Three-dimensional variable amplitude pseudo-derivative normal pulse polarography

J. Electroanal. Chem., 145 (1983) 21-34 Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands

21

T H R E E - D I M E N S I O N A L VARIABLE A M P L I T U D E PSEUDO-DERIVATIVE NORMAL PULSE POLAROGRAPHY THEORY, I N S T R U M E N T A T I O N AND ANALYTICAL APPLICATIONS

J.E. ANDERSON and A.M. BOND

Division of Chemical and Physical Sciences, Deakin University, Waurn Ponds, Victoria 3217 (Australia) (Received 1st April 1982; in revised form 30th August 1982)

ABSTRACT Using microprocessor based instrumentation, it is shown that the technique of variable amplitude pseudo-derivative normal pulse (pdnp) polarography can be extended to three dimensions with the measurement of current-time profiles on each pulse. Theory is presented for electrode processes with slow electron transfer and the ability to obtain variable amplitude, variable time data in a higly sensitive pulse mode from a single polarogram is considered to be most advantageous. The analytical application of this three-dimensional technique is experimentally examined in this work as an indicator of kinetic complications which lead to unrecognized forms of interference in the determination of unknown samples when standard analytical procedures are used. The combination of higher sensitivity, simpler theory and instrumentation, and greater versatility than differential pulse polarography should make the technique attractive in routine analytical chemistry.

INTRODUCTION

Modern polarographic techniques such as differential pulse polarography or alternating current polarography are now being more frequently used in analytical chemistry in preference to conventional dc polarography [1]. However, these transient techniques, whilst being considerably more sensitive than dc polarography, are more prone to subtle forms of interference which may not be readily recognized if the usual analytical procedures are followed. Concomitant with the use of these transient techniques is the ever increasing use of computers. In automated instruments the peak height and peak position of species to be determined are measured with the aid of the computer and referred to calibration curves obtained from standard solutions. The problem with this approach with transient polarographic techniques is that peak heights are often obtained at potentials where currents are controlled by kinetic phenomena. Interferences in the unknown sample may have in fact decreased the peak height by altering the rate of electron transfer or rate of a chemical step or increased the peak height by catalysis or adsorption related phenomena. This change in peak height can occur without any readily recognized shift in peak position or wave shape. In 0022-0728/83/0000-0000/$03.00

© 1983 Elsevier Sequoia S.A.

22 contrast, dc polarographic limiting currents may remain diffusion-controlled, even if the rate of electron transfer is altered because currents are being measured in a potential region uninfluenced by electrode kinetics. The difficulty with most forms of polarographic instrumentation in detecting interference is that all measurements are obtained from only one time domain. Computerized systems need in fact to be designed with multi-time domain or other capabilities to detect interference [2-5]. The difficulty with Fast Fourier Transform, pattern recognition techniques, etc., is that they are generally too complex to apply in the analytical laboratory for routine analysis. In a recent paper [6] we described the use of variable amplitude pseudo-derivative polarography. Using microprocessor based instrumentation the difference between data obtained at selected intervals from a sigmoidal shaped dc or normal pulse polarogram is plotted as a function of potential [6,7]. The result is that variable amplitude response can be obtained from a single experiment. When the normal pulse waveform is employed, the variable amplitude response is closely related to a series of single amplitude differential pulse polarograms obtained. Terms prior to application of the pulse are of course different, but for the reversible electrode process the two techniques converge and are identical. Whilst access to variable amplitude data is convenient, variable time domain data is likely to be more sensitive for detecting kinetic phenomenon and associated subtle losses of analytical interference [7,8]. In 1960, Reinmuth [9] proposed the use of three-dimensional surfaces (current-time-potential) to show the relationships among various time-dependent voltammetric techniques. These surfaces were obtained theoretically and appear to have been only used for educational purposes. Furthermore, they do not appear to be unique surfaces so that their value is limited for practical applications and, at that time, the experimental collection of such data would have been extremely difficult and time consuming and the data analysis difficult. However, now that computerized instrumentation is widely available, experimental difficulties are less of a problem and three-dimensional electrochemistry can be implemented in a practical format. Three-dimensional techniques have of course already proved invaluable in other areas of chemistry and the area of electroanalytical chemistry should prove to be no exception in this context. In this paper, we report on the collection of normal pulse polarographic data from several time domains in a single experiment. This data may be represented as the current-potential-time surfaces proposed by Reinmuth [9]. Likewise the variable amplitude pseudo-derivative normal pulse (pdnp) polarograms [6] may be generated from the data to produce additional surfaces, pdnp techniques obviously produce polarograrns retaining the attractive feature of differential pulse polarography. However, access to variable amplitude facilities and the absence of dc terms (theory is simpler) recommend this as the superior approach. The information obtained appears useful in detecting difference in the electron transfer rate of a given species in the standard and unknown samples which may affect the analytical response because the time and potential dependancies may be examined very

