)V1531_1 RETURNING MATERIALS: Place in book drop to LIBRARJES remove this checkout from .—;—. your record. FINES win - ~ be charged if book is returned after the date stamped be10w. v ~L2o ouc‘sv ACHIEVEMENT OF PULSED ELECTROANALYTICAL TECHNIQUES THROUGH THE USE OF CHARGE PULSE POLARIZATION: SIMULATION AND EXPERIMENT BY Kathleen Ann Fix A Dissertation Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1988 m ‘v. ya H'thv' $15“; 'VU .a‘iagure the Ce] :4; diffEre aid in“ ABSTRACT ACHIEVEMENT OE PULSED ELECTROANALYTICAL TECHNIQUES THROUGH THE USE OF CHARGE PULSE POLARIZATION: SIMULATION AND EXPERIMENT BY Kathleen Ann Fix The use of charge pulses to control the potential of an electrochemical cell virtually eliminates the errors inherent in potentiostatic control. Conventional instrumentation currently employs a potentiostat to control the potential of the working electrode of an electrochemical cell. The use of a constant current source results errors inherent in the techniques due to double layer charging and solution resistance. In the case of charge pulse polarization, charge pulses used to step the potential are separated from those used to maintain it and potential measurement is made between pulses with no net current in the cell. Modelling programs were written to simulate normal and differential pulse polarography and square wave voltammetry and implementations of those techniques using charge pulse polarization. The results of these programs were in good aura ' no». A J cnara< methoc agreement with those from physical experiments. The characteristics of the conventional and charge pulsed methods obtained from the models were compared. The charge pulsed methods were more sensitive in all cases and were faster in some instances. The optimum experimental values are predicted to be: a square wave amplitude of 25mv (or a pulse height of SOmV), a staircase step height of 1omv, and 25% of the cycle devoted to the forward pulse (for CPSWV). Lastly, for charge pulsed square wave voltammetry, results were obtained for a hypothetical ideal and currently realizable instrument. The resultant characteristics were analyzed in detail. Since the charge pulsed methods are instrumentally limited, the advent of faster, more sensitive components may make it possible to make further gains in the charge pulsed methods, which are currently limited by the maximum pulse rate and the range of practical charge injections. 2:321 filfifin v "v” :A‘, ‘9‘ e ACKNOWLEDGEMENTS I would like to thank Dr. C.G. Enke for all his help and guidance during my research career. I would also like to thank my guidance committee: Dr. A. Timnick, Dr. G. Babcock, and Dr. D. Nocera. I'd like to thank Dotty for being such a great friend and confidant over the past 4 years. Thanks go to Norman Penix for the building of the instrument and all the support over the past few years. I appreciate Pete Palmer's presence, a fellow Western New Yorker was welcome. I'd also like to thank the various members of the Enke group, especially the older ones and honoraries, for proving that craziness keeps you from going insane. Special thanks go to Mrs. D. Miller and Dr. Raymond O'Donnell for starting me off, and to my parents and Steve for encouragement and love. In the immortal words of Dr. Martin Luther King -- 'Free at last, free at last, thank God, ...[I’m] free at last!’ (or am I?) ii LIST or LIST'OF CHAPTER CHAPTER CHAPTER TABLE OF CONTENTS TABLES. . . . . . . . . . . . . . . . . . . . . vi FIGURES . . . . . . . . . . . . . . . . . . . .viii 1 PULSED ELECTROANALYTICAL TECHNIQUES . . . . . 1 A. Introduction to the Techniques . . . . . . . . 1 1. Normal Pulse Polarography . . . . . . . . . 2 2. Differential Pulse Polarography . . . . . . 6 3. Square Wave Voltammetry . . . . . . . . . .12 8. Theory and Practice. . . . . . . . . . . . . .15 1. Theoretical Equations . . . . . . . . . . .15 2. Practical Limitations . . . . . . . .‘. . .18 2 THE APPROACH AND DESIRABILITY OF IMPLEMENTING PULSED ELECTROANALYTICAL TECHNIQUES WITH CHARGE PULSE POLARIZATION. . . . . . . . . . . . . . . .27 A. History of Charge Pulse Polarization and its use to change potential. . . . . . . . . . . . . .27 8. Maintenance of Potential by Charge Pulse POlarization O O O O O O O O O O O O I O O O .30 C. Normal Pulse Polarography by Charge Pulse POIarizatj-on O O O O O O O O O O O O O O O O .36 D. Differential Pulse Polarography by Charge Pulse .POlarization O O O O O O O O O O O O O O O I .42 E. Square Wave Voltammetry by Charge Pulse Polarization . . . . . . . . . . . . . . . . .46 3 COMPUTER MODELLING OF PULSED ELECTROANALYTICAL TECHNIQUES USING CHARGE PULSE POLARIZATION. . . .50 A. Normal Pulse Polarography. . . . . . . . . . .52 1. Traditional normal pulse polarography . . .53 iii 2. Charge pulsed normal pulse polarography . .57 8. Differential Pulse Polarography. . . . . . . .63 1. Traditional differential pulse palarography O O O I O O O O O O O O O O O O 64 2. Charge pulsed differential pulse polarography. . . . . . . . . . . . . . . .66 C. Square Wave Voltammetry. . . . . . . . . . . .73 1. Traditional square wave voltammetry . . . .74 2. Charge pulsed square wave voltammetry . . .78 CHAPTER 4 STUDIES OF THE CHARACTERISTICS OF PULSED ELECTRO- ANALYTICAL TECHNIQUES USING CHARGE PULSE POLARIZATION BY COMPUTER SIMULATION . . . . . . .86 A. Normal Pulse Polarography. . . . . . . . . . .86 1. Comparison of continuous current model to physical experimental results . . . . . . .87 2. Comparison of results for continuous current and charge pulsed methods . . . . . ... . .90 8. Differential Pulse Polarography. . . . . . . 102 1. Comparison of continuous current model to physical experimental results . . . . . . 102 2. Comparison of results for continuous current and charge pulsed methods . . . . . . . . 107 C. Square Wave Voltammetry. . . . . . . . . . . 118 1. Comparison of continuous current model to physical experimental results . . . . . . 118 2. Comparison of results for continuous current and charge pulsed methods . . . . . . . . 120 CHAPTER 5 INSTRUMENTAL CONSIDERATIONS FOR CHARGE PULSED SQUARE WAVE VOLTAMMETRY . . . . . . . . . . . . 135 A. Description of Instrumental Characteristics. 135 1. Hypothetical ideal instrument . . . . . . 135 2. Instrumental characteristics of previously built instrument. . . . . . . . . . . . . 137 iv mu ,. R 1501‘ R In of van H .7375." ‘ Ul‘U .: as Irha .JD'.‘\"“ . «Hg ‘ EA 11. 3. Instrumental characteristics of current instrumentation . . . . . . . . . . . . . 137 B. Comparison of Characteristics for Charge Pulsed Square Wave Voltammetry for Hypothetical Ideal and Realizable Instruments . . . . . . . . . 139 CHAPTER 6 CONCLUSIONS: UTILITY OF CHARGE PULSE POWIZATION. O O O O O O C O O O O O O O O O O 157 A. Charge Pulsed Normal Pulse Polarography. 157 8. Charge Pulsed Differential Pulse Polarography. . . . . . . . . . . . . . . . 158 C. Charge Pulsed Square Wave Voltammetry. . . . 160 D. Comparison of the Advantages and Applications for the Use of Microelectrodes and Charge Pulsed TeChniques O O O O O O O O O O O O O O O O O 1 61 E 0 Final word 0 O O O O O O O O O O O O O O O O 1 64 LIST OF “FERENCES O O O O 0 0 O O 0 O O O O O O O O O O 1 66 APPENDIX A - L11, 8 Cdl Data 0 O 0 O O O O O O O O O O O 170 APPENDIX B - Computer Simulation Programs for the '4 Traditional and Charge Pulsed Electroanalytical HethOds O O O O O O O O O I O O O O O O O O O 17 6 Table LIST OF TABLES Table Page 4-1 Results of computer model and physical experiments for normal pulse polarography. . . . . . . . . . . . . . .89 4-2 Data for curves shown in Figure 4-1 . . .92 4-3 Results of computer model and physical experiments for differential pulse polarography. . . . . . . . . . . . . . 104 4-4 Data for curves shown in Figure 4-6 . . 106 4-3 Comparison of Christie's work to this work. 0 O O O I O O I O O O O O O O O O 119 A-l Double layer capacitance values for 1M KCl 0 O O O O O O O O O O O O O O O O O 1'71 A-2 Double layer capacitance values for 0.1M KCl 0 O O O O O O O O O O O O O O O O O 172 A-3 Double layer capacitance values for 0.01M KCl 0 O O O O O O O O O O O O O O O O O 173 A-4 Double layer capacitance values for 0.001M KC]. 0 O O O O O O O O O O O O O O O O O 174 A-5 Double layer capacitance values for 10'4M KCl 0 O O O 0 O O O O O O O O O O O O O 175 A-6 Double layer capacitance values for 10'5M KCl 0 O O O O O O O O O O O O O O O O O 176 B-l Mpdelling Program for Normal Pulse Polarography. . . . . . . . . . . . . . 177 8-2 Modelling Program for Charge Pulsed Normal Pulse Polarography. . . . . . . . . . . 184 8-3 Modelling Program for Differential Pulse Polarography. . . . . . . . . . . . . . 196 8-4 * Modelling Program for Charge Pulsed Differential Pulse Polarography . . . . 204 vi 8-5 Modelling Program for Square Wave valtmetry O O O O O O O O O I O O O O 217 Modelling Program for Charge Pulsed Square Wave Voltammetry. . . . . . . . . . . . 226 vii “I INDIE LIST OF FIGURES Figure Page 1-1 The potential program and current sampling scheme for normal pulse palarography O O O O O O O O O O O 0 4 1-2 A normal pulse polarogram showing the limiting current. . . . . . . . 5 1-3 The double layer charging current of a DME due to the expansion of the drop with time (Electrode in KCl at the PZC). . . . . . . . . . . . . . 7 1-4 The potential program and current sampling scheme for the ramp form of differential pulse polarography . . 8 1-5 The potential program and current sampling scheme for the step form of differential pulse polarography . . 9 1-6 A differential pulse polarogram showing the peak current difference . . . . 11 1-7 The potential program and current sampling scheme for square wave voltammetry . . . . . . . . . . . . 13 1-8 A square wave voltammogram showing forward, reverse, and difference currents. O O O O O O O O O O O O O 14 1-9 The equivalent circuit of an electro- chemical cell . . . . . . . . . . . 19 2-1 Charge pulse polarization . . . . . 31 2-2 Charge pulsed normal pulse polarography. . . . . . . . . . . . 38 2-3 Charge pulsed normal pulse polarography output . . . . . . . . 40 I 2-4 Charge pulsed differential pulse polarography. . . . . . . . . . . . 43 viii 2-5 2-6 3-2 3-3 3-4 3-5 3-7 3-8 3-9 3-10 3-11 4-2 4-3 Charge pulsed differential pulse polarography output . . . . . . . . 45 Charge pulsed square wave voltammetry . . . . . . . . . . . . 47 Charge pulsed square wave voltammetry output. . . . . . . . . 48 Flowchart for normal pulse polarography. . . . . . . . . . . . 55 Flowchart for charge pulsed normal pulse polarography. . . . . . . . . 60 Flowchart for charge pulsed normal pulse polarography. . . . . . . . . 61 Flow chart for differential pulse polarography. . . . . . . . . . . . 65 Flow chart for charge pulsed differential pulse polarography . . 69 Flow chart for charge pulsed differential pulse polarography . . 70 Flow chart for charge pulsed differential pulse polarography . . 71 Flow chart for square wave voltammetry . . . . . . . . . . . . 76 Flow chart for charge pulsed square wave voltammetry. . . . . . . . . . 80 Flow chart for charge pulsed square wave voltammetry. . . . . . . . . . 81 Flow chart for charge pulsed square wave voltammetry. . . . . . . . . . 82 Comparison of experimental results with simulated normal pulse polarogram. . . . . . . . . . . . . 91 Comparison of response for conven- tional and charge pulsed normal pulse polarography. . . . . . . . . 94 Plot showing how the time at which the current must be measured increases with increasing solution resistance for normal pulse polarography . . . 95 ix at» 41. 4-13 4-5 4-6 4-8 4-9 4-13 Comparison of minimum detectable concentration possible for conven- tional and charge pulsed normal pulse polarography. . . . . . . . . 98 Comparison of minimum detectable concentration possible for various electrode areas for charge pulsed normal pulse polarography . . . . .100 Comparison of the simulated differ- ential pulse polarogr with experi- mental results for 10' M Cd++ . . .105 Comparison of the response with respect to pulse height for conven- tional and charge pulsed differential pulse polarography. . . . . . . . .108 Comparison of peak half width with respect to pulse height for conven- tional and charge pulsed differential pulse polarography. . . . . . . . .109 Comparison of response with respect to staircase step height for conven- tional and charge pulsed differential pulse polarography. . . . . . . . .110 Comparison of response with respect to time for conventional and charge pulsed ifferential pulse polarography for 10' M Cd++. . . . . . . . . . .112 Comparison of minimum detectable concentration possible at various scan rates for conventional and Charge pulsed differential pulse polarography. . . . . . . . . . . .114 Comparison of minimum detectable concentration possible at various scan rates for different charge injection sizes for charge pulsed differential pulse polarography . .115 Comparison of minimum detectable concentration possible at various scan rates for different electrode sizes for charge pulsed differential pulse polarography. . . . . . . . .117 J 4‘. 4-14 4-16 4-17 4-20 4-21 5-2 Comparison of the response for various values of Esw for conventional and charge pulsed square wave voltam- metry . . . . . . . . . . . . . . .121 Comparison of the peak width at half height for various Esw valued for conventional and charge pulsed square wave voltammetry . . . . . .122 Comparison of response for different DE values for conventional and charge pulsed square wave voltammetry. . .124 Comparison of the response with time for conventional and charge pulsed square wave voltammetry . . . . . .126 Comparison of the response for various values of s for conven- tional and charge pulsed square wave voltammetry. . . . . . . . . .127 Comparison of minimum detectable concentration possible at various scan rates for conventional and charge pulsed square wave voltam- metry . . . . . . . . . . . . . . .129 The minimum possible concentration which may be determined for injec- tions of differing charge content for charge pulsed square wave voltammetry . . . . . . . . . . . .131 Changes in minimum detectable concentration with scan rates for charge pulsed square wave voltam- metry. Chasge content of injec- tion-5x10' . . . . . . . . . . .132 The effects of square wave amplitude on response for charge pulsed square wave voltammetry on a hypothetical ideal instrument. . . . . . . . . .141 The effect of square wave amplitude on the response of charge pulsed square wave voltammetry on a current instrument. . . . . . . . . . . . .142 ! xi 5-5 5-6 5-8 5-9 5-10 The effects of staircase step height on response for charge pulsed square wave voltammetry on a hypothetical ideal instrument. . . . . . . . . .143 The effect of staircase step height on the response of Charge pulsed square wave voltammetry on a current instrument. . . . . . . . . . . . .145 The effects of square wave asymmetry on response for Charge pulsed square wave voltammetry on a hypothetical ideal instrument. . . . . . . . . .147 The effect of asymmetric measurement on the response of Charge pulsed square wave voltammetry on a current instrument. . . . . . . . . . . . .148 The effects of scan rate while keep- ing a constant AB on the respose of charge pulsed square wave voltammetry on a hypothetical ideal instrument. . . . . . . . . .150 The effect of changing the scan rate while maintaining AE constant on the of charge pulsed square wave-voltam- metry on a current instrument . . .152 The minimum detectable concentra- tion possible with respect to scan rate for Charge pulsed square wave voltammetry on a hypothetical ideal instrument. . . . . . . . . .153 The minimum detectable concentra- tion possible at various scan rates for charge pulsed square wave voltammetry on a current instrument. . . . . . . . . . . . .155 xii CHAPTER 1 PULSED ELECTROANALYTICAL TECHNIQUES A. Introduction to the Techniques Around 1960, G.C. Barker (1) developed the techniques of pulse polarography. In these techniques, potential steps in the form of square waves are superimposed upon a constant base potential, a linear potential ramp, or a staircase waveform. The pulse polarographic techniques have since become some of the more widely used variations of DC polarography in electroanalytical applications. The increased sensitivity afforded by these techniques is also responsible, in part, for the resurgence of interest in electrochemical methods of analysis. Square wave voltammetry also originated with Barker in the 19503. Originally called square wave polarography (2), it was performed at a dropping mercury electrode (DME). Aware of the method’s shortcomings, however, Barker went on to develop differential pulse polarography. The shortcomings of square wave voltammetry arose from the limitations. of the electronics of that time. Square wave voltammetry is very similar to the implementation of pulse polarography which has potential pulses imposed upon a staircase waveform. In square wave voltammetry, however, I two potential pulses of the same magnitude are imposed in 2 opposite directions on the same staircase step. Recent work on the technique with modern electronics (3-6) has shown it to be very powerful, as well as one of the most sensitive electroanalytical methods available today. The pulsed methods all have the same inherent advantages of reduced interference from charging current and enhanced faradaic current over classical DC polarography. For these reasons, the pulsed electrochemical techniques have substantially lower levels of detectability than DC polarography. Each of the three pulsed electroanalytical techniques is described in greater detail below. . 1. Normal Pulse Polarography A Normal pulse polarography is performed at a DME (6-12). The working electrode is held at a base potential for the first 1-5 seconds of the drop life. For the study of a species by electrochemical reduction, the base potential, 83, is chosen to be well anodic of the formal reduction potential of the species. At this potential, little or no reduction of the electroactive species occurs. A fixed time after the beginning of the drop life, the potential is abruptly changed to a different, more negative value. This new potential is maintained for several tens of milliseconds and, at the end of the pulse, the potential is returned to E3, at which point, the current mercury drop is dislodged. Instead of monitoring the current constantly as in DC polarography, the current is sampled once in normal pulse polarography, near the end of the potential pulse. It is fibo an. I.— 3 not possible to measure the faradaic current at the beginning of the pulse because of the large charging current produced by the sudden change in the electrode potential. Each subsequent potential pulse increases in magnitude by a set amount and the current is sampled at the same time after the initiation of each pulse. The potential waveform is shown in Figure 1-1. The resultant waveform is a plot of the current sampled vs the potential of the related pulse. The curve produced is sigmoidal in shape and resembles the output of classical DC polarography without the spikes produced by the growth andffall of the mercury drops (Fig. 1-2). The height of the curve is proportional to the analyte concentration. Limits of sensitivity for this method are about 10‘7M. Classical DC polarography is limited to solutions of electroactive species of about 10‘2 to 10'5M. The greater sensitivity of normal pulse polarography results from two factors. The faradaic current is enhanced since reduction takes place only during the potential pulse, not throughout the drop life. The concentration of the analyte around the working electrode, therefore, does not become depleted by reduction during the early part of the drop life. Complete stirring of the solution is assumed at the time of drop fall; each new drop erases any. electrochemical history. Reduction of the charging current also increases the sensitivity of the method. At the time the current is I Potential (mV) i5 60- 1'1 . ‘ i4 ' 50-4 ‘ l3 40-1 W -l 32 30--l ...fi ‘ l1 20-1 -l ,0- , .——-J~ --— .mdrop 1+ drop 24 0 - i - v - u - u - 1 0 ‘I 2 3 4 5 Time (sec) Figure 1-1 The potential program and current sampling scheme for normal pulse polarography. In .10 il in. AS‘V “COLLJO 11001 900-1 1 N O o L 500.; 1 lim Current OLA) 300- Potential (V) Figure 1—2 A normal pulse polarogram showing the limiting current. sample zero. potent the 01 area, toward 6 sampled on the flat top of the pulse, dE/dt is essentially zero. The charging current produced by stepping to the new potential has decayed to a negligible value (hopefully) and the only contribution to charging current comes from the growth of the mercury drop. The charging current due to drop growth will be the same as for DC polarography at that time in the drop life. The rate of change in the surface area, and hence the charging current, begins to fall off toward the end of the drop life (Fig. 1-3). 2. Differential Pulse Polarography Differential pulse polarography is also performed at a DME*(6,10-18). This technique has two basic forms: in one case, the potential pulses are imposed upon a linear potential ramp; in the other, the pulses are imposed upon a staircase waveform. For studies of reducible species, the initial potential is a value positive with respect to the reduction potential of the species of interest. For the first case, as in normal pulse polarography, a potential pulse several tens of milliseconds in duration is made at the end of the life of the mercury drop (1-5 sec.) and is imposed upon a linear potential ramp (Fig. 1-4). In the other case, the potential pulse appears at the end of each staircase Step, which again corresponds to the end of the life of the mercury drop (Fig. 1-5). These potential pulses are maintained at a constant amplitude, which may range from 10 to 100 mV throughout the experiment. In these techniques the current is sampled twice, just prior to the potential drop fall dro D/ fair L. 300--l Current (pA) N 0 d 0 L4 o 1 2 Time (sec) Figure 1-3 The double layer charging current of a DUE due to the expansion of the drop with time. (Electrode in KCI at the P20) 501 50- '40. g ‘ 18 V 30- “ 15 3.5, ~ 1 ...J . c 204 13 3 l2 0 . “- 1o~ i1 «i 0.1 J—dropl-l-drop 2-| —1o -fi...r.f.r 0 1 2 3 4 5 ‘iime (sec) Figure 1-4 The potential program and current sampling scheme for the ramp form of differential pulse polarography. m>ch .OZCUuOQ ‘1 , (mV) Potential 70- ... L ' 16 I | ‘ 14 30-1 ‘ [2 i5 4 1 i3 10- ‘ 11 l-drop £+ drop 2-l -10- . . . . - o i i is 1 2'5 8 Time (sec) Figure 1-5 The potential program and current sampling scheme for the step form of differential pulse polarography. “I ('f 10 pulse and near the end of the pulse, as in normal pulse polarography. The output produced by differential pulse polarography is obtained by taking the difference of the two currents measured. This difference current is plotted with respect to the applied potential. The result is a peaked waveform, the height of which is proportional to the analyte concentration (Fig. 1-6). The occurrence of a peaked output provides better resolution along the potential axis than is seen for normal pulse polarography. Differential pulse polarography has detected species down to 10'3M. This increase in sensitivity is results from a reduction in charging current relative to that observed in normal pulse polarography. A. smaller charging current occurs by stepping the potential because the magnitude of the pulses is smaller. The pre-pulse and end-pulse currents are sampled near the end of the life of the mercury drop when the charging current due to the growth of the drop is falling off. Even this small contribution is further reduced by the differential measurement scheme. Moreover, this reduction of charging current in differential pulse polarography produces backgrounds that are generally flat, whereas those for DC and normal pulse polarography usually have a significant slope. These reductions in charging current more than make up for the loss in faradaic current relative to normal pulse polarography. I 11 0'125‘1 4_—. peak A current ' moo-i 3 ' 00075 A o.oso-l - .- A current 0.0254 0.000- r I 1 I v I --.50 --.60 -.7O -.80 Potential (V) Figure 1~8 A differential pulse polarogram showing the peak current difference. patenti . directio: pctentiai pulse pc Positive although, staircase PolaIOgra the merCl the end different The StairCaSe the Cage waveform height 12 3. Square Wave Voltammetry Square wave voltammetry may be performed at a DME but generally a stationary electrode is used (3-6,12-20). The potential waveform for this technique consists of two potential pulses of equal magnitude imposed in opposite directions upon a staircase step (Fig. 1-7). These potential pulses are smaller than those used in differential pulse polarography, generally less than 30 mV. These positive and negative pulses may be of equal width (3) although this is not always the case (4). The height of the staircase step is also relatively small-never more than 25 mv.f The technique is faster than differential pulse polarography as one does not have to wait for the fall of the mercury drop. The current is again sampled twice, at the end of each positive and negative pulse, as in differential pulse polarography. The difference of the two currents sampled on the same staircase step is plotted with respect to potential. As in the case of differential pulse polarography, a peaked waveform results. The peak is centered on Elm and its height is proportional to the analyte concentration (Fig. 1-8). Being'a relative of differential pulse polarography, square wave voltammetry has the qualities attributed to that technique as well as some advantageous characteristics of its own. Square wave voltammetry is faster than differential pulse polarography; a scan of 500 mV or more 501 m 4 1 d ..U 0 2 A>EV ., :Umucounvl 4‘ 10.. 0i 13 i4 501 I 4 12 mi . ---g _____ f); 7 ESW AE V‘SO-l ------ ---- E l +0 . c I I3 3 20“ I O 0- 4 I1) . I _. ‘0 , 0'" r 7' u o r . r s 0 50 100 Time (msec) Figure 1-7 The potential program and current sampling scheme for square wave voltammetry. f¢tc\ d“lnL-l\ < 14 2001 HAcurrent a fonnardcurrmt . o mcumnt 1504 A 3‘1OO-w 4.1, 5 t s a 501 '4 0.. ~50 -.55 -.30 ~35 -3o $75 -.'30 Potential (V) Figure 1—8 A square wave voltammogram showing forward. reverse. and difference currents. my. CC I8 tech: cone their 15 can be performed over one drop of a DME. This same scan would require perhaps 100 drops in differential pulse polarography. This speed, coupled with microcomputer control, provides the opportunity to do signal averaging by repetitively scanning the same experiment. The technique also shows good rejection of background currents and insensitivity to such things as nonplanar diffusion (6). Flexibility in the choice of various experimental parameters allows tailoring of the experiment to suit the system. The limit of sensitivity is about 10'3M when a DME is used. The detectability of square wave voltammetry is, therefore, comparable to that of differential pulse polarography, but, as stated above, runs much more quickly. B. Theory and Practice 1. Theoretical Equations Barker originally formulated the theory of the pulse techniques in the 19503 and 60s. Additional work has been done by Krause and Ramaley (3), and the Osteryoungs and their coworkers (4-6,10,12). For normal pulse polarography in which only cathodic processes occur, the current measured is given by i =- thC ‘/_12 fl? (1-1) m: + where P is P = exP[(nF/RT)(E-El/2)] (1-2) At potentials on the diffusion limited plateau the parameter P becomes negligible with respect to 1. Therefore, the 16 limiting current for normal pulse polarography is 111m :- nFAC [3 (1-3) ut In the case of differential pulse polarography, the differential current measurement scheme would suggests that the difference current would be given by the derivative of equation 1-1 A1 =- 32225943 «I 2 am RT fit (1+?) where AB is the pulse amplitude. This equation, however, is valid only for small amplitude potential pulses, less than RT/nF (approximately 25 mV at room temperature for n=19. The relevant equation for large amplitude pulses is Al - nFAC ‘/_p_- 23?? - EA (1-5) M(O+PAO+PA+PAG) where PA = explllEl+Ez)/2 - El/z](nF/RT)} (1-6) 0 = expillEz-Elll2]lnF/RT)} (1-7) and 82 - 31 = AE, the pulse amplitude. The peak occurs when PA equals 1. Therefore, the equation for the maximum diffusion current is Aimax - nFAC FEE £511 (1-8) Square wave voltammetry has a more complex equation since the flexibility of the technique introduces additional variables. The forward pulse is the pulse imposed on the staircase step in the same direction as the staircase waveform. At a time p11 during the jth staircase step, the current measured for the forward pulse is 17 ifm = nFAFE ‘Pf (1-9) M where Yf = P1 151-4117221le +Z:O(QZM(I’J'N+P1)IT% +GQ_1m+p1_02)mJ17l2) and the current measured at p21 for the reverse pulse is 1R”) = “FA AP :(sz (j-mwz) + 69'1””? “25-992) In these equations, terms of the type CN(k) correspond to the surface concentration of the oxidized species. N-l for the forward pulse while N-Z for the reverse pulse. The variable k is the period of the staircase step. The numbering begins at 0 for the variable j. C(0) and C(-1) are defined as C", the bulk concentration of the analyte. The surface concentration of the species of interest is determined by the potential of the working electrode. At a planar electrode for a simple reversible reaction, the surface concentrations are CN(k) - c*/(1+e(t)) (1-10) where 8(t) - exP[(nF/RT)(E1/2-E(k))] (1-11) For the forward pulses the potentials are 31(k) - si - kAE — ssw (1-12) and for the reverse pulses E2(k) . si - kAE + Esw (1-13) The differential current is then The A CORCEI 18 A1 ifm - iR(j) = nFAC" [I A‘I’lj) <1—14) m The NY function corresponds to the summation of surface concentrations from all previous steps. The peak of the output waveform for square wave voltammetry again occurs where elt)=1, or where E = 31/2- The specific equation for the peak current, however, is much more difficult to determine than those for the previous methods due to the number of variables involved in this technique. 