Theoretical Treatment of Staircase Voltammetric Stripping from the Thin Film Mercury Electrode Joseph
H. Christie'
and Robert A. Osteryoung'
Department of Chemistry, Colorado State University, Fort Collins, Colo. 80523
t
Staircase voltammetric stripping is an attractive alternative to both differential pulse and linear scan voltammetric stripping. This paper presents a theoretical treatment of this new stripping mode applied to the thln-film mercury eiectrode. For equivalent scan rates the faradaic response is somewhat smaller than that obtained by linear scan stripping.
_I
5 c W z
k TIME
It is becoming increasingly well recognized that differential pulsed voltammetric stripping has significant advantages over the more usual technique of linear scan voltammetric stripping (I). The most important of these advantages is the discrimination of the pulse technique against double layer charging contributions. A very approximate theory (2) for differential pulsed voltammetric stripping a t the thin-film mercury electrode indicates that the two techniques are roughly equivalent in their faradaic response, but the linear scan faradaic response is superimposed on a double-layer charging background while the differential pulse background is essentially flat. Perhaps the major disadvantage of the differential pulse stripping technique is the length of time required to perform the stripping experiment. The optimum scan rate (2 mV/s) and delay time (0.5s) result in the application of one pulse per millivolt of scan and require 500 s to scan 1 V ( I ) . This stripping time is unnecessarily long in comparison with the short plating times ( r - l I 2 .
RESULTS AND DISCUSSION Typical calculated staircase stripping function curves for several values of the thickness parameter 12/Dr are shown in Figure 2. For very thick films, the current function has the pronounced tail characteristic of staircase voltammetry under conditions of semiinfinite diffusion (2). This is the expected result since for small values of y , the function H3(y) has a value of unity and Equation 9 reduces to the same form as for semiinfinite diffusion (Equation 6 of ref 2).
The very thin film limit is of analytical interest. For small values of the thickness parameter, the shape of the stripping function becomes independent of the value of the thickness parameter. The potential of the maximum of the stripping function is shown in Figure 3 for several values of the step height. For very thin films the peak potential is a linear function of log (12/Dr)and for thick films approaches the infinite diffusion limit. Similar behavior has been noted for both linear scan and differential pulse stripping from thin-film electrodes ( 2 , 9 ) .
8
c
0 0
0
0
0
0
0
0
1 e)
AE ,mV
Figure 6. Step height dependence of maximum of thickness inde-
94
-2
0
pendent stripping function gp'
t2
log
Figure 4. Dependence of gp on thickness parameter. A€ = 2 (O), 5
KO, 10 (A) mV
'"I 1 1 o
thickness-independent function will be denoted as g'. Figure 4 shows the thickness dependence of the magnitude of g at the peak potential. Figure 5 shows the thickness-independent stripping function g' for several values of A E . Note that the magnitude of the peak current decreases with increased step height at constant scan rate although it increases with step height at constant step width. The latter result is a consequence of the fact that g decreases more slowly than (ilE)-l, Le., f increases with AB.These results imply that maximum sensitivity is obtained by choosing as small a value of T as possible and as large a value of AB consistent with adequate definition of the stripping peak. In the limit of very thin films, the peak current for linear scan stripping is given by (9)
*
I , = 11.6nuqm
4t
where the numerical factor 11.6 has units of V-I if V/s and for staircase stripping
;',
I
n (E-E I , s ) , rnV
Figure 5. Thickness independent stripping functions g' for A€ = 2 a),
(0
is in
,n l E I , = g, -9m
2
(.
u
o o),
10 (+++) mV
For comparison of the staircase stripping function with the linear scan stripping results of De Vries and Van Dalen (8, 9 ) , it is necessary to introduce the artificial "scan rate" parameter. Defining a new stripping function g = f / n A E , we can, with the stripping current, using Equation 10, arrive at nAE I=qlLlg The function g, in general, will be a function of both the step height LIE and the thickness parameter 12/Dr, but in the limit of very thin film is a function of ilE only; this
Figure 6 shows the step height dependence of gd.This plot again illustrates that the peak current decreases with increasing step height at constant scan rate and that the peak current for staircase stripping is somewhat less than for linear scan stripping. The decreased faradaic sensitivity is usually more than compensated by the insensitivity of staircase stripping to nonfaradaic processes. The results presented here indicate that staircase voltammetric stripping from the thin-film mercury electrode is indeed an attractive alternative to both differential pulsed and linear scan stripping, combining the best features of both techniques. Experimental work to verify the calculations presented here is in progress.