23

efficiently from a single experiment. The data appears useful in detecting other more complex use of multi-time domain (three-dimensional) electron transfer rate constants is also discussed

from different time domains also types of interferences. The possible voltammetry in the evaluation of in this paper.

EXPERIMENTAL

Instrumentation The microprocessor-based waveform generator and data acquisition system used has been described previously [6]. The software used in this work is described in the text and is available on request. The home-made potentiostat has also been described [10]. Unless otherwise stated the experiments were performed using a Static Mercury Drop Electrode (SMDE) from E.G. & G. Princeton Applied Research. The SMDE was used with a Pt auxiliary electrode and a Ag/AgC1 (saturated KC1) reference electrode. The theoretical work was performed on a DEC system 20 computer and all programs were written in FORTRAN. These programs are also available on request.

Reagents and procedures Analytical reagent grade chemicals were used throughout. All solutions were degassed with high purity nitrogen prior to the experiments. Microliter quantities of stock solutions were added to the test solutions to prevent dilution effects during the generation of calibration curves and standard addition curves. A sample volume of 10 ml was used throughout. All experiments were performed at (21 _ 1)°C. RESULTS A N D DISCUSSION

Figure 1 is a three dimensional pseudo-derivative pulse polarogram for reduction of 2 x 1 0 - 4 M Cd in 1 M KC1. All of this data was obtained from a single experiment. The variable amplitude responses are readily derived from the raw data (see subsequent discussion and figures) via software. The suggestion of Reinmuth [9] that three-dimensional electrochemistry would be a powerful technique becomes a reality with the microprocessor based instrumentation described in this paper. Visual inspection readily allows one to discern that the information content of an experiment of this kind is extremely high and this is confirmed by theory. The theory of three-dimensional electrochemistry and variable amplitude pdnp polarography is readily derived for an electrode process of the kind A+ne~B where slow electron transfer is rate determining. This case is considered in the present manuscript, with DA, DB, CA, Cb referring to diffusion coefficients or concentration o f A and B respectively.

24

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A convenient means of theoretically presenting the effect of k s on the peak characteristics of pdnp polarograms is a plot of the given variable vs. log k s. Access to the analytical mathematical solution available for the pdnp technique is of course

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Fig, 2. Variation of half p e a k width, p e a k p o s i t i o n a n d p e a k current w i t h c h a n g e in k s for variable a m p l i t u d e p d n p p o l a r o g r a p h y . T h e o r y is for a two electron r e d u c t i o n A + n e ~ B. C u r r e n t m e a s u r e m e n t times (from left to right) are 60, 50, 40, 30, 20 a n d 10 ms after a p p l i c a t i o n of the pulse for a n a m p l i t u d e of - 4 0 mV. Electrode area = 0.058 cm 2, d r o p time = 1 s, E l ~ 2 ~ E ° = 0 V, a = 0.50, D A = D B = 0 . 7 8 × 10 - 5 c m 2 s - i , CA = 10-3 M , c B = 0, T = 25°C. Peak p o t e n t i a l s are relative to E l ~ 2 = 0 V.