2. Practical Limitations The basis of all polarographic instrumentation is the potentiostat. The potentiostat is an instrument that controls the current between the working electrode-counter electrode pair in order to maintain a specified potential difference between the working and reference electrodes. The desired potential may vary with time according to the waveform supplied by a function generator. From the standpoint of the potentiostat, the electrochemical cell appears as a set of impedances (Fig. 1-9). Two of these impedances arise from the interfaces at the working and counter electrodes, and the other from the resistance 'of the solution contained in the cell. The solution resistance is divided into two fractions by the reference electrode. Ru, the fraction of the resistance between the working and reference electrodes, is called the umcompensated resistance. The size of the uncompensated Ref 19 Counter Electrode Rn Reference Electrode e ref Rf T Cdl 3 Working Electrode Figure 1—9 The equivalent circuit of an electrochemical cell. resista electr< electrc WI an era unccmpe _::ent' respect potenti values 20 resistance depends upon the position of the reference electrode and counter electrode with respect to the working electrode. Whenevercurrent is passed in an electrochemical cell an error in potential measurement will occur due to the uncompensated solution resistance (21-27). Since the potential is controlled to keep the measured potential with respect to the reference electrode at the desired value, a potential control error of iRu will occur. Even at small values of Ru, an appreciable error will occur when the current in the cell is substantial. A large current can occur in bulk electrolysis or experiments where dE/dt is large at any point. In combination with the capacitance of the double layer at the working electrode, Ru also contributes to a cell time constant of Rqu1- Therefore, if a significant change in potential is made instantaneously, the true value of the potential will lag that of the step according to the equation (28) etrue ' erefil ' GXPl-t/Rqu1)) (1'15). Consequently, experimental results will not be meaningful unless the cell time constant is small with respect to measurement'times. There are several methods available for the reduction of potential control error due to R“. One way is by increasing' the conductivity (thereby decreasing the resistance) of the solution. This may be done by increasing 21 the concentration of background electrolyte, increasing solvent polarity, or by decreasing the viscosity. Another method is to reduce Ru by moving the reference electrode closer to the working electrode. However, this can create problems by upsetting the uniformity of the field around the working electrode and, hence, has only limited effectiveness. The last method of correction involves the use of a positive feedback loop in the electronics of the instrumentation to provide compensation for Ru. This technique also has its problems. One would wish to compensate completely for Ru, but the electronics required to do so and to sense whether compensation has been achieved can introduce phase shifts and resultant time lags in the control circuitry. Overcorrection can result in effects such as overshooting, ringing, or high frequency oscillations which. may result in loss of cell control. Consequently, it is generally impossible or impractical to obtain total compensation for Ru. As we have seen earlier, there is another factor which ultimately limits the sensitivity of all conventional voltammetric methods. This arises from the effective capacitance that is part of the impedance of the working electrode.' The electrical behavior of the electrode- solution interface in ionic solutions resembles that of a capacitor (29-41). This double layer capacitance, Cdlr can be tens of microfarads per cmz. Therefore, even with no reducible species present in solution to provide electrical 22 conduction across the capacitor (the interface), an appreciable current will be required to charge the double layer capacitance as the electrode potential and/or area (as explained in a later paragraph) is changed. This behavior is evident from the following equations q 3 C V = Cdl A V (1‘16) fig = 1c = Cdl A Q! (1-17) dt dt where C is the size of the capacitor, V is the voltage to which it is charged, and A is the surface area of the electrode. Electrochemical reactions act as a resistive conductor connected across this capacitance. Thus, the measured current is always the sum of the faradaic and charging currents. To determine the faradaic current alone, some method of eliminating or compensating for the charging current must be devised. In the case of DC polarography, where a linear potential ramp is applied to the cell, the applied potential is constantly changing. This means that charging current (the current used to charge the double layer of the working. electrode to a new potential) is always present as shown in equation 3. The specific equation for the charging current in DC polarography is (42) 1c '3 VCdl + [(31- VCdJ) exp(__(-Et_ 1)] (1-18) RsC d where v is the voltage sweep rate and 31 is the initial potential. When potential step experiments are performed, 23 however, the error introduced in current measurement by the charging current can be reduced. When a potential step is made, the charging current appears as a surge at that point. The charging current then decays exponentially with time according to the following equation (43) i - AB exp; (1-19) Rst The. faradaic current is also at a maximum immediately following the potential step and decays with the square root of time. Therefore, the charging current decays at a faster rate than the faradaic current. For conventional polarographic methods, the charging current is generally negligible with respect to the faradaic current for analyte concentrations 2 10'3M. At concentrations of about 10'4M they are comparable and corrections must be made. For lower concentrations, the charging current is generally the larger of the two. For this reason, sensitivity is limited and accuracy falls off at low analyte concentrations. It is possible to reduce the value of the double layer. capacitance by reducing the size of the working electrode. However, since the measured faradaic current is directly proportional to the surface area of the electrode, one will also measure smaller faradaic currents. Compensation for the charging current error can also be made by determining the charging current contribution and correcting for it or by waiting until the charging current decays to a value negligible with respect to the faradaic current. The latter 24 technique, generally used in all electrochemical methods where the potential is stepped or pulsed, involves a tradeoff in results obtained. By sampling the current early in the step, . we obtain a larger measured current with a larger contribution from the charging current. However, if we wait for the charging current to decay to negligible value the faradaic current has also decayed to a small fraction of its initial value and, thus, sensitivity is decreased. The other contribution to charging current comes from the use of the OMB. As the surface area of the electrode increases throughout the life of the drop, an increased current will be required to keep it charged to the same potential q 3 Cdl A.V (1'20) ic - Cdl (Ez - E) dA/dt (1-21) where E2 is the Potential of Zero Charge for the electrolyte used. Since the relation for A is A - 4n (Jinn—9):” (1-22> 4fldfi . where m is the flow rate of the mercury and dug is its density, the equation for the charging current due to mercury drop growth is 1C - 0.00567Cd1(Ez - E)m2/3t'1/3 This is true for cases in which either potential sweep or potential step methods are used. The only ways to reduce this charging current contribution are to wait until near the end of the drop life when the area is increasing more 25 slowly or to use an electrode that does not change in size (i.e. a stationary electrode). DC polarography uses a linear potential ramp and can provide meaningful data only for moderately low analyte concentrations. Normal pulse polarography shows a marked increase in sensitivity since the faradaic current is enhanced. This occurs because the only time that reduction is taking place is during the potential pulses. For DC polarography, reduction is constantly taking place. Adso, error from charging current is reduced by waiting several milliseconds after the potential has been stepped to measure the\ current. Comparing ‘the equations for‘ the faradaic current produced by' DC and normal pulse polarography and with typical values, a significant increase of 6 times or more is seen for normal pulse polarography. This increase in faradaic current combined with the simultaneous reduction in the charging current measured results in an increase in detectability of two orders of’ magnitude over DC polarography. A further increase in detectability is seen for‘ differential pulse polarography. Since the peak faradaic current is never larger than the diffusion limited current in the corresponding normal pulse experiment, this increase must result from a further reduction in charging current contribution. The difference in sampled currents is used to subtract out much of the contribution from the growth of the mercury drop and to reduce the error from the double layer 26 capacitance. The result is an order of magnitude increase in detectability of differential over normal pulse polarography. Square wave voltammetry appears to have the potential to deal with ‘these and. other problems most completely. However, it has only recently come to light as a viable technique for trace analysis. It contains the differential measurement scheme of differential pulse polarography but is much faster; an entire voltammogram can be produced from an experiment performed within the life of one mercury drop. This will provide a slight increase in sensitivity over differential pulse polarography but square wave voltammetry generally has the same detectability associated with it. Pulsed electrochemical methods, of all the conventional potentiostatic methods, provide the best means of dealing with the problems associated with double layer capacitance. However, the electrode potential error is shared by all techniques that measure electrode potential under conditions in which the counter electrode is supplying a significant current . CHAPTER 2 APPROACH AND DESIRABILITY OF IMPLEMENTING PULSED ELECTROANALYTICAL TECHNIQUES WITH CHARGE PULSE POLARIZATION A. History of Charge Pulse Polarization and its use to Change Potential .G.C. Barker also developed and introduced the coulostatic method (44) in the early 60s. A short time later, P. Delahay and W.H. Reinmuth independently elaborated on \the method (45-48) . The coulostatic method produces a sharp change in the potential of the working electrode (and its associated double layer) by the injection of a current pulse with a specific charge content. The duration of the charge pulse is brief, on the order of microseconds, or less. It is designed to be fast enough so that, in the system under study, negligible charge transfer occurs during the time of the pulse. For charge transfer rate studies of very fast reactions, the pulse duration must be 100 ns or less. For diffusion controlled reactions at low concentrations, the pulse duration can be many microseconds. The quantity of charge provided to the system may be determined by applying a constant current for a short period of time or by injecting charge that has been stored on a capacitor charged to a known voltage. The pulse serves only to inject a charge increment and, under these conditions, 27 28 the actual shape of the injection pulse is unimportant (49). After the charge pulse is injected, the cell is placed in open circuit condition and the potential is monitored. If the potential is such that an electrochemical reaction can occur, the faradaic reaction current is supplied by the charge on the double layer capacitance of the working electrode. If no faradaic reaction is possible at that potential, the potential will not decay and Cdl retains the entire injected charge (50). The original coulostatic method for concentration determination (not for charge transfer rate) generally involved the injection of a large amount of charge, enough to ‘change the electrode from a potential positive with respect to the reduction potential of the species of interest (where if is essentially zero) to a point on the diffusion plateau. The cell was then placed in open circuit condition, i.e. no net current in the cell. The faradaic current can then only be supplied by a discharge of the double layer capacitance and, as charge is removed, the potential decays toward the equilibrium potential. The potential varies linearly with t“2 and the concentration of the species of interest can be determined from the slope of a AE vs t1/‘2 plot (45). The coulostatic method has some advantages over conventional potentiostatic methods. The potential measurement is made in open circuit conditions, and, therefore, with no net external current in the cell. This 29 effectively eliminates the ohmic drop error in potential measurements even in solutions containing low concentrations of analyte or background electrolyte. The result is that this method can be applied to most nonaqueous systems and contamination from adding supporting electrolyte salts can be reduced through the use of lower electrolyte concentrations. The interference from Cdl is also reduced since the charge required by the faradaic reaction is supplied by the discharge of the double layer capacitance. Therefore, the usual sharing of the total current between the faradaic and charging currents is replaced by an equality of if and ic. The faradaic current is known at any time by the rate of discharge of Cdl from the relation Cd1X(dvref/dt)' There are limitations in the coulostatic method. Large solution resistances will increase the 'time required 'to deliver the charge to the cell. There are specific requirements for electronic components used in the instrumentation, which, as of this writing, have been home- built by various experimenters (46,47,51—57). These' requirements are fairly stringent owing to the nature of the method and the measurements being made. Monitoring the potential decay presents problems in the interpretation of the curve. However, the application of a cell current through the use of charge impulses can provide advantages in other electroanalytical techniques. In this case, the rate at which charge injections are made can be 30 instrumentally controlled and cell potential measurement can be made with no iR drop error. The following section is a discussion of the development of’ ‘potentiostatic electroanalytical techniques through the use of charge pulse polarization. B. Maintenance of Potential by Charge Pulse Polarization The idea of using charge pulses to maintain a potential is not really new, but it has been only sparsely used. In the. early 19703 Goldsworthy and Clem (58,59) developed a 'bipolar digipotentiogrator'. The name arises from the fact that the instrument can be used as a potentiostat, as a current-to-frequency converter, and as a digital integrator. The only other instance of using charge injectione to maintain a constant potential comes from this laboratory (60). Using an instrument primarily designed by previous students (56,61), R. Engerer performed experiments in cyclic voltammetry by using a staircase waveform and charge injections. In both cases, the potential of the working electrode is controlled by injections of small charge pulses. of a constant size. Charge is injected as often as required to maintain a specified potential. Figure. 2-1 shows the details of stepping and maintaining a potential through the use of charge pulse polarization. The potential of the cell is stepped to a new value where a faradaic reaction may occur. This potential Potential 3]. -.650-1 -0625" NW thresholdP—-—-- --— - -- —-- ‘-—.600-4 -.575 charge I I content 5 l1 n L IL— ‘0550 r I I T I 0 5 10 15 20 25 Time (ms) Figure 2—1 The maintenance of a potential using charge pulse polarization. 32 step can be achieved in one of two ways. A constant current source can be switched into the cell for a given (very short) period of time to deliver a specific amount of charge to the working electrode. Another method involves charging a capacitor to a specific potential and dumping this stored charge to the working electrode. In either case, the shape of the charge pulse is unimportant (49). However, the speed with which the working electrode is charged is important. The potential must be stepped from one value to another in a sufficiently short time so that the charge introduced to the working electrode goes solely to charge the electrical double layer. This is the 'charging charge’, analogous to the charging current seen in potentiostatic methods since its only purpose is to charge the double layer' of ‘the working electrode to a new potential. When the potential has reached its desired value the cell is placed in an open circuit condition. In this case, there is no net external current in the cell. The faradaic reaction occurs only by removal of charge from the working electrode. As the electrode discharges in this manner, the' potential will begin to decay toward the reduction potential of the system. This potential decay is monitored and, when it reaches a threshold value (in other words, goes below the positive limit of the potential window), an injection of small cathodic charge content is used to bring the cell back within the specified limits. This charge injection takes an extremely short period of time (microseconds) and serves 33 only to replenish the charge removed by the faradaic reaction. After this small amount of charge is injected, and the electrode potential is made more negative, the faradaic reaction again begins removing charge from the working electrode. The potential decays in the positive direction and another injection is required to return the potential to a ‘value within the limits (i.e. within a specified potential window). The length of time required for a specified potential decay increases as the duration of the potential step increases since the concentration of the analyte species at the electrode surface decreases with time. Since the small charge injections all have the same charge content, the amount of charge required by the faradaic reaction is measured simply by counting the number of injections) made ‘while at the ‘potential of interest. Thus, the original analog potentiostatic technique is transformed into a digital method. The number of charge injections counted carries an error of up to one count (from whatever decay has occurred between the last charge injection and. the end. of ‘the potential step) and.'this' (including the reproducibility of the charge injection) provides an estimate of the precision of the measurement at that potential. If 100 charge injections are counted over a potential step, the maximum error in that measurement is 1%. Increasing the precision of the measurement requires only that the cell remain at the desired potential long enough to amass the necessary number of counts (up to the limiting 34 precision of the charge injections). The amount of charge needed by the faradaic reaction is determined by multiplying the number of injections counted by the charge content of each injection. This is, in essence, the integration of the faradaic current curve for the concentration of the analyte species at the specified potential. In other words, the area under the faradaic current/time curve is measured. The charge required to charge the working electrode up to a new potential was contained within the large charge impulse injected at the beginning of the step. In this manner, effective separation of if and 1c results and measurement of thexcharge consumed by the faradaic reaction carries none of the error attributed to charging current as is seen in traditional potentiostatic measurements. Different instrumental considerations are required when one wishes to step and maintain a specific potential as opposed to just changing the potential and monitoring the decay. In the latter case, the potential of the system is measured a specific time after the charge pulse has been injected. To maintain a potential, a method of determining' whether the current potential is within threshold values must be included. As explained in the previous paragraphs, the amount of charge injected must be relatively small and the rate of injection must be relatively high. The voltage measurement system must be able to discriminate small potential differences very quickly (less than a millisecond time scale). In other words, a fast monitoring system is 35 required as well as a system to inject very small charge pulses quickly and reproducibly. In its original form, the use of coulostatic or charge pulse polarization to change the jpotential of an electrochemical cell needed either a rapidly switched continuous current source or a capacitor charged to a given voltage by a battery or other constant voltage source. The decay curves could be recorded by various recording devices such as an x-y recorder, an oscilloscope, or, more recently, a computer. On the other hand, in an experiment where better control of the potential is needed, computer control of the instrument to perform these techniques is more suitable. Making large potential steps requires a system which will deliver a large amount of charge in a very short period of time. This means adequate voltage control (for charging the capacitors to the proper voltage to make the correct potential step size) and a fast switching system (to turn the current on and off at the proper times). A fast voltage measurement system is also required so that trimming' injections may be made if the potential at the end of the large or step charge injection is not at its correct value. These trimniing injections are of small charge content but serve only to get the potential of the working electrode up to its exact desired value and should not be confused with the small charge injections made during the potential pulse to maintain the current potential. 36 Maintenance of the potential also requires a fast voltage measurement system since only a small potential decay is allowed on the top of the step. The system must be able to quickly sense whether the potential has crossed the set threshold value. The measurement system must also be of sufficiently high resolution to differentiate between small potential differences. The control of the voltage source must also have relatively high resolution so injection of very. small amounts of charge can be :made on the step (potential excursions must be relatively small during the potential pulse to maintain a 'constant pulse potential' situation). These charge injections during potential maintenance must be small enough to provide precision voltage control. For example, for a Cdl of luF, a charge injection containing 5x10“9 coulombs will produce an electrode potential change of 5 mV. In addition, a high frequency clock is needed since charge injections for high analyte concentrations on the diffusion plateau can be required at frequencies greater than 10 khz. The more recent instruments built all use microcomputers to control and perform the experiments (53,54-57,61-65). C. Normal Pulse Polarography by Charge Pulse Polarization Charge pulsed normal pulse polarography is the name given to the technique whereby charge impulses are used to produce the input potential waveform of increasing potential pulses upon a constant base potential. The potential is 37 stepped by means of large charge injections and the potential at the top of each pulse is maintained with small charge injections. Since the base potential is chosen to be such that no faradaic reaction occurs there will be no small injections at that potential. However, the top of the potential pulses will show the effects of decay form the faradaic reaction and subsequent charge injection (Fig. 2-2). The rate of charge injection increases with increasing reduction current, i.e. as the potential of the pulses approaches and then passes the reduction potential of the species of interest. This rate will level off as the reaction becomes diffusion controlled. The rate of charge injection decreases the longer the pulse potential is maintained due to the partial depletion of the analyte at the electrode surface. This depletion effect is eliminated by the fall of the mercury drop. The drop fall produces a stirring motion which returns the surface concentration of the analyte to bulk concentration levels. Therefore, each new potential pulse begins with the same conditions. The amount of charge consumed by the faradaic process over the period of the potential pulse is equal to the amount of charge injected over that period. Since the amount of' charge per injection on the pulses remains constant, the charge required by the electrochemical reaction can be determined simply by counting the number of injections made; this counting is begun immediately after . a Potential 38 -06‘T '--.BO-< fall _058"i -.52- drop life——-l ”-‘8‘ r I r I I 0 4O 80 120 Time (ms) Figure 2—2 The potential program showing potential decay for charge pulsed normal pulse polarography. 39 the correct pulse potential is reached. The number of charge injections made during a potential pulse may be in the hundreds or thousands depending upon the solution involved and the values of the various system parameters used. This makes charge pulsed electroanalytical techniques digital in nature. The error in these measurements is some fraction of the charge pulse content (less than one charge injection). Therefore, an increase in precision can be gained by adjustment of system parameters to such that a larger number of charge injections are counted. In Figure 2-3, the number of small charge injections counted during each potential pulse is plotted with respect to the potential of the pulse for a system that initially contains only the oxidized. species (i.e. only reduction occurs during' the experiment). The resultant curve is sigmoidal in shape, like those produced by the traditional potentiostatic method. However, since charge pulsed normal pulse polarography is a digital technique, segmentation of the curve may be seen, especially at lower analyte concentrations where the number of small charge injections' counted on the diffusion plateau will be low. ‘ A consequence of using charge pulses to step and maintain the potential in a fashion resembling normal pulse polarography is that the charge required. to charge the double layer of the working electrode to a new potential is completely separated from the charge used by the faradaic reaction. Reduction of errors from the effects of Number of counts 40 ”200‘ I I I I -.50 -.60 -.7O -.80 --.90 Potential (V vs SCE) Figure 2-3 A charge pulsed normal pulse polarogram. 41 uncompensated solution resistance also occurs because the cell is maintained as an open circuit during the sensing and control of the electrode potential. As a result, charge pulsed electroanalytical techniques may be used in solutions of low electrolyte concentrations or nonaqueous systems. From theoretical calculations and the use of computer programs to model the technique, I have determined that charge pulsed normal pulse polarography can be used to determine a species concentration of 10’7M at 10 mV/sec scan rate at the detection limit. Higher scan rates can be achieved in charge pulsed normal polarography since counting of charge injections is begun immediately after the proper potential is attained. Concentrations above 10'6M can be determined at scan rates higher than 10 mV/sec and species at 10'4M or greater can. be determined. at greater' than lV/sec, whereas scan rates for conventional normal pulse polarography rarely exceed 5-10 mV/sec. The pulse width can be shortened at higher concentrations, which results in a higher scan rate, because there is no time wasted in waiting for the charging current to decay. Longer pulse widths must. be used for analyte concentrations below 10’5M to allow for accumulation of a reasonable number of counts. The reasons for these results are given in the fourth chapter. However, difficulty with this technique arises from the large potential steps which must be made. The large current required to make potential steps of 100 mV or more very 42 quickly necessitates low solution resistances, high current driver voltage capability, and very fast electronics. D. Differential Pulse Polarography by Charge Pulse Polarization The technique of charge pulsed differential pulse polarography has an input potential waveform of potential pulses of the same size imposed upon a staircase step function. The potential is stepped up and down by using large charge injections. Maintenance of the potential on top of the pulses and on the staircase step is achieved through the use of small charge injections (Fig. 2-4). The rate of charge injection on both levels will increase as the pulse potential and then the staircase potential approach and surpass the reduction potential. Charge pulsed differential pulse polarography is performed at a DME. This means that, after the drop fall at the end of the potential pulse, the surface conditions of the electrode are returned to bulk concentration levels. Also, the fall of the mercury drop removes any reduced analyte from the electrode so only reduction can occur on the staircase steps. A. traditional differential pulse polarogram is essentially the difference between two normal pulse polarograms, each started at a different potential, and a peaked output results. For the charge pulse implementation, the number of charge injections counted during the staircase Potential . r 43 “.651 illll M Nib drop -.80- fall —.55—l % KN“ drop life—-| -50 ‘ i ' I ‘ 1 ‘ I ' I . I ' fl 0 20 40 ‘ 60 80 100 120 140 Time (ms) Figure 2—4 The potential program showing potential decay for charge pulse differential pulse polarography. 44 step is subtracted from the number of charge injections counted during the pulse. This difference in the number of charge injections is plotted. with respect to the pulse potential. The resultant output waveform is peak shaped just as for the analog implementation (Fig. 2-5). Again, in the charge pulsed technique, segmentation of the curve may occur if the charge injection difference is small. There are advantages to controlling the potential waveform of differential pulse polarography with charge impulses. Following the same reasoning as in the previous section, charge pulsed differential pulse polarography is useful for solutions of low electrolyte concentrations and nonaqueous solvents. My use of computer simulations to model charge pulsed differential pulse polarography has shown the limits of detectability for this method to be approximately 5x10'8M at 10 mNYsec. Higher scan rates can be employed in charge pulsed differential pulse polarography owing to the increased efficiency of counting charge injections, which obviate the necessity of waiting for ichg to decay. Concentrations of 5x10'7M can be determined at scan rates greater than 10 mN/sec and concentrations above 5x10'5M can be determined at greater than 1V/sec, whereas, scan rates' above 10 mV/sec are uncommon for conventional differential pulse polarography. None of the problems inherent in taking large potential steps occur in this method since the potential pulses imposed upon the staircase Number of counts 45 350.- 250. - 1150.-1 --.50 -.so ' --.'70 -.'so -.90 Potential (V vs SCE) Figure 2-5 A charge pulsed differential pulse polarogram. 46 step are small compared to those used in normal pulse polarography. Reasons for these differences are given in Chapter 4. E. Square Wave Voltammetry by Charge Pulse Polarization Implementation of square wave voltammetry by charge pulse polarization is roughly similar to that of differential pulse polarography. Large charge injections are made to change the potential significantly. However, in square wave voltammetry potential excursion from one side of the reduction potential to the other side will cause a reversal in the electrochemical reaction. In other words, reduction of analyte can occur on a farward pulse, whereas oxidation of that species can occur on the subsequent reverse pulse. Since the potential always decays towards the reduction potential of the analyte, ’oxidizing' charge injections will be made to maintain the potential of the reverse pulse (until the vicinity of the reduction potential where reduction begins to occur) (Fig. 2-6). The difference in the number of charge injections on' the forward and reverse pulses is recorded with respect to potential. In the case of the anodic injections, their number is ‘added to those counted on the forward pulse to maintain a differential measurement scheme. As in the case of charge pulsed differential pulse polarography, a peaked output results (Fig. 2—7). Bacosou Potential -.651 -.60-4 -.55- forward pulse 47 reverse pulse /L____.L -.50 r O. 20. 