ANALYTICAL CHEMISTRY, VOL. 51, NO. 11, SEPTEMBER 1979
OL
A 20
40 60 ANTIDIURETIC HORMONE (mililunits per m l l
ac
L
lot
Figure 3. Standard curves. ADH dose-response curves for four different toad bladders. Non-ADH-dependent Na’ transport was subtracted before plotting each of the data points. At the time of addition of ADH, the serosal to mucosal osmolality gradient was 150 m0smollL. These studies were conducted at room temperature
over the electrode plus other factors not yet identified. However, for a given toad-bladder electrode preparation the sensitivity of the response to ADH appeared stable. Repeat determinations fall within *lo% of each other. Since the rate of change of sodium ion concentration in the mucosal solution is directly proportional to the concentration of ADH in the serosal solution, it should be possible to use this method to study and assay ADH. ADH currently is bioassayed using the rat-pressor method where change in blood pressure in the intact anesthetized rat is the end point ( 3 ) . The blood pressure of the rat is influenced by a multitude of factors besides the sample of pituitary extract (vasopressin) injected. Thus this assay procedure is only semiquantitative. T h e toad-bladder electrode is also subject to interferences. The toad bladder responds much more sensitively to ADH than to any other hormone. However, other hormones such
1645
as aldosterone, thyroxin, and angiotensin, and the hormone mediator cyclic adenosine monophosphate when present in high concentration can affect sodium ion and water transport. Transport of sodium ion and water across the toad bladder is known to be influenced by the concentration of hydrogen, potassium, and calcium ions. The toad-bladder electrode method responds more rapidly than the short circuit determination method (6,9),probably because of the small volume of fluid layered between the electrode and bladder. Transport of Na’ and H 2 0 in and out of this tiny diffusion limited layer is promptly sensed by the sodium electrode. Radioimmunoassay of ADH takes hours or days to perform ( 4 , 5 ) , but is more sensitive than the toad-bladder electrode method. However, the toad-bladder electrode method has ample sensitivity to assay the ADH activity of pituitary extract. Since this extract is being used clinically for its antidiuretic action, rather than for its pressor activity, we suggest the toad-bladder electrode be used instead of the rat-pressor method for bioassay of posterior pituitary extract (vasopressin, USP).
LITERATURE CITED (1) The United States Pharmacopeia, 19th ed., 1975,p 534. (2) Remington’s Pharmaceutical Sciences, Arthur Osol, Ed.. 1975,p 566. (3) S. Yoshida, K. Motohaski, H. Ibayashi, and S.Okimka, J. Lab. C h . M., 62, 279 (1963). (4, C. G. Beardwell, J . Clin. Endocrinoi. Metab., 33, 254 (1971). (5) J. J. Morton, P. L. Padfield, and M. L. Forsling, J . Endocrinol., 65, 411
_,.
11975) ~
(6) A. (7) R. (8) A. (9) A.
Leaf, Ergeb. Physiol., 56, 213 (1965). Hays and A. Leaf, J . G e n . Physiol., 45, 905 (1962). Leaf, J . G e n . Physiol., 41, 657 (1958). L. Finn, Am. J . Physiol.. 215, 849 (1968).
RECEIVED for review January 29,1979. Accepted June 7,1979. S.U. was recipient of an NIH Research Career Development Award. This work was supported by NIH GM 16133.
Theoretical and Experimental Studies of the Effects of Charging Currents in Potential-Step Voltammetry Lee-Hua Lai Miaw and S. P. Perone” Department of Chemistry, Purdue University, West La fayette, Indiana 4 7907
Digital simulations of current-time behavior in potential-step chronoamperometry and in staircase voltammetry have been generated which take into account the effects of potential-step charging currents as well as induced charging currents. Results revealed serious distortions of the current signals before four cell-time constants and significant interferencefrom the induced charging current at times between four cell-time constants and 30 cell-time constants. The theoretical predictions were verified experimentally, and the possibillty of extracting pure faradaic current from the measured signals was explored.
