthe valve-to detector distance was 15 cm.(a) ç=0.80-. I0 5 10 15Time (s)1.00.8o 0.600. 0.88Time (s)1.00.8o 0.600•° ç=0.84Time (s)(d) ç = 0.92Time (s)(f) =1.0015 15(e) C=0.96[\Time (s)0 5 10 15 0 5 10 15Time (s)2261.01cucj)cua)1.00 0-a)>Cua)0.99• SSE . ReIatke Peak Area1.020.85 0.90 0.95c0.200.160.12wCl)U) 0.980.80 1.00Figure 5-27. Effect of on (i) the sum of the squares of the errors (SSE) between thesimulated and experimental peaks, and (ii) the simulated peak area relative to theexperimental peak as shown in Figure 5-26.To consider the effect has on the flow profile at longer tube lengths, similarprofiles were compared for a valve-to-detector distance of 100 cm, as shown in Figure5-28. The flow rate was 2.0 mL min1 and the injection volume was 80 pL. There ismuch greater agreement near the peak maximum (between 10 and 20 seconds) for =0.80 (Figure 5-28b) than for = 1.00 (Figure 5-28f), however, there are now too manymolecules between 20 and 30 seconds, and not enough between 35 and 50 seconds.An optimal value again resides near 0.85, according to the SSE shown in Figure 5-29, the relative peak areas for all simulated values is too low by as much as 4%.2270.50.40.3° 5-28. Effect of on the simulated peak profiles (thick line) relative to theexperimental peak profile (thin line). The injection volume was 80 pL, the flow rate was2.0 mL min1, and the valve-to detector distance was 100 cm.(a) ç=0.75t\10 10 20 30 40 50Time (s)0.5(b) ç=0.800.4o 0.3C-)0.2[N0.10.00 10 20 30 40 50Time (s)0.5(d) ç=0.900.40.30.2 V0.10.00 10 20 30 40 50Time (s)0.5(c C=0.850 10203040 50Time (s)0.50.4oO.° =0.950.4°0.2 V0.10.0(f) =1.000 10 20 30 40 50Time (s)0 10 20 30 40 50Time (s)228(U0)(U0)00)>(U0)Figure 5-29. Effect of on (i) the sum of the squares of the errors (SSE) between thesimulated and experimental peaks, and (ii) the simulated peak area relative to theexperimental peak as shown in Figure 5-28.Although it may be concluded that the optimal value is not significantlyinfluenced by manifold length, it is much more dependent on the injection volume.Figure 5-30 shows the simulated results at higher injection volumes (160 and 240 pL)for three values of (0.60, 0.80, and 1.00). For the 160 pL injection, an optimal valuenear 0.80 (or possibly a little higher) is indicated by an excellent improvement in peaktail agreement. The contributions of plug-flow likely come form starting and stoppingthe flow periodically, and manifold non-ideality. Lack of agreement near the peakmaximum is still not understood or accounted for, although the overall peak heightagreement is improved at 0.80 as well. There is significant improvement in theagreement between the tailing portion of the peak (as well as peak height) for (= 0.80—--- SSE • Relative Peak Area0.400.350.300.25w0 0.2000. 0.80 0.85 0.90 0.950 10 20Time (s)30 0 10 20Time (s)229relative to (= 1.00 and = 0.60. At an even larger injection volume of 240 pL (Figure5-30d-f), the best agreement again appears to be near (= 0.80. This series of figures(Figure 5-30d-f) clearly demonstrates the ability to improve the peak shape agreementby reduction of the laminar flow profile, especially in the tailing region of the peak.1.0 1.00.8 0.8o0.60.4 0.40.2 0.20.0 0.01.0 1.00.8 0.8o 0.6 ° 0.60.4 °0.40.2 0.20.0 0.01.0 1.00.8 0.8o0.60.4 °0.40.2 0.20.0 0.030 30Time (s)Figure 5-30. Simulated and experimental peak profiles (thick lines and thin linesrespectively) for 160 and 240 pL injection volumes at 2.0 mL min1 with a valve-to-detector distance of 15 cm.300 10 20Time (s)30 0 10 20Time (s)300 10 20Time (s)0 10 20230All of the profiles shown thus far have used a flow rate of 2.0 mL min1. Sincelaminar flow conditions should be easier to attain at lower flow rates, the optimal valuefor would be expected to be inversely proportional to flow rate. Thus, flow profiles at0.5 mL mm1 would be expected to have an optimal value closer to 1.00, while flowprofiles at 4.0 mL min would be expected to have an optimal C value of less than 0.80.Figure 5-31 shows that this is indeed true. At 0.5 mL min1, the peak tail agrees best atC= 1.00, and is already “overshooting” at = 0.80. On the other hand, close inspectionof the profiles generated at 4.0 mL min’ indicates that an optimal C value liessomewhere between 0.80 and 0.60 (where it begins to “overshoot” as well).231(d) 4.0 mL min1, = 0.600 20 40Time (s)60 0 5 10Time (s)1.00.8o 0.6C) 0.5 mL miW1, = 0.800.8o 0.6000.40.20.00 20 40 60Time (s)1.0(c) 0.5 mL min1, = (s)1.0•0.80.600.