40. I r l 60. 80. 100. i 20. i 40. Time (ms) Figure 2-6 The potential program showing potential decay for charge pulsed square wave voltammetry. m w o n c O muCDOU *0 LUDEDZ 48 3501 H delta i a i forward a i reverse 0) 250-1 4.) C 3 O 1 0. V-I O 150- L 0 .D E 3 Z 50- cathodic . 3"---.. anodic .°""“°.. ~50 I. ' r f ' I r j -.50 --.60 -.7O -.80 -.90 Potential (V vs SCE) Figure 2-7 A charge pulsed square wave voltammogram. 49 Square wave voltammetry is not the best candidate for performance by charge pulse polarization since, as a traditional electroanalytical technique, it has the best means of reducing the errors due to charging current and uncompensated solution resistance. However, analysis of the results from a series of simulation experiments shows that charged pulsed square wave voltammetry still benefits from the characteristics inherent in the use of charge pulse polarization. A detection limit of 2x10'8M can be achieved by‘ this technique at a scan rate of 10 mV/sec. Concentrations of 5x10’7M can be determined at scan rates greater than 10 mV/sec and concentrations above 10'5M can be determined at greater than 1V/sec. As explained in the fourth chapter, lower electrolyte concentrations may be used and lower analyte concentrations can be detected simply by waiting at a given potential long enough to amass a reasonable number of counts. The wait for a significant amount of charge injections at a potential does mean a decrease in effective scan rate at lower analyte concentrations. The small potential pulses used in square. wave voltammetry, however, do make the method suitable for implementation by charge pulse polarization. CHAPTER 3 COMPUTER MODELLING OF PULSED ELECTROANALYTICAL TECHNIQUES USING CHARGE PULSE POLARIZATION Many systems are amenable to computer simulation. The following three terms are defined for subsequent discussion. The W contains the formulae from which the system response can be calculated for various situations. Simulatign is the process of using that model to predict the behavior of a system under various conditions. Simulations are the experiments performed by using the model. In order to produce a reasonable computer model, certain assumptions have to be made about the methodologies and characteristics attributed to the electrochemical system. Divalent cadmium in aqueous KCl was chosen as the model system because it is the most thoroughly understood and studied electrochemical system. The following characteristics apply to the system itself: 1. The reaction is diffusion limited. 2. The reaction is completely reversible. 3. The migration current is negligible. 4. Do a DR for amalgamated species. 5. The concentration gradient is calculated by using semi-infinite spherical diffusion equations. 6. There is no oxygen present in solution. 50 51 7. The background electrolyte is electrochemically inert. 8. The concentration of the background electrolyte does not affect the analyte (changing its form by complexation) or its reduction potential. 9. The double layer capacitance varies with potential according to the data presented by Grahame (31) and Lii (38) at 25°C. Lii's data are repeated in Appendix A for concentrations including 0.1M KCl. 10. Ionic adsorption on the electrode surface does not affect the measurement. : 11. The mercury drop is assumed to be spherical. 12. The mercury drop area does not change appreciably during the last half of its lifetime (i.e., a static mercury drop electrode is used). 13. There is no electrical noise present. The simulation models were written in FORTRAN 77 and run on a Digital Equipment Corporation vaxstation II. The average run time was under 10 seconds; however, choice of unreasonable values for some of the system parameters caused. the program to run an excessive length of time (over 30 minutes without completion of calculations). The run time should never be over 5 minutes. The simulation programs for all the named implementations follow a similar pattern. The first section of the program is devoted to variable I/O (input and output of variable values). The body of the model is next and each 52 contains a number of DO loops. The calculations required to model the specified technique are contained within these loops. The third section of each program allows the variable values to be read from a data file. The last section, not present in all models, contains the subroutines required by the model. A. Normal Pulse Polarography The initial step in formulating a computer model for any system or technique is to base the program on the theoretical equations that describe the system response. Thefequation relating the faradaic current and concentration for normal pulse polarography has been given previously (Eqn. 1-1) but is repeated here for convenience (10) i = nFACr (3-1) 1+P where P=expilnF/RT) (E-E1/2)]. Equation (3-1) must now be modified to correspond with the charge measurement method of charge pulsed normal pulse polarography (CPNPP) . Since i=dq/dt, this is done as follows i a fig - nFACr dt dq a rumor «REE: 97d dt qu - nFACl WJ{ 1+P q = 2nFAC (3-2) J: (.+.) The P term does not change with integration as the potential is assumed to remain constant over the width of the pulse. 53 The resultant equation (3-2) shows a significant change from the original. The factor of 2 is simply an integration constant; however, the movement of t from the denominator to the numerator of the square root term is an important difference. This difference makes evident one of the fundamental differences between charge pulsed potentiostatic methods and. their traditional analogs“ The longer' one remains at a given potential, the greater' will be the accumulated faradaic charge for that step, whereas the current at the end of the step decreases with increasing step duration. 1. Traditional Normal Pulse Polarography Formulation of the computer model begins with the equation for the faradaic current (Eqn. 3-1), which, for the purposes of simplicity, is split into three parts PTl I nFAC (3-3) PT2 - (D/nt)1/2 <3-4) PT3 - 1/<1+p) <3-5) Charging current contribution is calculated according to the usual theoretical equation (42) i - 45 exp (3'6) chg (Pscd It has been shown earlier that the use of a continuous current source, as with an analog potentiostat, produces an error in potential control due to iR drop across the solution. The true value of the potential is given by (66) Etrue ' E (1 ‘ exp §:%_{) (3'7) 8 dl 54 where Etrue is the true value of the potential, E is the desired potential, and the other variables have their usual meaning. The flow' chart for' the computer' model is shown in Figure 3-1. Complete listings of the modelling programs are found in Appendix B. After calling up the program, the user is asked if a file will be used to input the data. If so, the program assigns values to the parameters from the file. Otherwise, the user is prompted for input, line by line at the terminal. Each line provides the variable name and units. The name of the file which contains diffusion coefficient values is asked for and is entered by the user. The program reads the file and determines the proper value for D given the electrolyte concentration. The constants R, F, x, and T are specified and the variable values converted to the proper units for use in the equations. The user supplies a name for the output data file and the program writes the variable names and their values to it. Calculation of PT1 and PT2, which remain constant throughout the experiment, and the number of potential pulses in the scan follows. This value is calculated as the difference between the initial and final potentials divided by the potential difference between the pulses. The user is prompted for the name of the file containing the various values of the double layer capacitance with respect to potential. 55 C SW- D Operator input J 1 Conversion to proper utput values to /\ P Go to pulse potential Yes - . othe Yes End run? No No ‘ . A Find Cdl Stop Calc. Etrue. if! to. imea . Output potl l , VB imeas Figure 3-1 Flowchart for normal pulse polarography. 56 The next section of the model is the loop that performs the calculations for each potential pulse. The value for the double layer capacitance at the pulse potential is read from the file and used to calculate the cell time constant. For this purpose, it is assumed that the potential remains constant over the width of the pulse. The true potential is calculated for the time at which the current 'measurement’ is made. The value of the P term, 'and thus PT3 of the faradaic current equation, is determined by the Etrue value. The faradaic current contribution is then calculated from PT1*PT2*PT3~ The charging current contribution is determined by the potential step at the leading edge of the pulse and the cell time constant calculated earlier. The values of ifar and ichg are added to give the 'measured' current. The values of the pulse potential and 'measured' current are written to the data file as x,y pairs. The end of the potential pulse signifies the fall of the mercury drop and the surface concentration of the analyte returns to bulk concentration levels. The model then proceeds to the next pulse potential. It is unnecessary to return to the. base ;potential between each pulse (at least as far as simulation is concerned) since it is assumed that no faradaic reaction occurs at that potential and no measurement is made. The calculations required to step down and then up to the next pulse potential would simply take more time. When the program has gone through the loop the correct number of times, it signals an 'ALL DONE’ to the 57 terminal and asks the user if he/she wishes to perform another experiment. If so, it returns to the variable input section, otherwise, the user is returned to the computer's operating system. 2. Charge Pulsed Normal Pulse Polarography In the case of the charge pulsed implementation of normal pulse polarography the theoretical equation for the faradaic charge is that which was derived at the beginning of this discussion (Eqn 3-2). Again, for convenience, the equation was split into three parts PT1 =- 2nFAC (3-8) ~ PT2 = (Dt/n)1/2 (3-9) PT3 = l/(1+P) (3-10) The algorithm for charging current is not required in this case since it is assumed that the double layer is charged before the counting of charge pulses begins. This will be true as long as Cdl does not change during the step. Also, there is no need to include the equation for Etrue since measurements are not begun until the proper potential has been achieved and the potential measurement, always made. with no net current in the cell, always yields the true value. However, other algorithms are needed owing to the nature of the technique and the type of instrumentation needed to perform it. These are described below. The charge content delivered by the small injection is calculated as 58 SMQ = CHGV*CHGCAP (3-11) where CHGV is the voltage to which the capacitor is charged and CHGCAP is the size of the capacitor. The charge stored on the charging capacitor is transferred to the double layer when the switch is thrown and complete charge transfer is accomplished through the use of an operational amplifier. The time to make this small charge injection can either be set by the user (if 0, the effect of other variables is more easily seen) or calculated by the model as five cell time constants INJT = 5*Rs*Cd1 (3-12) since that is the time required to deliver 95% of the charge to the double layer. The size of the potential excursion caused by the small charge injection. is given. as ‘the charge content of ‘the injection divided by the working electrode capacitance. The time required for the potential to decay to the threshold value (assuming no electrical noise) depends upon the faradaic reaction and is calculated as DECAYT = 21 _sngg§_ 2 (3-13) 20 PT1*PT3 where SMCHG = DIF*WECAP. DIF is the potential difference from the threshold value and WECAP is the capacitance of the working electrode. The threshold values for the potential form a 'window' within which the potential should remain. It is assumed that the potential-correcting small charge injection occurs immediately as the cell potential crosses a threshold. 59 The last algorithm needed is for calculation of the analyte concentration at the surface of the working eletrode. The equation for the concentration gradient at a spherical electrode is (67) GRAD = 1 - BAD erfc DIST , (3-14) RAD+DIST 2(D*TIME) where GRAD is the proportion of the bulk concentration present at that time, RAD is the radius of the working electrode, DIST is the distance from the electrode surface (i.e., the diffusion layer thickness), and TIME is the time that has passed thus far within the pulse. The flowchart for this technique is shown in Figures 3-2 and 3-3. The program begins with operator input of the variable values either through reading a data file or direct input to a prompt. The user is asked for the name of the (data file which contains the values of the diffusion coefficient with respect to the concentration of the supporting electrolyte. The program then finds the proper value. After inputting several more values the user is asked if he/she wants to set the time required to make the small injection to a constant value or to allow the computer to calculate the time at each pulse potential. The user is prompted to name the output file. The constants are specified, variables converted to correct units, and these variable values written to the output data file. The operator is then asked for the name of the file containing the Cdl values and the correct value is found for the base 60 C J W -’| injut A Conversion 3 to proper utput l values to /\ (lie Make charge , injection At oulse pot No \ ‘? Yes /\ ~ Yes B . oothe Yes {End 0 run? 0 s?can No No Time-0 Stop #counts=0 0 Figure 3-2 Flowchart for charge pulsed normal pulse polarography. 61 Find Cdl l Calculate Decay time Return to Ebase Increment /h timer N oncentratio Calculate gradient Output # of counts vs cat! Figure 3-3 Flowchart for charge pulsed normal pulse polarography. rt pc 17.5 pu 62 potential. The variables whose values remain constant during the simulation are then calculated. The next part of the model contains one loop nested inside another. The outer loop contains a calculation of the time required to reach the pulse potential and the value of PT3. Also, the Cdl at that potential is found, as are the charge content of the small injection and the threshold values of the potential. The inner loop contains a calculation. of the time required for the potential to decay. If this time is greater than the pulse width the program exits the loop. Otherwise, the decay time is added to the time into the pulse. A small charge injection is made, the resultant potential excursion calculated, and the time required to make the injection is added to the total time into the pulse. If at any time this value becomes greater than the width of the pulse, the loop is exited. If not, a subroutine calculates the depletion of the analyte at the electrode surface and the loop is continued. After the nested loop has completed its cycling, the number of charge' injections required is calculated and written to the output data file with respect to the pulse potential. The potential is then stepped down to the base potential (useful in this case to allow determination of the time needed to achieve the pulse potential) and the surface concentration of the analyte returned to bulk concentration conditions. rea the rat: cal. ope: pole that and limb HUme Char Dela; "idti degre CURVE shCWs the e 63 The outer loop is cycled until the final potential is reached. The program then signals 'ALL DONE' and informs the user if the rate of potential decay is greater than the rate at which charge can be injected. A subroutine then calculates the 31/2 and the program ends by asking the operator if he/she wishes to run another experiment. B. Differential Pulse Polarography The equation for charge pulsed differential pulse polarography (CPDPP) is arrived at in the same manner as that for CPNPP Ai - gg - nFAC‘/_Q 53g? - Ea (3-15) dt 2(0'i‘0' PA+PA+PAa Aqu 3 nFAC Tf-D (It O+OPA+PA+PA261IIZ Aq = ZDFAC Q; Bag - R (3'16) V n (a+a PA+PA+P223) Again, the only differences between the current (10) and charge based equations are the integration constant (the number 2) and the movement of t from the denominator to the numerator of the square root term. In other words, the charge pulsed implementation of ' differential pulse polarography shows an increase in the measured charge as the width of the potential pulses increases as opposed to the decrease in the faradaic current with time seen in the conventional implementation. Here again, the final term shows no change from the integration since the potential at any level is assumed to remain constant. In the case of PA the equation is and pol CUT ffi O '1 The and in; Mgber cones 64 PA = eXPi[((El+32)/2)-El/2](HF/RTii (3-17) and for O 0 3 expiiifiz-ElilzlinF/RT)} (3-18) 1. Traditional Differential Pulse Polarography The modelling program for differential pulse polarography begins with the equation for the faradaic current (Eqn. 3-15) which is again split into three portions for easier handling PT1 = nFAC PT2 = (D/nt)1/2 p'r3= PAQZ_:_BA <3-19) o+PA02+PA+PAza The contribution from charging current is calculated via Rst1 and the true value of the potential is given by Etrue c E (1 - exp -; (3-21) Rst1 The flowchart for this technique is shown in Figure 3—4. As with the other modelling programs, the simulation begins by asking the operator if he/she wishes to input the variable values through the use of a data file. If so,'the model asks for the name of the file and values are read from it. If input is directly from the terminal, the user then assigns values to the various parameters through the use of a prompt. The user is prompted for the name of the file that contains the diffusion coefficient values and determines the proper value given the background electrolyte concentration. 'The program then asks for the name of the P 65 c ) Operator input 1 3 Conversion to prOper utput values to A\ Go to step Output pls * potential potl vs Al Yes , * 1 Output puls - -othe Yes End I a] run? at can ‘ potl vs ipls N0 NO I - Find Cdl Sta Find Cdl Calc. Etrue. P Calc. Etrue. if, ic, ipls if, ic._ istep and Al Output step ‘60 to pulse— potl vs iste potential Figure 3—4 Flowchart for differential pulse polarography. 66 output file. The constants are assigned and variables converted to the proper units. Then the variables and their values are written to the output data file. The first calculations within the model are for PT1 and the number of potential pulses in the scan. The user is next asked for the name of the file containing the double layer capacitance values and the program enters the loop. Calculations for the staircase step and pulse potentials are made within the same loop. The program begins with the calculation of the variables for the staircase step measurement. First, the values of PT2 and PT3 are calculated. Next is the calculation of ifar and ichg- These two variables are summed to give imeas- The potential is then stepped to the pulse level and the same calculations are repeated for the pulse values. The value of Ai is calculated as the difference between the current on the pulse and the current on the staircase step. The difference current is then written to the output file with respect to the pulse potential. A short section of code also determines the potential at which the highest current difference is observed and reports the result to the screen and writes the value to the output file. The program then signals ’ ALL DONE' and ends by asking the user if another run is desired. 2. Charge Pulsed Differential Pulse Polarography The equation for the faradaic charge for charge pulsed differential pulse polarography is that derived at the 67 beginning of this section (Eqn. 3-16). The three parts of the equation used in the model are PT1 = 2nFAC (3-22) 912 - (Dt/x)1/2 (3—23) pr3 ~‘__2 (3-24) U+Phg§-:—BA +PA+PAO Since charging current does not contribute to the measured charge in this method, its theoretical equation is not added nor is the equation for the true potential. The other algorithms required because of the difference in methodologies are included below. The charge content of the small charge injection is SMQ = CHGV*CHGCAP (3-25) where CHGV is the voltage on the charging capacitor and CHGCAP is the size of the charging capacitor. The time to) deliver this amount of charge to ‘the working electrode is either set by the user or calculated as follows INJT - 5*R3*Cd1 (3-26)3 The change in potential is calculated as the charge content of the injection divided by the capacitance of the working electrode. Assuming the absence of electrical noise in the system, the time in which the potential decays to the threshold value is pecan =- £1)(_§M§_fl§_)2 <3-27) ZD PT1*PT3 where SMCHG - DIF*WECAP. DIF is the potential difference 68 from the threshold value and WECAP is the capacitance of the working electrode. It is assumed that the potential is sensed immediately as it crosses the threshold. The concentration profile at the electrode surface changes while a potential is maintained and is calculated by GRAD - l - BAD erfc 215: (3-28) RAD+DIST 2 (D*TIME) where GRAD is the proportion of the bulk concentration present at that time, RAD is the radius of the working electrode, DIST is the distance from the electrode surface (i.e., the diffusion layer thickness), and TIME is the time into the current potential pulse. The flowchart for the charge-based form of differential pulse polarography is shown in Figures 3-5 through 3-7. To begin, the user is asked if a data file will be used to input the variable values. If so, he/she is asked for the name of the file and values are read from it. If not, the user is prompted for each variable by a line stating that variable's name and the units. During this input phase, the user is asked for the name of the file that contains the diffusion coefficient values and the correct value is read from the file. Three more variables are specified and the operator is then asked if he/she wishes to set the time required to make a small charge injection to a constant value. If not, the model calculates the time at each new potential. Next, the output file is named. The constants are specified and variable values converted to the proper units. The next section of code involves writing ‘the F 69 C Start ) W nput i A Conversion , to proper l Output 1 values to /\ fills _ Make charge injection ' A Yes Yes C - -othe Yes ()ngan 0 run? 7 ' No No - Time=0 Stop #counts=0 0 Figure 3-5 Flowchart for charge pulsed differential pulse polarography. '70 Find Cdl in Make charg injection 3]_ Difference in counts and output vs pls potl 0 utput counts vs ulse otl Increment timer timer and counter tfor i ,. Calculate I" once tire 10 I'd en sm inject ion A ' MARY of p\u1s/e Figure 3-6 Fl\/owchart for charge pulsed differential pulse polarography. Cal OnCe I'l '71 >i Calculate I © Decay time P ' I Increment A /\ timer 3 Output ,9 of counts vs ste at l Calcqla ] ncremen A once re 1011 timer and rad ient , . Figure 3-7 Flowchart for charge pulsed differential pulse polarography. variabj that calcule potenti the rad for in; of the Th4 which d_ small calcula: and Ste: correct 0f the c Calculat thresholi made (if Witt CUIrent F The time is determ that amo potential Pulse in injection lete c: by a “bra! 72 variable values to the output file. Then, those variables that remain constant throughout the experiment are calculated: PT1, the number of cycles to reach the final potential, the time spent at the lower potential (TRLX), and the radius of the electrode. The last prompt to the user is for input of the name of the file that contains the values of the double layer capacitance. The model next enters the loop section of the program, which does all the calculations required. There are two small loops within the larger, these involve the calculations for the small charge injections at the pulse and step potentials. First, within the large loop, the correct double layer capacitance is found for the potential of the current step. The content of the small injection is calculated as well as the values of PT3, the potential threshold values, and the time for a small injection to be made (if required). Within the first small loop, the difference between the current potential and the threshold potential is calculated. The time required for the potential to decay to that point is determined and the time within the pulse incremented by that amount. A small charge injection made and its potential change calculated and added, and the time into the pulse incremented by the time required to make the injectione .After each charge injection, the change in analyte concentration at the electrode surface is determined by a subroutine. If at any point the time within the pulse exceeds exiting that pc file. Th potentit The cal step, be double 1 concentr Exi larger, determin Pulse a: wl’itten Lastly, returned drop fal; StePped b Beyo 'ALL DON: Potential User is ac C. SqUar The C matiOn f '73 exceeds the given pulse width, the loop is exited. After exiting the loop, the number of charge injections made at that potential is determined and can be output to the data file. The potential is then stepped- to the next pulse potential as determined by the input waveform parameters. The calculations are done in the same manner as for the step, beginning with the finding of the proper value of the double layer capacitance and ending with calculation of the concentration profile at the electrode surface. Exiting the second small loop but still within the larger, the number of injections made on the pulse is determined and the difference between the counts on the pulse and step potentials calculated. This difference is written to the file with respect to the pulse potential. Lastly, the concentration at the electrode surface is returned to the bulk concentration value since the mercury drop falls at the end of the pulse and the potential is stepped back down. Beyond the end of the large loop, the program signals 'ALL DONE' to the screen. A subroutine determines the potential at which the largest difference occurs and the user is ashed if he/she wants to run another experiment. C. Square Wave Voltammetry The conversion from a current (20) to a charge based equation for square wave voltammetry. is performed in the Thes r for nor the fine no Chang this Cha Change S measurem Wave vol rePlaced °Ver th. re3u1t an' The veltanunet "1 bdrr Em; ‘ 74 same manner as for differential pulse polarography and produces identical results as follows: Ai - gg - nFAC [1’ NY <3-29) dt * A qu - nFAC AW]: dt Aq - 2nFAC‘/D_1 A‘I’ (3-30) It Thes resultant equation (3-30) shows the same effects as for normal and differential pulse polarography. However, the final terms in each of the other two techniques showed no changes. The ‘1‘ factors in this case do change, although this change is not related to the integration process. The changes in these final terms is due to the method of measurement in the charge pulsed implementation of square wave voltammetry. The p1 is replaced with 0' and the p2 is replaced with the number 1 since charge measurement is made over the entire width of the potential pulses. The resultant ‘1‘ terms are shown below v, - 92%;1411 +2292 Tanking/12‘“ 935%) m=0 and for ‘i’r ‘i’r921m_1_)_lC+ ..Q Jim—Q" ZI‘TQ'm (3-31) 2(m—M—E (3 -m+1) (j-1m+1-o) ) m==0 1. Traditional Square Wave Voltanuntery The computer model for traditional square wave VOltammetry is'expanded from the equation for the faradaic Current (Eqn. 3428) . Due to the nature of the calculations ’ We ti Dc "a Va the 75 in the model, this equation is split into three parts. The first two (PT1 and PT2) are the same as for traditional normal or differential pulse polarography. In this case, PT3 is the ‘1‘ term relating to the potential at which measurement is being made. The charging current contribution remains the same ichg - Ar. s_-t_exp( , (3-32) Rst1 and the true value of the potential is given by Etrue - E (1 - exp -t ) (3-33) Rscdl The flowchart for square wave voltammetry is essentially the same as for differential pulse polarography (Fig. 3-8). Differential pulse polarography is actually a subset of the various possible forms that can result from the manipulation of the parameters for square wave voltammetry. However, the current difference for square wave voltammetry is determined at the reverse pulse, i.e. at the end of the step back down from the pulse potential (exactly opposite to the measurement in differential pulse polarography). The simulation program begins, as usual, by asking if the operator wishes to use a data file to input the variable values. If so, the name of the file is entered and the values read from the file; otherwise, the operator inputs the proper values to each prompt. The user is then asked to provide the name of the file containing the diffusion coefficient values and the correct value is read from the '76 C “a“ ) Operator Yes i . othe run? No Stop inut i Conversion _ to proper utput values to Go to pulse f Output PIS potential potl vs Ai End Output step Yes [potl vs irev] No l , Find Cdl Find Cdl Calc. Etrue, Calc. Etrue. if, ic. irev' if, to. Mar and At l +_ I _ Output pls Go to step potl vs itor potential Figure 3-8 Flowchart for square wave voltammetry ‘77 file. Next, the output file is named. The constants of F, R, T, and x are specified and the variables whose units are inconsistent with those used in the equations are converted. The variable values are written to the output data file. The values of PT1, PT2, and the number of cycles are calculated. The question that asks for the name of the file containing the double layer capacitance values is the last statement before proceeding to the body of the model. The large loop, which corresponds to one cycle of a square wave voltammogram, contains two small loops nested within it. The initial calculations correspond to the first section of the ‘I’f calculation. The first small loop follows, which contains the remaining calculations required to determine the value of ‘Pf at that potential. These small loops for the ‘1’ terms are required because square wave voltammetry is performed at a stationary electrode. Therefore, the concentration of analyte at the working electrode is determined by all the previous steps in the experiment. Following calculation of PT3 (‘I’f), the faradaic current is determined. The value of Cdl is fpund for the forward pulse potential and the charging current contribution calculated. The measured current is the sum of ifar and 1559. The second small loop performs the calculations required to determine the value of PT3 for the reverse pulse OPr). The end of the large loop contains the rest of the calculations for the reverse pulse. The current due to the '78 faradaic reaction is found. The proper value for Cdl is determined and ichg calculated. The total measured current for the reverse pulse is the sum of the faradaic and charging currents. The measured current on the reverse pulse is subtracted from that found for the forward pulse and this difference is output to the data file with respect to the potential of the staircase step upon which these pulses were imposed. Following the large loop, a subroutine finds the potential at which the peak current difference occurs and the user is asked if he/she wishes to perform another experiment. 