25 attractive. Most other transient techniques would require a digital simulation or numerical method of analysis. Figure 2 shows a plot of peak width at half height, peak potential and the ratio of the peak current to the peak current for a reversible system Ip/lp (rev.) vs. log k s for variable amplitude pdnp polarography. The sets of each type of plot illustrates the effect of different measurement times after the application of the pulse (different pulse widths). The data will all be available from the three-dimensional surface shown experimentally in Fig. 1. The pulse measurement times in Fig. 2 were 60. 50, 40, 30, 20 and 10 ms (from left to right) with a pseudo-derivative amplitude ( A E ) of - 4 0 mV. The theory used to generate the curves in Fig. 2 was taken (corrected for sign errors--also see Acknowledgements section) from ref. 11 (eqn. 4.117) which gives the current flowing after a potential step at a spherical electrode when only the oxidized species is present and the diffusion coefficients of the reduced and oxidized species are equal. Access to an analytical solution, rather than the digital simulation required in differential pulse polarography is a significant advantage in the pdnp technique. As expected, for a constant value of k s, in the quasi-reversible region of curves a and b (s-shaped region), the system is closer to reversible for long measurement times (large pulse widths). Note that whereas the half peak width and the ratio of Ip/lp (rev.) begin to change at approximately the same value of log k s, the peak position is not affected until somewhat smaller values of k s are reached. Tables 1 and 2 show the variation in half peak width, peak potential and Ip/Ip (rev.) for constant measurement time (tp) with change in amplitude ( A E ) and constant AE with change in tp respectively. As may be seen from Table 1, for constant measurement time, the half peak widths for large values of k s, approach the theoretical value of 90.4/n mV [12,13] with decreasing values of AE. In addition, as predicted by reversible theory, the peak potential is at a value of E~/2 -AE/2 [ 12,13] for large values of k s. With respect to changes in the electron transfer rate; it is worth noting that the peak current is less affected by changes in rate constant for large values of AE. This is also true in differential pulse (dp) polarography [8]. It may also be seen that in the quasi-reversible range of rate constants, different pulse amplitudes would give seemingly different values of concentration with respect to a calibration curve made under reversible conditions. The same is true for Table 2 in that with constant AE, the concentration determined by the peak current would be different for different measurement times. Either of these multiple measurements of peak height could serve as indicators as to kinetic complication in an unknown sample compared with calibration curves obtained from standards (under reversible conditions). Comparison with dp polarography theory [8], shows that the current per unit concentration for reversible processes are essentially identical [6]. However, for the quasi-reversible or irreversible processes the pdnp technique appears to be theoretically superior because the current does not decay as fast with decreasing k s. This result is confirmed experimentally in Fig. 3. From many points of view the pdnp technique is superior to dp polarography [6,7,13]. The possibility of simple implementation in three dimensions adds to the advantages. To experimentally investigate the theoretical work presented above, variable

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amplitude pdnp polarography was performed with microprocessor based instrumentation which has been described previously [6]. The software used in this instrumentation contains an option not previously described which allows the current to be measured at regular intervals after application of the pulse. The number of samples per pulse is limited only by the amount of memory available for data. Therefore several experiments are performed simultaneously with different pulse widths. Upon completion of the experiment any of the polarograms at the various pulse widths may be examined. Alternatively, a variety of variable amplitude pseudo derivative polarograms may be generated by changing the value of AE. Figure 1 actually represents 6 of the possible pdnp polarograms collected in one experiment in three dimensional form as a current-potential-time surface. To experimentally investigate the effects of changes in rate constant on the analytical response as well as experimentally identify the presence of an interference, experiments were performed on Cd(II) reduction with and without the presence of surfactant. Surfactants are known to cause apparent decreases in electron transfer rate constant [2] and may be present in environmental samples. The surfactant used was cyclohexanol because only small quantities are required to cause significant changes in k s. Figure 4 reveals that analytical procedures based on digital ac polarography [14,15] and differential pulse polarography could have lead to an erroneous report of analytical data. The digital ac response has been shown to approach that of the conventional ac technique [15].

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E/V Fig. 4. Influence of the addition of approximately 10-5 M cyclohexanol to the reduction of 3 × 10 4 M cadmium in 1.0 M KCI at (21 + 1)°C in pseudo-derivativenormal pulse (pdnp), differential pulse (dp) and digital alternating current (ac) polarography. Pulse amplitude, AE = - 24 mV and peak width = 10 ms for pdnp and dp. Digital ac polarogram was obtained with an amplitude of 24 mV p-p. Ac polarograms are the total current response obtained at 90° with respect to the applied potential [14,15]. Drop time = 0.5 s, measurements made every 2 mV (dc ramp step). Upper set of curves contain cyclohexanol and lower set are standards obtained in the absence of cyclohexanol.Reference of upper curves to standards could lead to an erroneously low determination.