LITERATURE CITED (1) T. R. Copeland, J. H. Christie, R. A. Osteryoung, and R. K . Skogerboe. Anal. Chem., 45, 2171 (1973). R. A. Osteryoung and J. H. Christie, Ana/. Chern., 46, 351 (1974). J. H. Christie and P. J. Lingane, J. Elecboanal. Chem., 10, 176 (1965). R. G. Clem, G. Litton. and L. D. Ornelas, Anal. Chem., 45, 1306 (1973). D. K . Roe, Abstract 22, Division of Anal. Chem., presented at 169th National Meeting of the American Chemical Society, Philadelphia, Pa.. April
(2) (3) (4) (5)
ANALYTICAL CHEMISTRY, VOL. 48, NO. 6, MAY 1976
871
1975. (6) J. H. Christie, Anal. Chem., in press. 17) R. S. Nicholson and M. L. Olmstead. “Comouters in Chemistrv and Instrumentation, Electrochemistry,” Vol. 3,J. S: Mattson. H. B. Mbrk, Jr., and H. C. MacDonald, Jr.. Ed., Marcel Dekker. New York, N.Y., 1972, p 119. (8) W. T. De Vries, J. Electroanal. Chem., 9, 448 (1965). (9) W. T. De Vries and E. Van D a h , J. Electroanal. Chem., 14, 315 (1967).
RECEIVEDfor review October 20, 1975. Accepted February 2, l976. This work was supported in part by the National Science Foundation under Grant No. MP575-00332 and by the Office of Naval Research under Contract N00014-67A-0299-0007.
Fundamental and Second Harmonic Alternating Current Cyclic Voltammetric Theory and Experimental Results for Simple Electrode Reactions Involving Solution-Soluble Redox Couples Alan M. Bond* and Roger J. O’Halloran Department of Inorganic Chemistry, University of Melbourne, Parkville, Victoria 3052, Australia
lvica Ruzic‘ and Donald E. Smith’ Department of Chemistry, Northwestern University, Evanston, 111. 6020 7
A quantitative theoretical and experimental study of fundamental and second harmonic ac cyclic voltammetry is presented for a simple electrode reactlon lnvolvlng solutlonsoluble redox forms, and rate control by diffusion and/or heterogeneous charge transfer. Rate laws are presented for the ac cycllc responses at stationary planar and spherical electrodes, and their predictions surveyed. Experimental data for several redox couples with widely varying ks values are found to confirm detailed predictlons of the theory. Particular attention is paid the sltuation where the dc process Is non-Nernstian, under which conditions varlatlon of the kinetic status of the dc process leads to some lnteresting and useful effects in the ac observables. Some novel bases for characterizing the heterogeneous charge transfer rate parameters are revealed for the cyclic ac experiment. It is concluded that fundamental and second harmonlc ac cyclic voltammograms both complement and, in many cases, provide more sensitive and convenient insights about the electrode reaction than wldely-used conventional (dc) cycllc voltammetry.
Conventional (dc) cyclic voltammetry probably is the most widely used electrochemical relaxation method for studying electrode processes. The use of a triangular voltage at stationary electrodes allows both the oxidation and reduction pathways to be studied conveniently from one experiment, and quantitative theory has been extensively developed in a readily implemented form (1-13). However, the predominant use of the method remains qualitative (e.g., see references 14-25), because of restrictions inherent in the readout format ( 1 4 ) .Correction for charging current, particularly a t high scan rates, and data analysis from an asymmetric peak-shaped curve present two of the more important difficulties discouraging more widespread quantitative use of the method. The extension from dc to ac polarography has been extremely fruitful in terms of quantitative studies of electrode processes a t a dropping mercury electrode (DME) On leave from the Center for Marine Research, Ruder Boskovic Institute, Zagreb, Yugoslavia, 1972-75. 872
ANALYTICAL CHEMISTRY, VOL. 48, NO. 6. MAY 1976
(26-28). It follows that the same type of extension with stationary electrodes should be similarly advantageous, notwithstanding the fact that stationary electrode ac voltammetry has received relatively little attention. Recently (29, 3 0 ) ,data were presented to demonstrate that superposition of a sinusoidal alternating potential onto the triangular wave “dc” voltage ramp, a technique referred to as ac cyclic voltammetry ( 3 0 ) ,did indeed appear to exhibit the expected merits, relative to dc studies undertaken at stationary electrodes. All the well-known, attractive features for rapidly obtaining qualitative data under dc conditions, such as qualitatively easily interpretable readout, are retained with the ac mode. In addition, the availability of the dual time domain (dc scan duration and ac period) (26, 28) plus additional measurement modes, such as phase-selective detection (26-30), second harmonic detection (26-30), and phase angle measurements (26, 28), appear to provide greater scope for obtaining high-quality quantitative data. In particular, the methodology allows for discrimination against charging current and results in well-defined, symmetrical voltammograms, which in both cases represent considerable improvement over the situation existing in dc cyclic voltammetry. Our interest in ac cyclic voltammetry, therefore, is stimulated to some extent because we think the above-cited advantages should make it preferable to the dc approach in many instances. Also important is the simple consideration that ac cyclic experiments represent a natural approach any time ac data are desired a t a stationary electrode. Finally, an important incentive arises because the dc and ac readout formats often will be complementary, providing more information than either individual data format ( 2 8 ) . In this regard, it is of significance to recognize that modern instrumentation makes possible simultaneous measurement of the dc and ac (fundamental and second harmonic) responses (28, 31-33). Thus, access to both dc and ac data can be considered the natural result of a single experimental run. The concept of what we define as ac cyclic voltammetry appears to have originated with Okamoto (34-38),who developed instrumentation (with Saito) (34) and theory (35, 36) for the case where a small amplitude square-wave alternating potential is superimposed on a triangular wave dc
