Evaluation and improvement of the resolution of voltammetric measurements

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EVALUATION AND IMPRQVEMENT OF THE RESOLUTION OF VOLTAMMETRIC MEASUREMENTS JOSEPH WANG,* DEN BAI Luo and BASSAM FREIHA Department of Chemistry, New Mexico State University. Las Cruces, NM 8X003, U.S.A.

Summary--Two approaches for estimating and improving resoiution in ~bromatography analyses can be applied successfully to voltammetric measurements. It is shown that the resolution of vohammetric procedures yielding symmetric (or nearly symmetric) current peaks can be described by R = 2AE,!l.h99 (b, ,_ + h, 2,2) where AE, is the difference between the peak potentials of the two analytes, and b,,?,, and b, ‘,? are the peak half-widths. The window diagram approach is used to improve the resolution between neighbouring voltammetric peaks by optimization of the supporting electrolyte composition. The applicability of these approaches to differential-pulse anodic-stripping measurements at the mercury tilm electrode is demonstrated.

Differential-pulse or square-wave polarography and anodic-stripping voltammetry have become commonly used techniques for determining trace levels of electroactive species, and their sensitivity has been discussed several times.’ 4 On the other hand, many aspects of the resolution of voltammetric peaks have not been evaluated. in spite of selectivity problems associated with analysis of mixtures. The electroactive components of a mixture usually behave independently, so the voltamperogram is simply the summation of the individual peaks or waves. The three techniques mentioned give signals in the form of peaks, and differentiation of the sigmoidal response obtained with techniques such as hydrodynamic voitammetry’~h or normal pulse modulation polarography’ will also result in peaks. Clearly, for mixtures the resolution of adjacent voltammetric peaks depends on how far apart and how wide they are. We must decide what criterion for resolution is suitable. In chromatography, the resolution, R, of two adjacent peaks is defined as the ratio of the peak separation to the mean “base-line width” of the peak (measured as in Fig. 1):

The aim of the present work was to establish a similar method for estimating the resolution of two adjacent voltammetric peaks. We have found that for voltammetric techniques yielding symmetric, or nearly symmetric. current peaks, a reliable measure of the extent of overlap can be obtained, and that the window diagram approach”’ is very useful for improving the resolution and optimizing the conditions of voltammctric measurements. EXPERIMENTAL

The electrochemical cell and the reagents were those described previously’0 unless stated otherwise. Measurements were made with an EG&G PAR model 174 polarographi~ analyser. The differential-pulse anodic stripping measurements were made at the in situ plated mercury electrode. as described previously.” RESCLTS AND DISCtiSSION

Quantitutiw

nwsure

of f/wresolution

Various voltammetric procedures, such as linearscan voltammetry or stripping measurements at the hanging mercury drop electrode, produce asymmetric

Alternatively, if the widths are measured halfway between the base-line and and the tops of the peaks, the equation becomes R=-

Z(tz - f() I.699 ( w,,z. 1+ w, ,q.:.)

These equations are based both peaks are Gaussian.

on the assumption

(2) that

Fig. I. Definition of parameters used to define resolution.

*Author for correspondence. 397

398

JOSEPH

-

WANG

0.2v

Fig. 2. Differential pulse anodic stripping voltamperograms

for various binary mixtures: (A) cadmium (3 x 10-‘Mfthallium (3 x IO-‘M), (3) indium (4 x IO-‘iW)cadmium (4 x 10e7M), (C)copper (1 x 10..‘M)-bismuth (I x I)-“M) and (D) indjum (2 x 10. *~~thailium (1 x 10-“M). Mercury-coated glassy-carbon disk electrode rotated at 1600 rpm for 2 min deposition at - 1.I V. Stripping conditions, scan-rate, 2 mV&c: amplitude, 25 mV. Supporting electrolytes, I M HCI (A, B); LM WC1+ I M ethylenediamine (C. D).