•40.20.00 5Time (s)100 20(f) 4.0 mL min1, ç = 1.0040 60 0 5 10Time (s)Figure 5-31. Effect of on simulated peak profiles (thick line) at 0.5 mL min1 and4.0 mL min1 relative to experimental profiles (thin line) with an injection volume of80 pL and a valve-to-detector distance of 15 cm.Thus, it has been shown that improved agreement between the simulated andexperimental peak profiles can be accomplished by inclusion of an average-flow term(moderated by ) in the convection equation of the simulation. This is significant for232two reasons. First, it tells us that the experimental peak profiles have not been createdunder perfectly laminar conditions; if they were, they should exhibit much greatertailing. Second, by empirically determining the effect of the system parameters on(which is primarily influenced by flow rate), one could conceivably correct thesimulation to match the experimental profiles in the majority of cases. This would allowthe researcher to use the simulation as an accurate optimization tool for predictingexperimental peak profiles under various conditions. However, it should be kept inmind that laminar flow conditions which are free from the influence of secondary floware rarely found in practice. Hence, further work should first focus on incorporatingsecondary flow into the convective equation of the model.In the present state, the model can be used to accurately predict dispersionprofiles under flow conditions which are primarily dominated by laminar flow. Thisallows us to study the predicted output profiles for optimization purposes, and allows usto study the theoretical molecular distribution within the manifold tubing at any point intime. This will be the topic of the next section of this chapter.5.6.4 Cross-Sectional Molecular DistributionA significant advantage of developing an iterative model lies in the ability toexamine the progress of the simulated analysis at any point in time. This allows theresearcher to come to a greater understanding of the analytical procedure since thepredicted movement of the molecules within the manifold under varying analytical233conditions can be visualized. To facilitate this, the molecules within the tube can beplotted after each iteration (by the simulation software) in a frame which represents theactual manifold dimensions. This picture of the molecular cross-section can berecorded to disk as a bitmap file for subsequent examinationt.The sequential injection of two 80 pL zones at 2.0 mL mm1 with a valve-to-detector distance of 15 cm is shown in Figure 5-33, Figure 5-34, and Figure 5-35.Each frame represents a cross-section of the manifold tube with a vertical scale of0.84 mm (y-direction) and a horizontal scale of 58 cm (z-direction). The depth of theframe (x-direction) only includes molecules which are less than 10% of the tubediameter from the center of the tube (see Figure 5-32). In this way, the twodimensional cross-section represents an axial slice (or “slab”) through the tube withoutbias from the different thicknesses of the tube as seen from the side. The vertical lineclosest to the center of the frame is the multi-position valve interface, and the twovertical lines near the right represent the 7.85 pL detection zone. Molecules within thedetection zone are integrated to produce a detector response. The distance betweenthe valve and the left end of the tube is 40 cm, the distance between the valve and theright end of the tube is 18 cm, and the distance between the valve and the left edge ofthe detection zone is 15 cm.There are several utility programs available that operate in the Windows environment and allowsequential viewing of bitmap files with a time delay between each frame. Playing back the bitmappedfiles which are recorded during the simulation, produces an animation of the spatial distribution of themolecules as the analysis procedes.234(Tube Cross-Section(20% of Tube Diameter)Figure 5-32. Molecules found within the shaded “slab” are used in the cross-sectionalmolecular distribution plots.The simulation begins with the multi-position valve connected to the linecontaining the molecules to be injected (although the detector outline is still shown).The simulation allows the analyzer 1.00 s to turn to this position, and therefore, the