U s i n g t h r e e - d i m e n s i o n a l techniques, a set of calibration curves were generated for the reduction of C d ( I I ) to Cd(Hg) in the 10 - 4 M c o n c e n t r a t i o n range. Three values of - A E (20, 40, 60 mV) were used for the p d n p amplitudes a n d the pulse current was measured at times of 10, 20, 30, 40, 50 a n d 60 ms. O n e m a y envisage the result as a three-dimensional calibration curve. A n " u n k n o w n " sample c o n t a i n i n g approximately 10 -5 M cyclohexanol was then " d e t e r m i n e d " with use of these calibration curves. T a b l e 3 shows the results of this determination. The results in parenthesis are the c o n c e n t r a t i o n s d e t e r m i n e d without cyclohexanol present. As expected, w h e n cyclohexanol was present the d e t e r m i n e d c o n c e n t r a t i o n closest to the actual c o n c e n t r a t i o n was o b t a i n e d for the largest value of m e a s u r e m e n t time (tp) a n d largest pseudo-derivative a m p l i t u d e ( A E ) . The results indicate that the worst c o n c e n t r a t i o n d e t e r m i n e d was for small values of tp a n d A E (28% low). The difference i n d e t e r m i n e d c o n c e n t r a t i o n for different A E a n d tp enables the interference to be recognised a n d indicates that alternative analytical procedures must be applied. The use of the s t a n d a r d a d d i t i o n m e t h o d is n o r m a l l y r e c o m m e n d e d when matrix problems are suspected. It is of course more time c o n s u m i n g a n d therefore less c o n v e n i e n t for r o u t i n e d e t e r m i n a t i o n of multiple samples. This m e t h o d (Table 4) yielded a m e a n c o n c e n t r a t i o n approximately 6% lower t h a n that d e t e r m i n e d without the cyclohexanol present, a n d whilst providing superior data some interference remains. The greater c o n s t a n c y of r e s u l t s indicates to the analyst that the extent of

30 TABLE 3 Use of three-dimensional electrochemistry to indicate the presence of interference from approximately 1 0 - 5 M cyclohexanol in an analytical determination of cadmium referenced against standard solutions" [Ca]x 1 0 4 / M

t/ms - AE/mV

10 20 30 40 50 60

60 2.36 2.55 2.63 2.69 2.71 2.72

40 (2.90) (2.89) (2.91) (2.93) (2.92) (2.92)

2.23 2.43 2.54 2.56 2.63 2.64

20 (2.90) (2.93) (2.91) (2.91) (2.93) (2.90)

2.09 2.29 2.39 2.45 2.54 2.61

(2.93) (2.92) (2.95) (2.88) (2.94) (2.90)

a Actual concentration of cadmium is 2.92 x 10 4 in 1 M KC1. Values in parenthesis refer to determination of a sample in absence of cyclohexanol.

interference is now relatively small. The larger relative standard deviation obtained in the standard addition method (5% compared with < 1% for calibration curve) suggests that the actual mechanism of this interferent involves a concentration dependance. That is, the method of standard additions is not completely linear because the extent of interference depends on the ratio of cadmium to cyclohexanol. Detailed examination of the actual polarograms indicates that the presence of an interferent can be detected from careful examination of the peak position and half width under some of the conditions. Figure 5 shows the pdnp polarograms obtained with (a) and without (b) cyclohexanol present. The pseudo-derivative amplitude used was - 4 0 mV and the measurement times were (in decreasing peak current amplitude) 10, 20, 30, 40 and 50 ms. The shift in peak position and increase in peak width is most apparent for short pulse widths (curves a). For the Cd(II) system under

TABLE 4 Application of method of standard additions in the attempted determination of 2.0 x 10-4 M cadmium in 1 M KC1 and 10 5 M cyclohexanol using three-dimensional electrochemistry t/ms

[Cd] x 1 0 4 / M - AE/mV

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60

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20

1.79 1.84 1.87 1.91 1.88 1.91

1.79 1.84 1.86 1.86 1.88 1.95

1.82 1.81 1.86 1.97 1.88 1.84

31 reversible c o n d i t i o n s (curves b), the p e a k p o s i t i o n is i n d e p e n d e n t of m e a s u r e m e n t time. F r o m the three d i m e n s i o n a l profiles it is clear that s t a n d a r d s a n d " u n k n o w n s " are n o t identical. T h e ability to detect interference is clearly e n h a n c e d b y the three