2. Charge Pulsed Square Wave Voltammetry As usual the model is expanded from the equation for the faradaic charge which was derived above (Eqn. 3-30). Also, the new versions of ‘I’f and ‘Pr must be included. The equation is split into three parts for convenience, with PT1 and PT2 the same as for the charge pulsed implementations of the other two techniques. In this case, the value of PT3 is determined by ‘I'f or ‘I’r depending upon which pulse the model is on. The charge content of the small injections is calculated 'from SMQ . CHGV*CHGCAP (3-34) where CHGV is the voltage on the charging capacitor and CHGCAP is the size of the charging capacitor. The time 79 electrode is either set by the user or calculated as follows INJT - 5*R3*Cd1 (3-35) The change in potential due to the small charge injection can be calculated from the charge content of the injection divided by the capacitance of the working electrode. The time in which the potential decays to the threshold value is 133er - (21)<_aucn§_)2 (3-36) 2D PT1*PT3 where SMCHG s DIF*WF.CAP. DIF is the potential difference from the threshold value and WECAP is the capacitance of the working electrode. It is assumed that the potential is sensed inunediately as it crosses the threshold and that there is no electrical noise in the system. The ‘1' terms contain calculations for the concentration profile that results from each pulse. However, a means is still required to determine the concentration gradient during the pulse. This comes from the following equation GRAD - 1 - [ m erfc( >] (3-37) RAD+DIST 2(D*TIME)I72 where GRAD is the proportion of ‘the Ibulk concentration present at that time, RAD is the radius of the working electrode, DIST is the distance from the electrode surface (i.e., the‘diffusion layer thickness),.and TIME is the time that has passed thus far in the pulse. The flowchart for this implementation of square wave voltammetry is shown in Figures 3-9 to 3-11. The model begins with the question of whether a data file will be used 80 Conversion to proper ut ut K valueg to fills Make charge injection i At /\ . , End No Time==0 . Stop #countsao 0 Figure 3-9 Flowchart for charge pulsed square wave voltammetry. 81 Increment timer En ofp e 7 No I Calc la * cremen once ‘gra1t304 timer and a 3 en counter or am inec n 4" No End of p’ulse Yes Yes ' ut co1 u pu' o unts vs lise otl Figure 3—10 Flowchart for charge pulsed square wave voltammetry. 82 I , Calculate Decay time and direction erenc in coun an output Increment vs lac-2Q!- AK 3 timer flaiiit‘i A\ Figure 3-11 Flowchart for charge pulsed square wave voltammetry. 83 to input the data. If so, the file is named by the user and parameter values read. Otherwise, the operator is asked for each value by a prompt for each variable. The user is asked for the name of the file containing the diffusion coefficient values and the correct value read from the file. The last variable values are input and the operator asked to either set the time required to make a small injection or to allow the model to calculate the time required at each potential. The constants are specified and variable values converted to proper units as needed. The user is then asked to name the output file and the various values of the parameters written to it. Prior to the loop section of the model, PT1 is calculated as well as the number of cycles that will be performed, the widths of ‘the forward. and reverse pulses and the radius of the working electrode. The user is prompted for the name of the file that contains the double layer capacitance values, the value found for the initial potential, and the potential stepped to the value for the first forward pulse. Within the large loop that produces the cycles , are nested a series of four small loops. Before the_first small loop is the determination of the double layer capacitance value for the forward pulse. The first small loop performs the calculations to determine the value of PT3 for the forward pulse. The section before the second small loop contains calculations of the threshold potential values and the time required to make a small charge injection, if 84 necessary. The second small loop performs the calculations for potential decay and charge injection. The potential difference between the given potential and the threshold value is calculated, as well as the time needed for it to decay. The decay time is added to the time into the pulse, the small charge injection made and its subsequent potential excursion determined, and that time added. The last calculation in the loop is the subroutine that calculates the concentration profile at the electrode at that time within the pulse. This loop is exited when the time exceeds the forward pulse width. The number of charge injections made at that potential is recorded and the potential stepped to the next value for the reverse pulse. The double layer capacitance value is found and the third small loop entered. The third. and fourth small loops contain the same calculations as seen for the first and second, however the values obtained pertain to the reverse pulse. There is a difference that can and does occur on the reverse pulse. Due to the large potential excursion between the forward and reverse pulses and the fact that square wave voltammetry is performed at a stationary electrode, oxidation can occur due to the presence of reduced species in the mercury drop. Thus, ’positive' and 'negative' (or cathodic and anodic) charge injections will result because the potential will always decay in the direction of the reduction potential of the species of interest. However, oxidation will not occur until after reduction has taken place, so a ’negative' count 85 will not occur on the reverse pulse until after a ’positive' injection is counted on a forward pulse. The difference in the number of counts determined on the forward and reverse pulses is calculated following the fourth small loop. In the case of the negative injections, their number is numerically added to the number obtained in the previous forward pulse. Following the large loop, the model signals an 'ALL DONE’ to the user and determines the potential at which the count difference is a maximum. The values of two flags are also contained in the file. These flags indicate if the potential decayed at a rate faster than could be attained by the charge injector. Lastly the user is asked if he/she would like to perform another experiment. CHAPTER 4 STUDIES OF THE CHARACTERISTICS OF PULSED ELECTROANALYTICAL TECHNIQUES WITH CHARGE PULSE POLARIZATION BY COMPUTER SIMULATION Computer simulation has proven its ability to accurately model various types of instrumentation and chemical systems. The following chapter is devoted to the comparison of the results of the computer experiment to the corresponding physical experiment and to the characterization of three charge pulsed electroanalytical techniques. As Normal Pulse Polarography Normal pulse polarography was developed at the same time as differential pulse polarography. Since differential pulse polarography showed an increased sensitivity due to the subtraction of charging currents, normal pulse polarography has not been a widely used electroanalytical technique. The fellowing sections include a comparison of the results obtained through physical and computer experiment, as well as a comparison of the response with respect to the values of various system parameters for both conventional and charge pulsed normal pulse polarography. 86 87 1. Comparison of the Continuous Current Model to Physical Experimental Results The next step in the process was to see if the simulation models accurately portrayed the events of an instrumentally controlled experiment. Cadmium ions, being the most studied and best suited cations, were studied with a background electrolyte of KCl. The instrument used to perform the physical experiments was a PAR (8686 Princeton Applied Research) Model 364 Polarographic Analyzer in conjunction with a PAR Model 303 Static Mercury Drop Electrode. Substitution of the values of the instrumental parameters into the simulation program for conventional normal pulse polarography allows for direct comparison of the two experiments. The instrument settings used are as follows: 5ettinga_cf_the_instrument Initial potential -O.352 v Scan direction negative Scan rate 5 mV/sec Operating mode Normal Pulse Current range varies Output offset off Wings Mode DME Drop Size small* Purge 4 min 88 W Pulse width 50 msec Current sampled last 16.7 ms Drop time 1 sec Purge gas N2 Background Electrolyte 0.1 M KCl Reference electrode Ag/AgCl The values used in the computer model were input from the terminal as follows Metal ion & electrolyte Cd++ in KCl Reference electrode Ag/AgCl Number of electrons 2 Surface area of electrode 0.01017 cm2* Concentration of analyte varies Background electrolyte conc. 0.1M Pulse width 50 msec Time of measurement 33.3 msec Diffusion coefficient 7.15x10"6 cmZ/s Base Potential -0.350 V Reduction potential -0.6438 v Final potential -O.950 V Step size between pulses 5.0 mv Uncompensated resistance 50 ohms Double layer capacitance varies Relaxation time (DROPT-TPLS) 950 msec *This value was obtained for the PAR Model 303 SMDE. Ten mercury drops were dispensed into a weighed beaker, the 89 setting on the electrode was ’small’. The weight of the mercury in the beaker was measured. From this weight, the density of mercury, .and the assumption that the mercury drops were spherical, the average volume of one mercury drop was obtained. The volume of a sphere is mr3 and the surface area of a sphere is defined as 4/3nr2. Through calculation of the radius of an individual drop,‘ the value for the surface area of one ’small’ mercury drop was obtained. Both sets of experiments (physical and simulation) were run on concentrations of Cd++ ranging from 10"6 to 5x10'4M. Comparison of the diffusion current resulting from these experiments is shown in Table 4-1. Table 4-1 Results of computer model and physical experiments gg++ ggng(M) Sim, val§mg1 Avg, exp;.(mA) Std, gev § dif 1 x 10"6 0.0162 0.0161 0.00395 0.617 s x 10‘6 0.0811 .0.0837 0.00409 3.20 1 x 10"5 0.162 0.167 0.00497 1.23 5 x 10‘5 0.811 0.814 0.00961 0.370 1 x 10"4 1.62 1.59 0.0580 1.85 5 x 10‘4 8.11 8.15 0.263 0.493 As can be seen from the final column of this table, the computer' model accurately' predicts the. diffusion current value for a normal pulse experiment. 90 Another means of testing the accuracy of the model is to see how well the experimental points fit the predicted curve from the computer program. This is shown in Figure 4-1 for a 10'5M CdH’ solution in 0.1M KCl. There is an extremely good fit between the physical and simulation experiments (values used for each curve shown in Table 4-2). It can be seen that the model accurately’ portrays the current measured for a reversible, two electron, electrochemical reaction. Therefore, the theoretical equations modified to produce the equations for the charge pulsed implementation is accurate and can be used to model a reversible, two electron system. 2. Comparison of Results for Continuous Current and Charge Pulsed Methods The next logical step was to compare the relationships between the various system parameters and the response of the conventional and charge pulsed implementations. Fewer variables are needed to characterize the system for normal pulse polarography. The first parameter to be studied was the potential difference between pulses. The diffusion current or charge measured does not change with the potential difference between the pulses. In other words, .for both cases, the relation between the limiting current or charge and the step size between pulses is a straight line of slope=0. However, an increase in the voltage difference between pulses results in a loss of voltage definition of 91 .Eo._uo..o_oa 3.2. .056: 33.25» 53 3.33.. 330.53%» .0 canton—coo «iv 0.53m mom 8, >V .2238 out 05.! 00.... own! 9.... F p u p i— n — p Noel... 350a Bop 3305.390 n . 3.38 com—235$ .l... . T ..Nod ..ood r ..ofio 11.0 T (v1!) iusuno 92 Table 4-2 Data for curves shown in Figure 4-1 Measured values Simulated values Pntl_i!l__9urrent_imA) Potl (V) Current_lmAl -0.4938 0.00000 -0.490 0.136x10"5 -0.500 0.240x10’5 -0.51o 0.494x10‘5 -0.520 0.106x10"4 -0.530 0.231x10'4 -0.5438 0.00100 -0.540 0.502x10'4 -0.550 0.109x10"3 -0.560 0.238x10'3 -0.570 0.517x10"3 -0.580 0.00112 -0.5938 0.00320 -0.590 0.00243 -0.6038 0.00700 -0.600 0.00519 -0.6088 0.00990 -0.6138 0.0143 -0.610 0.0109 -o.6188 0.0203 -0.6238 0.0283 -0.620 0.02199 -0.6288 0.0385 -0.6338 0.0511 -0.630 0.04131 -0.6388 0.0655 -0.6438 0.0811 -0.640 0.06921 -0.6488 0.0970 -0.6538 0.111 -0.650 0.1003 -0.6588 0.124 -0.6638 0.134 -0.660 0.1264 -0.6688 0.142 -0.6738 0.148 -0.670 0.1436 -0.6788 0.152 -0.6838 0.155 -0.680 0.1531 -0.6938 0.159 -0.690 0.1579 -0.700 0.1602 -0.710 0.1613 -0.720 0.1618 -0.730 0.1620 -0.7438 0.162 -0.740 0.1622 -0.7538 0.162 -0.750 0.1622 93 the output curve, so a relatively small potential difference should be used. Figure 4-2 shows the limiting response for conventional and charge pulsed normal pulse polarography for different sweep rates. The potential difference between pulses is maintained at a constant 10 mv so the change in sweep rate is achieved by a proportional change in the width of the potential pulses. An increase in the measured current with respect to sweep rate is seen for the conventional implementation. However, potentiostatic control makes current measurement later in the pulse a necessity since time is required to decrease the error due to charging current. Inn the charge based implementation, an increased measurement time means that more counts are amassed. Therefore, it would be well to use a lower sweep rate for charge pulsed normal pulse polarography. This means that a reasonable compromise must be made for.specific experimental conditions between the number of counts desired and the amount of time spent at each potential for the charge based method. Solution resistance presents some difficulties in both cases. An increase in Rs results in an increase in the charging current time constant and, hence, requires a measurement time later in the potential pulse. This can be seen from Figure 4-3. The charging current curves were calculated by using uncompensated resistance values of 50, 100, and 200 ohms. The analyte concentrations used to 94 $383.63.. 3.2. .252. 3 posse encore use an .ocozcgcoo to. encode! .0 cootanoo «It Boot An\>v 3a.. coo... mo. An\>v 30.. coon mo. 97. I ...I . I . I .. F . 9m . o...§ 0 pr . om . orMOd a... .86 w. . O :30 0 w. . n m IS.O w e . m. M .8... I. . m w." 18.. ( u w 9 ION.— .? I. . rat.“ Current 04A) 95 5.0-1 ' i ' 1 -— Faredaic current 4.0+ 3,0... . 2'0“ inc. cone. J \ \ 1.0- “ 0.0.- ‘ -: 7 t I t : t ; j 0 20 4O 60 80 100 Time at which current is measured (ms) Figure 4-3 Plot showing how the time at which the current must be measured increases with increasing solution resistance for normal pulse polarography. 96 determine the faradaic current curves were 1, 2, and 5x10‘5M. As can be seen from the Ru curves, an increase in the uncompensated resistance (related to a higher solution resistance) has the effect of causing an increase in the time needed to allow the charging current to decay to a negligible value. Even for an analyte concentration of leO‘sM, a wait of over 30 ms is required to reduce the charging current, for a resistance of 200 ohms, to 10% of the faradaic current. There is an evident loss of sensitivity in waiting many tens of milliseconds to measure the current. A higher solution resistance also results in an increased error in potential control for conventional normal pulse polarography. For this reason, high background electrolyte concentrations are used for any technique whose potential is controlled potentiostatically. Charge pulsed normal pulse polarography does not encounter this problem. A high solution resistance can increase the time required to make large potential steps. The potential excursion caused by a charge injection is a result of the charge content of the injection and the double layer capacitance of .the working electrode. For large potential steps, the maximum charge in a single injection may not be sufficient to produce the potential change desired. Therefore, multiple charge injections may be required to attain the proper potential. An increase in the time to step to the correct potential can result in a decrease in the surface concentration of the analyte. This reduces the amount of 97 charge measured after that potential has been achieved. It is also possible that, towards the end of a scan where potential steps of >1V may be required, the charge injector would not be fast enough to produce the required potential step. In other words, for very large potential steps, the charge injector may never get there. The next figure (4-4) shows the relations between the scan rate (produced by a proportional change in the drop time, pulse width, and measurement time) and the minimum detectable concentration. A signal to noise ratio of 10 on the diffusion plateau was used to determine the minimum detectable concentration. This means that the faradaic current measured was ten times the charging current for conventional normal pulse polarography and that at least ten charge injections were counted for charge pulsed normal pulse polarography. As can be seen, a decrease in scan rate, and thus, an increase in the time at which the current measurement is made, increases the minimum concentration which may be detected in the conventional method. The limit arises from a combination of the charging current .and background noise in current measurement. The relation is reversed for charge pulsed normal pulse polarography. A low analyte concentration results in an increase in the time required for the potential to decay to the threshold value. Therefore, a slower scan rate allows a lower concentration to be detected. This plot shows that the dynamic range of the charge pulsed implementation for one specific set of 98 Santana—ca 3.3... .250: an mania encore pee an 3335230 to.— eZfinoa cow-Sees lcoo 033033 6255.: Co coatanoo elv Esau An\>v 30.. coon no. Am\>v oboe coon mo. e s II e I. elm m e 0 II 0 II sill o.ol - ow . om . 2.3... 6 are . ow . cm . 2.06.. o Blots—Iv I w o 2163.... .7... m. o 3193.... I .m: o alopxplv I n ...o.nl Tndl m D. m. .3... o .31 w. m ml 10 Hi m Inc“- w 3.7 e U . n. . as It 3 -o.n.. new.“ -9... o u uogionusouoo slqaiosiep ulnulgugm bol 99 conditions is at least an order of magnitude. Changes in the experimental parameters result in movement of this curve up or down to encompass a range of concentrations from 10‘3M to 10'7M. The series of curves in Figure 4-4b shows the minimum concentration that may be detected by the technique of charge pulsed normal pulse polarography at various scan rates with charge injections carrying different charge content. The minimum detectable concentration is determined as that at which at least ten charge injections are counted on the diffusion current plateau. It is evident, from the curves, that the injection of a smaller amount of charge into the cell allows lower analyte concentrations to be detected. This is because charge injections containing less charge produce smaller potential excursions and, therefore, the potential decay to the threshold value requires less time. Hence, more charge injections are needed to maintain the proper potential for a constant analyte concentration. It can then be inferred that smaller charge injections will result in detection of lower analyte concentrations.. A charge content of lO‘lOC is the smallest practical charge injection for an electrode of large surface area (about 0.05 cmz) with a background electrolyte concentration of 0.1M. The current measured in traditional normal pulse polarography is in direct proportion to the working electrode area. Figure 4-5 shows the effects of a change in the surface area of the working electrode for charge pulsed log minimum detectable concentration 100 -4.5-1 -5.0- -5.5-4 -8.0- H A-0.05 cmZ H A-0.025 cmz H A-0.01 cm2 -B-5 - . - . - . -1i.0 -2.0 -i .O 0.0 log scan rate (V/s) Figure 4-5 Comparison of minimum detectable con— centration possible for various electrode areas for charge pulsed normal pulse polarography. 101 normal pulse polarography. As in the case of the traditional implementation, the response is directly proportional to the electrode area. Therefore, for charge pulsed normal pulse polarography we see that, as a result of larger surface area, the analyte concentrations that can be detected are lower. Normal pulse polarography' can, be 'used. to determine species from molar quantities down to a limit of approximately 10'5M. This limit arises from the error introduced by the charging current. Charge pulsed normal pulse polarography, however, has upper and lower limits. The lower limit of 10'7M is obviously not due to charging current error, instead, it is derived from the electrical noise in the system and the minimum amount charge that can be reproducibly delivered to the cell. The maximum concentration that can. be determined. by this method is 10‘3M. This upper limit is due to the maximum rate at which charge injections may be made. The development of new and better electronic components cannot aid potentiostatically controlled potential step techniques. However, since charge pulsed normal pulse polarography is instrumentally limited, the advent of new and innovative integrated circuits may provide an.increase in detectability under reasonable time constraints. 102 B. Differential Pulse Polarography Differential pulse polarography has seen much use as an electroanalytical technique. The technique held the advantage of subtraction of charging currents over normal pulse polarography, as well as a peak shaped output which allowed for easier current measurement and increased resolution. Square wave voltammetry seems to be replacing this method as experimenters discover its increased sensitivity and faster scan rates. 1. Comparison of the Continuous Current Model to Physical Experimental Results Physical experimental differential pulse ‘polarograms were obtained from the PAR Model 364 Polarographic Analyzer with the Model 303 SMDE. The polarograms were obtained for the Cd++ in KCl system. The values of instrumental settings were input into the computer' model to derive simulated differential pulse polarograms. Comparisons can be readily made. The instrument settings used are as follows: WW Initial potential -0.352 V Scan direction negative Scan rate 5 mV/sec Operating mode Difl Pulse Pulse height 50 mV Current range varies Output offset off 103 W Mode DME Drop Size small* Purge 4 min cher.2ertinent_!alnsa Pulse width 50 msec Current sampled last 16.7 ms Drop time 1 sec Purge gas N2 Background Electrolyte 0.1 M KC1 Reference electrode Ag/AgCl The parameter values used in the computer model were input from the terminal as follows Metal ion & electrolyte Cd++ in KCI Reference electrode Ag/AgCl Number of electrons 2 Surface area of electrode 0.01017 cm2* Concentration of analyte varies Background electrolyte conc. 0.1M Pulse width 50 msec Time of measurement 33.3 msec Diffusion coefficient ' 7.15::10"6 cmz/s Base Potential -0.350 V Reduction potential —0.6438 V Final potential -0.950 V Pulse height 50 mV Step size between pulses 5.0 mV 104 Uncompensated resistance 50 ohms Double layer capacitance varies Relaxation time (DROPT-TPLS) 950 msec *Previously explained for normal pulse polarography. The physical and simulated experiments were performed on concentrations of Cd++ ranging from 10"6 to 10'4M. These results also compare favorably with one another as seen in Figure 4-6. The experimental polarogram fits the predicted curve produced by the simulation model well for 10’6M Cd++. Table 4-3 contains the peak difference currents for the simulated polarogram and physical experimental determinations. Table 4-3 Results of computer model and physical experiments W1 Ldif 1 x 10"6 0.1186 0.1212 2.19 5 x 10'6 0.5929 0.6003' 1.25 1 x 10‘5 1.186 1.226 3.37 5 x 10'5 5.929 5.978 ' 0.83 1 x 10‘4 11.86 12.45 4.97 Therefore, the theoretical equations used to calculate the measured current difference is accurate for a reversible, two electron system. The program for charge pulsed differential pulse polarography, resulting from the theoretical equations modified to represent charge pulse polarization, should also be accurate in its determination of the behavior of the Cd++/KC1 system. 105 .++_uo 3516— ..8 3.33; .3coEtoaxo £3 Ea..mo..o_oa om._:a 33:0 Icon—to pauo_sE_n 05 Co contanoo ole 0.52... now 9 3 .2288 0.! 5| m.l m.l F p — n — . NooI 350a Bop .3coEtoaxm I 3.33: pogo—seem I INOd 1 Iwod 1.o—d f (v11) iueJJna eouelsiigg 106 Table 4-4 Data for curves in Figure 4-6 Simulated values Potl (V) Current_1mAL Measured values 29:1 (2) Current (mAl -0.550 0.0009 -0.5538 0.0000 -0.555 0.00154 -0.5588 0.00150 -0.560 0.00238 -0.5638 0.00156 -0.565 0.00352 -0.5688 0.00313 -0.570 0.00508 -0.5738 0.00938 -0.575 0.00887 -0.5788 0.0125 -0.580 0.01294 -0.5838 0.0188 -0.585 0.01836 -0.5888 0.0234 -0.590 0.02383 -0.5938 0.0297 -0.595 0.02973 -0.5988 0.0375 -0.600 0.03844 -0.6038 0.0469 -0.605 0.04854 -0.6088 0.0594 -0.610 0.05975 -0.6138 0.0719 -0.615 0.07224 -0.6188 0.0828 -0.620 0.08135 -0.6238 0.0938 -0.625 0.09513 -0.6288 0.1063 -0.630 0.1069 -0.6338 0.1141 -0.635 0.1155 -0.6388 0.1188 -0.640 0.1205 -0.6438 0.1218 -0.645 0.1216 -0.6488 0.1188 -0.650 0.1186 -0.6538 0.1125 -0.655 0.1129 -0.6588 0.1070 -0.660 0.1050 -0.6638 0.1000 -0.665 0.09610 -0.6688 0.0891 -0.670 0.08613 -0.6738 0.0766 -0.675 0.07438 -0.6788 0.0656 -0.680 0.06404 -0.6838 0.0563 -0.685 0.05414 ~0.6888 0.0500 -0.690 0.04518 -0.6938 0.0438 -0.695 0.03875 -0.6988 0.0375 -0.700 0.03254 -0.7038 0.0297 -0.705 0.02667 -0.7088 0.0250 -0.710 0.02136 -0.7138 0.0188 -0.715 0.01645 -0.7188 0.0141 -0.720 0.01250 -0.7238 0.0109 -0.725 0.01072 -0.7288 0.00781 -0.730 0.00895 -0.7338 0.00781 -0.735 0.00756 -0.7388 0.00625 -0.740 0.00618 -0.7438 0.00469 -0.745. 0.00424 -0.7488 0.00156 -0.750 0.00290 -0.7538 0.0000 -0.755 0.00198 -0.760 0.00134 -0.765 0.00091 -0.770 0.00062 107 2. Comparison of the Results for the Continuous Current and Charge Pulse Methods The following paragraphs contain a discussion of the system responses for conventional and charge pulsed differential pulse polarography. The same experimental parameters are studied as for normal pulse polarography with the addition of the behavior of the system with respect to the amplitude of the pulse potential, for which the effects are shown first (Fig. 4-7). The current and charge differences are those measured at the.apex of the resultant peak. In both implementations, there is an increase in the peak response with an increase in the pulse amplitude. It would therefore seem evident from the plot that the best response may be obtained by using the largest pulse amplitude possible. However, figure 4-8 shows that the width of the peak at half height increases with increasing pulse amplitude. Therefore, the experimenter must be careful to choose a pulse amplitude which is large enough to produce an adequate response while maintaining a reasonable peak shape and voltage resolution. . Figure 4-9 relates the height of the staircase step to the behavior of the system for both implementations. There is little 'change in the peak current difference measured with increasing step height for conventional differential pulse polarography. This is also the case for charge pulsed differential pulse polarography. Since no significant difference in response is observed the only precaution which 108 .3 p 9.5 :32. 66.5.. .3 .ON . p .on .0— 3.... .68 Too» ..ooo Tacon T82 .68. £33 .68. 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F.33 s 6.3 (v11) wanna aoumamo 111 needs to be taken is to keep the step height small enough to maintain peak shape and definition. A change in sweep rate is produced by changing the width of the potential cycle while maintaining the staircase step size at 10 mv. Figure 4-10 shows how the responses of the two implementations vary with a change in sweep rate. In the case of conventional differential pulse polarography, an increased sweep rate results in a larger measured current. However, the peak charge difference obtained for charge pulsed differential pulse polarography has the opposite relation. Slower scan rates provide a longer time over which charge injections can be counted and result in a higher charge difference. The solution resistance affects both implementations of differential pulse polarography. The solution resistance must be maintained at a relatively low value ~to keep the charging current contribution negligible and maintain adequate potential control in traditional differential pulse polarography. For charge pulsed differential pulse polarography, the problem is not potential control, but that increased solution resistance increases the time needed to make large potential steps. The time to achieve the proper potential dbes not decrease the width of the potential pulse over which charge injections are made. However, the longer the time spent in trying to reach the potential, the larger the difference in the surface concentration of the analyte species. Generally, the size of the potential excursions in 112 ?\>V 3a.. coon mo. ON... . 9.. 3| :18 3:2 3. Eugenia 8.3 ascents an v.32. 092.0 pea Ao .ocozcgcoo to. 05: 3 «cannot 5.: 02.2.»! to cootanoo o—lv 0.50m An\>v BE coon mo. suouoofug sfiJoqo go asumswp 0...! O.Nl . ofil an 0.6 rad (v11) wanna soustma 113 charge pulsed differential pulse polarography is small enough to preclude difficulties in that area. The curves seen in Figure 4-10 provide an explanation for the effects seen in figure 4-11. Here the detectability was determined at a signal to noise ratio of ten (10). The minimum practical charge injection size is 10'10C and the minimum current difference which can be detected for the conventional implementation is in the nanoampere range. In the charge based implementation, the charge difference determined increases with increased measurement time, whereas, the faradaic current decreases with time for conventional differential pulse polarography. The minimum detectable concentration for conventional differential pulse polarography is lower for faster scan rates. The inverse is true for the charge pulsed implementation. In other words, for charge pulsed differential pulse polarography, the longer the wait, the more counts amassed, and the lower the concentration that may be detected. Figure 4-12 contains the curves for the minimum detectable concentration with respect to the size of .the charge injection made. As with charge pulsed normal pulse polarography (Fig. 4-4), it is evident that the smallest charge content will result in the best precision in the method, and can be used to determine lower analyte concentrations than can be determined with larger charge injection sizes. ?\>v 38 $520808. 3...... 35:935.. 3 93.2. 09.2.0 poo Ac Eco—«:2, Icon to. n32 :3» got? an 03.32. .330ch Icoo 033033 £35.55 .0 canton—too :lt 0.52“. 114 coon m2. Am\>v 38 coon mo. 8w: 8.7 .m 86 8.... 8.~.. 8.7 p 0.“. w P p n p B P Ooh- M a m a..- . w . p m... .66... a .06.. m. a m... 5...... 9 . m i w -97 a w. 3 II J an ll 56.. m. .3: a U uonmiueouoo elqoioaiap wnwgugw bol log minimum detectable concentration 115 . -5e07 -B.O" . e—e q-mo-s C H q-5x10-10 C H q-2x10-10 C _7 O H q-‘lx‘lO—‘IO C - ' I ' I ' I ~3.00 -2.00 -1 .00 0.00 log scan rate (V/s) Figure 4—12 Comparison of minimum detectable con- oentrotlon possible at various scan rates for different charge injection sizes for charge pulsed difierentiol pulse polarography. 