signal peaks even for reversible systems. Mowever, for stripping measurements at the mercury film electrode, differential-pulse, square-wave or a.c. polaro~raphy, and various procedures based on differentiation of sigmoidal signals, symmetric (or nearly symmetric) response peaks are obtained. Like those in practical chromatographic measurements these peaks are generally not truly Gaussian in shape. It is almost afways a mistake to assume chromatographic peaks are Gaussian in shape,‘2- is and exponentially modified Gram-Charlier,‘* Gaussian~ 16 bi-Gaussian,‘3.‘7 Poisson’3 and a combinationi of Gaussian, exponential and hyperbolic tangent shapes have been employed. The exact mathematical current-potential functions for most voltammetric techniques are not available. Boudreau and Perone*’ found that the function which best fitted square-wave voltammetric peaks is a combination of Gaussian and Cauchy functions (with the Gaussian component having the greater effect on the peak shape). Stripping measurements at the mercury film electrode can be described by an approximate Gaussian function.” Hence an analogue of equation (2) can obviously be made the basis for estimating the resolution of symmetric, or nearly symmetric, voltammetric peaks with a relatively flat base-iine: 2AE, where AE, is the difference between the peak potentials and bit2 is the peak width at half height. As bij2 is commonly used in voltammetric measurements, equation (3) is preferred to the anaioguc of equation ( 1). and its utility is illustrated in Fig. 2, which shows

et

ai,

that though for the cadmium-thallium (A) and indium-cadmium (B) mixtures AEp is essentially the same (0.07 V), the extent of overlap of the peaks is very different. The value of R is 0.68 and 0.97 for the cadmium-thallium and indium~admium mixtures. respectively. A similar observation applies to the copper-bismuth (C) and indium-thallium (ID) systems, which have AE, values of 0.17 and 0.14 V and R values of 2.6 and 1.3 respectivefy. The value of R clearly provides a reliable estimate of the resolution. The 6,:, value is inversely proportional to the number of electrons {Q) participating in the electrode reaction and increases with decreasing rate of electron transfer (once the reaction becomes totally irreversible, the width remains unchanged). For example, the pseudo derjvative polarographi~ techniq~les (pulse, a.c. and square-wave polarography) show a limiting b,,Z value of 90.6/n mV.2’ For the voltamperograms shown in Fig. 2 the stripping reactions involve transfer of one (TI), two (Cd, Cu) or three (In, Bi) electrons, and it is clearly the one-electron thallium reaction that creates the most severe overlap problems. Table 1 summarizes the R values obtained for differential-pulse stripping measurements of several binary systems; only the cadmium-indium couple exhibits significant overlap (cf: B in Fig. 2). As bl,‘*is inversely proportional to the number of electrons transferred, for two reversible systems which both have the same n value, R is proportional to nA&,, which is the estimate frequently used for evaluating the resolution of voltammetric measurementszo However, this estimate is not useful when the two redox reactions involve different numbers of electrons or different rates of electron transfer. However, in such cases R does provide a reliable measure of the resolution, as it takes into account the different factors (n, reversibility) affecting the peak width. For truly Gaussian peaks, nearly complete resolution (0.3% overlap) is obtained at R = 1.5. For

Table I. R v&es and peak-potential separations for different pairs of metals measured by differential pulse anodic strippjng voltammetry* Binary system Cd-Pb Cd-in Cd-Cu Cd-Pi Cu-Pb CU-in Cu-Bi Pb-ln P&E Bi-ln

A&, P’ 0.21 0.07 0.39 0.57 0.18 0.31 0.20 o.t3 0.37 0.50

R

2.9 0.9‘7 5.2 9.1 2.3 4.2 2.9 I.5 5.9 s.t

*5 x IO-‘M bismuth, copper and indium; 3 x IO-‘M lead and cadmium; sup porting electrolyte, IM HCI. Other conditions as for Fig. 2.

399

Resolution of voltammetric measurements A

I

Pb

1.5

1.0 Lqond

I

02v +

cont.

2.0

(Ml

8

0.3

4

Fig. 3. Differential pulse anodic stripping voltamperogram for 4 x IO-‘M indium and lead in IM HCI. Conditions as

_

0.2 I

2 L1

for Fig. 2.