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F/V Fig. 5. Use of variable amplitude pdnp polarogram obtained from three dimensional electrochemical curves to indicate presence of interference. System is reduction of 2 x 10-4M cadmium in 1 M KCI at (21 + 1)°C. Drop time = 1 s. Curves a contain 10-5 M cyclohexanol and curves b are obtained from the standard solution. AE = -40 mV and in decreasing peak current amplitude time of current measurement = 10, 20, 30, 40 and 50 ms respectively. Interference not readily observed at 50 ms is easily seen at 10 ms.

d i m e n s i o n a l electrochemistry a n d since all d a t a are o b t a i n e d from a single experim e n t n o loss in time is associated with the technique. A second investigation involved a m o r e c o m p l e x t y p e of interference; that of r e a c t a n t a d s o r p t i o n . This type of interference causes an e n h a n c e d p e a k current a n d a shift in p e a k p o t e n t i a l if the a d s o r p t i o n is sufficiently strong in differential pulse p o l a r o g r a p h y [16]. Because of the e n h a n c e d p e a k current it has actually b e e n c o n s i d e r e d an a d v a n t a g e [17] u n d e r c o n t r o l l e d conditions. This k i n d of interference is similar to that resulting from a change in electron transfer b u t p r o d u c e s erroneously high (rather t h a n low) results. This interference can b e r e a d i l y o v e r l o o k e d using s t a n d a r d a n a l y t i c a l procedures. I n n o r m a l pulse p o l a r o g r a p h y the diffusion limiting p l a t e a u is actually smaller t h a n in the absence of this t y p e of interference while at sufficiently short pulse widths the p o l a r o g r a p h i c wave develops the shape of the pulse c o m p o n e n t in d p p o l a r o g r a p h y [ 18]. F i g u r e 6 shows the variable a m p l i t u d e p d n p p o l a r o g r a m s of 3 x 1 0 - 4 M C d ( I I ) in 1.0 M KC1 with (a) a n d w i t h o u t (b) 0.01 M N a I . I o d i d e has been used to cause r e a c t a n t a d s o r p t i o n in studies of this

32

phenomena [17]. However, adsorption may also arise from naturally occurring species such as humic and fulvic acid [19]. As is apparent from Figure 6, the enhancement effect is most pronounced at short measurement times. Under the

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E/v Fig. 6. Three dimensional electrochemistry enables interference (enhanced currents) from adsorption to be detected. System is reduction of 3 × 10 -4 M cadmium in I M KCI at (21 + 1)°C. Drop time = 1 s. Curves a contain 0.01 M NaI and curves h are obtained from the standard solution. AE = --40 mV and the time of current measurement in order of decreasing peak current amplitude is 10, 20, 30, 40 and 50 ms respectively. Interference not seen at longer current sampling times is readily apparent at 10 ms.

conditions used (AE = - 4 0 mV, tp = 10, 20, 30, 40 and 50 ms) the effect is greatly diminished at 40 and 50 ms such that reference to a calibration curve made in the absence of iodide yields an accurate result. However, its effect could have gone unnoticed using the results from 20 ms (5% high) had the measurement been made at l0 ms. The shape of the 10 ms peak may be understood by reference to the non-sigmoidal shape of the original normal pulse polarogram (maxima present). The above theoretical and experimental data indicates the analytical advantages of three dimensional pdnp polarography with respect to detection of interference. The microprocessor based instrumentation which now makes three dimensional voltammetry a real possibility could easily be extended to provide the measured parameters (time, current, potential, width, height, amplitude, etc.) automatically, thereby improving the reliability of polarographic analysis. Future work will proceed in this direction.