116 Again, as in the results seen in Figure 4-5, the curves in Figure 4-13 show that an increased electrode area allows for detection of a lower concentration of the species of interest. This is because a larger working electrode surface area results in an increased response in both implementations. The parameter to compare for the two implementations of differential pulse polarography is the concentration range of species that may be detected. Conventional differential pulse polarography allows for detection of species from molar concentrations to approximately 10’7M. The charge pulsed technique has a minimum and maximum concentration detection limit owing to instrumental.considerations. The upper limit of 10'3M results from the highest rate of charge injection that may be instrumentally achieved. The detection limit of 2x10'8M results from a combination of the electrical noise in the system and of the smallest amount of charge that can be reproducibly injected. The problems associated with potentiostatic control cannot be easily resolved. However, the limitations of charge pulsed differential pulse polarography may be reduced by development and use of more sophisticated electronic components.’ log minimum detectable concentration -5.0-4 . -6.0-4 H A-0.05 em2 H ”-0.025 cm2 __7 0 H A-0.01 cm2 O 7* U 1 T 1 --3.00 --2.00 ---1.00 0.60 log scan rate (V/s) Figure 4-13 Comparison of minimum detectable con— centration possible at various scan rates for different electrode sizes for charge pulsed differential pulse polarography. 118 C . Square Wave Voltammetry Square wave voltammetry has an advantage of time over the pulse polarographic techniques. In pulse polarography, the time required to scan a potential range can be relatively long. At low analyte concentrations, a long drop time is required to increase the ratio of faradaic to charging currents; the result is low sweep rates. Much higher scan rates can be used for square wave voltammetry, which also shows good discrimination against double layer charging currents. 1. Comparison of the Current Based Model and Physical Experimental Results Instrumentation required to perform the physical experiments for square wave voltammetry are not available at Michigan State University. Therefore, a direct comparison of the simulation model and experimental results was not possible. However, the results obtained by the simulation model were compared with the digital simulation results obtained by Christie, Turner, and Osteryoung (20). The subsequent paper (67) shows the excellent correlation between their simulation model and the results of physical experiments in which the cadmium and ferric oxalate systems were used.’ The key element in the theoretical equations is ‘P. All other variables are constant at a given potential but ‘1’ shows the entire electrochemical history of the scan. Therefore, the values calculated for ‘I’f and ‘Pr by the simulation model discussed in Chapter 3 are compared to 119 obtained by Christie, Turner, and those peak values Osteryoung (20) in their Figures 2, 8, and 9. As seen in the table below, the results of the model I have derived from the theory compare favorably with Christie, et.al. (20) Table 4-5 Comparison of Christie’s work to this work ’ w w W la 0.383 0.252 0.391 0.260 1b 0.522 -o.054 0.524 -0.053 1c 0.698 —0.239 0.694 -0.250 2a 1.442 0.265 1.430 0.280 2b 0.585 -0.122 0.587 -0.117 2c 0.347 -o.878 0.345 —0.858 3a 1.907 -0.565 1.978 -0.527 3b 1.731 -l.185 1.776 -1.133 3c 1.157 -1.352 1.216 -1.350 For set 1 the conditions are AE=2.5mV, o=0.5, pl=0.499, p2=0.999, and a: Esw=2.5mV, b: Esw=5mV, and c: Esw=0.7§mv. For set 2 the conditions are AE=2.5mV, Esw=10mv, p1=a—0.001, p2-0.999, and a: (7-0.1, b: (Ia-0.5, and c: 6-0.9. For set 3 the conditions are the same as for 2 with the exceptions p1=0.049 and p2=o+0.049. As can be seen, the results from the simulation model correspond fairly well with the published results. The 120 comparison of values for parts 3a and 3b shows deviation but the accuracy of the model here is still good. 2. Comparison of the Results for the Continuous Current and Charge Pulse Methods Simulated charge pulsed square wave voltammograms were generated for several values of the experimental parameters. These simulation 'experiments' provide the means to characterize this technique. The number of charge injections counted at the peak for various values of Esw (the square wave amplitude) is shown in Figure 4-14. The evident conclusion is that the analytical response can be increased by increasing the square wave amplitude. This effect is seen in other pulsed techniques as well. However, as we have seen before an increased square wave amplitude leads to broadening of the resultant peak as shown in Figure 4-15. As a result, proper care must be taken'to choose a square wave amplitude large enough to produce a reasonable response while maintaining an adequate peak shape. Similar results are seen for traditional square wave voltammetry (20). The total response with respect to Esw produces.the same curve in both cases. The value of the response rises with increasing Esw but levels off at larger values. The peak width at half height is also affected by Esw. There are two differences seen in the curves for conventional and charge pulsed square wave voltammetry (Fig. 4-15). The minimum in the curve shown for the traditional implementation does not appear in the case of charge pulsed 121 $53.53.? 26: 22.0» 3 28.3 092.0 one Ao 3:00.338. to. sum 00 «no.3 «3013 use encoder. e5 .0 contooEoo e —l+ 0.50: 9.5 :0 9.5 in 0.0N 0.0a 0......— 0.0— 0.0 0.0 0.3 0.0m 0.9 0.9 0.0 0.0 r P - p L 8|! P n b P b one- D. 9 ‘3 m . w .86 .8. o 0 v I, O . 100N W. 100 0 . m 68 m. . m. r8.— 858 .8261 I lone m. «:5 e833. I 8.53 Page. I . .0... “Shoe Russo... one 853 .38. e..e w «c230 3o.— I m 00.— 3 .88 at (w!) zuouno souermg HID 3 T8 122 8 T é .baeEEozg 263 Booe- 3 25.3 092.0 one he 3.30553 to» 323 you esoto> to. 292. :2. so 52; so... .5 .6 esteesoo 2... 2:2... 9.5 3am 0N ON 0— 0— m 0 n n P b b 3 m m D. D. 17 11 U. i. U. D D 1. 1.. u. . u. D D H... 18 ..Ifl U. U. m. m. 6 . 6 U. U. 1' ‘0- ) )6 w w .A. . m . Au ll. .00 123 square wave voltammetry. This result is like that seen for differential pulse polarography (10) where the minimum peak width is at EswsO. Thus, the square wave amplitude does not produce the same distortional effects seen in traditional square wave voltammetry. The other difference in this curve is that the widths determined for n=2 are approximately 10 mV larger for conventional square wave voltammetry. This means that charge pulsed square wave voltammetry has slightly better resolution than the traditional method. The duration of the potential steps increase if AB is increased while maintaining a constant sweep rate. The effects of changes in AB while maintaining a constant sweep rate (Fig 4-16) show results that strongly resemble those for. Esw. This effect is not seen in the traditional implementation at all: the peak height remains relatively constant, only a 6% increase from AE=0.5 mv to 5 mV (20). However, there is a significant increase (500%) in peak height for a change from 2 to 10 mv for charge pulsed square wave voltammetry. This results from an increase in the potential excursion from the reverse pulse (where .the previous difference measurement was made) to the forward pulse. Since the measurement made in the charge pulsed implementation is an integration of the faradaic current, this increase arises from the increased faradaic reaction rate at the beginning of the forward pulse. Here again the problem of increased peak width with increased AB results. There is also a loss of definition of the peak since a 124 ON 9.5 ma 0 — ..SoEEozg 261 Bongo 3 non—an 09.2.0 uco Au .ocozcgcoo to. «022. m4 «actor—o to. 3:33.. .o contanoo o 74 2:2... 2.... 9.5 ma 3 F O.N . o.— 3 03 m 00.0 n” m 1 m .86 o a r roe mu: 19.6 a U: r m T .w flood m. a. 1 K . flag 3 tom 0 P... m f 8 An .I. (vii) iuauno ooumama 125 smaller number of points are used to define it at higher AE values. Therefore, a relatively small AB is required to provide adequate peak definition. A AE of 10 mV maintains a reasonable peak shape while keeping the half width less than 75 mV for n=2. An important point to recall is that the number of charge injections counted at the peak depends on the time period over which the charge injections are made. Figure 4-17 shows the effect of sweep rate upon the number of charge injections at the peak. The A3 value here is held constant at 10 mv so the effect seen is due to the increased measurement time. It is evident that it is advantageous to use lower sweep rates for the technique of charge pulsed square wave voltammetry. This is exactly opposite to the behavior seen for traditional square wave voltammetry (20), where the measured current decreases exponentially with time. Other time/scan rate related responses are explained in the paragraphs below. The effect of square wave asymmetry is shown in Figure 4-18. This is quite different from the results seen in the conventional method (20). For the traditional implementation of square wave voltammetry, where the current is measured at the end of the pulses, the peak current measured goes through a minimum at o=0.5. The curve in Figure 4-18 is more like that for traditional square wave voltammetry when the current is measured at the beginning of the pulses, a maximum is reached at o=0.5. Since currents ...caoEEogg 26: 826» an ton—an 092.0 one an 55:52.3 .3. 0:5 5.! cocoa—not 05 .0 cantanoo h—lv 2:2... 126 An\>v 30.. coon mo. An\>v 30.. coon mo. 3 a..- 3“: 3 3: 34.... P p P f G p b u n b 86 P . u... 4 18' m . m .8... I: m t . 0 18a. 1. 196 o . u. . .82 m 6 .86 . a 13 m. . filo . m 186 .69“ 9 m r A. .l 8 a. ..l lg lg; (v1!) wanna souelsmo 127 4505833) 263 803..» 3 vegan 092.0 are ac .2395on 53 b .o 2.22, «not? to. 3:83.. 05 yo contodEoo 51... 950E Admin Boston. to; cozootv .o Avoid p.633 to“. concoct b OFF. . .Wo. . .opo. - .for. . .Nwo- - .cdonF ow- . .nno. . .mwo. . -30. . -NM. . .0606 i r m... . n” . m . menu m . m 1 o 1o.— ..SN 1. . o t u. r r D .8». m H 1. .3 a .m. IO?” 0 1 HM" w . m AD I fin s A0 II. o 3 (v71). wanna eoualamq 128 are not measured instantaneously in charge pulsed square wave voltammetry this curve actually shows the effects of changing the measurement time on the forward, pulse in relation to the reverse pulse. Oxidation on the reverse pulse occurs at a slower rate than the reduction on the forward pulse. Due to the fast initial rise in the number of charge injections counted at the beginning of a potential pulse, a large percentage of the total counts is measured early on the forward pulse. Therefore, the largest number of charge injections will be measured at a point where the pulse width of the forward pulse is some fraction of the reverse pulse. In this case, the optimum difference occurs when the forward pulse is 25% and the reverse pulse is 75% of tau. A value of 25% for s is recommended since a higher sensitivity will be achieved. in all. measurements. .All response curves for charge pulsed square wave. voltammetry have used this value. Figure 4-19 shows the variation in ndnimum detectable analyte concentration with varying sweep rate. A signal to noise ratio of 10 (10 charge injections counted) was used to determine detectability. The charge content of the" injections was chosen to be 2x10'lo coulombs. This charge content will produce a 2 mV potential excursion in a solution of Cd++ in 0.1M KCl where the working electrode capacitance is assumed to be luF. The potential excursion produced by the small charge injection must be larger than the electrical noise in the system, which is assumed to be $505.03.? 0.6... 20:00 an 000...... 092.0 2.0 no 3:09.328 to. 038 0000 «not? .0 03.0000 00:05:02.8 03300.00 506.58 .0 canton—coo «7.4 050—“. 129 Am\>v 0.0.. 00030 00. Am\>v 0.0.. 0003» mo. I I m... I I m L Pb P N nomin- 5 P m 5 v. F N O00- M. U ..w: ..oKI n w 'Oocll 10.0.... D. 9 a. .9? O m N 70.?! .3... m r o 0.”- U 0 W 10.NI a I. m. .o 1. [comic Nldu r50." 0 U uononueouoo egqoioaiep umuIIquJ 60] 130 lmV. Consistent with the results seen in Figure 4-17, the longer the period of time over which charge injections are made, i.e. the lower the sweep rate, the lower the concentration that can be detected. The absolute minimum and maximum detectable analyte concentrations, however, are dependent upon the values of the various experimental parameters, as shown below. The curves shown in Figure 4-20 are for charge pulsed square wave voltammetry. The maximum scan rate is determined as that at which at least 10 charge injections are counted at that concentration. The curves are produced for small injections of different charge content. It can be seen that differing charge injection content changes the dynamic range of the technique. At analyte concentrations from about 10'4M to 10‘7M, a higher scan rate may be used in the case of charge pulsed square wave voltammetry. Specifically, at 10'6M a three fold increase in scan rate is possible. The last figure (Fig. 4-21) shows the change in dynamic range for differing system jparameters. The same basic concentration range is maintained (about 1.2 orders of' magnitude) but concentrations within ‘that range decrease with increasing values of the electrode surface area, the square wave amplitude, and the staircase step size. This does not differ significantly from the current based form of square ‘wave ‘voltammetry since :measured. current increases with increasing electrode surface area and square wave log minimum detectable concentration 131 -5.5- -6.5-+ / . v—v 5 x 10-10 0 H 2 x 10-10 0 H 1. x 10-10 a ‘ H 5 x 10-11 0 0—0 _7.5 - I ‘ ' . 2 x'10-11 e‘ -I‘.i.0 -2.0 --1 .0 0.0 log maximum scan rate (V/s) Figure 4-20 The minimum possibie concentration which may be determined for injection: of differ- ing charge content for charge pulsed square wave voltammetry. 132 .o opiowxmlcom00~£ .0 2.0.000 092.0 450:. 153.2. 0.63 0.6000 00030 09.2.0 ..0. 000.2. ..0.0E 1800 .0805“. .0c0>00 .0. 0.0. 0000 5.3 0090... 1:00:00 03300.00 €06.58 0. 00002.0 31+ 0.50.... Am\>v 0.0.. c000 :58.on mo. O.— 6.0 o. ..1 O.Ni O..ni e F b h p n b n b 005' >50..de atom-.5 .NEOflOdI< Ola >50 wlm< .>Enul30m .NEonNO.OI< Ola >Enlw< $5.05 .NEu FO.OI< I f '00”- Icon-l. uogonusouoo elqoioeiep wanqu 60' 133 amplitude. However, for the charge based implementation, there are four system parameters that can be adjusted to produce the best response for a given concentration (AB, Esw, electrode area, and charge content of injection) as opposed to the two for conventional square wave voltammetry. This variation, however, presents a problem. One set of system parameters cannot be used for all analyte concentrations in charge pulsed square wave voltammetry. A much larger range of concentration values (approximately 5-6 orders of magnitude) can be determined with one set of parameter values for square wave voltammetry. The limit of 1.2 orders of magnitude for the charge based implementation is the result of time constraints: too short an amount of time to count injections at the higher scan rates, and a I value of 1 second at the low end. A larger range and, hence, lower detectable analyte concentrations are possible at much lower scan rates. However, since the number of charge injections made at a given potential is related to the inverse of the analyte concentration squared (Eqn. 3-35), not much. more of an increase could. be achieved without significant increases in the time involved. The technique of charge pulsed square wave voltammetry has limits' to the concentrations that it can be used to determine. The highest concentration that can be determined is 10‘3M; this limitation is due to the highest rate at which charge may be injected to the cell. At the other end of the scale, the detection limit is 2x10‘8M and this limit 134 results from the electrical noise in the system. A maximum cycle width of 5 seconds was used to determine this limit. The detection limit reported for the conventional method (3) is 4.7x10'8M for n=2. Charge pulsed square wave voltammetry has some interesting differences as compared to the conventional implementation. The use of charge impulses to step and maintain the potential greatly reduces the errors in the measurement process and allows measurement in low concentrations of background electrolyte. A square wave amplitude of 25 mv provides a higher number of counts while maintaining a peak width at half height of less than 75 mV. A staircase step of 10 mV maintains peak definition while slightly increasing the response. An asymmetrical waveform (6=0.25) provides greater precision. However, the greatest difference is seen in the variation of the analytical response with respect to the time over which the measurement is made. Greater precision of measurement can be achieved by reduction of the scan rate. In the case of charge pulsed square wave voltammetry, lower concentrations can. be determined by variation of experimental parameters. Theoretically, any trace amount of analyte can be determinedf as long as we are willing to wait as long as it takes to amass a reasonable number of counts. In other words, without the limitation of tgs seconds, it is possible that even lower concentrations can be detected by charge pulsed square wave voltammetry. CHAPTER 5 INSTRUMENTAL CONSIDERATIONS FOR CHARGE PULSED SQUARE WAVE VOLTAMMETRY The discussion of charge pulsed square wave voltammetry in the previous chapter focussed on theoretically predicted results for the charge pulsed method. The following two sections introduce the relation of the parameters with the results that can be expected for the charge pulsed method if implemented. by two instruments on opposite ends of ‘the spectrum. The first instrument is a hypothetical ideal instrument. The projected results from such an instrument are compared in Section B with those based on the characteristics of an instrument which could .be produced from currently available components. A. Description of Instrumental Characteristics 1. Hypothetical Ideal Instrument This discussion will begin with the definition of a hypothetical ideal instrument. Hypothetical is defined as a situation based upon a tentative assumption in order to test out its empirical consequences. Ideal means that it exists as a mental image only, and is the ultimate goal for achievement. Therefore, the hypothetical ideal instrument (HII) is the perfect instrument for the job that does not, 135 136 and perhaps cannot, exist containing all those characteristics we wish it could have. In the case of an instrument to perform charge pulsed techniques, the instrument would probably be called a programmable charge pulse polarizer. It would be very fast, be able to discern and produce extremely small potential changes, and be able to perform any programmed experiment in a fully reproducible manner. In greater detail, the specific characteristics are as follows: freedom from electrical noise absence of hysteresis effects negligible current or charge leakage unlimited current capacity 1. 2. 3. 4. 5. ability to sense minute potential differences 6. ability to achieve a small potential window 7. infinitely variable charging voltage 8. infinitely variable charging capacitors 9. capable of instantaneous charge injection 10. negligible variance in charge injections 11. ability to maintain any rate of charge injection The results shown and discussed in the next section are provided by the simulation model for charge pulsed square wave voltammetry described in Chapter 3. The parameter values used in the computer program correspond to the characteristics described above. Only those relations which show significant deviations from the results shown in the previous chapter will be discussed. 137 2. Instrumental Characteristics of Previously Built Instrument A programmable coulostatic polarizer has been previously built in this laboratory (56,59,58). It consisted of a microcomputer controlled system to measure potential and make the required charge injections. C.C. Lii used it to perform a series of experiments in chronopotentiometry and was able to increase the limits of detection three orders of magnitude using charge pulses (59). Robert Engerer also performed experiments on this instrument by using the technique of cyclic voltammetry. He was able to determine Cd++ concentrations down to a detection limit of 10'7M (58). However, this instrument was built starting in 1974 and, therefore, operates at a slower rate than can. be achieved. with. the 'presently available components. The maximum rate of injection attainable with this instrment was 5 kHz; the injection time was 50 us. The electrical noise in the system was approximately 1mv. Norman Penix is currently building a similar instrument of new components that will be faster and more sensitive than the previous incarnation (68). 3. Instrumental Characteristics of Current Instrumentation The new Penix instrument contains qualities and components (68) which make it closer to the hypothetical ideal than that previously used. In comparison to the hypothetical ideal described. in the first half of ‘this 138 chapter its characteristics are as follows: 1. electrical noise of lmV present 2. slight hysteresis in threshold sensing (this will not hurt results as long as it is constant and fairly reproducible) 3. current leakage (in the switches) of $5 picoamperes 4. current capacity of 550 mA 5. ability to determine potential differences to a resolution of 1.22 mV (limited by the resolution of the ADC) 6. ability to produce potential windows of 10, 5, and 20v 7. ability to control charging capacitor voltage to a resolution of 2.44mv (limited by resolution of the DAC) 8. variation in charging capacitor size limited by those commercially available 9. ability to inject charge within 10ms 10. error in charge injections of i1% 11. rate of charge injection limited to 100kHz The results provided in the next section are calculated by the simulation model for charge pulsed square wave voltammetry. These results show a strong correlation with those described in the Chapter 4 since some of the limitations of the current instrument were used there. 139 B. Comparison of the Characteristics for Charge Pulsed Square Wave Voltammetry for the Hypothetical Ideal and Best Current (Penix) Instrument The system variables are the same as those described in the Chapter 4. To reiterate, the system parameters to be studied are Esw, AB, 0, measurement time (as changed by a change in scan rate), and the minimum detectable concentrations possible with scan rate. The charge difference relation obtained from the simulation model for both instruments will be compared and contrasted with respect to the parameters stated above. A Cd‘Ur concentration of 10'5M was used in all cases. The background electrolyte is 0.1M KCl. The major difference between the ideal and practical instrument arises in the area of charge injections. The ideal instrument is able to detect smaller potential differences, and make smaller charge injections more quickly. One of the key elements limiting the size of an injection in a practical instrument is the electrical noise in the system. Since an ideal instrument has no noise, the electrode’s response to an infinitesimal charge injection can be detected. However, even the simulation model cannot realistically handle an infinitely small charge injection. Therefore, a size of 1 picocoulomb was chosen since it will produce a change in electrode potential which is relatively small but can still be seen in the significant figures carried in the calculations. .A charge injection of 1 140 picocoulomb will produce a potential change of luv in a solution with a double layer capacitance of luF. The results shown below use this-value to provide a basis for comparison with the practical instrument, which uses a charge injection size of 20 nC. The first system parameter evaluated is Esw. The difference in charge injections with respect to square wave amplitude for the hypothetical ideal instrument are shown in Figure 5-1. The resulting curve is almost linear at lower Esw values but it begins to fall off at square wave amplitudes greater than 35 mv. The difference in anodic and cathodic charge injections is taken when the reverse pulse is 2xEsw mv more positive than the forward pulse potential. Consider the placement of the peaks for the anodic and cathodic reactions (Fig. 2-7). When the ‘value of' Esw becomes more than half of the potential difference between those peaks the charge difference measured will begin to fall off due to diffusion limitations. Therefore, the measured charge difference will reach a limiting value at large Esw. The simulated charge difference fOr various values of square wave amplitude with the realistic instrument is shown in Figure 5-2. The curve rises sharply for lower values and then falls off with increasing Eswu Just as for the hypothetical instrument, this is due to the increase in the potential difference between the pulses. If the difference is too large, the measurement is beyond the peak values for Thousands of charge injections 30.4 20- 10- 141 ' I ' I ' r f I ' o 10 20 30 40 5'0 Square wave amplitude (mV) Figure 5—1 The effects of square wave amplitude on response for charge pulsed square wave voltammetry on a hypothetical ideal instrument. Hons Injec # of charge 750.01 700.0- 6500- 500.04 550.0- 500.0-1 450.0~ 400.0-l 350.0 142 a. 1'0. 25. 33. 4b. 50. square wave amplitude (mV) Figure 5-2 The effect of square wave amplitude an the response of charge pulsed square wave voltammetIy on a current instrument. 143 either the forward or reverse pulse and the response falls off. However, the limiting charge difference is reached at much lower Esw values for the practical instrument. This difference in response results from the difference in charge injection size between the two instruments. Since an electrochemical reaction requires a significantly greater rate of charge injection on the ideal instrument, less charge difference loss is seen at larger square wave amplitudes. The slowing of the faradaic reaction produces a much more striking limitation of the charge difference measured for the practical instrument. AB is the amplitude of the staircase step for charge pulsed square wave voltammetry. Maintenance of a constant scan rate while changing the value of AE requires an increase in the duration of the potential step. The charge difference for a hypothetical ideal instrument is shown in Figure 5-3. The rise in the curve results from an increase in the potential excursion between the reverse pulse and the subsequent forward pulse. This increase in potential difference produces an increase in the number of charge injections counted on the forward pulse that results from the increased faradaic reaction at the beginning of the pulse. The next curve (Fig. 5-4) gives the system response for a change in AF: while maintaining a constant scan rate f°r the realistic instrument. In this case, there is an ‘n increase in the difference of charge injections counted Wit 144 so. lOflS soJ t mice 30- 20-4 IO-l Thousands of charge I I I I I O. 5. i O. 1 5. 20. 25. AE (staircase step height—mV) Figure 5—3 The effects of staircase step height on response for charge pulsed square wave voltammetry on a hypothetical ideal instrument. mCO..OO.C.. OOLOIO ..O x. ions t misc 1} of charge 145 300.4 100. I I 1 O. 5. 1 O. i 5. 20. 25. staircase step height (mV) Figure 5-4 The effect of staircase step height on the response of charge pulsed square wave square wave voltammetry on a current instrument. p1 cl 01 Pt ga th US in Che Opt re 146 increasing staircase step amplitude. The charge difference begins to fall off at larger staircase step sizes for both instruments due to diffusional limitations. However, a large value results in loss of peak definition so a value of 10mv was used in all cases. The effect of an asymmetric square wave was tested by varying the parameter a. The results for the ideal instrument are shown in Figure 5-5. The curve is very different from that seen in the previous chapter (Fig. 4- 19). Since the potential excursion for the hypothetical ideal instrument (1mV) is so much less than that used in the previous chapter (1mV), the H11 is much more sensitive to the faradaic reaction seen at the beginning of the potential pulses. Since this instrument can maintain any rate of charge injection, it is able to keep up with the high rate of discharge from the double layer at the beginning of the pulses, which approached lMHz at 0=0..8. In this case, a gain is realized in allowing more time for the reaction on the forward pulse to occur. The optimum value of 0.80 is used for all other response curves in this section. The charge difference measured on the practical instrument for asymmetric square wave pulses is shown in Figure 5-6. Similar to the curve seen in the previous chapter (Fig. 4-19), a maximum is reached at 0=0.2. This optimum value is produced by a balance in the rate of reaction on the forward and reverse pulses. Since the reverse reaction occurs at a slower rate and a large a. M K K 050500.?5. OULOIO $0 MUCOMJOE... 147 5? j on O 1 Thousands of charge injections . N O O 0 I r I I I I I I I fl 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0' (fraction devoted to the forward pulse) Figure 5—5 The effects of square wave asymmetry on response for charge pulsed square wave voltammetry on a hypothetical ideal instrument. Icc..tc.c. OOLO£O .0 w. fions Injec # of charge 700.0-« 148 V t r I .0 0.2 03 016 ofs 11.0 0 (fraction devoted to forward pulse) Figure 5—6 The effect of asymmetric measurement on the response of charge pulsed square wave square wave voltammetry an a current instrument. 149 percentage of the counts realized for the forward pulse is determined near the beginning of the pulse, the maximum is seen when the forward pulse is shorter than the reverse. The optimum value of 0.2 was used for all other response curves for the realistic instrument. This is very different from Fig. 5-5 (the ideal instrument). The faster cathodic reaction results in a significant increase in the smaller charge injections used by the hypothetical (instrument. Since the reduction reaction has a higher initial response than the subsequent oxidation, there is a significant advantage in increasing the time over which charge injections are counted on the forward pulse for the hypothetical ideal instrument. Maintaining the staircase step height at a constant value while changing the scan rate results in a change in the time over which the charge injections are counted. The linear relation of charge difference and scan rate (with a constant AB) is shown for the ideal instrument in Figure 5-7. As expected for a charge pulsed technique, a slower scan rate, and therefore a longer measurement time, results in the measurement of a larger number of charge injections. A change in the scan rate while maintaining a constant staircase step amplitude produces a change in the time over which charge injections are counted. An increase in the number of charge injections counted is expected with decreasing scan rate for a charge pulsed method. The resulting charge difference measured for a realistic ions 1: misc log it of charge 8.0-. 