2 0.1 -

differential-pulse stripping measurements (at the mercury film electrode) this would occur at about R = 1.6, as calculated from the data in Fig. 3. At R < 0.75 (i.e., 2 50% overlap) the resolution is unsatisfactory for most purposes (e.g., A in Fig. 2). These criteria pertain to approximately equimolar mixtures. Higher resolution may be needed when the concentrations for the two components differ considerably. Various experimental conditions, e.g., scan-rate, pulse-amplitude or supporting electrolyte, may affect the voltammetric peak potential and peak-width, so to control and improve the resolution the analyst must know how R varies with these conditions. Table 2 shows the effects of the pulse-amplitude and potential scan-rate on the resolution of the peaks of indium and lead, two metals giving rise to overlapping stripping peaks in many media. The best resolution was obtained with 2 mV/sec scan-rate and 50 mV amplitude. These data indicate that the scan-rate has the dominant effect on the resolution; a tenfold increase in scan-rate decreased R by a factor of approximately 3-4, whereas a similar increase in pulse amplitude changed R by only 5-20%. Obviously, changes in the sensitivity or speed associated with these changes in the experimental conditions

Table 2. R values for the lead-indium pair as a function of the differential pulse amplitude (AE) and scan-rate (v)* AE, mV v, mV’jsec

2 5 IO 20

10

25

50

100

2.0 1.56 1.05 0.72

2.05 1.59 1.01 0.60

2.09 1.55 0.99 0.65

1.95 1.46 0.96 0.55

‘5 x tOS7M indium and lead; supporting ehxtrolyte, acetate buffer (pH 4.5). Deposition at - I.1 V for 1 min.

0.0

0.5

15

2.0

Fig. 4. (A) Dependence of the stripping peak potential on ethylencdiamine concentration for indium (I 1.thallium (2), lead (3), copper (4) and bismuth (5). (B) Window diagram for these metals over the O--2M ligand concentration range, in the presence of 1M HCI.

should be taken into account when optimizing the overall performance. Overall, equation (3) provides a reliable measure of the resolution, which can be utilized effectively when various solution or instrumental conditions are changed to improve the separation of nei~hbouring peaks. lmproaed

resolution by the window diagram approach

The window diagram approach uses the resolution of all possible pairs of peaks in the sample to obtain the best separation of the worst separated pair of peaks. Most applications of this approach have been in chromatography~,~ but it can be exploited in any situation in which optimization of one (or more) of the experimental conditions with respect to one of the dependent variables is required. For example, the method was used successfully with lanthanide-shift nuclear magnetic resonance spectra.” Similarly, polarographic measurements can be improved by optimizing the solution PH.*~ In this section, we examine the utility of the window diagram approach for optimizing the supporting electrolyte composition to improve the resolution in anodic stripping voltammetry. This possibility results from the fact that most supporting electrolytes have some tendency to complex metal ions, thus affecting the position of the stripping peaks on the potential axis. Figure 4 shows (A) the effect of ethylenediamine concentratjon on stripping peak potential for five

400

JOSEPH

WANG

et al.

is observed with zero and 0.9M ethylenediamine concentrations, respectively; dete~ination of these metals is not feasible under these conditions. As a result of the optimization obtained by the window diagram approach, the five metals can be measured on the same voltamperogram. within a relatively narrow potential range (from -0.2 to -0.8 V). Additional metals (e.g., zinc, nickel, gallium, antimony) may also be measured within the entire potential range of the mercury working electrode. (The ability to perform such multi-element measurements would also depend on the absence of inte~eta~i~ interferences.) The same strategy for improving the resolution in anodic stripping measurements can be achieved by changing other solution or instrumental factors. For example, a change in the mercury film thickness or potential scan-rate alters the peak position to different extents, depending on the number of electrons involved.25 Other approaches for improving the resolution of stripping measurements have been reviewed.’ I -3.0