Since the double-layer charging current has always been recognized as the major background current in potential-step voltammetric studies, it has been common practice to collect the data at times longer than four or five cell-time constants, when presumably the double-layer charging current has almost completely decayed. Alternatively, if data at shorter times 0003-2700/79/035 1-1645$01 .OO/O
are of interest, they have been corrected for double-layer charging current contributions by performing the same experiment with electrolyte solution only, to obtain a “blank”. The latter approach is inappropriate because the desired potential is not obtained before three or four cell-time constants; the former approach cannot handle short-time data. In addition, both approaches ignore the existence of the induced charging current, which results from the flow of time-varying faradaic current, and hence is not observable in the blank experiment ( I , 2). In fact, it, is impossible to correct experimentally for the background interference due to the induced charging current at times shorter than 30-35 cell-time constants. Moreover, the presence of induced charging current and faradaic current postpones the achievement of the desired step potential by 25-30 cell-time constants. Theoretically, the total charging current may be considered as the sum of two current components; Le., the charging current due to the application of a potential step, and the charging current induced by the flow of faradaic current. Therefore, in potential-step voltammetry, the total measured 1979 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 51, NO. 11, SEPTEMBER 1979
current, iT,consists of three components: the faradaic current, iF, the step charging current, ic(step), and the induced charging current, iC(mdu&). Fratoni and Perone ( I , 2) have demonstrated the effect of induced charging currents in chronoamperometric studies of flash photolytic processes. Delahay, Pilla, Berntsen, and co-workers (3-7) also acknowledged the phenomenon of induced charging current and the inseparability of faradaic and charging current, but their work did not provide an explicit approach for the correction of chronoamperometric data for induced charging currents. In Berntsen’s work, digital simulation was employed to study the effects of uncompensated ohmic distortions in potential-step experiments, but the effects of induced charging currents in voltammetric experiments were not considered ( 7 ) . In Fratoni and Perone’s work ( I , 2 ) ,the potentials of interest were located on the diffusion plateau; hence the Cottrell equation was used to describe the faradaic i-t behavior. In the work reported here we have considered charging current effects in potential-step voltammetry. This study seems particularly appropriate at this time because of the widespread acceptance of cyclic voltammetry as an investigative tool. Because modern computer-based instrumentation will shortly replace this tool with the more powerful cyclic staircase voltammetry (cyclic SCV), it seems particularly timely to describe here the limitations imposed by charging currents in potential-step voltammetry. In the study of effects of potential-step and induced charging currents in SCV, the faradaic i-t behavior is dependent on potential, which is a complex function of time. Thus, an analytical description could not be obtained, and digital simulation was employed here in the theoretical treatment of charging current phenomena in SCV. For the present, only reversible and diffusion-controlled processes have been considered. Experimental verification of results are also reported here.
THEORY Boundary Value Problem. In this study we will be concerned mainly with the reversible heterogeneous reduction, 0 + ne R, under diffusion-controlled conditions. The diffusion coefficients of 0 and R are assumed to be equal; Le., Do = DR The boundary value problem is expressed as follows: t = 0, for all X, Co = C O * , CR = CR* =O, E D L = E, (1) t > 0, EDL= f(t,E,,AE,J),J = step number (2) x - m
CO
=
CO*,
C R = CR* = 0
x = o
(3)
Do(
z) z) z) = -DR(
iF = nF*(
x=o
Fick’s Second Law
(7)
where all the symbols have their usual electrochemical significance. Some additional useful relationships are as follow:
iT iCitotal
=
=
iF
(11)
-t iC(mduced)
(12)
iC(total)
k(step)
-k
where ic(step,is charging current due to the potential step, iT is the total cell current, i~ is the faradaic current, iC(mduced) is the induced charging current, iC(total) is the total charging current, Ru is the uncompensated cell resistance, CDL is the double layer capacitance, AE is the potential step, Erefis the reference electrode potential, and E D L is the potential across the double layer. From the preceding relationships a digital simulation technique was used to predict current-time behavior in potential-step chronoamperometry and SCV. Because the basic approach is well-documented in the literature (e),the details are not presented here. However, a complete discussion is available (9).