5.0-l 150 T 1 U I I -2.5 -2.0 -i .5 -i .0 -.5 0.0 0.5 log scan rate (V/s) Figure 5—7 The effects of scan rate while keeping a constant AE on the response of charge pulse square wave voltammetry on a hypothetical ideal instrument. ma Ch Us is ex; th. is mag Ex; 151 instrument is shown in Figure 5-8. The deviation at higher scan rates is due to the time required for each injection. The time between charge injections consists of the time for the potential to decay to the threshold value and the time it takes to inject the charge to the cell. Since a smaller number of charge injections is made at higher scan rates, less time (cumulative) is required in each pulse for charge to be injected. Therefore, the slope of the curve is lower at higher scan rates. The response with respect to scan rate is quite similar for both sets of instrumental characteristics. If one were to measure charge difference for the ideal instrument at a much higher scan rate (>10 V/s), the slope of the curve would decrease in the same ’manner as seen for the practical instrument at rates of >0.5 v/s. Figure 5-9 shows the minimum analyte concentration that may be detected with various scan rates. A difference of 10 charge injections between the forward and reverse pulses was used to determine the limit of detectability. The response is seen to be linear with respect to scan rate. This is the expected result for an ideal charge pulsed experiment. From the figure, an lO-fold improvement in analyte detectability is achieved by decreasing the scan rate two orders of magnitude. Therefore, a Cd++ concentration of 10‘12M could be determined using a scan rate of 2x10"11 V/s, but this experiment would take 3200 years! This, of course, is the result for a charge injection size of 1pA. Since the E E ll‘LLLILL‘IJ 0. ~3.0 0 C O '35 8 E 1500. ° 3 g . .c 1000.1 0 s.- O '0: 500. ‘AJLQLA 152 I T F I I -2.5 -2.0 -1.5 -1.0 -.5 log scan rate (V/s) I 0.0 Figure 5—8 The effect of changing the scan rate j 0.5 while maintaining AE constant on the response of charge pulsed square wave voltammetry on a current nstrument. log minimum detectable concentration .55.. 4.04 -7.5-. 153 -800 1 I I r r I 1 -3.0 “2.5 -2.0 “1 .5 - 1 .0 ".5 0.0 0.5 log scan rate (V/s) Figure 5—9 The minimum detectable concentration possible with respect to scan rate for charge pulsed square wave voltammetry on a hypothetical ideal instrument. 154 detection limit has been previously defined as the lowest concentration for which ten charge injections are counted, a smaller charge injection would provide better sensitivity. In other words, for a charge injection size of 0.1pA, ten charge injections would be made in the time it took for one injection using a 1pA charge pulse. Therefore, the maximum scan rate that could be used for the 10‘12M Cd” solution would increase by an order of magnitude and the experiment would take less time. The minimum detectable concentration decreases with decreasing scan rate (Fig. 5-10). The slope of the curve also decreases with decreasing scan rate. The reason for this is the relation between concentration and the time required for the potential to decay (Eqn. 3-36). Since the decay time is related to the inverse of the concentration squared, the minimum concentration that may be detected will not decrease to the same extent at lower scan rates as it does at higher scan rates. The technique of charge pulsed square wave voltammetry can be used only on a specific range of analyte concentrations on a realistic instrument. For the instrumental characteristics described in the previous section, the maximum concentration is 5x10'4M. This limitation is imposed by the 10ms charge injection time. The minimum concentration is limited by the electrical noise in the system, which limits the size of charge injection which can be used, is 2x10'3M. The ideal instrument, not log minimum detectable concentration -5.5-« -600d -6.5- 155 I I I I I i “3.0 “-2.5 ”2.0 -1 .5 -1 .0 -.5 0.0 0.5 log scan rate (V/s) Figure 5-10 The minimum detectable concentration possible at various scan rates for charge pulsed square wave voltammetry on a current instrument. 156 having the above limitations, could be used for any analyte concentration. The optimum parameter values determined for the technique of charge pulsed square wave voltammetry (Chap. 4, Section C, Part 2) are close to those found for the instrument being built by Norman Penix (68). A square wave amplitude of 25 mv and staircase step height of 10 mv still provide good response while maintaining adequate peak shape. A forward pulse of 20% of tau (the width of the staircase step) results in the best response. The greatest variation results from an increase in the measurement time, as seen for a decrease in scan rate. The range of concentrations that can be determined is limited to about. 1.2 orders of magnitude for one set of system parameters. However, this range can be moved up or down by changing such factors as the magnitude of the charge injection and electrode size. CHAPTER 6 CONCLUSION: UTILITY OF CHARGE PULSE POLARIZATION The previous chapters dealt with the characteristics of three voltammetric techniques whose potential program is controlled by multiple charge injections. The following is a discussion of the usefulness of injecting charge pulses to control the potential of an electrochemical technique. A. Charge Pulsed Normal Pulse Polarography Charge pulsed normal pulse polarography, as described in Chapter 4, provides a lower detection limit than the conventional method. The charge pulse implementation can also be performed at higher scan rates. However, the use of charge pulse polarization to achieve the large potential steps required by the technique of normal pulse polarography is limited by the maximum charging rate. Towards the end of a scan, the potential step may be larger than can be attained in a sufficiently small fraction of the step duration. The limitation described in the previous pararaph is instrumental in nature. Contributing factors include capacity of the operational amplifier, maximum charge content of the injections, and maximum rate of injection. Improvements could be achieved by using higher current and 157 158 higher voltage electronic components in the charge pulse generator. Even with the necessary charging capability, the resulting characteristics are not equal to those of the charge pulse implementations of other pulse polarographic techniques. Therefore, as with conventional potentiostatic methods, other charge pulse techniques prove much more attractive than charge pulsed normal pulse polarography. B. Charge Pulsed Differential Pulse Polarography Differential pulse polarography, as performed by charge pulse polarization, has a lower detection limit than the traditional implementation. Charge pulsed differential pulse polarography can also use higher scan rates than conventional differential pulse polarography. The smaller potential steps taken in the differential pulse method make the technique more amenable to~performance by charge pulse polarization. The charge pulse implementation can provide better responses in~ various situations. For those solutions with high electrolyte concentrations, say 114 or 0.1M, analyte concentrations of IO'GM or greater can be detected more quickly by using charge pulses. Traditional differential pulse polarography generally employs scan rates of 5-10 mV/s. Analyte concentrations from 10‘5M to the detection limit can be determined at the above mentioned scan rates with the traditional implementation more quickly than for charge pulsed differential pulse polarography. However, reduction 159 of errors introduced by impurities in electrolyte materials can be achieved only by purification of the materials or by lowering the concentration of the background electrolyte. Decreasing electrolyte concentrations poses problems for the traditional method due to increased solution resistance. A higher solution resistance increases the time constant of the charging current, thus increasing the time required for it to decay to a negligible value. This, in turn, decreases the sensitivity of differential pulse polarography. There is also an error in potential control induced by the continuous current used. These problems do not arise in the charge pulse implementation. Therefore, if lower electrolyte concentrations are recommended or for solutions such as groundwater where one may not wish to add electrolyte, charge pulsed differential pulse polarography will give the best response and. maintain its detection limit. The limitations of the two implementations have differing origins. The charging current, although reduced in the differential technique, is still the limiting factor in detection of lower analyte concentrations for the traditional method. The major limitation for charge pulsed differential pulse polarography is the electrical noise in the system. For an instrument with 1mV of noise, the minimum practical charge injection size is 10"10 coulombs for an electrode capacitance of 10F. Reduction of the noiSe would lower the detection limit of the method. Then, 160 however, other instrumental limitations may become significant, such as minimum reproducible charge injection size and threshold sensing precision. In conclusion, charge pulsed differential pulse polarography can be used to advantage in cases of high solution resistance. Also, the use of charge impulses would allow 10"3 to 10’5M species to be detected at higher scan rates than seen in conventional methodology; In other words, fast charge pulsed differential pulse polarography would essentially be a form of square wave voltammetry. C. Charge Pulsed Square Wave Voltammetry Square wave voltammetry has only recently come to light as a viable electroanalytical technique. Its speed and ability to discriminate against charging currents makes it an attractive alternative to other methods. Charge pulsed square wave voltammetry shows some advantages over the traditional method, although not to the extent seen for other techniques. Charge pulsed square wave voltammetry has a slight advantage over conventional square wave voltammetry in the detection limit. Analyte concentrations of >2x10'5M can be determined more quickly with charge impulses, whereas solutions within two orders of magnitude of the detection limit are scanned faster conventionally. Also, as stated above for charge pulsed differential pulse polarography, the response for charge pulsed methods does not change with 161 solution resistance. Therefore, these solutions are better suited to determination by charge pulsed square wave voltammetry. Again, as explained previously, the conventional method is limited by inherent errors in the methodology itself. Noise in the nanoampere region presents problems in conventional system current measurement. However, it is electrical noise in the voltage measurement system which produces the accuracy limitation for charge pulsed square wave voltammetry. 5 The conclusions drawn for charge pulsed square wave voltammetry are the same as for charge pulsed differential pulse polarography. It is better for low concentrations and high solution resistances and faster for species of 10'3M to 2x10‘5M. All in all, due to its error reducing characteristics, square wave voltammetry stands to gain the least by using charge injection potential control. I). Comparison of the Advantages and Applications for the Use of Microelectrodes and Charge Pulsed Techniques Exploitation of the advantages of microelectrodes has been researched since the early 19708. Growing use of these devices results from the reduction or elimination of many of the undesirable aspects of electrochemical methodology. The improvements seen in the quality of electrochemical data obtained are a consequence of several characteristics of microelectrodes (69,70). First, currents in the 162 picoampere range can be measured with relative ease. Second, iR losses are reduced at small electrodes because of the proportionally lower electrolysis current of the species of interest. The reduction in iR losses also permits the use of a two electrode system as well as work in novel solvent systems. Third, charging currents are reduced to insignificant values since the double layer capacitance of microelectrodes is much lower than for those of conventional size. This decrease in capacitance also allows the potential of the electrode to be changed very rapidly, permitting voltammetric measurement on the microsecond time scale. The reduced double layer capacitance also reduces the faradaic currents measured but the dimensions of the diffusion layer can greatly exceed the dimensions of a microelectrode. In other words, mass tranport rates increase with decreasing electrode size and faradaic current to electrode area ratios are higher for microelectrodes than for conventional electrode systems. The unusual characteristics of microelectrodes permit the use of voltammetric methods in areas of application heretofore unexplored. The reduction of 1?. losses opens a wide area of application in such conditions as absence of background electrolyte, in organic solvent systems, in low temperature glasses and eutectics, and gas phase measurements. However, highly resistive solutions require maintenance of a reference potential, change the diffusion coefficients of species, and may introduce migration 163 effects. Rapid heterogeneous or homogeneous reaction rates can be measured due to the decrease in double layer capacitance (and the resultant decrease in cell time constant). Since the ratio of faradaic to background currents remains the same as for conventionally sized electrodes, background subtraction of the voltammograms is required. However, useful voltammetric data can be obtained at scan rates greater than 105 V/s. The high mass transfer rates seen at microelectrodes allow electroanalytical measurements to be made at low analyte concentrations. The most interesting area of application, however, relates directly to the small size of the electrodes. Micro- and ultramicroelectrodes are often used to stimulate and monitor physiological processes. The exploitation of size is also seen in measurements of very small volumes of solution. Lastly, electrodes on the micrometer scale can. be used to probe processes at discrete locations such as neurochemical detection in the brain, chemical dispersion in the case of laminar flow, or views of electrochemical processes at larger electrodes. Charge pulsed implementations of various electroanalytical techniques with electrodes of conventional size share some of the advantages and applications seen above for microelectrodes. As described previously, the use of charge pulses to obtain electrochemical information results in elimination of iR losses and in effective separation of 'charging’ and faradaic charge. Higher scan 164 rates can often be used for higher analyte concentrations (about 1V/s) and lower analyte concentrations can be detected (down to about 10'8M). The limitations in these last two improvements are the result of the characteristics of instrumental components. As far as applications are concerned, charge pulsed techniques find use in a subset of the areas in which microelectrodes are used. Charge pulsed voltammetric methods can be used in any of those areas considered as traditional electrochemical domains (i.e. inorganic and organic species in aqueous solutions) as well as conditions involving high solution resistances such 'as reduced background electrolyte concentrations or solvents with low dielectric constants. ' It may be possible to incorporate microelectrode use into the realm of charge pulse voltammetric~techniques. However, the low Cdl would require impulse charges smaller than we are able to produce at the current time. Therefore, if possible, combination of microelectrodes with charge pulse polarization would prohibit work at low analyte concentrations. However, measurements might be obtained at somewhat higher scan rates and at concentrations greater than 10'3M. E. Final Word Charge pulse polarization introduces advantages to a greater or lesser extent to any electrochemical technique 165 for which it is used. These advantageous characteristics include elimination of potential measurement error and an effective separation of the charge required to change the potential of the working electrode from that used by the faradaic reaction. However, the gains incurred. by the method whose potential program is controlled by charge impulses depends greatly on the type of technique upon which it is used. Techniques such as DC and Tast (or sampled current DC) polarography and cyclic voltammetry have no means of reducing the inherent errors of using a continuous current to create a linear potential ramp. Other methods that use staircase waveforms to approximate linear ramps, e.g. staircase voltammetry and normal pulse polarography, already have a means of reducing charging current error. The wait of several tens of milliseconds not only reduces charging current but also allows for reduction in potential measurement error (Eqn. 3-7). Other potential step techniques (differential pulse polarography and square wave voltammetry) further reduce the errors through the use of a differential current measurement scheme. The result is that the latter techniques have the least to gain from the use of charge pulse polarization while the type of technique mentioned in the first sentence have the most to gain. In conclusion, the use of charge pulses to control the potential of an electrochemical cell reduces the measurement errors of any' conventional electroanalytical. method. 166 Measurements may generally be made more quickly, in solutions with large uncompensated resistances, and to lower concentrations than seen with traditional implementations. However, those traditional techniques which are already capable of the best error reduction do not see as much improvement through the use of charge pulse polarization. As a result, the most sensitive of the electroanalytical techniques based upon a continuous current source would be better performed in the conventional manner unless very low electrolyte concentrations are required. New electronic technology may extend the range of advantages for charge pulse polarization in the future. BIBLIOGRAPHY 167 BIBLIOGRAPHY l. G.C. Barker, A. Gardner, 2. Analyt. Chem., 113, 79(1960). 2. G.C. Barker, I.L. Jenkins, Analyst, 11J 685 (1952). 3. M.S. Krause, Jr., L. Ramaley, Anal.Chem., $1, 1365 (1969). 4. J.H. Christie, J.A. Turner, R.A. Osteryoung, Anal. Chem., 42, 1904 (1977). .5. JuJ. O'Dea, J. Osteryoung, R.A. Osteryoung, Anal. Chem., 53, 695 (1981). 6. J.A. Osteryoung, R.A. Osteryoung, Anal. Chem., 51, 101A (1985). 7. A.J. Bard, L.R. Faulkner, "Electrochemical Methods Fundamentals and Applications", John Wiley and Sons, Inc., New York, 1980, pg. 186. 8. A.M. Bond, "Modern Polarographic .Methods in Analytical Chemistry”, Marcel Dekker, New York, 1980, pg. 243. 9. J.A. Plambeck, "Electroanalytical Chemistry: Basic Principles and Applications”, John Wiley and Sons, Inc., New York, 1982, pg.322, 327. 10. E.P. Parry, R.A. Osteryoung, Anal. Chem., 31, 1634 (1965). . 11. J.H, Christie, R.A. Osteryoung, J3 Electroanal. Chem., 12, 301 (1974). 12. J. Osteryoung, J. Chem. Educ., 50, 296 (1983). 13. A.J. Bard, L.R. Faulkner, "Electrochemical Methods Fundamentals and Applications", John Wiley and Sons, Inc., New York, 1980, pg. 190. 14. A.M. Bond, "Modern Polarographic Methods in Analytical Chemistry", Marcel Dekker, New York, 1980, pg. 259. 168 15. J.A. Plambeck, "Electroanalytical Chemistry: Basic Principles and .Applications", John Wiley and Sons, Inc., New York, 1982, pg.323, 327. ' 16. D.E. Burge, J. Chem. Educ., 41, A81 (1970). 17. J.B. Flato, Anal. Chem., 44, 75A (1972). 18. R.L. Birke, Anal. Chem., 50, 1489 (1978). 19. L. Ramaley, M.S. Krause, Jr., Anal. Chem., 41, 1362 (1969). 20. J.H. Christie, J.A. Turner, R.A. Osteryoung, Anal. Chem., 42, 1899 (1977). 21. A.J. Bard, L.R. Faulkner, ”Electrochemical Methods Fundamentals and Applications", John Wiley and Sons, Inc., New York, 1980, pg. 22. - 22. D. Skoogy D. West, "Fundamentals of .Analytical Chemistry”, Holt, Rinehart, and Winston, New York, 1976. P9. 491. . 23. P. Kissinger, W. Heineman, "Laboratory Techniques in Electroanalytical Chemistry", Marcel Dekker, Inc. 1984, pg. 193. 24. H.H. Bauer, P.J¢ Elving, .Anal. Chem., .30, 334 (1958). 25. H. Schmidt, M. van Stackelberg, J. Electroanal. Chem., 1, 133 (1959/60). 26. H.H. Bauer, P.J. Elving, JACS, 82, 2091 (1960). 27. D.J. Kooijman, J.H. Sluyters, Electrochim. Acta, 11, 1147 (1966). 28. A.J. Bard, L.R. Faulkner, "Electrochemical Methods Fundamentals and Applications", John Wiley and Sons, Inc., New York, 1980, pp. 569-573. 29. ibid, pg. 6. 30. D.C. Grahame, Chem. Rev., 41, 441 (1947). 31. D.C. Grahame, JACS, 11, 2975 (1949). 32. D.C. Grahame, B.A. Soderberg, J. Chem. Phys., 2;, 449 (1954). 33. D.C. Grahame, JACS, 16, 4819 (1954). 169 34. D.C. Grahame, JACS, 12, 2093 (1957). 35. D.C. Grahame, JACS, 22, 4201 (1958). 36. J.J. McMullen, N. Hackerman, J. Electrochem. Soc., 1.05. 341 (1959) . 37. J.H. Sams, Jr., C.W. Lees, D.C. Grahame, J. Phys. Chem., 22, 2032 (1959). 38. G.H. Nancollas, C.A. Vincent, Electrochim. Acta, 12, 97 (1965). 39. L. Ramaley, C.G. Enke, J. Electrochem. Soc., 112, 943 (1965). 40. P. Delahay, R.D. Levie, A.-M. Giuliani, Electrochim. Acta, 11, 1141 (1966). 41. J.H. Frischmann, A. Timnick, Anal. Chem., 22, 507 (1967). 42. A.J. Bard, L.R. Faulkner, "Electrochemical Methods Fundamentals and Applications", John Wiley and Sons, Inc., New York, 1980, pp. 13. 43. ibid, pg. 11. 44. G.C. Barker, "Trans. Symp. Electrode Proc.", Philadelphia, 1959 (E. Yeager, Ed.), John Wiley and Sons, Inc., New York, 1961. ~ 45. P. Delahay, Anal. Chim. Acta, 21, 90 (1962). 46. P. Delahay, Anal. Chim. Acta, 21, 400 (1962). 47. P. Delahay, Anal. Chem., 25, 1267 (1962). 48. W.H. Reinmuth, Anal. Chem., 21, 1272 (1962). 49. H.P. van Leeuwen, Echim. Acta, 22, 207 (1978). 50. A.J. Bard, L.R. Faulkner, "Electrochemical Methods Fundamentals and Applications", John Wiley and Sons, Inc., New York, 1980, pg. 273. 51. A. .Aramata, P. Delahay, Anal. Chem., .22, 1117 (1972). 52. P. Delahay, Y. Ide, Anal. Chem., 22, 1119 (1972). 53. J.M. Kudirka, R. Abel, C.G. Enke, Anal. Chem., 11, 427 (1972). 170 54. J.E. Davis, N. Winograd, Anal. Chem., 51, 2152 (1972). 55. T.A. Last, Anal. Chem., 21, 2327 (1982). 56. Spyros E. Hourdakis, PhD Dissertation, Michigan State University, 1978. 57. Norman E. Penix, PhD Dissertation, Michigan State University, 1988. 58. Robert Engerer, PhD Dissertation, Michigan State University, 1985. 59. Ching Cherng Lii, PhD Dissertation, Michigan State University, 1982. 60. W.W. Goldsworthy, R.G. Clem, Anal. Chem., 52, 1718 (1971). 61. W.W. Goldsworthy, R.G. Clem, Anal. Chem., 51, 1360 (1972). 62. P.H. Daum, M.L. McHalsky, Anal. Chem., 22, 340 (1980). 63. M.A. Schreiber, T.A. Last, Anal. Chem., 52, 2095 (1981). 64. A.C. Barnes, T.A. Nieman, Anal. Chem., 25,, 2309 (1983). . 65. S.R. Mikkelsen, W.C. Purdy, Anal. Chem., 52, 244 (1987). 66. A.J. Bard, L.R. Faulkner, "Electrochemical Methods Fundamentals and Applications", John Wiley and Sons, Inc., New York, 1980, pg. 569. 67. J.A. Turner, J.H. Christie, M. vukovic, R.A. Osteryoung, Anal. Chem., 42, 1904 (1977). 68. N.E. Penix, Private Communication. 69. S. Pons, M. Fleischmann, Anal. Chem., 52, 1391A (1987). 70. R.M. Wightman, Science, 240, 415 (1988). APPENDICES APPENDIX A 171 Table A-1 W cm. AS A FUNCTION or po'ruvs scsi FOR 1M KCL -00173'004653-4 '0.211,0.43OE-4 '0.250,0.410E-4 '0.238,0.408E-4 '0.327,0.4203-4 -O.365,0.430E-4 -0.404,0.445E-4 -O.442,0.4553-4 '0.481,0.44SE-4 '0.519,0.415E-4 ’0.558,0.380E-4 -00596100335E-4 “0.635,0.295E-4 '0.573,0.265E-4 '0.712,0.23SE-4 '0.750,0.220E-4 '0.789,0.200E-4 '0.827,0.195E’4 '0.866,0.130E-4 -009041001758-4 '0.943,0.17SE-4 -00981’001703-4 '1.020,0.167E-4 -1.212,0.157E-4 '1.251,0.175E-4 '1.289,0.175E-4 “1.328,0.1353-4 '1.366,0.137E-4 -10405’001908-4 172 Table A-2 v 1 M K CDL AS A FUNCTION OF POTL(VS SCE) FOR 0.1M KCL -0.096,0.445E-4 '0.134,0.415E-4 -0.173,0.390E-4 '0.211,0.390E-4 -0.250,0.395E-4 -0.288,0.410E-4 -O.327,0.415E-4 -0.365,0.407E-4 *0.404,0.385E-4 -0.442,0.345E-4 -0.481,0.300E-4 -0.519,0.265E-4 '0.558,0.240E-4 -0.596,0.222E-4 -0.635,0.215E-4 -0.673,0.ZOSE-4 -0.712,0.197E-4 -00750100192E’4 -00789,001853-4 '0.827,0.180E-4 -0.866,0.175E-4 '0.904,0.175E-4 “0.943,0.175E-4 -0.981,0.170E-4 -1.020,0.170E-4 -1.135,0.170E-4 -1.174,0.175E-4 -1.212,0.175E-4 -1.251,0.180E-4 -1.289,0.182E-4 -1.328,0.185E-4 “103661001923-4 ‘10405100197E‘4 173 Table A-3 WW CDL As A FUNCTION OF po-ers scs) FOR 0.01M KCL -0.019,0.440E-4 -0.057,0.397E-4 -0.096,0.380E-4 -O.134,0.37OE-4 -00173,003728-4 -0.211,0.37SE-4 -0.250,0.377E-4 -0.288,0.367E-4 -0.327;0.345E-4 -0.365,0.295E-4 -0.404,0.235E-4 -0.442,0.180E-4 -O.481,0.157E-4 -0.519,0.157E-4 -0.558,0.170E-4 -0 0596' 00 175E-4 “0.635,0.185E-4 -0.673,0.187E-4 -0.712,0.187E-4 -0.750,0.180E-4 -0 .789, 00 1778-4 -0.827,0.175E-4 -0.866,0.170E-4 -0.904,0.168E-4 -0.943,0.163E-4 ~0.981,0.157E-4 -1.020,0.157E-4 -1.058,0.ISSE-4 -1.097,0.152E-4 -1.134,0.155E-4 -1.174,0.155E-4 -1.212,0.169E-4 -l.251,0.170E-4 -l.289,0.172E-4 -1.328,0.175E-4 -1 0 366’ 0 0 175E'4 174 Table A-4 W 001. AS A FUNCTION OF POTL(VS scsI FOR 0.001M KCL 0.0200,0.389E-4 -0.0l9,0.375E-4 ’0 0 057' 0 0 3778-4 -0.096,0.381E-4 -O.134,0.380E-4 '0.173,0.360E-4 '0.211,0.342E-4 -0.250,0.27SE-4 -0.288,0.205E-4 -O.327,0.135E-4 -0.365,0.095E-4 -0.404,0.0BSE-4 -O.442,0.070E'4 -O.481,0.082E-4 -0.519,0.105E-4 -0.558,0.127E-4 '0.596,0.145E-4 -0.635,0.155E-4 '00673'00167E-4 -O.712,0.171E-4 -00750'001713-4 -007891001733-4 ‘0.827,0.171E-4 '0.866,0.167E-4 -0.904,0.165E-4 -0.943,0.162E-4 -0.981,0.158E-4 -1.020,0.156E-4 -100581001558-4 -1.097,0.155E-4 -1.l35,0.154E-4 -1.174,0.157E-4 ‘1.212,0.157E-4 -1.251,0.162E-4 '1.289,0.167E-4 -1.328,0.167E-4 -10366100167E-4 -10405,00170E'4 175 Table A-5 D0ubls_laxsI_CapaCitanae_xaluss_far_lnlint£§l CDL AS A FUNCTION OF POTL(VS SCE) FOR 10'4M KCL -0.019,0.328E-4 -0.057,0.328E-4 '000961003248’4 -0.134,0.3123-4 -0.173,0.305E-4 '0.211,0.275E-4 -0.250,0.220E-4 -0.288,0.14BE-4 -0.327,0.089E-4 -0.365,0.050E-4 -0.404,0.034E-4 -0.442,0.045E-4 -O.481,0.067E-4 -0.519,0.087E-4 -0.558,0.100E-4 '0.596,0.116E-4 -0.635,0.130E-4 -0.673,0.140E-4 -0.712,0.150E-4 -0.750,0.1523-4 -O.789,0.158E-4 -0.827,0.157E-4 -0.866,0.157E-4 -0.904,0.156E-4 -0.943,0.155E-4 -009811001523-4 -1.058,0.152E-4 -1.097,0.150E-4 -102511001503-4 -1.289,0.152E-4 -1.328,0.153E-4 -1.366,0.153E-4 -1.405,0.155E-4 '104431001563'4 176 Table A-6 WWW COL As A FUNCTION OF POTL(VS scs) FOR 10‘5M KCL -0.019,0.294E-4 -0.057,0.280E-4 -0.096,0.277E-4 '0.134,0.247E-4 -00173,002013-4 '0.211,0.152E-4 '0.250,0.102E-4 '0.288,0.067E-4 -0.327,0.037E-4 -0.365,0.023E-4 '0.404,0.0183-4 -0.442,0.028E‘4 '0.481,0.048E-4 -0.519,0.064E-4 '0.558,0.077E-4 -0.596,0.085E-4 -0.635,0.095E-4 ’0.673,0.107E-4 -0.712,0.117E-4 -O.750,0.128E-4 -O.789,0.138E-4 -O.827,0.143E-4 -0.866,0.145E-4 -0.904,0.148E-4 -O.943,0.145E-4 -100581001458-4 -1.097,0.170E-4 '1.135,0.142E-4 ‘1.289,0.142E-4 -1.328,0.144E-4 -103661001473-4 -10405'00150E-4 APPENDIX B 177 Table B-1 THIS PROGRAM PRODUCES A SIMULATION OF A NORMAL PULSE POLARO- GRAM. IT CALCULATES I FAR. I CHG. I TOTAL. PERCENT FARADAIC CURRENT. AND MEASURES THE CURRENT AT THE SAME TIME DURING EACH STEP. I FAR IS DEPENDENT ON THE NUMBER OF ELECTRONS IN THE SYSTEM. THE AREA OF THE ELECTRODE. THE CONCENTRATION OF THE ANALYTE. THE DIFFUSION COEFFICIENT OF THE 0! SPECIES. THE TIME OF THE MEASUREMENT. AND THE POTENTIAL. I CHG DEPENDS ON THE STEP . SIZE. THE SOLUTION RESISTANCE. THE DOUBLE LAYER CAPACITANCE. AND THE TIME OF THE MEASUREMENT. I TOTAL IS SIMPLY THE SUM OF THE THO. COMPLETED 1’26/95 NRITTEN BY KATHLEEN A. FIX UPDATED 6’86 OOOOOOOOOOOOOOOOOOOOO SPECIFICATION OF VARIABLES CHARACTEROIS CFILE CHARACTEROI DANS CHARACTEROIS DFILE CHARACTERGIS DOFILE CHARACTER’AS NAME CHARACTEROIS OFILE CHARACTER’I RANS CHARACTER§4 REF CHARACTER'SO SYS CHARACTER94 HE CHARACTEROI YESANS !FILE CONTAINING CDL VALUES! !ANS TO DEFAULT FILE CUES! !NAME OF FILE NITH DEFAULT VALS! !NAME OF FILE NITH DIFN COEF VALS! !DUMMY FOR FILE HEADER! !NAME OF OUTPUT FILE! !ANS TO ANOTHER RUN CUES! !KIND OF REFERENCE ELECTRODE! !NAME OF METAL AND ELECTROLYTE! !KIND OF WORKING ELECTRODE! !YES ANS TO ANY CUES! INTEGER N !I OF ELECTRONS PASSED! INTEGER NTIMS !0 OF TIMES THRU THE LOOP! REAL AREA !SURFACE AREA OF THE ELECTRODE! REAL B REAL BI REAL BR REAL CDL !THE VAL OF THE DBL LAYER CAP! REAL CONC !CONCENTRATION OF THE ANALYTE! REAL CI REAL 02 REAL D !DIFN COEF OF THE OX SPECIES! REAL DELTE !THE DIF BETHEEN POTL PLSES! REAL DROPT !TIME FOR ONE HG DROP TO FALL! REAL DI REAL DR REAL E !THE POTENTIAL OF THE SYS! REAL EBASE !THE BASE POTENTIAL! REAL EFIN !THE FINAL POTENTIAL! REAL ERED !THE REDUCTION POTENTIAL! REAL ETRUE !THE REAL POTL THEN! REAL F !THE FARADAY! REAL ICHG !THE CHGING CURRENT THEN! REAL IFAR !THE FARADAIC CURRENT THEN! REAL IMEAS !TOTL I MEASD AT TIME! REAL ITOTL !SUM OF IFAR AND ICHG! REAL M REAL P !P TERM IN PART 3! REAL PERFAR !1 OF TOTL I HHICH IS FAR! REAL PI REAL PTI REAL PT2 REAL PT3 REAL PI REAL P2 REAL R REAL RU REAL TEMP REAL TIMCON REAL TIME REAL TPLS REAL TRLX 1f78 !THE VALUE OF PI! !PART I OF THE EON! !PART 2 OF THE EON! !PART 3 OF THE EQUATION! !THE GAS CONSTANT-8.31441! !THE UNCOMP RESISTANCE! !THE TEMP IN KELVIN! !EXP PART OF TIME CONSTANT! !TIME “HEN I IS MEASURED! !THE HIDTH OF THE POTL PLS! !DROPTIME MINUS PULSE UIDTH! 00000 USE OF DEFAULT FILE YESANSI'Y' HRITEI3.3) FORMATI'CUSING DEFAULT DATA FILE?IY/N] ') READ(3.6)DANS FORMATIAI) IF (DAN8.EO.YE8AN8) oo '70 300 00000 0‘ U 23 12 IS I7 33 .o $3 2%) 60 INPUTTING OF VARIABLES URITEI5.20) FORMAT(‘$NAME OF METAL AND ELECTROLYTEz') READ(5.23)SYS FORMAT(ASOI) URITEI5.I2) FORMATI'SHORKING ELECTRODEz') READ!S.IS)HE FORMATIAAI) HRITE(S.I7) FORMAT('$REFERENCE ELECTRODE:') READ(S.IS)REF NRITEI5.SO) FORMAT('ONUMBER OF ELECTRONSz') READ(5.SS)N FORMATII?) NRITE(3.40) FORMAT( ' ALL THE FOLLOHING NUMBERS INPUTTED MUST INCLUDE S DECIMAL POINTS') HRITEI5.SO) FORMAT('$AREA OF ELECTRODECCA*02]:’) READ($.33)AREA FORMAT(GIS.5) HRITE(5.60) FORMAT('$CONCENTRATION OF ANALYTEIMiz') 179 READ($.33)CONC HRITEIS.I70) I70 FORMAT('OCONCENTRATION OF BACKGROUND ELECTROLYTEIM):‘) READ(5.53)BCONC HRITE(5.70) 7O FORMATI'CPULSE HIDTthSlz') READ(5.53)TPLS HRITEIS.SO) SO FORMATI'CTIME OF MEASUREMENTIQSJ:') READIS.33)TIME NRITEI3.I00) I00 FORMATC'OBASE POTLIAVlz') READ($.SSIEBASE NRITE($.IIOT IIO FORMATI'CREDN POTLImVlz’) READI5.$3)ERED HRITEI5.I20) 120 FORMATI'GFINAL POTLIMVJ:') READ(5.53)EFIN NRITEI5.ISOI I30 FORMAT(’$STEP SIZEthlz‘) READI3.53)DELTE HRITEI5.140) 140 FORMATI'CUNCOMPENSATED SOLN RESISTANCECohmslz') READI5.53)RU HRITE(S.ISO) ISO FORMAT(‘$DROP TIMEISiz') READI5.33)DROPT 200 HRITEC5.93) 93 FORMATI’CFILE CONTAINING VALUES OF DOX: ’) READIS.97)DOFILE 97 FORMAT(AI$) C HERE HE GO THRU A DATA FILE AND GET THE CORRECT VALUE C FOR THE DIFFUSION COEFFICIENT OPEN(UNIT-4.NAME-DOFILE.STATUSI'OLD') READI4.90)NAME 90 FORMATI4SAI) DO 195 L-I.II READ(4.I35)BI.DI I55 FORMAT(20I5.S) IF (BI.GE.BCONC) GO TO 137 160 READ(4.I$5)B2.DZ IF (B2.EO.BCONC) GO TO 163 IF (B2.GT.BCONC) THEN M-(BCONC-BI)/(B2-BI) B-MD(D2-DI) D-DI+B GO TO 165 180 ELSE BI-82 01-02 GO TO 160 END IF I95 CONTINUE I63 DI-DR I57 D-DI I65 CLOSEIUNIT-A) SPECIFICATION OF CONSTANTS 00000 F-964SA.6 !IN COUL/MOLE! PI-3.14I59 R-S.SIA4I !IN J/MOLE DEGREE K! TEMP-298.15 !IN DEGREES K! CONC'CONC/IOOO TPLS-TPLS/IOOO TIME-TIME/IOOO EBASE-EBASE/IOOO ERED-ERED/IOOO EFIN-EFIN/IOOO DELTE-DELTE/IOOO CREATION OF DATA FILE NRITEI5o5) FORMAT('$NAME OF OUTPUT FILE? ') READI5.97)OFILE OPENIUNIT-3.NAME-OFILE.TYPE-'NEH'.CARRIAGECONTROLI'LIST’. 