firstmolecules are seen moving into the tube towards the left at 1.10 s. The parabolic flowprofile is immediately evident in the first step the molecules take, since, as anapproximation, the model assumes the flow rate and laminar flow profile startinstantaneously. By dividing the tube into 1 cm segments and integrating the numberof molecules in each cylinder created, an axial dispersion profile of the molecules canbe shown for each iteration (thin line on top of the molecular distribution). The injectionof the first zone continues for a total of 2.40 s with an iteration period of 0.10 s.Although a frame was recorded for each simulation iteration, several frames have beenleft out in these figures for brevity.By 3.40 s the injection period is complete and the flow is stoppedinstantaneously (also an approximation). It is interesting to note that very few235molecules are predicted to be near the walls of the tube throughout the zone, and thuswall interaction calculations in the model would play a relatively minor role at this point.The zone of molecules is now over 30 cm in length, which is over 15 cm longer than an80 pL zone would be under plug flow conditions. From 3.40 s to 4.40 s the flowremains stopped as the injection valve moves to the next position (the detector line).During this time, the molecules are allowed to take their diffusion steps withoutconvective steps. Although the injected zone does not appreciably lengthen during thistime, it does appear to be slightly more radially diffused at 4.40 s (e.g., examinemolecular concentrations at the center of the tube nearest the valve). As such, it isimportant to include this pause with molecular diffusion in the model.From left to right, the concentration gradient is shown to increase quickly at first,and then more gradually for the majority of the injected zone, until it reaches a valuenear C° at the valve interface. A key point can now be made based on the molecularconcentration gradient across the injected zone. Simplification of the model, by makingthe assumption that this zone has a constant concentration throughout, and cantherefore be injected as a usquare plug” (as in flow injection or chromatography models)would be oversimplifying the situation too much since the concentration gradientthroughout the zone is significant. By the use of this unique injection procedure, it isnow possible to visualize the true concentration gradient in the simulated tube.At 4.50 s, the first molecules of the second zone to be injected have steppedthrough the multi-position valve. The concentration profile must now be considered236since, in black and white, it is difficult (if not impossible) to see the difference betweenthe molecules of each zone (a colour animation of the two different molecular zonesprovides a much greater contrast). By 6.80 s the second zone is completely injected,and, not surprisingly, it has a similar concentration profile as the first zone at 4.40 s.The tailing (right-most) edge of the first zone now has a concentration gradient which isthe inverse of its leading (left-most) edge. With this model, the nature of thesepredicted axial concentration profiles can be shown for the first time. The overlap ofthese profiles is the most likely point of reaction, and would constitute the productconcentration profile. Although the overlap appears to be skewed to the left at 6.80 s, itwill be shown in the next section that the product concentration across the zone isactually quite symmetric when radial molecular distribution is taken into account.By 7.80 s the molecules have been allowed their diffusional steps (withoutconvection) for one second as the valve moves to the detection line. At 7.90 s the flowis reversed and the molecules begin to move back through the valve, towards thedetection zone. The initially abrupt concentration profile at the valve interface nowbegins to disperse. By 9.00 s, 40 pL of the second zone have moved back through thevalve and the concentration gradient across this zone is approximately symmetrical. Atthis point, molecules of this zone are just entering the detector. By consideration of theconcentration profile appearing in the detector over the next four frames, one canunderstand why the detector response increases so quickly and “washes away” soslowly, creating a very skewed peak profile.237At 10.30 s, the isodispersion point is