RESULTS OF THEORETICAL COMPUTATIONS A Single Potential-Step Experiment. To illustrate the effects of charging currents on potential-step chronoamperometry, the example considered here involved a single cathodic potential step of 300 mV, starting at 150 mV anodic of the half-wave potential. Different conditions were considered, including various initial concentrations and cell time constants. Figure 1 illustrates the simulated prediction of current-time behavior in a potential-step experiment. Here, the initial concentration of the oxidizing agent used was 1.0 X M, with a cell time constant of 50 ~ s As . can be seen, the total charging current and the total current decay continuously with time during the entire experiment, while the faradaic current increases a t first, reaches a maximum, and then decays with time. The behavior of the faradaic current can be understood best by realizing that EDLis actually “scanning” toward its final value. Thus, the actual faradaic current has the appearance of a peak-shaped polarogram obtained in linear sweep voltammetry. A maximum in the current is observed after about 1 cell-time constant (R,CDL). Ultimately, (after about 20 cell-time constants) the current approaches Cottrell behavior, where current decays with l/tl/*. Figure 2 shows that the total charging current is the dominating component a t the early stage in the potential-step experiment whereas the faradaic current is the primary contribution a t later times. More importantly, a substantial charging current contribution (- 15%)is predicted after five cell-time constants, and contributions from total charging current of 7 % , 4 % , 2 % , and 1.4% are predicted for times of 10, 15, 25, and 35 cell-time constants, respectively. These are very much different from what one might expect if only the step charging current were involved. If the initial concentration is lowered to 1.0 X M, then a less negative contribution from the induced charging current is predicted, resulting in higher positive contributions to the total current a t short times. An increase in cell-time constant increases the negative contributions from the induced charging current a t short times, resulting in less positive contributions to the total current. The effect of the induced charging current in a potential-step experiment can also be demonstrated through the Cottrell plot, as shown in Figure 3. Curve A is the plot of the total current, and it is noted that Cottrell behavior is not
ANALYTICAL CHEMISTRY, VOL. 51, NO. 11, SEPTEMBER 1979
1647
0
0
0
2.50
0.00
5.00
7.50
10.00
12.50
15.00
TIME. ( T / R C l
9 0
0.10
0.15
0.20 [
Figure 1. Theoretical current-time curve in a single-step experiment. (A) Total current, i,; (B) faradaic current, i,; (C) total charging current, M; R , = 500 Q, CDL = 0.1 pf, R,CD, = iqtotal,. C,' = 1.0 X 50 ps; (E,- E,,,) = 150 mV, A€ = -300 mV; A = 0.01 cm'; Do = D, = 1.0 X cm2/s
C.25
T/RCIB.I
0.30
0.35
1
0.40
-1/2 1
Figure 3. Cottrell plot of theoretical total current and faradaic current. C,' = 1.0 X M; R , = 500 8 ; C ,, = 0.1 pf; R,C, = 50 ps. A = 0.01 cm2;Do = D, = 1.0 X cm2/s;(E, - E,/,)= 150 mV; A € = -300 mV. (A) Total current; (B) pure faradaic current; (c) theoretical Cottrell plot in absence of charging current. Line C intercepts at 0 current at time infinity
0
t
L
5 La
'0.0
j
l 2.50,
l 5.00
, 7.50
, 10.00
, 12.50
, 15.00
TIME. [T/RCI
Figwe 2. Thewetical percentage contributions from current components for single-step experiment. C,' = 1.0 X M; R , = 500 R, CDL = 0.1 pf, R,Cm = 50 ps; A = 0.01 cm2;Do = D, = 1.0 X cm2/s; (Ei - E,,,) = 150 mV, A € = -300 mV. (A) Faradaic current; (B) total charging current; (C) step charging current; (D) induced charging current followed until after 35 cell-time constants. On the ot,her hand, if the pure faradaic component is plotted against l/t'/', Cottrell behavior is observed for times longer than 20 cell-time constants (Curve B). This observation underscores the very
significant fact that pure diffusion-limited currents are not obtained in a potential-step experiment until after about 20 cell-time constants; moreover, if no correction for induced charging current contributions is made, diffusion-limited currents are not obtained until after about 35 cell-time constants. These facts contrast sharply with the usual assumption that valid data can be obtained after 4RC in a potential-step experiment (IO). SCV Experiment. In the study of effects of induced charging currents in staircase voltammetry, we would expect to see behavior for each step similar to that described for a large single-step experiment. The simulated predictions for SCV are illustrated in the following sections. For the first example described here, the starting potential used was 150 mV anodic of the half-wave potential. The potential was then scanned cathodically, with 20-mV steps; the step time was 15 RC, and a total of 15 steps were considered. The faradaic currents for several steps are plotted in Figure 4. Each shows a time dependence similar to the single-step experiment discussed previously. The amount of faradaic current increases with the step number as the potential is approaching the half-wave potential, then decreases after the potential reaches a relatively cathodic value. For each step, the maximum faradaic current occurs at a time around 1 RC, indicating that the voltammogram of pure faradaic current extracted from the total current measurement taken at about 1 RC will have the highest peak current. It is also interesting to consider the variation in charging current contributions to the total current at each step. Figure 5 demonstrates that the potential dependence of the charging current background is considerably different when the current is sampled at 1 RC compared to 4 RC.