5 FMM- 'FORMATTED '3 ' (I 00000 HRITEI5.I0) NRITEI3.10) IO FORMAT(' NORMAL PULSE POLAROGRAPHYIcurrcntJ') HRITE(3.26)SYS 26 FORMAT(' NAME OF METAL AND ELECTROLYTE: '.A30) NRITEIS.II)UE II FORMATI' NORKING ELECTRODE: '.A4) HRITE(S.I5)REF I5 FORMATI' REFERENCE ELECTRODE: ’.A4) HRITEI3.36)N 36 FORMAT(' NUMBER OF ELECTRONS: '.I2) HRITE(3.56!AREA 56 FORMATI' AREA OF ELECTRODECcnfifi21: ’.GI5.5) NRITEIS.65!CONC 65 FORMATI' CONCENTRATION OF ANALYTEIKMJ: '.GI5.5) HRITE(3.67)BCONC 181 67 FORMATI' CONCENTRATION OF BACKGROUND ELECTROLYTEIM): '.GIS.5) HRITE(3.75)TPLS 75 FORMAT(' PULSE HIDTHISJ: '.OI5.5) NRITEIS.S$)TIME 85 FORMAT(' TIME OF MEASUREMENTISJ: '.OI3.5) HR!TE(3.95ID 95 FORMAT(’ DIFN COEF OF OXIcniGZIsJ: '.OI$.5) HRITE(S.IOSIEIASE Io: FORMATI' BASE POTLIVJ: '.OI$.$) URITE(3.II$)ERED II: FORMAT(' REDN POTLIVJ: '.OI$.5) HRITE(3.I25)EFIN 123 FORMAT(' FINAL POTLIVJ: '.015.5) HRITE(3.I39)DELTE 135 FORMAT(’ STEP SIZEIVJ: '.OIS.5) WITEIS. IQSIRU 145 FORMATC' UNCOMPENSATED SOLN RESISTANCEtohnsJ: ‘.OI:.5) HR!TE(3.ISS)DROPT I85 FORMAT(’ DROP TIMEtnS): '.OIS.5) HRITEI3.2IOI . 210 FORMATC' POTLIVI CURRENTEAJ') c _ _ _ —- ..... ._ C C CALCULATION OF PART I OF EON. NUMBER OF TIMES THRU C THE LOOP. PART 2 OF THE EON AND OTHER CONSTANTS C C PTI-NQFoAREAGCONC NTIM8-IFIX((EBASE-EFINIIDELTE) PT2-SORT(D/(PI§TIME)) TRLx-DROPT-TPLS E-EBASE URITEC5.240) 240 FORMAT('$FILE CONTAINING CDL VALUES: ') READI5.97)CFILE c .......... C . C LOOP HHICH PRODUCES POLAROGRAM THRU CALCULATION OF PART 3 C OF EON C c _. __ ——- — —---- DO 230 J2'1.NTIMS !NE DETERMINE THE CORRECT VALUE FOR CDL AT THE !CURRENT POTENTIAL FROM A DATA FILE OPENTUNIT-2.NAME-CFILE.STATUS-'OLD’) READ(2.90)NAME DO 245 II-I.40 READ(2.I55)PI.CI IF (PI.LE.E) GO TO 250 182 255 READ(2.I55)P2.C2 IF (P2.EO.E) GO TO 260 IF (P2.LT.E) THEN M-(E-PIIIIP2-PI! B-MOIC2-CI) CDL-CI+B GO TO 265 ELSE PI-P2 CI-C2 GO TO 255 END IF 245 CONTINUE 260 CI-C2 250 CDL-CI 265 CLOSEIUNIT-2) TIMCON-EXP(-TIME/(CDLCRU!D ETRUE-E*(I - TIMCON) P-EXPI((ETRUE-EREDIONRF)/(RRTEMPII PT3-I/(I+P) IFAR-PTIOPT2OPT3 ICHO-((DELTEO(J2-II)IRUIOTIMCON IMEAS-IFAR+ICHG PERFAR-(IFAR/IMEASIGIOO NRITE(3.222)E.ICHG HRITE(S.224)E.IFAR HRITEIS.220)E.IMEAS 220 FORMATI'RD ’.2GI5.5) 222 FORMATC'IC '.2GI2.5) 224 FORMAT(’IF '.2GI2.5) E-E-DELTE 230 CONTINUE HRITEI5.270) 270 FORMATI' ALL DONE') CLOSE(UNIT-S) NRITE(5.2SG) 280 FORMAT('$DO ANOTHER RUN7IY/NJ ') READI5.6)RANS IF (RANS.EG.YESANS) GO TO 290 GO TO 999 OPENING AND READING THE DEFAULT FILE '— §00000 HRITEI5.3I0) FORMATI’SDEFAULT FILE NAME: ’) READ(5.90)DFILE OPEN(UNIT-2.NAME-DFILE.STATUSI'OLD’) READ(2.S20)SYS 320 FORMATI20X.A30) READ(2.330)NE 330 FORMATI2OX.A4) READ(2.330)REF READ(2.340)N 3‘0 FORMAT(20X.I2) READI2.350)AREA 0 u 0 350 999 183 FORMATI20X.GI5.5) READ(2.350)CONC READ(2.350)BCONC READI2.350)TPLS READ(2.350)TIME READ(2.350)EBASE READI2.S50)ERED READ(2.350)EFIN READ(2.350)DELTE READI2.350)RU READ(2.350)DROPT CLOSEIUNIT-2) GO TO 290 CALL EXIT END 0000000000000000000000000 184 Table B-2 0' O O--. 0...----- ------ o a .0- 0- 0 -I 0---- - 0- .~- .. - 9 -------- THIS PROGRAM SIMULATES NORMAL PULSE POLAROGRAPHY AS PERFORM- ED BY CHARGE PULSE POLARIZATION. IT IS INTENDED TO SIMULATE THE OPERATION OF A CHARGE INJECTOR BEING BUILT BY NORMAN PENIX. A LARGE SECTION OF THIS PROGRAM IS DEVOTED TO VARIABLE I/O. THE MORE COMPACT AREA TOWARD THE END CONTAINS THF PART OF THE PROGRAM NHICH CALCULATES THE VARIOUS COMPONENTS REQUIRED BY THE FORMULA OF A POLAROGRAM. THE LARGER OF THE THO LOOPS PERFORMS THE STEPS UP AND DOHN. CALCULATING THE NUMBER OF CHARGE INJECTIONS AND THE TIME REQUIRED. THE SECOND HALF OF THAT LOOP (NHICH FOLLONS THE SMALLER LOOP) OUTPUTS THE RESULTS TO THE OUTPUT DATA FILE. THE SMALLER. INSIDE LOOP DOES THE CALCULATIONS EQUATING IT TO THE INSTRUMENTAL APPLI- CATION OF SMALL CHARGE INJECTIONS TO MAINTAIN THE POTENTIAL OF THE PULSE. THE THEORETICAL EQUATIONS USED ARE FROM PARRY AND OSTERYOUNG. ANAL CHEM. VOL 37. PG I6SQ. I965. COMPLETED 7/I2/S5 HRITTEN BY KATHLEEN A. FIX ' O..- . 0-- - 1'--- - ---- --..’----. n-------- - ------- o . -- ------»o --c ..‘C-. o---- SPECIFICATION AND EXPLANATION OF VARIABLES CHARACTER'I ANS - !ANS TO QUES TO REPEAT! CHARACTER’I DANS !ANS TO DEFAULT FILE QUES! CHARACTEROI5 CFILE !NAME OF CDL FILE! CHARACTEROIS DFILE !NAME OF DEFAULT FILE! CHARACTEROI5 DOFILE !NAME OF D OX FILE! CHARACTEROI5 FILE !NAME OF OUTPUT FILE! CHARACTEROI IANS !ANS TO INJEX QUES! CHARACTER'45 NAME !DUMMY VARIABLE! CHARACTEROI RANS !ANS TO QUES FOR ANOTHER RUN! CHARACTEROA REF !NAME OF REF ELECTRODE! CHARACTERO20 SYS !NAME OF ANALYTE SYS! CHARACTERRA NE !NAME OF NORKING ELECTRODE! CHARACTERfiI YESANS !YES ANSWER! INTEGER INJCNT !. OF SM CHG INJEX DURING PULSE! INTEGER INJFLG !II IF INJT SET CONSTANT VALUE! INTEGER MCNT !0 OF NEG COUNTS ON PULSE! INTEGER N !0 OF ELECTRONS TRANSFERRED! INTEGER NTIMS !0 OF TIMES THRU LG LOOPIPULSES)! INTEGER PCNT !G OF PLUS COUNTS ON PULSE! INTEGER PTH !TELLS IF HIT MAX INJEX SPEED! REAL AREA !SURFACE AREA OF N. ELECTRODE! REAL B !INTERCEPT OF VARIOUS LINES! REAL BCDL !DBL LAYER CAP AT BASE POTL! REAL BCONC !CONC OF THE BACKGRND ELECTROLYTE! REAL BHECAP !CAP OF HORK ELECTRODE AT BASE POTL! REAL BI !FIRST VALUE OF B.E. CONC! REAL B2 !SECOND VALUE OF B.E. CONC! REAL CDL !DOUBLE LAYER CAPACITANCE! REAL CHG !AMT OF CHG DUMPED INTO CELL! REAL CHGCAP !SIZE OF CHGING CAP! REAL CHGV !VOLTAGE USED TO CHG CHGCAP! REAL CHGVDN !CHG V REQD ON CHGCAP TO STEP DOHN! REAL CHGVUP !CHG V REQD ON CHGCAP TO MAKE PULSE! REAL CONC !CONC OF ANALYTE! REAL CI !FIRST VALUE OF CDL! 00000 I0 008 REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL USE OF DEFAULT DATA FILE INJFLG'O C2 D DECAY DECAYT DELTE DIF DIFF DROPT DI D2 EBASE EFIN EHALF ERED p GRAD INJT LGCHG LOHER M p PI PTI PT2 PT3 PI P2 R RAD RS SMCHG SMQ TEMP THERE TIME TIMS TOTLT TPLS TRLX UPPER VWE WECAP WEP CARRAYI200) PARRAYI200) YESANS-‘Y' WRITE(5.IOT FORMATI'OUSING DEFAULT DATA FILE7tY/NJ ') READ(5.20TDANS FORMATIAI) IF (DANS.EQ.YESANS) GO TO 700 185 !SECOND VALUE OF CDL! !DIFN COEFFICIENT OF OX SPECIES! !AMT OF POTL DECAY ALLOWED ON STEPS! !TIME REOD TO DECAY XmV ON PULSE! !POTL DIF BETWEEN SUCCESSIVE PULSES! !DIF TWEEN POTL AND LOWER LIMIT! !DIF TWEEN POTL AND BASE POTL! !LIFE LENGTH OF MERCURY DROP! !FIRST VALUE OF DOX! !SECOND VALUE OF DOX! !BASE POTENTIAL! !FINAL POTENTIAL! !CALCULATED HALF WAVE POTENTIAL! !FORMAL REDUCTION POTENTIAL! !THE FARADAY! !THE CONC GRADIENT FROM RELAX TIME! !TIME REQUIRED FOR I CHG INJEX! !AMT OF CHG IN A LG CHG INJEX! !VALUE OF LOWER LIMIT OF DECAY! !SLOPE OF LINE FOR DOX OR CDL! !FACTOR IN POLAROGRAM FORMULA! !VALUE OF THE CONSTANT PI! !VALUE OF IST PART OF FORMULA! I I C an I I D g 2 C U Imp . I N 2 !FIRST VALUE OF POTL! !SECOND VALUE OF POTL! !THE GAS CONSTANT! !RADIUS OF THE WORKING ELECTRODE! !SOLUTION RESISTANCE! !SMALLEST AMT OF CHG CAN GO TO CELL! !SMALLEST AMT OF CHG CAN BE MEASURED! !THE TEMP OF THE SYSTEM! !HOW LONG IT TAKES TO GET ----! !TIME IN PLS WHEN MEAS IS STARTED! !0 OF TIMES THRU SM LOOPCINJCNT)! !SUM OF INJEX & TURNAROUND TIMES! !LENGTH OF POTL STEP! !DROPT - TPLSIRELAXATION TIME)! !UPPER LIMIT OF DECAY POTL ON PLS! !POTL ON THE WORKING ELECTRODE! !CAPACITANCE OF WORKING ELECTRODE! !WORKING ELECTRODE POTENTIAL! !ARRAY TO HOLD VALUES OF CHARGE! !ARRAY TO HOLD VALUES OF POTL! 186 INPUTTING OF VARIABLES FROM TERMINAL 90 I00 IIO I20 I25 I30 I40 I50 I60 I70 ISO I90 WRITEI5.30) FORMATI'SNAME OF METAL AND ELECTROLYTEz') READI5.40)SYS FORMATI20AI) WRITEI5.50) FORMATI'CTYPE OF WORKING ELECTRODEz') READ(5.60IWE FORMATI4AII WRITEI5.70) FORMATI'CTYPE OF REFERENCE ELECTRODE:'I READ(5.60IREF WRITEI5oSOI FORMATI'SNUMBER OF ELECTRONS:') READ(5.90)N FORMATII2) WRITEI5.I00) FORMATI' ALL THE FOLLOWING NUMBERS INPUTTED MUST INCLUDE 5 DECIMAL POINTS') WRITEI5.IIOT FORMATI'SSURFACE AREA OF ELECTRODEIcnOi2lz') READ(5.I20TAREA FORMATIGI5.5) WRITEI5.I30) FORMATI'CCONCENTRATION OF ANALYTEIMJt’) READI5. I20ICONC WRITE(5.I40) FORMATI'SCONC OF BACKGROUND ELECTROLYTEIMlz') READI5.I20IBCONC WRITE(5.I50) FORMATI'SPULSE WIDTHIaSlz’) READ(5.I20ITPLS WRITEI5.I60) FORMATI'CDROP TIMEISEClz’) READ(5.I20IDROPT WRITE(5.I70) FORMATI'STIME OF MEASUREMENTIQSlz') READ(5.I20ITIME WRITE(5.ISOI FORMATI'CBASE POTLIquz') READI5.I20)EBASE WRITE(5.I90) FORMATI'GREDN POTLInVlz') READI5.I20)ERED WRITE(5.200) 200 2I0 220 00 235 240 250 260 265 270 298 296 485 187 FORMATI'SFINAL POTLthJ:') READI5.I20)EFIN WRITEI5.2IOI FORMATI'CPOTL DIFFERENCE BETWEEN PULSESIAVlz') READI5.I2OIDELTE WRITEI5o220) FORMATI'CSOLUTION RESISTANCEIohnst’) READ(5.I2OIRS WRITE(5.230) FORMATI’CFILE CONTAINING VALUES OF DOX? ’) READI5.SIO)DOFILE HERE WE SEARCH A FILE TO FIND THE CORRECT VALUE FOR THE DIFFUSION COEFFICIENT OPEN(UNIT-4.NAME-DOFILE.STATUS-'OLD') READI4.2S5)NAME FORMATI4SAI) DO 260 L-I.II READ(4.240)BI.DI FORMAT(2GI5.5) IF (BI.GE.BCONC) GO TO 270 READI4.240)B2.D2 IF IB2.EQ.BCONC) GO TO 265 IF (B2.GT.BCONC) THEN M-(BCONC-BI)/(B2-BI) B-M*(D2-DII D-DI+B GO TO 280 ELSE BI-B2 DI-D2 GO TO 250 END IF CONTINUE DI-D2 D'DI CLOSEIUNIT-4) WRITEI5.290) FORMATI'QSIZE OF CHGING CAPIUFJ:') READI5.I2OICHGCAP WRITEI5.293) FORMATI'SVOLTAGE ON CHGING CAPIVJ:’) READ(5.I20TCHGV WRITEI5.296) FORMATI’SAMT OF V DECAY ON PULSESIAVJ:') READ(5.I20IDECAY WRITEI5.4SSI FORMATI'SHAVE INJT A SET VALUE7IY/NJ') READI5.20)IANS IF (IANS.EQ.YESANS) THEN WRITEI5.49OI 188 49o FORMATI'QVALUE or INJEX TIME (US):') READ¢:.IzoIINUI ELSE INUFLG-I END IF c-- -_ - ................. c c CREATION or DATA FILE c c ____ _ _ UNITE(s.aooI aoo FORMATI'SNAME or OUTPUT FILEz') READI5.SIOIFILE 3.0 FORMATIAIS) OPEN(UNIT-3.NAME-FILE.TYPE-'NEW'.CARRIAOECONTROLI'LIST'. 5 FORM-'FORMATTED') c- _-- -------- c g SPECIFICATION or CONSTANTS AND CONVERSION TO SI UNITS c ............ r-95494.5 !IN COOL/MOLE! PI-3.I4I39 ‘ R-S.SI44I !IN JIMOLE DEGREE K! TEMP-29S.I5 !IN DEGREES K! PTH-O CONCICONC/IOOO TPLS-TPLS/IOOO TIME-TIME/IOOO EBASE-EBASE/IOOO ERED-ERED/IOOO EFIN-EFIN/IOOO DELTE-DELTE/IOOO CHOCAP-CHOCAP/I.0E6 DECAY-DECAY/IOOO INJT-INJT/I.OE6 UNITE¢5.320. WRITE(3.320) 320 FORMAT(' CHARGE PULSED NORMAL PULSE POLAROGRAPHY') c .- _ - A -----..---..- --_-- --_-—--- c c WRITING VARIABLE VALUES TO DATA FILE c c __ -- __ __ _ _=_-_ 32: WRITEIS.SSO)SYS aoo FORMATI' NAME or METAL AND ELECTROLYTE: '.20AI) un:rz¢a.aao.uc 340 FORMATI' WORKING ELECTRODE: '.4AI) WRITE(3.SSO)REF 3:0 FORMATI' azrsnche ELECTRODE: '.4AI) WRITE(3.360)N 360 FORMATC' NUMBER OF ELECTRONS: '.12) S70 WRITEIS.S7OIAREA FORMATI' AREA OF ELECTRODEICAOO2J: '.GIS.5) 390 400 4I0 420 430 440 450 460 470 490 520 530 189 MITEI3.SSOICCNC FORMAT(' CONCENTRATION OF ANALYTEIIMJ: '.GI5.5) WRITEIS.390)BCONC FORMATI' CONC OF BGRND ELECTROLYTECM]: '.GI5.5) WRITE(S.400)TPLS FORMAT(’ PULSE WIDTHISJ: '.GI5.5) . WRITE(S.4IO)DROPT FORMATI' DROP TIMEISECT: '.GI5.5) HRITE(S.420)TIME FORMATI’ TIME OF MEASUREMENTISJ: '.GI5.5) WRITEIS.4SO)D FORMATI’ DIFFUSION COEF OF OXICORREII): '.GI5.5) WRITE(3.440)EBASE FORMAT(’ BASE POTLIVJ: '.GI5.5) WRITEIS.450IERED FORMAT(' REDN POTLIV): '.GI5.5) WRITE(3.460)EFIN FORMAT(' FINAL POTLCVJ: '.GI5.5) WRITE(3.470IDELTE FORMAT(' STEP SIZEIVJ: '.GI5.5) WRITE(8.4SOIRS FORMATI' SOLN RESISTANCEIohADJ: '.GI5.5) WEP-EBASE WRITEI5.520I FORMATI'SFILE CONTAINING CDL7’) READI5.3I0!CFILE OPEN(UNIT-2.NAME-CFILE.STATUSI'OLD’) READI2.235)NAME FROM A FILE. THE CORRECT VALUE OF THE DOUBLE LAYER CAPACITANCE IS FOUND FOR THE BASE POTENTIAL DO 540 II-I.40 READC2.240)PI.CI IF (PI.LE.WEP) GO TO 550 READ(2.240)P2.C2 IF IP2.EQ.WEPI GO TO 545 IF (P2.LT.WEP) THEN M-(WEP-PI)/(P2-PII B-MOIC2-CI) BCDL-CI+B GO TO 560 ELSE PI-P2 CI-C2 GO TO 530 END IF 190 540 CONTINUE 545 CI-C2 550 BCDL-CI 560 BWECAP-AREAOBCDL CLOSEIUNIT-2) WRITEIS.500)CHGCAP 500 FORMATI' CHGING CAPACITOR SIZEIFJ: '.GI5.5) WRITE(3.503)CHGV 503 FORMATI' VOLTAGE ON CHGING CAPIV]: '.GI5.5) NRITEC3.506)DECAY 506 FORMAT(’ AMT OF DECAY ON PULSESIVJ: '.015.5) IF (INJFLG.EQ.I) GO TO 496 WRITEIS.49S)INJT 49S FORMATI' INJECTION TIMEISJ: ‘.GI5.5) c- -- C C CALCULATION OF NUMBER OF TIMES THRU LOOP TO PRODUCE C POLAROGRAM. AND INITIALIZATION OF SOME VARIABLES C c A __ 496 PTI-2ONOFOAREAOCONC NTIMS-IFIX((EBASE-EFIN)IDELTE) WRITE(3.5I0) 5I0 FORMAT(' POTLIVJ 0 OF COUNTS’) TRLX-DROPT-TPLS TOTLT-0.0 VWE-EBASE RAD-SQRTIAREA/(4OPI)) C ---= C C LOOP WHICH PRODUCES POLAROGRAM THRU CALCULATION OF PARTS 2 C (SQUARE ROOT TERM) AND SIFROM POTENTIAL) OF THEO EQUATION C c -- DO 660 I-I.NTIMS CHGVUP-BWECAPGDELTENIICHGCAP 610 CHG-CHGVUPGCHOCAP 620 VWE-VWE-CHGIBWECAP C CALCULATE HOW LONG IT TAKES TO GET THERE WITH A IOmA C CURRENT SOURCE THERE-CHOI.OIO TOTLT-THERE P-EXPII(VHE-ERED)ONOF)I(R.TEMP)) PTSII/(IOP) WEP-WEP-(DELTEOI) C IN THIS SECTION. THE CURRENT VALUE OF CDL IS DETERMINED AND C THE WORKING ELECTRODE CAPACITANCE AND OTHER RELATED NUMBERS C ARE OBTAINED AND/OR CALCULATED 191 OPENIUNITI2.NAME-CFILE.STATUS-'OLD') READ(2.235)NAME DO 580 I2-I.40 READI2.240)PI.CI IF (PI.LE.WEP) GO TO 590 570 READ(2.240)P2.C2 IF (P2.EQ.WEP) GO TO 585 IF (P2.LT.WEP) THEN M-(WEP-PI)/(P2-PI) BIMGIC2-CI) CDLICI+B GO TO 595 ELSE PI-P2 CI-C2 GO TO 570 END IF 590 CONTINUE 5S5 CI-C2 590 CDL-CI 595 WECAP-AREAPCDL CLOSEIUNIT-2) SMQ-CHGVPCHGCAP !AMT OF CHG FROM SM INJECTION! TIMS-TPLSCI.0E5 !MAX NUMBER OF INJEX POSSIBLE! IF (INJFLG.EQ.I) INJT-SACDLiRS PCNT-0 MCNT-0 UPPER-WEP-(.5PDECAY) !UPPER AND! LOWER-WEP+(.59DECAY) !LOWER LIMITS OF WINDOW! c _ _ - .......... C C THIS DO LOOP MEASURES THE DECAY OF THE PULSE AND INJECTS C SMALL AMOUNTS OF CHARGE OF THE SAME SIZE TO MAINTAIN THE C PULSE POTENTIAL AT A CONSTANT VALUE. THE NUMBER OF CHARGE C INJECTIONS MADE DETERMINES THE AMOUNT OF CHARGE REQUIRED C BY THE FARADAIC REACTION“ C c — — - ----------------- DO 630 J-I.TIMS IF (TOTLT.GE.TPLS) GO TO 640 IF (VWE.GT.LOWER) THEN !IF YOU AREN'T IN DECAYT-1.0E-6 !THE WINDOW KEEP GO TO 64I !INJECTING CHARGE ELSE !TIL YOU’RE THERE C IF IN WINDOW CALC TIME TO DECAY TO LOWER LIMIT DIF-LOWER-VWE SMCHG-DIFOWECAP DECAYT-(PI/D)O(SMCHG/(PTIGPTS))992 !FLAG IF HIER THAN INJEX FREQ IF (I.NE.NTIMS) GO TO 65! IF (J.NE.TIMS/2) GO TO 651 C WRITEI5.652)DECAYT 652 FORMATI'DTIl '.GI5.5) 65I IF (DECAYT.LT.I.0E-6) PTH-I END IF 64I PT2-SQRTIDGDECAYT/PI) CHG‘PTIOPT2OPTS VWE-VWE+CHG/WECAP !MEANWHILE. THE VOLTAGE TOTLT-TOTLT+DECAYT !DECAYS 192 IF (TOTLT.GE.TPLS) GO TO 640 VWEIVWE-SMQIWECAP IF (TOTLT.GE.TIME) PCNTIPCNTOI C WE START COUNTING THE 0 OF INJEX AFTER THE MEAS TIME HAS PASSED TOTLT-TOTLT+INJT C CHECK IF YOU'RE BACK IN THE WINDOW 636 IF (VWE.GE.UPPER .AND. VWE.LT.LOWER) THEN GO TO 638 ELSEIF (VWE.LT.UPPER) THEN PT2-SQRTIDOINJT/PI) !IF ABOVE CHG-PTIGPT29PT3 VWE-VWE+CHG/WECAP VWEIVWE+SMQIWECAP MCNT-MCNT+I !ANODIC INJECTION! TOTLT-TOTLT+INJT GO TO 636 ELSE PT2-SQRTIDUINJT/PI) !IF BELOW CHG-PTIOPT2OPTS VWE-VWE+CHG/WECAP VWE-VWE-SMQ/WECAP PCNT-PCNT9I TOTLT-TOTLT+INJT GO TO 636 END IF !CALC ANALYTE DEPLETION DUE TO REDUCTION 6SS PTI¢2§N5FGAREAOCONCOGRAD(TOTLT.D.RAD.TPLS) 630 CONTINUE 640 INJCNT-PCNT-MCNT CARRAY(I)-INJCNT PARRAY(I)-VWE WRITE(3.650)VWE.INJCNT 650 FORMATI'RD'.EI5.5.I6) !STEP BACK WEP-EBASE DIFF-WEP-VWE CHGVDN-WECAPODIFF/CHGCAP CHG-CHGVDNPCHGCAP VWE-VWE+CHG/WECAP !DOWN TO BASE POTL BWECAP-AREARBCDL TOTLT-0.0 PTI-2ONDFOAREAOCONC !DROP FELL. BACK TO BULK CONC 660 CONTINUE WRITEI5.670) 670 FORMATI' ALL DONE ') WRITE(5.675)PTH WRITE(S.675)PTH 675 FORMATI' PTH - '.II) EHALF-HALFWPINTIMS.PARRAY.CARRAY) WRITEI5.6SO)EHALF WRITE(3.6SO)EHALF 6SO FORMATI' EI/2 IS CALCULATED AS: '.GI5.5) CLOSEIUNIT'S) WRITEI5.690) 690 FORMATI'SDO ANOTHER RUN7IY/NJ ') READ(5.20)RANS IF (RANS.EQ.YESANS) GO TO I25 193 GO TO 999 OPENING AND READING THE DEFAULT FILE 0000 c.. ..— 700 WRITEI5.7I0) 710 FORMATI'CDEFAULT FILE NAME: ') READ(5.SIO)DFILE OPENIUNIT-2.NAME'DFILE.STATUS-'OLD’) READ(2.720)SYS 720 FORMATI2OX.A20) READ(2.730)WE 730 FORMATI2OX.A4) READ(2.730)REF READ(2.740)N 740 FORMATI2OX.I2) READI2.750)AREA 750 FORMATI20X.GI5.5) READ(2.750)CONC READ(2.750)BCONC READ(2.750)TPLS READ(2.750)DROPT READ(2.750)TIME READ(2.750)EBASE READ(2.750)ERED READ(2.750)EFIN READ(2.750)DELTE READ(2.750)RS CLOSE (UNIT-2) GO TO 225 999 CALL EXIT END THIS SECTION OF THE PROGRAM CONTAINS THE FUNCTIONS REQUIRED TO CALCULATE THE CONCENTRATION GRADIENT OF THE ANALYTE IN SOLUTION AT A DMEIOR SMDE). THE GRADIENT IN THE SYSTEM IS CALCULATED USING A LOOP AND REQUIRING THE USE OF THE ERROR FUNCTION COMPLEMENT. 000000000 FUNCTION GRADITOTLT.D.RAD.TPLS) REAL DIST.D.DNOM.TOTLT.FCNC.VALU.GRAD DIST-5.0E-4 DNOM-2OSQRTIDGTOTLT) FCNC'DIST/DNOM IF (FCNC.GE.I.6) THEN VALU-CERFIFCNC) ELSE VALU-ERFCIFCNC) END IF GRAD-I.O-IRADPVALU/(RAD+DIST)) RETURN END c--n=__ ........................................ 000000 ' 194 CALCULATION OF THE ERROR FUNCTION COMPLEMENT FOR THOSE NUMBERS GREATER THAN 1.6 WHICH THE APPROXIMATION OF THE FUNCTION ERF DOES NOT WORK FOR. FOR PROPER EXPANSION OF THE ALGORITHM SEE CERF.FTN OR ERR.FTN. FUNCTION CERFIFCNC) X-FCNC CERF I (2./SQRT(S.I4I59))0(EXP(-ID(XOC2))II2DX))O I (I‘ II(2O(XOO2))+ S/(4OIXOO4))- ISIISOIXGOS))* 2 IO5/(I6PIXOOI6))) RETURN END CALCULATION OF THE ERROR FUNCTION COMPLEMENT 00000 FUNCTION ERFCIFCNC) ERFCOI.O-ERF(FCNC) RETURN END 000000 c-.. ——. C- .- .— v w ‘— CALCULATION OF THE ERROR FUNCTION. FOR PROPER EXPANSION OF THE ALGORITHM SEE ERFC.FTN OR ERFCTST.FTN. FUNCTION ERFtFCNC) ERF-Z/SORT(3.14159)O(FCNC -(FCNC*¢3/3.0) +(FCNC!O$/I0.0) 5 -(FCNC9¢7I42.D) +(FCNC999/(216.0I)) RETURN END C C C C CALCULATION OF THE E I/2 VALUE INDICATED BY THE POLAROGRAM PRODUCED. c------- ‘ FUNCTION HALFWPITIMES.POTS.CHGS) REAL POTS(200).CHGS(200).Q.CHI.CH2.PI.P2.CNET.QNET REAL PERCNT.PNET.VNET INTEGER CNT.TIMES Q-CHGS(TIMES)/2 CNT-O DO S50 J2-I.TIMES CNT-CNT¢I IF (CHGS(J2).GE.Q) GO TO S60 CONTINUE CHI-CHGSICNT-I) CH2-CHGSICNT) PI-POTSICNT-I) P2FPOTSICNT) CNET-CH2-CHI QNET-Q-CHI PERCNT-QNET/CNET 195 PNET-n-P I VNET-PNETOPERCNT HALFWP -P I .VNET RETURN END OOOOOOOOOOOOOOOOOOOO y...‘ 196 Table B-3 THIS PROGRAM PRODUCES A SIMULATION OF A DIFFERENTIAL PULSE POLAROGRAM. IT CALCULATES I FAR. I CHG. I TOTAL. AND MEASURES THE CURRENT AT THE SAHE TIME DURING EACH STEP. I FAR IS DEPENDENT ON THE NUMBER OF ELECTRONS IN THE SYSTEM. THE AREA OF THE ELECTRODE. THE CONCENTRATION OF THE ANALYTE. THE DIFFUSION COEFFICIENT OF THE OX SPECIES. THE TIHE OF THE MEASUREMENT. AND THE POTENTIAL. I CHG DEPENDS ON THE STEP SIZE. THE SOLUTION RESISTANCE. THE DOUBLE LAYER CAPACITANCE. AND THE TIME OF THE MEASUREMENT. I TOTAL IS SIMPLY THE SUM OF THE THO. COHPLETED 4/15/86 HRITTEN BY KATHLEEN A. FIX SPECIFICATION OF VARIABLES !ANS TO DEFAULT FILE QUES! !ANS CUES FOR ANOTHER RUN! !ANY YES ANSHER! !TYPE OF REFERENCE ELECTRODE! !TYPE OF HORKING ELECTRODE! !NAME OF FILE HITH CDL VALUES! !NAME OF DEFAULT DATA FILE! !NAME OF FILE HITH DIFN COEFS! !NAME OF OUTPUT FILE! !METAL AND ELECTROLYTE USED! !DUMMY VARIABLE FOR HEADER! CHARACTERGI DANS CHARACTEROI RANS CHARACTEROI YESANS CHARACTERO4 REF CHARACTERGA HE CHARACTEROIS CFILE CHARACTERGIS DFILE CHARACTER’IS DOFILE CHARACTER*15 FILE CHARACTER'SO SYS CHARACTERDQS NAME INTEGER N !G OF ELECTRONS PASSED! INTEGER NTIHS !0 OF TIMES THRU LOOP! REAL AREA !SURFACE AREA OF HORKING ELECTRODE! REAL B REAL BCONC !CONCN OF BACKGROUND ELECTROLYTE! REAL BI REAL B2 REAL CDL !THE DOUBLE LAYER CAPACITANCE! REAL CONC !CONCENTRATION OF THE ANALYTE! REAL CI REAL C2 REAL D !DIFN COEF OF THE 0! SPECIES! REAL DELTE !THE DIF BETHEEN SUCCESIVE PLSES! REAL DELTI !DIFFERENCE OF ISTEP AND IPLS! REAL DROPT !LIFE OF MERCURY DROP! REAL DI REAL D2 REAL E !THE POTL AT ANY TIME! REAL EBASE !THE BASE POTENTIAL! REAL EFIN !THE FINAL POTENTIAL! REAL EPEAK !POTL WITH PEAK CURRENT DIF! REAL EPLS !THE HEIGHT OF THE POTL PLS! REAL ERED !THE REDUCTION POTENTIAL! REAL ETRUE !HHAT THE POTL REALLY IS! REAL F !THE FARADAY! REAL ICHG !THE CHGING I AT ANY TIME! REAL IFAR !THE FARADAIC I AT ANY TIME! REAL IMEAS !ITOTL AT THE CORRECT TIME! !THE CURRENT MEASD ON THE PULSE! 197 REAL ISTEP !THE CURRENT MEASD ON THE STEP! REAL ITOTL !SUM OF IFAR AND ICHG! REAL M REAL P !THE P TERM IN PART 3! REAL PI !THE VALUE OF PI! REAL PTI !PART I OF THE THEORETICAL EON! REAL PT2 !PART 2 OF THE THEORETICAL EON! REAL PT3 !PART 3 OF THE THEORETICAL EON! REAL PI REAL P2 REAL OI REAL 02 REAL R !THE GAS CONSTANT-8.31441! REAL RS !THE SOLUTION RESISTANCE! REAL TEMP !THE TEMP IN KELVIN! REAL TIME !THE TIME "HEN I IS MEASURED! REAL TPLS !THE PULSE HIDTH! ()OOOO USE OF DEFAULT FILE YESANSI'Y’ HRITE(5.3) FORMAT('$USING DEFAULT FILE?IY/NJ ') READ(5.6)DANS FORMAT(A IF (DANS. E0. YESANS) GO TO 700 INPUTTING OF VARIABLES ISO 153 33 40 HRITE(5.20) FORMAT(‘$NAME OF METAL AND ELECTROLYTEz') READ(5.23)SYS FORMAT(30AI) HRITE(5.ISO) FORMAT('$TYPE OF HORKING ELECTRODE: ') READ(5.I$3)HE FORMATIQAI) HRITE(5.160) FORMAT('$TYPE OF REFERENCE ELECTRODE: ') READ(5.153)REF HRITE(5.30) FORMAT('$NUMBER OF ELECTRONS: READ(5.33)N FORMAT(I2) HRITE(S.40! FORMAT(' ALL THE FOLLOHING NUMBERS INPUTTED MUST INCLUDE 5 DECIMAL POINTS’) HRITE(5.50) FORMAT(’$AREA OF ELECTRODECcni'2JI') READ(5.53)AREA 198 53 FORMAT¢GIS.S) HRITE(S.60I 60 FORMATI’CCONCENTRATION OF ANALYTEIMlz') READ(3.53)CONC HRITE(5.67) 67 FORMAT('OBACKGRND ELECTROLYTE CONCIMlz') READ(5.53)BCONC HRITE(5.7OI 7O FORMATC'SPULSE HIDTHCQSJt’) READ(S.$3)TPLS HRITE(5.SOI SO FORMATI'OTIME OF MEASUREMENTIQSJ:') READIS.53)TIME HRITEI5o90) 90 FORMAT('CDROP TIMEISECJz’) READI5.53)DROPT HRITEI5.IOO) IOO FORMATI'CBASE POTLIQVJ:') READI3.53IEBASE HRITEC5oIIO) IIO FORMAT('$REDN POTLI-Vlz’) READI3.53)ERED HRITE(3.I20) I20 FORMATI'BFINAL POTLInVlz') READ(5.53)EFIN HRITE(5.I27I I27 FORMAT('$PULSE HEIGHTIIVJz‘) READIS.S3)EPLS HRITE(3.130) 130 FORMATI'tSTEP SIZEIIVlz') READI5.53)DELTE HRITE(5.I40) .I40 FORMAT(’$SOLN RESISTANCEIohmslz’) READ(5.53)RS 240 HRITEI5.230) 250 FORMATI'CFILE CONTAINING Don? ') READ(5.260IDOFILE 260 FORMAT(AI$) OPEN(UNIT-A.NAME-DOFILE.STATUS-'OLD') READ(4.270)NAME 270 FORMAT(45AI) DO 300 L-I.II READ(4.2SO)BI.DI FORMAT(2GI$.$I IF (BI.GE.BCONC) GO TO 320 READI4.2SO)B2.D2 IF (B2.EO.BCONCI GO TO 310 IF (B2.GT.BCONC) THEN §§ § 310 “°“"“§§ I.) 40 00000 36 $6 199 M-(BCONC'BIIIIB2-BI) B-M'(D2-DI) D-DIOB GO TO 330 ELSE BI-B2 DI-D2 GO TO 290 END IF CONTINUE DI-D2 D-DI CLOSEIUNIT-A) CREATION OF DATA FILE =— w ----- HRITE(S.340) FORMAT('CNAME OF OUTPUT FILE: ') READ(5.260)FILE OPEN(UNIT-3.NAME-FILE.TYPE-'NEH’.CARRIAGECONTROLI’LIST'. 5 FORM-'FORMATTED') SPECIFICATION OF CONSTANTS F-95484.6 !IN COUL/MOLE! PI-3.14159 R-S.SI44I !IN J/MOLE DEGREE K! TEMP-298.15 ' !IN DEGREES K! CONC‘CONC/IOOO TPLS-TPLS/IOOO TIME-TIME/IOOO EBASE-EBASE/IOOO ERED-ERED/IOOO EFIN-EFIN/IOOO EPLS-EPLS/IOOO DELTE-DELTE/IOOO HRITEIS.IG) HRITEC3.IOI FORMATI' DIFFERENTIAL PULSE POLAROGRAPHYIcurrontJ’) HRITING VARIABLE VALUES TO DATA FILE NRITEI3.26)SYS FORMATI' NAME OF METAL AND ELECTROLYTE: ’.30AI) HRITE(3.36)N FORMATI' NUMBER OF ELECTRONS: '.I2) HRITEI3.56)AREA FORMATI' AREA OF ELECTRODECcnifi2J: ’.GI$.7) HRITE(3.63ICONC 200 63 FORMATI' CONCENTRATION OF ANALYTEIKMJ: '.GIS.7) HRITE(3.69IBCONC 69 FORMATI' BACKGRND ELECTROLYTE CONCCM): '.GI5.7) NRITEI3.7SITPLS 73 FORMAT(' PULSE HIDTHISJ: '.GIS.7) HRITE13.SSITIME SS FORMATI' TIME OF MEASUREMENTISJ: '.GIS.7) NRITEI3.S7IDROPT S7 FORMATI' DROP TIMEISI: '.GI$.7) HRITEI3.99)D 95 FORMATI' DIFN COEF OF OX[¢.'02/QJ: '.GIS.7) HRITEC3oIOSIEBASE 105 FORMAT(' BASE POTLIVJ: '.GI5.7) HRITEI3.II3)ERED IIS FORMAT(' REDN POTLIVJ: '.GI$.7) HRITE(3.I23)EFIN I23 FORMAT(' FINAL POTLIV.: ’.GI5.7) HRITE(3.I29)EPLS I29 FORMATI' PULSE HEIGHTCVJ: '.GI$.7) HRITEI3.135)DELTE 135 FORMATI' STEP SIZEIVJ: ’.GIS.7) HRITEI3.I45)RS I49 FORMATI' SOLN RESISTANCEIORIQJ: 'oGI5.7) c a- -- C C CALCULATION OF NUMBER OF TIMES THRU LOOP HHICH PRODUCES C POLAROGRAM. PART ONE OF EOUATION. AND PART THO C c--. —— _— ----—- PTI-NlCONCOAREAGF NTIMSIIFIX¢(EBASE-EFINIIDELTEIOI E-EBASE HRITE(5.400) 400 FORMAT('$FILE CONTAINING Cdl: ') READIS.260ICFILE NRITE(3.2IO) 2IO FORMAT(' POTLIVJ CURRENTCAJ') CC- ---------------o ...n... ._ ‘“ C C LOOP NHICH PRODUCES POLAROGRAM THRU CALCULATION OF PART 3 C OF EON C c _ __ -- _ — _ -_- —————— DO 230 J-I.NTIMS PT2'SORTID/(TIME‘PIII P-EXPII(E-ERED)CN§F)/(R9TEMP)) 201 PT3-I/(I*P) IFAR-PTIOPT2OPT3 !STEP-IFAR COOOOOOOOOOHOOQQD‘IOOOO...IG‘IOQ‘IOOGOOOOOOGOODDODOODOODOQOOGODOOCCDO I D§§§§OII§ C 560 570 590 230 350 380 CALCULATION OF VALUES AND VARIABLES FOR THE PULSE E-E-EPLS PT2-SORTID/(TIMERPIII P-EXPI((E-EREDIiNOF)I(ROTEMPII PT3-II(I+P) IFAR-PTIOPT2iPT3 OPENIUNIT'2.NAME-CFILE.STATUSI'OLD') READ(2.270)NAME READ(2.2BO)PI.CI IF (PI.LE.E) GO TO 590 READ(2.2BO)P2.C2 IF (P2.EO.E) GO TO 370 IF (P2.LT.E) THEN M-(E-PIIIIP2-PII BIMGIC2-CI) CDL-CI+B GO TO 590 ELSE PI-P2 CI-C2 GO TO 560 ENDIF CI-C2 CDL'CI CLOSE(UNIT-2) HRITE(3.223)E.IFAR FORMAT!’RF'.2GI5.3) !MULPLT FILE! ICHG-(DELTE/RSIOIEXPI-TIME/(CDLORS)I) HRITEI3.226)E.ICHG FORMAT('RC'.2GIS.5) !MULPLT FILE! IPLS-IFAR+ICHG EIE+EPLS-DELTE CONTINUE DELTI-IPLS-ISTEP HRITEIS.22OIE.DELTI NRITE‘3.220)E.DELTI FORMAT('RD'.2GI$.5) !MULPLT FILE! IF (J.EO.I) OI-DELTI O2’DELTI IF (O2.GT.OI) THEN EPEAK-E ELSE 01-62 END IF CONTINUE HRITE(5.350) FORMAT!‘ ALL DONE') HRITE($.380)EPEAK HRITE!3.3SO)EPEAK FORMAT(' POTL AT PEAK CURRENT DIF IS: ’.GI$.5) CLOSE(UNIT-3) HRITEI5.360) 360 202 FORMATI'ODO ANOTHER RUN?[YINJ ') READ(5.6)RANS IF IRANS.EO.YESANS) GO TO 370 GO TO 999 OPENING AND READING THE DEFAULT FILE 00000 7IO 720 730 740 750 999 v — _ HRITE(5.7IO) . FORMAT('$DEFAULT FILE NAME: ’) READ(5.260)DFILE OPENIUNIT-2.NAME-DFILE.STATUS-'OLD') READI2.720)SYS FORMATI2OX.A20) READ(2.730)HE FORMAT(20X.A4) READ(2.730)REF READ(2.740)N FORMAT!2OX.I2) READ(2.750)AREA FORMAT(20X.GI3.$) READ(2.750)CONC READI2.750IBCONC READI2.730)TPLS READ(2.750)TIME READ(2.7SO)EBASE READ(2.750)ERED READ(2.750)EFIN READI2.7SO)EPLS READ(2.730)DELTE READ(2.750)RS CLOSEIUNIT-2) GO TO 240 CALL EXIT END 900‘ 10 ' 00 . o ,._O‘ ' ‘0 D 9 ‘1 H. P - THIS PROGRAM SIMULATES DIFFERENTIAL PULSE POLAROGRAPHY AS” PERFORMED BY COULOSTATIC POLARIZATION. IT IS INTENDED TO SIMULATE THE OPERATION OF A CHARGE INJECTOR BEING'BUILT BY NORMAN PENIX. A LARGE SECTION OF THIS PROGRAM IS DEVOTED TO VARIABLE I/O. THE LARGER OF THE THO LOOPS PERFORMS THE STEPS UP AND DOHN. CALCULATING THE NUMBER OF CHARGE INJECTIONS AND THE TIME REOUIRED. IT ALSO FINDS THE VARIATIONS OF THE DOUBLE LAYER CAPACITANCE THROUGHOUT THE SCAN AND CALCULATES THE EFFECTS OF THESE VARIATIONS. THE STARRED LINE REPRESENTS THE BOUNDARY BETHEEN THE CALCULATIONS FOR THE STEPS UP AND DOHN. THE LAST THIRD OF THE LARGER LOOP (HHICH FOLLOHS THE SECOND OF THE SMALLER LOOPS) OUTPUTS THE RESULTS TO THE OUTPUT DATA FILE. THE SMALLER. INSIDE LOOPS DO THE CALCULA- TIONS EOUATING IT TO THE INSTRUMENTAL APPLICATION OF SMALL CHARGE INJECTIONS TO MAINTAIN THE POTENTIAL OF THE PULSE OR STEP. THE LAST SECTION CONTAINS THE FUNCTIONS REOUIRED TO CALCULATE THE CONCENTRATION PROFILE. THE VERY LAST FUNCTION IS USED TO CALCULATE THE POTENTIAL OF THE SOLUTION AT HHICH THE PEAK CHARGE DIFFERENCE OCCURS. THE THEORETICAL EOUATION COMES FROM THE PAPER BY PARRY AND OSTERYOUNG IN ANAL CHEM 37. PG 1634. I965. COMPLETED 7/IQ/SS HRITTEN BY KATHLEEN A. FIX 0000000000000000000000000000000 ...7 ---==— ___ — -- SPECIFICATION AND EXPLANATION OF VARIABLES CHARACTEROI ANS !ANS TO OUES TO REPEAT! CHARACTER'I DANS !ANS TO DEFAULT FILE OUES! CHARACTERiI IANS !ANS TO OUES ABOUT INJEX TIME! CHARACTEROIS CFILE !NAME OF CDL FILE! CHARACTER'IS DFILE !NAME OF DEFAULT FILE! CHARACTERGIS DOFILE !NAME OF D OX FILE! CHARACTERGIS FILE !NAME OF OUTPUT FILE! CHARACTER‘AS NAME !DUMMY VARIABLE! CHARACTERGI RANS !ANS TO OUES FOR ANOTHER RUN! CHARACTEROQ REF !NAME OF REF ELECTRODE! CHARACTER§2O SYS !NAME OF ANALYTE SYS! CHARACTEROQ HE !NAME OF HORKING ELECTRODE! CHARACTEROI YESANS !YES ANSHER! INTEGER INJCNT !. OF SM CHG INJEX DURING PULSE! INTEGER INJFLG !II IF INJECTION TIME IS CONSTANT! INTEGER MCNT !. OF NEG INJEX ON PULSE! INTEGER N !I OF ELECTRONS TRANSFERRED! INTEGER NTIMS !0 OF TIMES THRU LG LOOPIPULSES)! INTEGER PCNT !0 OF POS INJEX ON PULSES ! INTEGER PINJCT !0 OF INJEX COUNTED ON PULSE! INTEGER PTH !-I IF FREO OF INJEX TOO HI ON PULSE! INTEGER SINJCT !I OF INJEX COUNTED ON STEP! INTEGER 8TH !-I IF INJEX FRED TOO HI ON STEP! REAL AREA !SURFACE AREA OF HORKING ELECTRODE! REAL B !INTERCEPT OF VARIOUS LINES! REAL BCONC !CONC OF BACKGROUND ELECTROLYTE! REAL BI !FIRST VALUE OF B.E.CONC! REAL B2 !SECOND VALUE OF B.E. CONC! REAL CHG !AMT OF CHG DUMPED INTO CELL! REAL CHGCAP CHGVUP SMCHG SMO STEPDN SHECAP TEMP THERE TIME TIMS TOTLT TPLS TRLX UPPER VHE HEP CARRAY¢2OOI PARRAYI2GO) 204 !SIIE OF CHGING CAP! !VOLTAGE ON CHGING CAPACITOR! !VOLTAGE REOD TO MAKE STEP DOHN! !VOLTAGE REOD TO MAKE POTL PULSE! !CONC OF ANALYTE! !FIRST VALUE OF CDL! !SECOND VALUE OF CDL! !DIFN COEFFICIENT OF OX SPECIES! !AMOUNT OF VOLTAGE DECAY ON PULSES! !TIME REOD TO DECAY I.22nV ON PULSE! !POTL DIF BETHEEN SUCCESSIVE PULSES! !DIF THEEN POTLS ON PULSE! !DIF THEEN PULSE AND STEP! !DISTANCE FROM SURFACE OF HE! !LIFE LENGTH OF MERCURY DROP! !FIRST VALUE OF DOX! !SECOND VALUE OF DOX! !BASE POTENTIAL! !FINAL POTENTIAL! !VALUE OF POTL AT PEAK CHARGE DIF! !FORMAL REDUCTION POTENTIAL! !STEP HEIGHT!"‘ !THE FARADAY! !TIME REOUIRED FOR I CHG INJEX! !LOHER LIMIT OF DECAY ON PULSES! !SLOPE OF LINE FOR DOX OR CDL! !FACTOR IN POLAROGRAM FORMULA! !DBL LAYER CAP AT PULSE POTL! !VALUE OF THE CONSTANT PI! !VALUE OF IST PART OF FORMULA! 2 I U M N I I I 2 U I an I I C 2 !CAPACITANCE OF HE AT PLS POTL! !FIRST VALUE OF POTL! !SECOND VALUE OF POTL! !THE GAS CONSTANT! !RADIUS OF THE HORKING ELECTRODE! !SOLUTION'RESISTANCE! !DBL.LAYER CAP AT STEP POTL! !SMALLEST AMT OF CHG CAN GO TO CELL! !SMALLEST AMT OF CHG CAN BE MEASURED! !DIF THEEN POTL PULSE AND STEP! !CAPACITANCE OF HE AT STEP POTL! !THE TEMP OF THE SYSTEM! !TIME IT TAKES TO GET ----- ! !TIME IN PLS HHEN MEAS IS STARTED! !0 OF TIMES THRU SM LOOPIINJCNT)! !SUM OF INJEX & TURNAROUND TIMES! !LENGTH OF POTL STEP! !DROPT - TPLS(RELAXATION TIME)! !UPPER LIMIT OF DECAY ON PULSES! !POTL ON THE HORKING ELECTRODE! !HORKING ELECTRODE POTENTIAL! !ARRAY TO HOLD VALUES OF CHARGE! !ARRAY TO HOLD VALUES OF POTL! USE OF DEFAULT DATA FILE TO INPUT VARIABLE VALUES p O 2055 INJFLG-O YESANSI'Y' HRITE(S.IO) FORMATI'tUSING DEFAULT DATA FILE?IY/NI ') READ(S.20)DANS FORMATIAI) IF (DANS.EO.YESANS) GO TO 700 INPUTTING OF VARIABLES FROM TERMINAL 8 00000 3 70 SO I00 IIO I20 I25 I30 I40 ISO I60 I70 HRITEIS.3OI FORMATI'CNAME OF METAL AND ELECTROLYTEz') READ(S.40)SYS FORMATI20AI) HRITECSoSOI FORMAT('CTYPE OF HORKING ELECTRODEz’) READIS.60)HE FORMATIQAI! HRITEIS.70) FORMATI'CTYPE OF REFERENCE ELECTRODEz') READIS.60DREF HRITE(5.80) . FORMATI‘QNUMBER OF ELECTRON8:') FORMATIIRI HRITEISoIOOI FORMATI' ALL THE FOLLOHING NUMBERS INPUTTED MUST INCLUDE S DECIMAL POINTS') HRITEIS.IIG) FORMATI’QSURFACE AREA OF EIECTRODEICQO§2J:') READIS.I20)AREA FORMATIGIS.S) HRITEIS.I30) FORMAT('0CONCENTRATION OF ANALYTEIM):') READIS.I20ICONC HRITEISoI40) FORMATI'SCONCENTRATION OF BACKGROUND ELECTROLYTEIM):') READIS.I20)BCONC HRITEIS.ISO) FORMATI'GPULSE HIDTHIuSlz') READIS.I20ITPLS HRITEIB.I60I FORMATI'CDROP TIMEISEClz'I READ(S.I20)DROPT HRITEIS.I70) FORMATI‘CTIME OF MEASUREMENTIQSJt‘) READ(5.I20)TIME 206 HRITEIS.ISOI ISO FORMATI'GINITIAL POTENTIALIQVlz') READCS.I2OIEBASE HRITEIS.I90) 190 FORMAT('CREDUCTION POTENTIALCnVlz') READIS.I20IERED HRITEISo2GG) 200 FORMAT('$FINAL POTENTIALInVlz') READIS.I2OIEFIN HRITEIS.2OS) 203 FORMATI'OPULSE HEIGHTCnVlz’) READ(5.I20)DELTE HRITEIS.2IGI 2I0 FORMATI'GSTAIRCASE STEP SIZEInVlz') READIS.I20)ESTEP HRITEIS.22G) 220 FORMATI'GSOLUTION RESISTANCEIOhnslz') READIS.I20)RS 22S HRITE(S.230) 230 FORMAT('$FILE CONTAINING VALUES OF DOX? ’) READ(S.310)DOFILE C HERE HE FIND THE CORRECT VALUE OF THE DIFFUSION . C COEFFICIENT FOR THE ANALYTE CONCENTRATION ' OPENIUNIT-Q.NAME-DOFILE.STATUS-’OLD') READ(4.23S)NAME 235 FORMAT(4SAII DO 260 L-I.II READ(4.240IBI.DI 240 FORMATI2GIS.SI . IF (BI.GE.BCONC) GO TO 270 250 READ(4.240)B2.D2 IF (B2.EO.BCONC) GO TO 263 IF IB2.GT.BCONC) THEN M-(BCONC-BI3/(B2-BI) B-M9(02-DI) o-oxon on To 290 ELSE 91-32 01-02 _ co to 2:0 END Is 260 CONTINUE 265 01-02 270 0-01 290 cLOEE READ(5.BIO)CFILE c -— - _____ _ . __ ............ c g LOOP HHICH PRODUCES POLAROGRAM c __ no 660 I-I.NTIMS OPEN(UNIT-2:NAME-CFILE.STATUE-'OLD') READ(2.2SS)NAME c HERE HE CALCULATE (FIND) THE CAPACITANCE as THE HORKING c ELECTRODE AT THE CURRENT STEP POTENTIAL no 540 11-1.ao READ(2.240)PI.CI IF (P:.LE.NEH ad to 3:0 :30 READ(2.240)P2.C2 IF (P2.E0.HEP) on T0 545 IF (P2.LT.HEP) THEN M-(HEP-P1)/(P2-P1) a-N.