reached at the valve, where the mutualoverlap of the concentration profiles is quite symmetric. This point would actually beanticipated at 10.20 s which is exactly 2.40 s (equivalent to 80 pL) after the flow wasreversed. At this point in the analysis we have, in essence, an 80 pL zone positionedon either side of the injection valve, with each zone partially dispersed into the other.The concentration of each zone at this interface is approximately 0.5 C°. Thisdemonstrates unequivocally that mutual dispersion between two injected zones in anarrow bore tube is possible with zero net movement of fluid, according to the random-walk model [12-13]. This was one of the advantages presented in favour of thesequential injection method since zero net movement of fluid means sample andreagent consumption are minimized.As the flow continues to the right, the overlapped zone becomes more skewedand the isodispersion point reaches the detector at 11.80 s. After this point, theconcentration of the zone on the right slowly decreases while the concentration of thezone on the left increases slightly until its peak maximum is reached in the detector.Finally, the concentration of both zones slowly diminishes to zero, with the moleculesalong the walls of the tubes lingering the most; in fact, some molecules are still seennear the walls as far as 20 cm to the left of the valve, even at 20.00 s.238Figure 5-33. Cross-sectional molecular distribution during injection of an 80 pL samplezone through the valve (central vertical line).bOOs1030s11 00 s239Figure 5-34. Cross-sectional molecular distribution during injection of an 80 pL samplezone through the valve (central vertical line).:.••,.-N gccCD—1(710iCool—C-)(DO C,)<0—0<(1)(D 00CDD1 <2.CDCD—32-CD0C 0 0 C -‘ D CD 2 CD 0 0 CD co 0 Cl) CD 3-D CD1) . C2415.6.5 Cross-Sectional Zone PenetrationThe mutual overlap of two zones does not necessarily mean that radial mixing inthe area of overlap is complete or homogeneous. Again, this can be shown with therandom-walk model as a function of time. The simulation tube was divided axially into1.0 mm segments to produce several hundred individual cylinders. Each cylinder wasfurther divided into 50 concentric cylinders of equal volume. During each iteration ofthe simulation, a point is made on the simulation tube for each cylinder with at least onemolecule from each of the two zones. A point is plotted at the corresponding axialposition of the cylinder (z - position) and the positive and negative y - position for thatcylinder, thus creating a distribution profile which is symmetric about the tube axis. Inthis way, the actual zone-penetration can be shown as a cross-section in a planeparallel to the axial center of the tube without bias due to radial positioning. Thepenetrated zones thus shown, indicate the most probable location of chemical reactionand therefore product formation. The concentration of these penetrated zones can beintegrated over the axial distance of the tube (at 1.0 cm intervals as before), thusshowing the predicted concentration of the product zone at any point in time.The axial and radial zone penetration for the two 80 pL zones examined in theprevious section, are shown in Figure 5-36, Figure 5-37, and Figure 5-38 as a functionof time. Each frame represents a 60 cm long tube with an internal diameter of 0.84 mmand a valve-to-detector distance of 15 cm. The simulation starts by pausing for 1.0 s,injecting the first zone for 2.4 s, pausing for another 1.0 s, before beginning injection of242the second zone at 4.40 s. At 4.50 s the second zone has made its first step into theinjection tube, and subsequently the zone penetration initially appears as a very thinregion at the interface between the two zones. As the injection proceeds, the zonepenetration increases in thickness, and distorts parabolically down the length of thetube according to the laminar flow profile. The concentration profile of the penetratedzones increases in width proportionally, and increases in height approximately equallyover the entire zone. This indicates that the height of the overlapping area at say7.80 s in the previous simulation (Figure 5-34) is not indicative of the productconcentration. That is, if the entire tube is taken into consideration at any instant intime, the isodispersion point would not be expected to have a greater concentration ofproduct (using equivalent sample and reagent concentrations) due to the radialseparation of the two zones. A detector response, however, is still likely to maximizenear the isodispersion point since the product concentration will increase with time (asthe two zones pass through the detector) and then minimize when the sample orreagent concentration in the flow-cell approaches zero.At 7.80 s the flow is reversed and the molecules are propelled towards thedetector. Inversion of the radial distribution of the penetrated zones can be seen from8.00 s to 11.00 s in Figure 5-37. At 10.20 s the simulation is again at the point of zeronet fluid movement and the peak height of the concentration profile of penetrated zonesis predicted to be maximum at the valve interface. This indicates that the optimallocation for detection of product is at the valve. Future designs of multi-position valveswhich incorporate a sensor (e.g., a fiber-optic cable) within the valve mechanism might243see improved sensitivity at reduced sample and reagent consumption. This is inexperimental agreement with the decreased injection volume necessary to achievemaximum sensitivity when using the shortest manifold lengths (Chapter 4). If a longerreaction time is necessary, the flow can be stopped while the product maximum issituated in the detection zone. Progression of the zone penetration towards thedetector causes the concentration to diminish such that a maximum of approximatelyone-half of the height reached at the valve interface is realized at the detector.244Figure 5-36. Axial cross-section of zone-penetration between two 80 iJL zones injectedsequentially at 2.0 mL min1.245Figure 5-37. Axial cross-section of zone-penetration between two 80 pL zones injectedsequentially at 2.0 mL min1.246Figure 5-38. Axial cross-section of zone-penetration between two 80 pL zones injectedsequentially at 2.0 mL min1.247By monitoring the zone penetration concentration profile as a function of time, itcan be shown that the peak height of this profile increases slowly and approximatelylinearly as the second zone is loaded. Then, the rate of increase in peak height isincreased as the flow is reversed, with a maximum height being reached at the point ofzero net fluid movement. Figure 5-39 shows this effect as a function of time. Afterpeak maximum is reached, the maximum concentration of the penetrated zones quicklydecays at an exponential rate. Thus, it may be concluded that the random-walk modelpredicts a significantly narrower and taller concentration profile of penetrated zoneswhen the displacement is at zero net fluid movement. Greatest sensitivity would,therefore, likely be achieved at this manifold position. Similar results would beexpected if three stacked zones were considered, except that the point of zero net fluidmovement occurs when the middle zone is centered at the valve interface.248IjO. 0.2‘C0Figure 5-39. Relative peak maximum for zone penetration as a function of time, aspredicted by the simulation.5.7 CoNcLusioNsA numerical simulation based on the random-walk model has been proposedand developed for the sequential injection process. This is the first time this analyticalprocess has been modeled. A unique injection procedure is incorporated into themodel which simulates the sequential stacking of up to four zones in the manifoldtubing. There is generally good agreement between simulated and experimental peakprofiles created under laminar flow conditions. The model is able to successfullypredict peak profiles created at a variety of flow rates, injection volumes, and valve-to-LoadingFirstZoneFlowReversal0 2 4 6 8 10 12 14 16Time (s)249detector distances typical of sequential injection analysis. It was found that inclusion ofan average-flow term (the magnitude of which is controlled by ) in the convectivemovement equation of the model improves the correlation (especially in the peak tail)between the simulated and experimental peak profiles. As expected, the degree oflaminar flow () achieved in the experimental profiles is shown to be inverselyproportional to the flow rate.The model has been used to improve our fundamental understanding of theprocesses occurring during the injection process and flow reversal. The molecularconcentration gradients of two zones as a function of time have been shown, and usedto prove (theoretically) that mixing can indeed