OBSERVATIONS The simulated predictions of currents in a single potential-step experiment indicate that the desired potential across
-
0,'
Currents with Respect to Different Initial Concentrations -Single Potential-Step ExperimentD
(0
% 9E m (r
5
-
+-
z
k
w (r E
2 9-
-
A
9 STEP
TINE.
lT/RC)
Figure 4. Theoretical faradaic current-time behavior for potential steps in SCV. C o s = 1.0 X M; R , = 500 Q; CpL = 0.1 pf; RUCDL= 50 ps. A = 0.01 cm2; Do = D, = 1.0 X 10- cm2/s; ( E , - E,,,) = 150 mV; A € = -20 mV; step-time = 15 RC, 15 steps
the double-layer is not reached before 20 to 25 cell-time constants, resulting in deviations of the faradaic current and the total measured current from Cottrell behavior before 20 to 25 and 30 to 35 cell-time constants, respectively. The positive deviation before the currents reach Cottrell behavior indicates that more than diffusion-limited current exists between the region of 1 RC to 25 RC. A maximum demonstrated in the faradaic current-time profile shows that the highest amount of faradaic component can be obtained if the current is sampled a t about 1 RC. However, with different initial concentrations, in two otherwise identical systems, the ratio of the currents is not directly related to the ratio of the concentrations, and it varies with respect to elapsed time, as is illustrated in Table I. In Table I, two concentrations, 1.0
0.525 0.550 0.618
10.0 12.0 15.0
1.052 1.064 1.040
(c,*),
fn
9,v)
03
E 2
; 9,
; 9z m
3
0.8 1.0 1.2
b
zr: 2w p: a
1.113 1.097 1.084 1.073
9-
a
=Lo)
6.0 7.0 8.0 9.0
pl
E?
-
0.998 0.954 0.794 0.596
9 a
e
p:
0.01 0.2 0.4 0.6
(co*),
e
r:
ratio
M, are considered; the ratios in the X M and 1.0 X table are those of the predicted faradaic currents normalized with respect to the initial concentrations. As can be seen, only 5 times as much current is predicted a t times around 1 RC, while the concentration ratio is 10. The ratios approach unity after 25 to 30 RC, as would be expected. The behavior of each step in SCV is similar to that described for a single potential-step experiment. However, in a staircase voltammogram, contributions from charging current vary with the applied potential; also, if the sampling time falls between 1 and 20 RC, more faradaic current is expected than predicted by simple SCV theory based on
9
m
t/RC
concentrations of sample 1 , and sample 2, respectively. Ratio = (iF)l/(iF)2 x ( c o * ) ~ / ( c o * ) ~ ~
9 2-
- 2-
ratio
= 1.0x 10-3 M; = 1.0 x i o - 4 M; = 50 S2 ; CDL = 0.1 fif, RuCDL = 50 f i =~ RC; A = 0.010 c m z , Do = D R = 1.0 x cm2/s. ( E , - E , , , ) = 150 mV, A E = -300 mV. (Co*),, (C,*), = Initial a
R,
9
21
t/RC
r:
3-
z
W p:
a
= l
R
C
ANALYTICAL CHEMISTRY, VOL. 51, NO. 11, SEPTEMBER 1979
a
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b
T I M E , fMlCROSEC1 TIME, [PIICROSEC) Figure 6. Comparison of theoretical and experimental current-time behavior for long cell time constant in single-step experiment. (Fe(Ox)?-) cm2/s;( E , - E,,2) = 150 mV; M: R , = 465 9; ( C & = 0.722bf, (R,C& = 335 1 s ; A = 0.0182 cm2; Do = 3.11 X = 6.05 X A € = -300 mV. Solid lines. theoretical results: dotted lines, exDerimental results; (A) Total current (measured),(B) total charging current (calculated), (Cy faradaic current (calcuiated). diffusion control only, and the relative deviation is not constant with respect t o the applied potential. Experimental verification of simulated predictions described above is presented in t h e following sections.