I

I

-0.7

-0.4

I - 0.t

E IV1

Fig. 5. ~i~er~nt~a~ pulse anodic stripping voltam~~rograms for 6 x IO-‘M thallium, 9 x IO-‘M indium, 3 x lO-‘M lead, 5 x 10-‘M copper and bismuth with (a) 0, (b) 0.65 and (c) 0.90M ethylenediamine and IM HCI. Deposition for I-min at - 1.1 V. Scan-rate, I mV/sec, Rotation speed and amplitude as for Fig. 2.

metals. and (3) the window diagram generated from the data in (A). ft is clear that the changes in peak potential differ from metal to metai, as they are dependent on the formation constants of the complexes.) ft should be noted that the plot for the thallium peak potential crosses those for indium, lead and copper over the range of ligand concentration covered. To construct the window diagram, the differencein peak potential of the pair most difficult to resolve is plotted as a function of the ligand concentration. Two “windows” of separation are clearly evident, and define the conditions under which complete separation of the mixture is possible. In practice, the window at a ligand concentration of 0.65M offers the best separation of the peaks of ail the metals (under these conditions, AE, for the least separated pair is 92 mV>. This is illustrated in Fig. 5, which shows the stripping voltamperograms for these metals at three ligand concentrations. With the optimal ligand concentration, O&M, the peaks are well from other (b); only the each resolved indium-thallium pair exhibits some overlap (R = I .I). All five metals present can conveniently be determined. In contrast, severe overlap of the thallium-indium and thallium-lead peaks (R < 0.4)

~~~~ow~e~~~~enf-~is work was supported in part by the National Institutes of Health, grant No. GM30913-02. REFERENFES I. A. M , Bond, Modern Polarographic Techniques irt Anafytical Chemistry, Dekker, New York, 1980. 2. Anal. Chem., 1980, 52, 229A. 3. J. Wang, Stripping Analysis: Principles, instrumentation and Applications, VCH Publishers, Deerfield-Beach, FL, 1985. 4. G. E. Batley and T. M. Florence, J. Efectroanal. Chem., 1974. s5, 23. 5. J. Wang, Tafanta, 1982, 29, 805. 6. B. MiIler and J. M. Rosamilla. Anal. Cbem.. 1983, 55,

1281.

7. J. E. Anderson and A. M. Bond, ibid., 1981, 51 504. 8. R. J. Laub and J. H. Purneil. ibid.. 1976. 48, 799. 9. S. N. Deming and M. L. H. Turoff,‘ibi& i978, SQ, 546. 10. J. Wang, Tufunta, 1982, 29, 125. 11. J. Wang and D. B. Luo, ibid., 1984, 31, 703. 12. A. H. Anderson, T. C. Gibb and A. 3. Littlewood, J. Cbromaro~. Sci., 1970, 8, 640. 13. E. Grushka, M. N. Myers and J. C. Giddings, Anal. Chem., 1970, 42, 21. 14. J. T. Lundeen and R. S. Juvet, ibid., 1981, 53, 1369. 15. J. P. Poley and J. G. Dorsey, ibid., 1983, 55, 730. 16. H. M. Gladnev, B. F. Dowden and J. D. Swalen, ibid.,

1969, 41, 883: 17. T. S. Buvs and K. de Clark. ibid.. 1972. 44. 1273. i8. 0. Grubher, ibid., 1971, 43,‘1934. 19. S. N. Chesler and S. P. Cram, ibid., 1973, 43, 1354. 20. P. A. Boudreau and S. P. Perone, iX& 1979, Sf, XI i. 21. ~.$to$$ and Z. Kubhk, J. Efectroanaf. Chem., 1979, 22.

W. b. Gutknecht and S. P. Perone, Anal. Chem., 1970, 42, 906.

23. R. L. Laub, A. Pelter and J. H. Purnell, ibid., 1979,5t, 1878. 24. L. B. Anderson and R. J. Laub, J. Eleetroanal. Chem..

1981, 122, 359. 25. K. Wikiel and Z. Kublik, ibid., 1984, 163, 71