(c2-c1» BCDL-61+! 00 TO :50 ELSE 91-92 C1-C2 co TO :30 END IF :40 CONTINUE 54: cx-cz 5:0 sen-c: sea SHECAP-MEAOSCDL CLOSE(UNIT-2) SMO-CHGVfiCHGCAP 210 IF (I.NE.I) CHGVDN-PHECAPGSTEPDN/CHGCAP CHG-CHGVDNOCHGCAP 620 VHE-VHEOCHG/PHECAP THERE-CHGI.OIO !HOH LONG HITH 100A CURRENT SRC P-EXP(((VHE-EREDIUNOF)I(R§TEMP)I PT3-I/(IOP) TIME-TRLXOI.OES PCNT-O MCNT-O SINJCT-O UPPER-HEP-(.SlDECAYI LOHER-HEP+(.SODECAY) C IF (INJFLG.EG.I) INJT-SORSOSCDL C C THIS DO LOOP MEASURES THE DECAY OF THE STEP AND INJECTS C SMALL AMOUNTS OF CHARGE OF THE SAME SIZE TO MAINTAIN THE C STEP AT A CONSTANT VALUE. THE NUMBER OF CHARGE INJECTIONS C MADE DETERMINES THE AMOUNT OF CHARGE REOUIRED BY THE ' C FARADAIC REACTION. C c- _ __ DO 630 J'Io TIHS IF (TOTLT.GE.TPLS) GO TO 640 IF (VHE.GT.LOHER) THEN !IF NOT IN HINDOH DECAYT-IO.E-6 GO TO 641 ELSE DIF-LOHER-VHE SMCHG-DIFGSHECAP DECAYT-(PIIDIOISMCHG/(PTI'PTSI)flfi2 !FLAG IF INJEX FREO TOO FAST ' IF (DECAYT LT.I.OE-6) STH-I END IF . ' IF (DECAYT.LT.I.0E-6) DECAYT-I.OE-6 64I PT2-SORT(DRDECAYTIPII CHG-PTIOPTEUPT3 VHE-VUE+CHG/SHECAP !THE VOLTAGE DECAYS SO TOTLT-TOTLT+DECAYT !HE KICK IT UP IF (TOTLT.GE.TPLSI GO TO 640 ' VHEIVHE-SMO/SHECAP !TO HHERE IT BELONGS IF (TOTLT.GE.TIME) PCNTIPCNT+I C HE START COUNTING THE 0 OF INJEX AFTER THE MEAS TIME HAS PASSED TOTLT-TOTLT+INJT 636 IF (VHE.GE.UPPER .AND. VHE.LE.LOHER) THEN GO TO 638 !IF IN HINDOH ELSEIF (VHE.LT.UPPER) THEN !IF ABOVE HINDON PT2-SORT(DDINJT/PI) CHG-PTIOPTQOPTS VHE-VHE+CHGISHECAP VHE-VHE+SMO/SHECAP MCNT-HCNT+1 TOTLT-TOTLT+INJT GO TO 636 ELSE !IF BELOH HINDOH PT2-SORT(DCINJTIPI) CHG-PTIDPT20PT3 211 VHE-VHE+CHGISHECAP VHE-VHE-SMO/SHECAP PCNTtPCNTOI TOTLT-TOTLT9INJT GO TO 636 END IF C CALCULATE CONCENTRATION GRADIENT HHILE ON PULSE 638 PTI-2*NOFGAREAOCONCOGRAD(TOTLT.D.RAD.TRLX) 630 CONTINUE 640 HEP-HEP-DELTE SINJCTUPCNT-MCNT !0 OF INJEX COUNTED ON STEP COG... OCSOIOCOCOOOGOOOO‘IO‘IOSOISOOOOSGOSSSOOSOOSOOOOO‘IGGOGOSOI’OQOS{O SSOOIOS‘ISOS DIFF-VHE-HEP CHGVUP-SHECAPODIFF/CHGCAP CHG-CHGVUPPCHGCAP PTI-2ONOFOAREAOCONC THERE-CHG/.GIG IN THIS SECTION. THE CURRENT VALUE OF CDL IS DETERMINED AND THE HORKING ELECTRODE CAPACITANCE AND OTHER RELATED NUMBERS ARE OBTAINED AND/OR CALCULATED FOR THE PULSE 000 OPEN(UNIT-2.NANE-CFILE.STATUE-'OLD') READ(2.235)NANE DO 580 12-1.40 READC2.240)P1.CI IF (P1.LE.HEP) 00 To 390 570 READ(2.240)P2.C2 IF (P2.EO.HEP) 00 To 585 IF (P2.LT.HEP) THEN M-IUEP-PI)/(P2-PI) I-H9(cz-CI) PCDL-CI+I 00 To 595 ELSE 91-92 et-ca 00 To 570 END IF 380 CONTINUE :85 et-cz 590 PCDL-CI $9: PHECAP-AREAGPCDL CLOSECUNIT-a) TOTLT-0.0 B20 VHE-VHE-CHG/SHECAP P'EXPII(VHE-EREDIUNIFI/(ROTEMP)I PT3-I/(14P) TIMSITPLSRI.OES PCNT-0 MCNT-0 UPPER-HEP-(.S§DECAYI LOHER-HEP+(.SDDECAY) IF (INJFLG.EO.I) INJT-SARSOPCDL 00000000 212 THIS DO LOOP MEASURES THE DECAY OF THE PULSE AND INJECTS SMALL AMOUNTS OF CHARGE OF THE SAME SIZE TO MAINTAIN THE PULSE AT A CONSTANT VALUE. THE NUMBER OF CHARGE INJECTIONS MADE DETERMINES THE AMOUNT OF CHARGE REOUIRED BY THE FARADAIC REACTION. SAI 836 SSS 830 SAG 6S2 6S4 650 DO 830 JI-I.TIMS IF (TOTLT.GE.TPLS) GO TO 340 IF (VHE.GT.LOHER) THEN DECAYT-IO.E-6 GO TO SCI ELSE DIF-LOHER-VHE SMCHG’DIF'PHECAP DECAYT-(PIlDI'ISMCHG/(PTI'PTSI)ffi2 IF (DECAYT.LT.I.OE-6I PTH-I END IF IF (DECAYT.LT.I.OE-6I DECAYT-I.OE-6I PT2-SORT(DODECAYT/PII CHG-PTIOPT2OPT3 VHE-VHE+CHG/PHECAP !MEANHHILE. THE VOLTAGE TOTLTOTOTLT+DECAYT !DECAYS IF (TOTLT.GE.TPLSI GO TO S40 VHE-VHE-SMO/PHECAP !TO HHERE IT BELONGS IF (TOTLT.GE.TIMEI PCNT-PCNT+I HE START COUNTING THE C OF INJEX AFTER THE MEAS TIME HAS PASSED TOTLTOTOTLT+INJT IF (VHE.GE.UPPER .AND. VHE.LE.LOHER) THEN GO TO SSS ELSEIF (VHE.LT.UPPER) THEN PT2-SORTIDUINJT/PI) CHG-PTIGPT2GPT3 VHE-VHE+CHG/PHECAP VHE-VHEOSMO/PHECAP MCNT-MCNTOI TOTLT-TOTLTOINJT GO TO SS6 ELSE PT2-SORTIDAINJT/PI) CHG-PTIAPT2GPT3 VHE-VHE+CHG/PHECAP VHE-VHE-SMO/PHECAP PCNT-PCNT+I TOTLT-TOTLT9INJT GO TO S36 END IF PTI-2ONOFOAREARCONCOGRAD(TOTLT.D.RAD.TPLS) CONTINUE PINJCT-PCNT-MCNT INJCNT-PINJCT-SINJCT CARRAY(I)-INJCNT PARRAY(I)-VHE ' HRITEI3.6S2)VHE.SINJCT FORMAT('RS'.EIS.S.I6) HRITE(3.6SA)VHE.PINJCT FORMATI'RP'.EIS.S.I6) HRITE(3.6SO)VHE.INJCNT FORMATI'RD'.EIS.S.I6I 213 HEP-HEP‘STEPDN TOTLT-0.0 C DROP FALLS. RETURN TO ORIGINAL BULK CONCENTRATION PTID2ONDFDAREA0CONC 660 CONTINUE HRITEIS.670) 670 FORMATI' ALL DONE 'I EPEAK-PKPOT(NTIMS.PARRAY.CARRAY) HRITEIS.6SG)EPEAK HRITE(3.6SOIEPEAK 6SO FORMATI' POTENTIAL AT PEAK CHARGE DIF IS: '.GIS.S) CLOSEIUNITISI HRITEIS.690) 690 FORMATI'SDO ANOTHER RUN? 'I READIS.20)RANS IF (RANS.EO.YESANS) GO TO I2S GO TO 999 c--- — .. -.. ........ C ' OPENING AND READING THE DEFAULT FILE c-.. 700 HRITE(S.7IOI 7IO FORMATI'SDEFAULT FILE NAME: ') READ(S.310)DFILE OPENIUNIT-2.NAME-DFILE.STATUS-'OLD') READI2.720)SYS 720 FORMAT(2OX.A20) READ(2.730)HE 730 FORMAT(2OX.A4I READ(2.730)REF READ(2.740)N 740 FORMAT(2OX.I2) READ(2.7SO)AREA 7SG FORMATI2OX.GIS.SI READI2.7SO)CONC READ(2.7SO)BCONC READI2.7SOITPLS READ(2.7SOIDROPT READI2.7SO)TIME READI2.7SO)EBASE READ(2.7SO)ERED READ(2.7SO)EFIN READ(2.7SO)DELTE READ(2.7SO)ESTEP READI2.7SO)RS CLOSE (UNIT-2) GO TO 225 999 CALL EXIT ------ o —— _‘ ‘ ------ THIS SECTION OF THE PROGRAM CONTAINS THE FUNCTIONS REOUIRED TO CALCULATE THE CONCENTRATION GRADIENT OF THE ANALYTE IN SOLUTION AT A DMEIOR SMDE). IT ALSO CALCULATES THE AMOUNT 00000 214 C RETURNED TO BULK CONCENTRATION LEVELS AFTER THE RELAXATION C TIHEI THE TIHE AT HHICH THE SYSTEH I8 RETURNED TO BASE POTL) C HAS ELAPSED. THE GRADIENT IN THE SYSTEM IS CALCULATED USING C A LOOP AND REQUIRING THE USE OF THE ERROR FUNCTION COMPLEMENT. C c ......... --_------______. A .......... FUNCTION GRADITOTLT.D.RAD.TIHEBI REAL DIST.D.TIHES.DNOH.TOTLT.FCNC.VALU.GRAD DIST-5.06-4 DNOH-zESORT(D9TOTLT) FCNc-DIST/DNOH IF (FCNC.GE.I.6) THEN VALu-CERFIFCNC) ELSE VALu-ERFCIFCNC) END IF GRAD-I.o-(RADAVALU/(RAD+DISTI) RETURN END C _ c c CALCULATION OF THE ERROR FUNCTION COHPLEHENT FOR THOSE C NUHDERB GREATER THAN 1.6 HHICH THE APPROXIMATIDN OF THE C FUNCTION ERF DOES NOT HORK FOR. FOR PROPER EXPAN8ION~ : OF THE ALGORITHH SEE CERF.FTN OR ERR.FTN. C _ _-—_-—_ _ — - FUNCTION CERFIFCNCT x-FCNC CERF - (2.!80RTI3.141:9)IUIEXPI-IOIXO92))/(QUXT)9 I (I- III:9(X992))+ 3!:49IXGOATT- IS/(SfiIXGOS))+ 2 IOS/(I6DIXOOI6IIT RETURN END c __ _ _ _ --— C C CALCULATION OF THE ERROR FUNCTION COMPLEMENT C c __ —_= _ _ - = ..... FUNCTION ERFCIFCNC) ERFc-I.o-ERF(FCNC) RETURN END c .. _-- .- C C CALCULATION OF THE ERROR FUNCTION. FOR PROPER EXPANSION C OF THE ALGORITHM SEE ERFC.FTN OR ERFCTST.FTN. C c- .--.. __ -—-——_ FUNCTION ERFIFCNC) ERF-G/SORTIS.IQIS9)9(FCNC -(FCNC903/3.0) +(FCNCGOS/I0.0) s -¢FCNc§c7/42.0) +(FCNC909/(2I6.0)T) RETURN END c___ -_-_ _ - ________ _ _ -------------- 215 CALCULATION OF THE E 1/2 VALUE INDICATED BY THE POLAROGRAN PRODUCED. 0000 830 FUNCTION PKPOTITIHESoPOTB.CHGS) REAL POTSIQOO).CHG8(QOO).CPK.EPK INTEGER CNT.TINES.CNTN CNT-O CPK-CHOSCI) EPK-POTS(I) DO 850 JEOIoTIHES IF (CHOS(J2+II.LT.CPK) THEN. CNT-CNTPI CNTH-NOD(CNT.4) IF (CNTH.E0.0) GO TO 860 ELSE CPKICHOBCJZ+I) EPK-POTS(J2+I) END IF CONTINUE ‘ CNT-O PKPOT-EPK RETURN END OOOOOOOOOOOOOOOOOOOOOO 216 Table B-5 THIS PROGRAM PRODUCES THE THEORETICAL CURVES FOR THE PERFORMANCE OF A SQUARE HAVE VOLTAMMETRIC EXPERIMENT FROM THE EQUATIONS GIVEN GY CHRISTIE. TURNER. AND OSTERYOUNG IN ANAL CHEM (49). I977. P.IS99. THE INITIAL SECTION OF THIS PROGRAM IS DEVOTED TO VARIABLE IIO. THE LARGEST LOOP ESSEN- TIALLY PERFORMS THE STEPS FOR ONE CYCLE IN THE INPUT CURVE. THE THO MIDDLE LOOPS PERFORM THE CALCULATIONS FOR THE FORNARD AND REVERSE PULSES AND THE CHARGES PRODUCED. THE SMALL SECTION FOLLOHING THE LARGE LOOP OUTPUTS THE POTENTIAL AT HHICH THE PEAK CHARGE DIFFERENCE OCCURS. THE VERY LAST SECTION BEFORE THE EXIT IS HHERE VALUES ARE INPUTTED FROM THE DEFAULT FILE. COMPLETED 2/26/86 HRITTEN BY-KATHLEEN A. FIX SPECIFICATION OF VARIABLES CHARACTEROI ANS !ANS TO CUES TO REPEAT! CHARACTEROIS CFILE !NAME OF CDL FILE! CHARACTERII DANS !ANS TO DEFAULT FILE OUES! CHARACTER'IS DFILE !NAME OF DEFAULT FILE! CHARACTER'IS DOFILE !NAME OF D O! FILE! CHARACTERPIS FILE !NAME OF OUTPUT FILE! CHARACTERR4S NAME !DUMMY VARIABLE! CHARACTER§4 REF !NAME OF REF ELECTRODE! CHARACTEROQO SYS !NAME OF ANALYTE SYS! CHARACTER'4 HE !NAME OF HORKING ELECTRODE! CHARACTER'I YESANS !YES ANSHER! INTEGER EMM ” !NUMBER OF ITERATIONS IN SUM! INTEGER JAY !G OF CYCLES IN EXPT SO FARIO—7)! INTEGER KAY !G OF CYCLES USED IN CALCULATION! INTEGER N !0 OF ELECTRONS TRANSFERRED! INTEGER NTIMS !0 OF TIMES THRU LG LOOP(PULSES)! REAL AREA !SURFACE AREA OF N. ELECTRODE! REAL B !INTERCEPT OF VARIOUS LINES! REAL BCONC !CONC OF BACKGROUND ELECTROLYTE! REAL BOTTOM !VALUE OF BOTTOM OF CONC. DIVIS! REAL BI !FIRST VALUE OF B.E.CONC! REAL B2 !SECOND VALUE OF B.E. CONC! REAL CDL !DBL LAYER CAP OF SOLN! REAL CHGCAP !SIZE OF CHGING CAP! REAL CONC !CONC OF ANALYTE! REAL CI !CONC FRAX FROM FORHARD PULSE! REAL C2 !CONC FRAX FROM REVERSE PULSE! REAL D !DIFN COEFFICIENT OF OX SPECIES! REAL DELTI !CURRENT DIF THEEN STEP/PULSE PAIR! REAL DI !FIRST VALUE OF DOX! REAL 02 !SECOND VALUE OF DOX! REAL EBASE !BASE POTENTIAL! REAL EFIN !FINAL POTENTIAL! REAL EK !POTL AT KTH CYCLE IN EXPT! REAL EPEAK !VALUE OF POTL AT PEAK CHARGE DIF! REAL EPS !VALUE OF EPSILON CALCULATED! REAL ERED !FORMAL REDUCTION POTENTIAL! REAL ESTEP !STEP HEIGHT! REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL REAL ESN ICHG IFOR IR ITOTF ITOTR M p PI POTL PTI PT2 PT3 PTSF PTSR PI P2 GI 02 R RHOI RHO2 RS SIGMA STEPDN STEPUP TAU T TIME TOP 217 !HALF PULSE SIZE FROM STEP HEIGHT! !THE FARADAY! !CHGING CURRENT FOR THE STEP! !CURRENT FROM FDRNARD PULSE! !CURRENT FRDN REVERSE PULSE! !IFAR + ICHO FDR F. PULSE! !IFAR + ICHO FOR R. PULSE! !SLOPE OF LINE FOR DOX 0R CDL! !FACTOR IN POLAROGRAM FORMULA! !VALUE OF THE CONSTANT PI! !POTL AT HHICH VALUES ARE REPORTED! !VALUE OF IST PART OF FDRNULA! ! - - 2ND - ~ ! E I I 3RD I I I 9 !FIRST VALUE OF POTL! !SECOND VALUE OF POTL! !THE GAS CONSTANT! !PT HHEN CURRENT TAKEN IN STEP! !PT HHEN CURRENT TAKEN IN PULSE! !UNCOMPENSATED SOLUTION RESISTANCE! !FRAX OF CYCLE ATTRIBUTED TO F. PULSE! !POTL DIF FOR STEP DOHN! !POTL DIF FOR STEP UP! !HIDTH OF ONE CYCLE OF EXPT! !THE TEMP OF THE SYSTEM! !TIME OF MEASUREMENT IN CYCLE! !VALUE OF TOP OF DIVISION FOR CONC! c-- c c USE OF DEFAULT DATA FILE c c _._._ YESANSI'Y' HRITE(3.ID) !o FORMAT('$USING DEFAULT DATA FILE?IY/NJ ,, READ(:.20!DANS 20 FORMATIAI) IF (DANS. ED. YESANS) GO TO 700 c--------------- c c INPUTTING OF VARIABLES c c ............................ __ URITE!5.30> so FORMAT('$NAME OF METAL AND ELECTROLYTEz') READ(3.40)SYS 4o FDRNATcaoAx! HRITE(3.30) so FORHATI'CHORKINO ELECTRODEz') READI5.60)HE so FORMATIQAII URITE(:.70! 7o FORMATI'DREFERENCE ELECTRODEz') 90 I00 IIO I20 I25 I30 I40 I50 I60 I67 I74 I80 I90 205 210 218 READ(5o60)REF HRITEIS.SO) FORMATI'SNUMBER OF ELECTRONS:') READI5a9OIN FORMATII2) HRITEISTIOOI FORMAT(' ALL THE FOLLOHING NUMBERS INPUTTED MUST INCLUDE S DECIMAL POINTS') HRITEISoIIOI FORMATI’SAREA OF ELECTRODEICIO¢2J:’) READCSoI2OIAREA FORMATIGIS.SI HRITE(S.ISOI FORMAT('SCONCENTRATION OF ANALYTEIM12’) READ(S. I20)CONC HRITEISo140) FORMATI’SCONC OF BACKGROUND ELECTROLYTEIMlz') READISoI2GIBCONC HRITECSoISOI FORMATI'SHIDTH OF ONE CYCLEIQS]:') READISTI2OITAU HRITEISoI60) FORMAT('$FRAX OF CYCLE FOR FOR. PULSE ’) READ(S.I20)SIGMA HRITEISo167) FORMATI'SFRAX OF CYCLE HHEN STEP SAMPLING OCCURSI’) READISTIZOIRHOI HRITE(S.I74) FORMATI’SFRAX OF CYCLE HHEN PULSE SAMPLING OCCURSz'! READISoI2OIRHO2 HRITE(5aISO) FORMATC'SBASE POTLImVlt') READCSTI2OIEBASE NRITE(5.190) FORMAT('$REDN POTLInVlz’) READ(5.I20IERED NRITE(5.200) FORMATI'SFINAL POTLIonz'! READIS.I20)EFIN NRITE($.205) FORMATC’SSOUARE HAVE AMPLITUDEI-Vlz’) READISoI2OIESN NRITEISo2IO) FORMATI’SSTEP SIZEIAVJ:') READ(S.I20)ESTEP 219 HRITEI3a220! 220 FORMATI'DUNCOMPENSATED RESISTANCEIOHMSJz') READI5.I20)RS 223 HRITEISa230! 230 FORMATI'SFILE CONTAINING DOX? ') READ(5.310)DOFILE OPENIUNIT-QoNAME-DOFILE:STATUS-’OLD') READ(4.235)NAME 235 FORMAT(45AI) DO 260 L-IoII READ(4.240)BI.DI 240 FORMATI2GIS.$I IF (BI.GE.BCONC) GO TO 270 250 READ(4.240)B2.D2 IF (B2.EQ.BCONC) GO TO 265 IF (B2.GT.BCONC) THEN M-(BCONC-BI)/(B2-BII B-MO(D2‘DII D-DI+B GO TO 280 ELSE BI-B2 DI-D2 GO TO 250 END IF 260 CONTINUE 26$ DI-D2 270 D-DI 280 CLOSE(UNIT-4I C“ -— ——— — — - C 2 CREATION OF DATA FILE c _=____=- ._ _ _ HRITE(5.300) 300 FORMAT(’$NAME OF OUTPUT FILE:') READ(5.310)FILE 310 FORMATIAIS) OPEN NRITE(3o424)RHO2 . FORMAT!’ FRAX OF CYCLE AT PULSE SAMPLE: ’.015.5) “RITE(30‘3°,D FORMATI' DIFFUSION COEF OF OXICA§921812 '.GI$.5) HRITECSp44OIEBASE FORMATI' BASE POTLIIVU: ’.GI$.$) EBASE-EBASE/IOOO NRITE(3o450)ERED FORMAT(' REDN POTLIQVJ: 'TGIS.5) ERED-ERED/IOOO HRITEI3o460IEFIN FORMATI’ FINAL POTLIQVJ: ’oGI5.5) EFIN-EFIN/IOOO NRITEIS.470)ESU FORMAT!’ SQUARE HAVE AMPLITUDEIMV): ’aGIS.3) ESH-ESN/IQOO NRITE(3.47SIESTEP FORMAT!’ STEP HEIGHTIMVJ: 'oGIS.5) ESTEP-ESTEP/IOOO NRITE(3.490!RS FORMAT(' UNCOMPENSATED RESISTANCEIOHMS]: ’.GI5.5) 0000000 221 CALCULATION OF PART ONE OF EQUATION oNUMBER OF TIMES THRU LOOP HHICH PRODUCES THE POLAROGRAM. AND PART THO OF THE EQUATION 500 510 c-- ‘--—- C C C C PTI-NRFOAREAGCONC PT2-SORTID/(TAUOPI)! NTIMS-IFIX((EBASE-EFINIIESTEP) HRITEISTSOOI FORMAT('$FILE CONTAINING CDL? ') READISTBIOICFILE HRITEISoSIOI FORMATC' POTLIVJ DELTA CURRENTIIJ') LOOP HHICH PRODUCES VOLTAMMOGRAM 520 DO 570 I-IoNTIMS JAY-I KAY-JAY EK-EBASE-(KAYGESTEPI-ESN EPS-EXP((NGFIIRGTIIOIERED-EK)) CI-I/(I+EPS) KAY-JAY-I EK-EBASE-(KAYPESTEP)+ESH EPS-EXP((NGF/(ROT))§(ERED-EK)) C2-I/(I+EPS) IF (KAY.LE.0.0) C2-I TOP-C2-CI BOTTOM-SORTIRHOI) PT3-TOP/BOTTOM DO 520 J-I.JAY KAY-J-I EK-EBASE-(KAVDESTEPI-ESH EPS-EXP((NRFI(RGT)IO(ERED-EK)I CI-I/(I+EPS) IF (KAY.LE.0.0) CI-I.0 KAY-J-Q EH-EDASE-(KAYPESTEPI+ESH EPS-EXPIINCFI(ROT))PIERED-EK)! C2OI/(1+EPS) IF IKAY.LE.0.0) C2-I TOP-C2-CI EMM-J-I SOTTOMISORT(JAY-EMM+RHOII PT3-PT34TOP/BOTTOM KAY-J-I EK-EBASE-(KAYPESTEPI+ESH EPS-EXP((NOF/(R§T))!(ERED-EK)I C2-I/(I+EPS) IF (KAY.LE.0.0) C2-I.O TOP-CI-C2 BOTTOM-SORT(JAY-EMM+RHOI-SIGMA) PT3-PT3+TOP/BOTTOM CONTINUE fl 521 522 526 528 $29 542 530 SSI 222 URITEI3.$2I)PT3 FORMAT('PT3F-':GI5.SI STEPDN-29(ESH9ESTEP) IF (I.EQ.I) STEPDNOESH*ESTEP IFOR-PTIlPT2RPT3 OPENCUNIT-2oNAME-CFILEaSTATUS-'OLD’! READI2.235)NAME READI2.240)PI:CI IF (PI.LE.EKI GO TO 528 READC2a240)P2aC2 IF (P2.EQ.EK) GO TO 526 IF (P2.LT.EKI THEN M-(EK-PI)/(P2-PI) D-HP(C2-CI) CDL-CI+B GO TO 329 ELSE PI-P2 CI-C2 GO TO 522 ENDIF CI-C2 CDL-CI CLOSEIUNIT-2) TIRE-TAUPRHOI ICHG-(STEPDN/RSIOIEXPI-TIME/(COLORS))) ITOTF-IFOR+ICHG ‘HRITE(3.S42IPOTL.ICHG FORMATI'CF'.2GIS.S) PT3-0.0 DO 530 JI-I-JAYOI KAY-JI'I EK-EBASE-(KAYRESTEPI-ESH EPS-EXP((NiF/(ROT))G(ERED-EK)) CI-I/(IOEPS) IF (KAY.LE.0.0) CI-I.0 KAY-JI-E EK'EBASE-(KAYGESTEP)+ESH EPS'EXPIINOFIIRRT)IO(ERED-EK)) C2-I/(I+EPS) IF (KAY.LE.0.0) C231 EMM-JI-I TOP-CE'CI BOTTOM-SQRT(JAY-EMM+RH02I PT3-PT3+TOPIBOTTOM KAY-JI-I EK-EBASE-(KAYOESTEP)¢ESH EPS-EXPIINlF/(RGT))OIERED-EKII CEII/(I*EPS) IF (KAY.LE.0.0) C2'I.O TOP-CI-C2 BOTTOM-SORT(JAY-EMM+RHO2-SIGMA) PT3IPT3+TOPIBOTTOM CONTINUE HRITE(3.531!PT3 FORMAT('PT3R-’.GIS.5) 223 STEPUP-IZPESH)+ESTEP IR-PTIFPTEGPTO OPEN(UNIT-2.NAME-CFILE.STATUSI'OLD') READ‘20233,NAHE READ(2.240)PI.CI IF (PI.LE.EK) GO TO 338 532 READ!2.240)P2.C2 IF (P2.EQ.EK) GO TO 536 IF (P2.LT.EK) THEN M-(EK-PI)/(P2-PI) B-HOIC2-CI) CDL-CI+D GO TO 539 ELSE PI-P2 CI-C2 GO TO 532 ENDIF 336 CI-C2 $38 CDL-CI $39 CLOSEIUNIT-z) TIME-TAUOIRHO2-SIGMA! ICHG-(STEPUP/RSIOIEXPI-TIME/(CDLORSII) ITOTR-IR-ICHG PT3-0.0 DELTI-ITOTF-ITOTR POTL-EBASE-ESH-((JAY-IIOESTEP) c HRITE(3.544IPOTL.ICHG S44 FORMAT('CR':2GI5.S) P HRITE!3.340)POTL.ITOTF 540 FORMAT(’RF'.2GIS.S) HRITE(3.550)POTL.ITOTR 530 FORMAT(’RR'.2GI5.5I HRITE(3:560IPOTL.DELTI 560 FORMAT('RGT'.2GI$.5) IF (I.EQ.II QI-DELTI Q2-DELTI IF (Q2.GT.QII THEN EPEAK-POTL ELSE QI-Q2 END IF $70 CONTINUE HRITE(3.SSOIEPEAK HRITEI5oSSOIEPEAK $80 FORMAT(' POTL AT PEAK CURRENT DIF IS: 'oGIS.5! CLOSEIUNIT-G) GO TO 999 C _ -_- _ _ ........ C C OPENING AND READING THE DEFAULT FILE C c = .=__ ---. ......................... 700 HRITE(5.7IO) 710 FORMAT(’$DEFAULT FILE NAME: ') READISTSIOIDFILE. OPENIUNIT-2.NAME-DFILETSTATUSI’OLD') READ!2.720)SYS 720 730 740 750 999 224 FORMAT!20X.A20! 'EAD‘20730,HE FORMAT(20X.A4) READ!2.730)REF READ(2.740)N FORMATI2OXoI2) READ<2o750DAREA FORMATI20!.GIS.S) READC2o7SOICONC READ(2.7SO)BCONC READ(2.7$0)TAU READ!2.750)SIGMA READ(2.750)RHOI READ(207SO’RH02 READ‘2075°)EBASE READ(2.7SO)ERED READ(2.750)EFIN READI2T7SOIESH READ¢2o7SOIESTEP READ(2.750)RS CLOSE (UNIT-2! GO TO 225 CALL EXIT END 225 Table B-6 UPO‘ eu f0_ 1e WoV‘ V0 sun‘ THIS PROGRAM SIMULATES SQUARE HAVE VOLTAMMETRY AS PERFORMED BY COULOSTATIC POLARIZATION. IT IS INTENDED TO SIMULATE THE OPERATION OF A CHARGE INJECTOR BEING BUILT BY NORMAN PENIX. A LARGE SECTION OF THIS PROGRAM IS DEVOTED TO VARIABLE IIO. THE LARGER OF THE THO LOOPS PERFORMS THE STEPS UP AND DOHN. CALCULATING THE NUMBER OF CHARGE INJECTIONS AND THE TIME REQUIRED. IT ALSO FINDS THE VARIATIONS OF THE DOUBLE LAYER CAPACITANCE THROUGHOUT THE SCAN AND CALCULATES THE EFFECTS OF THESE VARIATIONS. THE STARRED LINE REPRESENTS THE BOUNDARY BETHEEN THE CALCULATIONS FOR THE STEPS UP AND DOHN. THE LAST THIRD OF THE LARGER LOOP (HHICH FOLLOHS THE SECOND OF THE SMALLER LOOPS) OUTPUTS THE RESULTS TO THE OUTPUT DATA FILE. THE SMALLER. INSIDE LOOPS DO THE CALCULA- TIONS EOUATING IT TO THE INSTRUMENTAL APPLICATION OF SMALL CHARGE INJECTIONS TO MAINTAIN THE POTENTIAL OF THE PULSE OR STEP. THE LAST SECTION CONTAINS THE FUNCTIONS REQUIRED TO CALCULATE THE CONCENTRATION PROFILE. THE VERY LAST FUNCTION IS USED TO CALCULATE THE POTENTIAL OF THE SOLUTION AT HHICH THE PEAK CHARGE DIFFERENCE OCCURS. THE THEORETICAL EQUATIONS USED IN THIS PROGRAM ARE FROM CHRISTIE: TURNER. AND OSTERYOUNG IN ANAL. CHEM. (49). I977. P. I999. COMPLETED 4121/87 HRITTEN BY KATHLEEN A. FIX I SPECIFICATION OF VARIABLES 0000000000000000000000000000000 REAL X.T.Z CHARACTEROI ANS CHARACTEROI DANS CHARACTEROI IANS CHARACTEROIS CFILE CHARACTERPIS DFILE CHARACTEROIS DOFILE CHARACTERIIS FILE CHARACTERO4S NAME CHARACTEROI RANS CHARACTERO4 REF CHARACTEROQO SYS CHARACTEROA HE CHARACTEROI YESANS INTEGER CHGCK INTEGER EMM INTEGER INJCNT INTEGER INJFLG INTEGER INTEGER INTEGER INTEGER INTEGER INTEGER INTEGER INTEGER INTEGER INTEGER INTEGER !ANS TO QUES TO REPEAT! !ANS TO DEFAULT FILE QUES! !ANS TO INJEX TIME QUES! !NAME OF CDL FILE! !NAME OF DEFAULT FILE! !NAME OF D OX FILE! !NAME OF OUTPUT FILE! !DUMMY VARIABLE! !ANS TO QUES FOR ANOTHER RUN! !NAME OF REF ELECTRODE! !NAME OF ANALYTE SYS! !NAME OF HORKING ELECTRODE! !YES ANSHER! !TELLS IF I IS ANODIC OR CATH! !NUMBER IN SUMMATION SECTION! !0 OF DIFFERENCED SM CHG INJEX! !-0 IF INJEX TIME IS CONSTANT! !0 OF CYCLES IN EXPT SO FAR(0-?)! !0 OF CYCLES USED IN CALC! !0 OF NEG INJEX APPLIED! !0 OF ELECTRONS TRANSFERRED! !0 OF TIMES THRU GRADIENT LOOP! !0 OF TIMES THRU LG LOOP(PULSES)! !R OF POS INJEX APPLIED! !0 OF TIMES THRU SM LOOPIINJCNT)! !R OF TIMES EXCEED MAX FREQ! !R OF TIMES EXCEED MAX FREO! !0 OF SM CHG INJEX ON PULSE! INTEGER SINJCT REALOS REALPS REALPS REALPS REALPS REALOS REALPS REALPS REALPS REALPS REALPS REALPS REALOS REALOS REALPS REALPS REALOS REALPS REALOS REALPS REALRS REALOS REALPS REALGS REALIS REALOS REALPO REALOS REALRS REALPS REALPS REALPS REALPS REALPS REALPS REALOS REALPS REALPS REALPS REALPS REALOS REALPS REALPS REALPS REALPS REALPS REALPS REALPS REALGS REALOB REALOS REALPS REALPS REALPS REALPS REALGS REALPS REALPS REALPS AREA 3 BCONC BOTTOM a! 32 CDL CHG CHGCAP cuov CHGVDN CHGVUP CONC CPK CI C2 D DECAY DECAYT DELTAV DELTD DELTD DENOM DIF DIFF- DIST DISTNC DNOM DROPT DI D2 EBASE EFIN EK EPEAK EPK EPS ERED ESTER ESH F FCNC INJT LDUER n p PI PLSCHG PTI PT2 PT3 PHECAP PI P2 OF OR 01, 02 R 226 !R OF SM CHG INJEX ON STEP! !SURFACE AREA OF H. ELECTRODE! !INTERCEPT OF VARIOUS LINES! !CONC OF BACKGROUND ELECTROLYTE! !VALUE OF CONC DENOMINATOR! !FIRST VALUE OF B.E.CONC! !SECOND VALUE OF B.E. CONC! !VALUE OF DBL LAYER CAP! !AMT OF CHG DUMPED INTO CELL! !SIZE OF CHGING CAP! !VOLTAGE APPLIED TO CHGING CAP! !VOLTAGE REQD TO MAKE STEP DOHN! !VOLTAGE REQD TO MAKE POTL PULSE! !CONC OF ANALYTE! !VALUE OF PEAK CHG! !FIRST VALUE OF CDL! !SECOND VALUE OF CDL! !DIFN COEFFICIENT OF OX SPECIES! !DECAY HINDOH ON PULSES! !TIME REQD TO DECAY X nV ON PULSE! !AVG DIST OF RETURN OF ANALYTE ION! !DISTANCE INTERVAL AROUND HE! !CHARGE DIF THEEN STEP/PULSE PAIR! !VALUE OF INTEGRATED EQN FOR CALC! !DIF THEEN VHE AND LOHER THRESHOLD! !DIFF THEEN HEP AND VHE! !DISTANCE FROM SURFACE OF HE! !LIFE LENGTH OF MERCURY DROP! !FIRST VALUE OF DOX! !SECOND VALUE OF DOX! !BASE POTENTIAL! !FINAL POTENTIAL! !POTL AT KTH CYCLE IN EXPT! !VALUE OF POTL AT PEAK CHARGE DIF! I I I I I I IO U I !VALUE OF EPSILON CALCULATED! !FORMAL REDUCTION POTENTIAL! !STEP HEIGHT! !SQUARE HAVE POTENTIAL! !THE FARADAY! !TIME REQUIRED FOR I CHG INJEX! !LOHER THRESHOLD OF VOLTAGE HINDOH! !SLOPE OF LINE FOR DOX OR CDL! !FACTOR IN POLAROGRAM FORMULA! !VALUE OF THE CONSTANT PI! !FAR CHARGE FROM PULSE! !VALUE OF IST PART OF FORMULA! I I N 2ND I M It I 2 I I up ~ I I N ! !CAPACITANCE OF HE AT PLS POTL! !FIRST VALUE OF POTL! !SECOND VALUE OF POTL! !CHARGE RESULT OF FOR PULSE! !CHARGE RESULT OF REV PULSE! !THE GAS CONSTANT! REALPS REALPS REALPS REALOS REALOS REALOS REALOS REALOS REALPS REALOS REALOS REALPS REALOS REALOS REALOS REALGS REALOS REALOS REALPS REALPS REALPS REAL-8 RAD RS SIGMA SMCHG SMQ STEPDN STEPUP STPCHG SHECAP TAU TEMP THERE TIME TIMES TOP TOTLT TPLS TRLX UPPER VALU VHE HEP REAL CARRAYI200) REAL PARRAY(200) REAL VHEPIIOOI REAL VHES(I00! 227 !RADIUS OF THE HORKING ELECTRODE! !SOLUTION RESISTANCE! !FRAX OF CYCLE FOR FOR PULSE! !SMALLEST AMT OF CHG CAN GO TO CELL! !SMALLEST AMT OF CHG CAN BE MEASURED! !DIF THEEN POTL PULSE AND STEP! !DIF THEEN POTL STEP AND PULSE! !FARADAIC CHARGE FROM STEP! !CAPACITANCE OF HE AT STEP POTL! !HIDTH OF ONE CYCLE OF EXPERIMENT! !THE TEMP OF THE SYSTEM! !TIME TO MAKE STEP H/IOMA CURRENT SRC! !TIME IN PLS HHEN MEAS IS STARTED! !VALUE OF TOP OF CONC DIVISION! !SUM OF INJEX & TURNAROUND TIMES! !LENGTH OF POTL STEP! !DROPT - TPLSIRELAXATION TIME)! !UPPER THRESHOLD OF VOLTAGE HINDOH! !POTL ON THE HORKING ELECTRODE! !HORKING ELECTRODE POTENTIAL! !ARRAY TO HOLD VALUES OF CHARGE! !ARRAY TO HOLD VALUES OF POTL! !ARRAY TO HOLD PULSE POTLS! !ARRAY TO HOLD STEP POTLS! c---._ C C USE OF DEFAULT DATA FILE C c--' -- 0 w _ -------------- INJFLG-O YESANS-‘Y' HRITEISoIGI I0 FORMATI'CUSING DEFAULT DATA FILE?[Y/NJ ’) READ(ST20)DANS 20 FORMATIAII IF (DANS.EQ.YESANSI GO TO 700 c _ _. _ =_ __ -_--_-----_-_ C C INPUTTING OF VARIABLES C c _ _ _ HRITEISoSO! SO FORMAT('$NAME OF METAL AND ELECTROLYTE:') READ(S.40)SYS 40 FORMATIA20) HRITE(5o30) 30 FORMATI'DHORKING ELECTRODEz') READ($.60)HE 60 FORMATIA4) HRITEIST70) 70 FORMAT('$REFERENCE ELECTRODEt’) READ(5060’REF HRITE!3.SO) SO FORMATI’CNUMBER OF ELECTRONSz') 90 I00 IIO I20 I25 130 I40 ISO 160 I70 I80 I90 200 205 2I0 220 228 READ(5o90)N FORMAT(I2) HRITEISoIOOI FORMAT(' ALL THE FOLLOHING NUMBERS INPUTTED MUST INCLUDE 3 DECIMAL POINTS') HRITEISTIIOI FORMAT(’$AREA OF ELECTRODECCNGO2JI') READISoIROIAREA FORMAT(GIS.S) HRITE(S-ISO) FORMATI'DCONCENTRATION OF ANALYTEIMJr') READISTI2OICONC HRITEISoI40) FORMATI‘SCONC OF BACKGROUND ELECTROLYTEtMlz’) READ(5.I20IBCONC HRITEIBaISOI FORMAT('$HIDTH OF ONE CYCLEIaSlz') READ‘50‘2°,TAU HRITEISoIbOI ' FORMATI'GFRAX OF CYCLE FOR FOR PULSEz') READ(S.I20!SIGMA HRITECSoI70) FORMATI'CTIME OF MEASUREMENTIaSlz') READISTI2OITIME HRITE(5.ISO) FORMATI'SBASE POTLthlz‘) READ‘SoI2OIEBASE HRITE(S.I90) FORMATI'SREDN POTLInVlz') READISoISGIERED HRITE(5.200) FORMATI'SFINAL POTLImVlz’) READ(5.I20)EFIN HRITE(5.205) FORMATI'DSQUARE HAVE POTLInVlz') READISoI2OIESH HRITEIST2IOI FORMAT('$STEP SIZEInVJI’) READ(S.I20IESTEP HRITE(5.220I FORMATI'SSOLUTION RESISTANCEIGhnslz’) READISTI2OIRS HRITE($:230) FORMATI’SFILE CONTAINING DOX? ') READ(S.3IO)DOFILE 235 240 230 260 263 270 290 293 296 490 49: c--- O --- C C C c-.. 229 OPENCUNIT-4.NAME-DOFILE.STATUS-'OLD') READI4.23$)NAME FORMAT(4SAI) DO 260 L-IoII READ!4.240)BI.DI FORMATI2GIS.SI IF (BI.GE.BCONC) GO TO 270 READ(4.240)B2.D2 IF (B2.EQ.BCONC) GO TO 265 IF (B2.GT.BCONC) THEN M'(BCONC-BI)I(B2-BI) B-MRIDR-DI) D-DI+D GO TO 280 ELSE 01-32 01-02 GO TO 230 END IF CONTINUE DI-D2 D-DI CLOSE(UNIT-4) HRITE($.290) FORMATI'OSIZE OF CHGING CAPIUFlz’) READ(5oI20)CHGCAP HRITE(5.293) FORMAT('SVOLTAGE ON CHGING CAPIVlz') READ(S.I20)CHGV HRITEI5o296) FORMATI’SSIIE OF VOLTAGE DECAY HINDOHIMVJ: ’) READ!S.I20)DECAY HRITEISo490) FORMATI'SHAVE INJEX TIME A CONSTANT VALUE?IY/NJ ') READIS.20)IANS IF (IANS.EQ.YESANSI THEN . HRITEISo49SI FORMAT('SVALUE OF INJEX TIMEIUS]: ') READISTIROIINJT ELSE INJFLG-I END IF SPECIFICATION OF CONSTANTS F-9b4S4.6 !IN COUL/MOLE! PI-3.I4IS9 R-S.3I44I !IN J/MOLE DEGREE K! TEMP-29S.IS !IN DEGREES K! PTH‘O STH-G CONC‘CONC/IOOO TAU-TAU/IOOO 230 TIME-TIME/IOOO EBASE-EBASE/IOOO ERED-ERED/IOOO EFIN-EFIN/IOOO ESH-ESH/IOOO ESTER-ESTEP/Iooo CHGCAP-CHGCAP/1.0E6 DECAY-DECAYIIOOO 29: URITEI:.320! 320 FORMATI' CHARGE PULSED SQUARE HAVE VOLTAMMETRY') c------- — ““ A __ "‘ __ C C CREATION OF DATA FILE c C: ____ ........................... URITE(s.aoo! 300 FORMAT(’SNAME OF OUTPUT FILEz’) READI:.310!FILE an FORMATIAIS) OPEN(UNIT-3.NAME-FILE.TYPE-'NEN'.CARRIAGECONTROL-’LIST'. s FORM-'FORNATTED’) c . _ —— _ _ --- c c HRITING VARIABLE VALUES TO DATA FILE C c-- '.--- — v ---=—— —— HRITE(3.S20) URITE(a.aao)svs aao FORMAT!’ NAME OF METAL AND ELECTROLYTE: ’.2OAI) URITEIO.340!NE 340 FORMATC' HORKING ELECTRODE: '.4A1) URITEca.aso!REF 350 FORMAT(' REFERENCE ELECTRODE: '.4AI) HRITE(3.360)N 350 FORMAT(' NUMBER OF ELECTRONS: '.I2) URITEI3.370!AREA 370 FORMATI’ AREA OF ELECTRODEICARG2J: '.oxs.s! HRITE(3.SSO)CONC aao FORMAT(' CONCENTRATION OF ANALYTEIINT: '.GI$.3) URITEI3.390!DCONC 390 FORMAT(’ CONC OF BGRND ELECTROLYTECMJ: '.GI$.S) HRITE¢3.400)TAU aoo FORMAT!’ HIDTH OF ONE CYCLEtS): '.CI:.3! URITE¢3.4Io!annA 4:0 FORMATI’ FRAX OF CYCLE FOR F PULSE:'.GIS.5) HRITE(3.420)TIHE 420 FORMAT(' TIME OF NEASURENENTIS); '.GI5.5) HRITEIS.430)D 430 FORMATI' DIFFUSION COEF OF OXICQOR2/SJ: ’.GI5.S) «o 450 450 470 475 480 503 $05 8 231 HRITEI3o44OIEBASE FORMAT!’ BASE POTLIVJ: ’oGI$.3) HRITE(3.450IERED FORMATI' REDN POTLCVJ: '0015.5) HRITEI3.460)EFIN FORMAT(' FINAL POTLIVJ: '.GI$.5) HRITEIST47OIESH FORMAT(' SQUARE HAVE POTENTIALIVJ: 'oGI5.5) HRITE(3.475)ESTEP FORMATI' STEP HEIGHTIV]; '.GIS.5) HRITE(3o4SO)RS FORMATI' SOLUTION RESISTANCEIORQIJ: 'oGI5.5) HRITE(3.500)CHGCAP FORMATI' CHGING CAPACITOR SIZEEFJ: 'oGIS.S) HRITE(3.503)CHGV FORMATI’ VOLTAGE ON CHGING CAPCVJ: ’oGIS.5) HRITEISTSOSDDECAY FORMAT!’ VOLTAGE DECAY ON PULSESIV]: 'oG15.5) IF (INJFLG.EQ.I) GO TO 6I0 HRITE(3o600IINJT FORMATC'CINJEX TIMEISJ: ’oGIS.SI CALCULATION OF PART ONE OF EQUATION oNUMBER OF TIMES THRU LOOP HHICH PRODUCES THE VOLTAMMOGRAM 00000000 on O 510 S20 KAY-I PT1-2RNRFRAREARCONC NTIns-IIDNNTI(EBASE-EFINIIESTEP) HRITE(STSIOI FORMATI' POTLIVJ 0 OF COUNTS') TOTLT-0.0 HEP-EBASE VHE-EBASE STEPUP-(ESTEP+ESH)O2 STEPDN-(2PESH)*ESTEP TPLS-SIGMAOTAU TRLX-TAU-TPLS HRITEISTS20) FORMAT('SFILE CONTAINING CDL7‘) READ(5.310)CFILE OPEN(UNIT.2ONA"E‘CFILEOSTATUS.'DLD') READIZTRSSINAME DO 524 II-Io40 READI2T24OIPITCI 1232 IF (PI.LE.HEPI GO TO 528 S22 READI2.240)P2.C2 IF (P2.EQ.HEPI GO TO 325 IF (P2.LT.HEP) THEN M-(HEP-PI)I(P2-PII B-MOIC2-CI) CDL-CI*B GO TO 529 ELSE PI-P2 CI-CR GO TO 322 END IF S24 CONTINUE 326 CI-C2 328 CDL-CI 529 SHECAP-AREARCDL CLOSE(UNIT-2) CHGVUP-SHECAP!(ESTEP+ESHI[CHGCAP CHG-CHGVUPPCHGCAP C LET'S CHARGE THE CAPACITORS. DUMP THE CHARGE. AND STEP UP THERE-CHG/.0I0 !TIME TO STEP HIIOnA CURRENT SRC! VHE-VHE-(CHG/SHECAPI VHEP(I)-VHE RAD-SQRT(AREA/I4RPII) HEP-EBASE-(KAYOESTEPI-ESH c ___ .. —- - — —- —-_----_------— C C LOOP HHICH PRODUCES VOLTAMMOGRAM C c _ DO 660 I-IoNTIMS SMQ'CHGVOCHGCAP JAY-I OPEN!UNIT-2.NAME-CFILE.STATUS-'OLD') READI2.2SS!NAME DO 500 ‘A-SO4O READ(2.240)PI.CI IF (PI.LE.HEP) GO TO 550 530 READ(2.240)P2.C2 IF IP2.EQ.HEP) GO TO 545 IF (P2.LT.HEP) THEN M-(HEP-PIIIIP2-PI) B-MOICR-CI) CDL'CI+B GO TO 560 ELSE . PI-P2 CI-C2 GO TO 530 END IF $40 CONTINUE S43 CI-C2 330 CDL-CI 360 $65 233 PHECAP-AREAOCDL CLOSE(UNIT-2) KAY-JAY EPS-EXP((N9FIIROTEMP))O(ERED-VHEP(JAY)I) CI-I/(I+EPS! KAY-JAY-I IF (KAY.LE.0.0) THEN C2-I.0 GO TO 363 ELSE EPS-EXP(((N.F!/(ROTEMP))OIERED-VHESCJAY-I))) C2-I/(I+EPS) END IF TOP-C2-CI BOTTOM-SQRT(SIGMA) PT3-TOP/BOTTOM VHESIIIOEBASE SQUARE HAVE SUMMATION STEP FOR THE CALCULATION OF THE CONC ENTRATION FACTOR 835 845 835 S95 — v DO 895 K CONTINUE I-I.JAY-I HMM-KI-I IF (MMM.LE.O) THEN CI-I.O GO TO SSS ELSE EFS-EXPIINRF/(ROTEMP))O(ERED-VHEP(MMM))) END IF CI-II(I+EPS! HRH-RI-z IF (NRH.LE.O! THEN C2-I GO TO 949 ELSE EPs-EXPIINRF/(RGTEMP))RIERED-VHES(MNM)I) END IF CS-I/(I+EPS! TOP-C2-CI EMM-KI-I DOTTOH-SORTIJAV-EHH+SIONA! PT3-PTS+TOP/DOTTOR MMM-KI-I IF mm. LE. 0! THEN C2-I GO TO SSS ELSE EPSIEXPIINRF/(ROTEMP))§(ERED-VHES(NMM))) END IF ca-I/(I+EPS! TOP-CI-C2 DOTTOH-SORT(FLOATIUAv-ENN)T PTO-PT3+TOP/DOTTON IF (PT3.EQ.0.0! PT3-I.0E-6 PCNT-0 2234 MCNT‘Q TOTLT-0.0 TIMS-TPLSDI.OES IF (INJFLG.EQ.I) INJT-SDRSPPCDL UPPER-HEP-(.5'DECAY) LOHER-HEP+(.S*DECAYI HRITE!3.3)PT3 THIS DO LOOP MEASURES THE DECAY OF THE PULSE AND INJECTS SMALL AMOUNTS OF CHARGE OF THE SAME SIZE TO MAINTAIN THE STEP AT A CONSTANT VALUE. THE NUMBER OF CHARGE INJECTIONS MADE DETERMINES THE AMOUNT OF CHARGE REQUIRED BY THE FARADAIC REACTION. 0000000000 DO 630 J-I.TIMS IF ITOTLT.GE.TPLS! GO TO 540 IF (VHE.GT.LOHER) THEN DECAYT-I.E-6 GO TO 641 ELSE DIF-LOHER-VHE SMCHG-DIFRPHECAP DECAYT-(PI/D)R(SMCHG/(PTIOPTS))fii2 IF (DECAYT.LT.I.OE-6) PTH-I END IF HRITE(S.S)SMCHG URITEEaASE GO TO 775 9:2 HRITE(S.9$4) 9S4 FORMAT(’SFINAL POTENTIALIVJz’) READ($.I20)EFIN GO TO 775 ' 956 HRITE($.9SS) 953 FORMAT('$SOUARE HAVE POTLthJ:') READ(5.I20)ESH ESH-ESH/IOOO . GO TO 775 960 HRITE($.962) 962 FORMAT('SSTEP HEIGHTthJ:’) READ(5.120)ESTEP ESTEP-ESTEP/Iooo GO TO 775 964 HRITE(5.966) 966 FORNATI'CSOLN RESISTANCEtohmsJ:') READ(5.I20)RS GO TO 773 968 HRITEIS.970) 97o FORMAT(’$CHGING CAPACITOREUFJ:') READ(5.I20)CHGCAP CHGCAP-CHGCAP/I.0E6 GO TO 775 969 HRITE(5.97I) 97! FORMAT(’4VOLTAGE ON CHGING CAPCVJ ’) READ(5.I20)CHGV GO TO 775 241 972 HRITE(S.974) 974 FORMATI'SVOLTAGE DECAYthlz') READ(0.I20IDECAY DECAY-DECAY/IOOO GO TO 773 980 HRITE(5.983! 98$ FORMATI'SREADY TO RUN AGAIN7IY/NJ ') READ(S.765)ANS IF (ANS.EQ.YESANS) GO TO 293 990 HRITE(5.99$) 99S FORMATI' END OF PROGRAM') GO TO 999 c-- —— -- ___ .................. C C OPENING AND READING THE DEFAULT FILE C c-- _- -_-_---_--------- 700 HRITEI5.710) 710 FORMAT('$DEFAULT FILE NAME: ‘) READ(0.310)DFILE OPEN(UNIT-2.NAME-DFILEoSTATUSI'OLD') READ(2.720)SYS 720 FORMAT(20X.A20) READ(2.730)HE 730 FORMAT(20X.A4) READI2.730)REF READ(2.740)N .740 FORMAT(20X.I2I READ(2.7SOIAREA 750 FORMATI20X.GIS.S) READ(2.7SO)CONC READI2.TSOIDCONC READ(2.750)TAU READ¢2.750!SIGNA READI2.7SD!TINE READ¢2.750!EDASE READI2.750!ERED READI2.7:O!EFIN READI2.7SOIESN READ!2.730!ESTEP READ(2.7SO)RS CLOSE (UNIT-2) GO TO 225 999 CALL EXIT END THIS SECTION OF THE PROGRAM CONTAINS THE FUNCTIONS REQUIRED TO CALCULATE THE CONC GRADIENT OF THE ANALYTE IN SOLN AT AN SMDE. IT ALSO CALCS THE AMT RETURNED TO BULK CONC LEVELS AFTER THE RELAXATION TIME HAS ELAPSED. 00000000 FUNCTION GRADITOTLT.D.RAD.TIMES) REALP8 DIST.D.TIMES.DNOM.TOTLT.FCNC.VALU.GRAD DIST-5.0E-4 DNOM-2GSQRT(DPTOTLT) 242 FCNc-(DISTIIDNOM IF (FCNC.GT.I.6) THEN VALU'CERF(FCNC) ELSE VALU-ERFC(FCNC) END IF GRAD-I.O-IRAD'VALU/(RAD+DIST)) RETURN END 0(50M1 CALC OF THE ERROR FCN COMPLEMENT FOR LARGER VALUES c__ __ FUNCTION CERFIFCNC) X-FCNC . CERF - (2.]SQRTI3.I4I$9II¢IEXP(-I*(X¢R2))/(2GX))R I (I- I/(2PIXGO2!)+ 3/(4OIXOO4II- I5/(SPIXRC8))+ 2 I05/(I6OIXGOI6III RETURN END C C C CALC OF ERROR FCN COMPLEMENT c---------------------__ - ---- FUNCTION ERFCIFCNC) ERFC-I.0-ERF(FCNC) RETURN END (50¢5(50 065(30t5 FUNCTION ERF(FCNC) ERF-2/SQRT(3.I4I6) l(FCNC ~(FCNCGO3/3I +(FCNCCPS/(SOFLOAT(IFACTRI2I))) S -(FCNCPG7/(7§FLOAT(IFACTR(3)I!) +(FCNCPP9/(9OFLOATIIFACTRI4)II)! RETURN END CALC OF FACTORIALS REQD FUNCTION IFACTRIJS) IFACTR-I DO 2 “3.10” IFACTR-IFACTROK3 CONTINUE RETURN END