occur with no net fluid movement. Aswell, the cross-sectional distribution of zone penetration has been examined and usedto determine that the theoretical maximum penetration increases upon flow reversal,reaching its highest point at the valve interface. Further use and modification of thismodel will provide new insight into the sequential injection method.Further improvements in the agreement of the model with experimental peakprofiles might be attained if the approximation of instantaneous flow rate change at thestart and stop of an injection period was refined. As well, the model may be improvedby accounting for the true valve and detector geometry. An attempt could also be madeto improve the laminar flow characteristics of the experimental peak profiles, whichhave been shown to be somewhat less than perfect probably due to (i) the valve anddetector geometry, (ii) the pulsing caused by the peristaltic pump, or (iii) the repeated250starting and stopping of the flow. Further investigation could be done with the currentmodel using tracer dyes with different diffusion coefficients, and the effect oftemperature could be investigated.The next major obstacle to overcome with this model is to account for secondaryflow characteristics found when the manifold tubes are coiled. This would enable theresearcher to develop optimal experimental methods with the model which can beimplemented in practice. As a final step towards reality, incorporation of the effects ofchemical concentration gradients and reaction kinetics should be attempted. It isassumed that the computational power of the personal computer will continue toincrease in future years enabling the inclusion of these calculations without asignificant delay in generation of simulated peak profiles.2515.8 REFERENcEs[1] D. Betteridge, C. Z. Marczewski, and A. P. Wade, Anal. Chim. Acta, 165 (1984),227.[2] C. D. Crowe, H. V. Levin, D. Betteridge and A. P. Wade, Anal. Chim. Acta, 194(1987), 47.[3] Wentzell, M. R. Bowdridge, E. L. Taylor and C. MacDonald, Anal. Chim. Acta,278 (1993), 293.[4] A. Einstein, Ann. Phys., 17 (1905), 549.[5] C. A. Whitney, Random Processes in Physical Systems, Wiley, New York, 1990.[6] A. G. Marshall, Biophysical Chemistry, Wiley, New York, 1978.[7] E. C. Hemenway and A. P. Wade, J. Chem. Ed.,69(2) (1992), 123.[8] J. C. Giddings, J. Chem. Ed., 35 (1958), 588.[9] J. C. Giddings, Dynamics of Chromatography, Part 1, Principles and Theory,Dekker, New york, 1965.[10] G. Taylor, Proc. R. Soc. London, Ser. A, 219 (1953), 186.[11] M. von Stackelberg, M. Pilgram, and V. Toome, Zeitschrift fur Elektrochemie,57 (5) (1953), 342.[12] J. Ruzicka, G. D. Marshall, and G. D. Christian, Anal. Chem., 62(1990), 1861.[13] J. Ruzicka and G. D. Marshall, Anal. Chim. Acta, 237 (1990), 329.252[14] H. Wada, S. Hiraoka, A. Yuchi, and G. Nakagawa, Anal. Chim. Acta, 179 (1986),181.[15] J. W. Atkins, Physical Chemistry, Wiley, New York, 1978.[16] J. P. Tullis, Hydraulics of Pipelines: Pumps, Valves, Cavitation, Transients,Wiley, Toronto, 1989.2536. Conclusions andFurther Work“The measure of our intellectual capacityis the capacity to feel less and less satisfiedwith our answers to better and better problems.”C. W. Churchman6.1 SEQuENTIAL INJECTION ANALYSIS SYsTEMFor the first time, a significant step towards simplification of method developmentfor sequential injection analysis has been made. The virtual manifold presented inChapter 2, combined with the greater hardware simplicity of a sequential injectionsystem has proven to be a synergistic combination. Not only can new chemistries beincorporated without physically reconfiguring the manifold (one of the design ideals ofsequential injection analysis), but with the new interface, almost all system variablescan be automatically explored with a “few clicks of the mouse.” This removes thecomplexity of the software interface from the hands of the researcher who can thenfocus greater attention on developing new methods or exploring new reaction kineticsor chemistries. Increased utilization of graphical user interfaces which simplify complex254software control over mechanical systems will become more and more apparent as thisscience evolves. In essence, it is a graphical model on a computer screen that hasbeen established in order to make this field more understandable, and more useful, toresearchers across the disciplines.6.2 