33 A l t h o u g h n o t specifically discussed a b o v e it is readily a p p a r e n t that the use of t h r e e - d i m e n s i o n a l electrochemistry in electrode kinetics m u s t be considered, In other areas, the usefulness of c o m p a r i n g theoretical and e x p e r i m e n t a l surfaces for the u n d e r s t a n d i n g of systems c o n t a i n i n g m o r e t h a n two variables has b e e n i n d i c a t e d [20] a n d a p p l i c a t i o n in electrochemistry should be equally significant. T h e d a t a o b t a i n e d in the e x p e r i m e n t s d e s c r i b e d i s ideally suited to the s t u d y of electrode kinetics using the m e t h o d s d e s c r i b e d b y Y a m a d a a n d T a n a k a for the e v a l u a t i o n of kinetic p a r a m e t e r s [21] since the required c u r r e n t - t i m e a n d c u r r e n t - p o t e n t i a l d a t a are o b t a i n e d simultaneously. F o r t u n a t e l y , the differential equations which m u s t be solved for m o s t classes of electrode process are m u c h simpler for n o r m a l pulse p o l a r o g r a p h y than in other pulse techniques such as differential pulse p o l a r o g r a p h y when dc terms are present. The S M D E used in this work, provides a c o n s t a n t e l e c t r o d e area a n d even further simplifies the t h e o r y relative to the d r o p p i n g m e r c u r y electrode. T h e a p p l i c a t i o n of three d i m e n s i o n a l electrochemistry in studies of electrode kinetics will b e investigated as p a r t of o u r future research p r o g r a m in this area. N o r m a l pulse p o l a r o g r a p h y is ideally suited to t h r e e - d i m e n s i o n a l electrochemistry f r o m an i n s t r u m e n t a t i o n p o i n t of view. T h e extension to o t h e r m u l t i p l e m e a s u r e m e n t (difference) techniques such as differential pulse p o l a r o g r a p h y is c o m p l i c a t e d b y the v a r i a t i o n in the time b e t w e e n m e a s u r e m e n t to be s u b t r a c t e d with time d o m a i n of m e a s u r e m e n t (pulse width). ACKNOWLEDGEMENTS T h e a u t h o r s gratefully a c k n o w l e d g e the A u s t r a l i a n R e s e a r c h G r a n t s C o m m i t t e e for the financial s u p p o r t a n d the c o n t r i b u t i o n o f K . W . H a n c k in the theoretical w o r k p r e s e n t e d in this p a p e r a n d for m a n y helpful discussions. REFERENCES 1 A.M. Bond, Modern Polarographic Techniques in Analytical Chemistry, Marcel Dekker, New York, 1980. 2 R.J. Schwall, A.M. Bond and D.E. Smith, Anal. Chem., 49 (1977) 1805. 3 D.E. Smith, Anal. Chem., 48 (1976) 221A; 48 (1976) 517A and references cited therein. 4 M. Ichise, H. Yamagashi and T. Kojima, J. Electroanal. Chem., 94 (1978) 187 and references cited therein. 5 M. Ichise, H. Yamagashi, H. Oishi and T. Kojima, J. Electroanal. Chem., 106 (1980) 35, 108 (1980) 213, 132 (1982) 85 and references cited therein. 6 J.E. Anderson and A.M. Bond, Anal. Chem., 53 (1981) 504. 7 A.M. Bond, J. Electroanal. Chem., 118 (1981) 381. 8 K. Aochi and J. Osteryoung, J. Electroanal. Chem., 110 (1980) 19 and references cited therein. 9 W.H. Reinmuth, Anal. Chem., 32 (1960) 1509. 10 J.E. Anderson, R.N. Bagchi, A.M. Bond, H.B. Greenhill, T.L.E. Henderson and F.L. Walter, Am. Lab., 13 (Feb. 1981) 21. 11 D.D. Macdonald, Transient Techniques in Electrochemistry, Plenum Press, New York, 1977, p. 84. 12 E.P. Parry and R.A. Osteryoung, Anal. Chem., 37 (1965) 1634. 13 A.H. Rahier and B.P. Gilbert, J. Electroanal. Chem., 130 (1981) 327.

34 14 15 16 17 18 19

J.E. Anderson and A.M. Bond, Anal. Chem., 53 (1981) 1394. J.E. Anderson and A.M. Bond, Anal. Chem., 54 (1982) 1575. F.C. Anson, J.B. Flanagan, K. Takahashi and A. Yamada, J. Electroanal. Chem., 67 (1976) 253. J.B. Flanagan, K. Takahashi and F.C. Anson, J. Electroanal. Chem., 81 (1977) 261. J.B: Flanagan, K. Takahashi and F.C. Anson, J. Electroanal. Chem., 85 (1977) 256. W.T. Bresnahan, C.L. Grant and J.H. Weber, Anal. Chem., 50 (1978) 1675 and references cited therein. 20 J.W. Frazer, Anal. Chem., 52 (1980) 1205A. 21 A. Yamada and N. Tanaka, Anal. Chem., 45 (1973) 167.