ExPERIMENTAL DESIGN AND SYSTEM CHAcTERlzATloNNever before has the control over injection volume and peak shape been soevident in a flow system. This control results in peak shapes that vary widely, and bydirect manipulation of the method, virtually any degree of dispersion can be achievedwithin the same physical manifold. The results from a comprehensive empiricalinvestigation of peak shape is presented in Chapter 3 in an attempt to gain new insightinto the sequential injection technique. The study took advantage of the ability of theanalyzer to quickly and independently perform a large number of experiments(over 6,000). All of the data were stored within an efficient database for rapid recalland display. Peak moments are found to be useful for characterizing sequentialinjection peak shape, The reproducibility and periodicity of the injection volume whenusing a peristaltic pump is demonstrated. In addition, the random-walk model is shownto hold for the sequential injection process, thus validating its use, in Chapter 5 forsimulation purposes.2556.3 OPTIMIzATIoN OF DISPERSION IN SEQUENTIAL INJECTION ANALYSISIn Chapter 4, the concept of zone penetration was further explored with the useof the analyzer created in Chapter 2 and the dataset tabulated in Chapter 3. The majorfactors influencing the mutual penetration of two adjacent zones are injection volume,flow rate, and valve-to-detector distance. In this study, only coiled tubes are taken intoconsideration since this is usually the format that the manifold takes on in practice;straight tubes greater than one metre in length are awkward to work with on a realanalyzer. Four parameters which allow a relative measure of the degree of samplezone penetration, sensitivity, reagent economy, and throughput of the analysis wereintroduced, and were considered under conditions of varying analytical requirements.A composite function was used which enabled the search for optimum conditions usingtwo or more of the four “essential” optimization parameters. It was found that thesample zone penetration and the sensitivity parameters are the most important whendesigning a method. When only these two parameters were considered, the optimalvolumes of sample and reagent to inject were found to be independent of valve-to-detector distance and flow rate (assuming fast reaction conditions). Additionally, it wasfound that increasing the distance between the valve and the detector beyond theminimum necessary to physically connect them provides no significant advantage forzone penetration, and only decreases the sensitivity. Longer manifold lengths can besimulated by further aspiration of the injected zones towards the pump before sendingthe mixture to the detector for measurement (or via multiple flow reversals). However,this requires extension of the distance between the pump and the valve to ensure that256the injected zones never reach the pump. Finally, a study should be done to confirmthe utility of these optimization descriptors with a real, suitable chemistry.6.4 RANDOM-WALK MODEL FOR SEQUENTIAL INJECTION ANALYSISThe random-walk model has provided the first simulation tool for studying thesequential injection technique. The model was shown to correlate well with sequentialinjection peak profiles which are created under laminar flow conditions, and possibleareas of further refinement of the model were discussed. The addition of anaverage-flow term in the convective step was able to correct for the discrepancy in the tailingportion of the peaks. Other discrepancies in the correlation between the simulated andexperimental profiles may be attributed to “developing flow” when the laminar flowprofile is created at the beginning of fluid movement. The model alsoallowedvisualization of the (theoretical) cross-sectional concentration gradients which occurduring the sequential injection process. This model should have a significant impact onstudying heterogenous chemistries such as the use of magnetic beads in biotechnologyapplications since the model works at the physical I particle level. Reactionkineticsand variation in manifold geometry could be implemented with little difficulty,It is forthese reasons that the random-walk model will likely be the most useful aid instudyingsequential injection analysis for quite some time.


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