EXPERIMENTAL Chemicals. K2C204,0.2 M, (Analytical grade, Mallinckrodt) was used as the supporting electrolyte in the experiments. Ferrioxalate solution, 1.046 X M, in 0.2 M KzCzO4 was obtained by dissolving the proper amount of FeNH4(S04)2-12H20 crystals (Analytical grade, Malliickrodt) in 0.2 M K2C204solution. The concentration of the ferrioxalate solution was determined as described in Reference 11. The concentration of the sample solution used in the study of the induced charging current was a 6.05 X lo4 M ferrioxalate in 0.2 M K2C204solution, which was prepared by dilution of the M ferrioxalate solution. Distilled deionized water was used for all solutions. Electrodes. A 3-electrode cell was used. Platinum coil was used as the counter electrode; a Coleman 3-710 calomel electrode was used as the reference electrode. A hanging mercury drop (Brinkmann E-410) was employed as the working electrode. The drop area used in all experiments was either (0.0141 f 0.0001)cm2 or (0.0182 f 0.0001)cm2. Potentiostat and Computer Instrumentation. A conventional 3-electrode potentiostat and current measurement circuitry were used (9). A variable resistance was placed in series with the working electrode to adjust the uncompensated resistance (and hence the cell time constant) a t will. The potentiostat rise time (99%) was 20 ps for an application of a 300-mV potential step, and 10 ps for a 20-mV step. A laboratory minicomputer system (Hewlett-Packard 2116B) was used for programmed potential-step experiments and for data acquisition and data reduction. The system included a 14-bit DAC (&lo V, Analog Devices DAC-l4QM), an 11-bit ADC (& 10 V, Analog Devices 12QM), the timing logic, a programmable clock, a Teletype, a high speed tape reader, a high speed tape punch, and an oscilloscope. The output signal could be digitized every 30 ps. Experimental Procedures. The half-wave potential of 6.05 X 10” M ferrioxalate solution at pH 8.3 was determined with cyclic voltammetry to be -242 mV vs. SCE. All sample solutions were deaerated prior to the beginning of the experiment by bubbling high purity nitrogen gas through the solutions for 20 min. For each experiment, the appropriate potential function was applied to the cell, and the output signal was digitized and stored as described above. Because the output current for the large po-
tential step had a relatively high value at short times and decayed rapidly, the measurement circuit was adjusted so that a lower gain was used to monitor the signal at short times without saturation and a higher gain at longer times to detect even slight changes in the output. Ensemble averaging and moving-window smoothing were utilized to improve the signal-to-noise ratio. Because it was known that the double-layer capacitance in the oxalate system varies with the applied voltage, it was necessary to determine the double-layer capacitance as a function of potential. To accomplish this, a potential step of‘ 10 mV initiated at various potentials covering the entire voltage span of interest was imposed on a cell of the blank electrolyte solution. The decay of the charging current from each potential step was recorded. Assuming little change in double-layer capacitance over the 10-mV range, the decay of the step charging current, ic(step),can be related to the elapsed time, t, the potential step size, 1E,the cell-time constant, RuCDL,and the uncompensated resistance, R,, as described by Equation 9. Therefore, the cell-time constant, R,CDL, and the uncompensated resistance, R,, were determined, respectively, from the slope and the intercept of a plot of In i ~ ( ~ ~ ~ , vs. time. Once R, and R,CDL were known, the double-layer capacitance, CDL,was readily calculated. In the study of the effects of the induced charging current in a potential-step experiment, 6.05 X M ferrioxalate solution in 0.2 M K2C204was used. Starting at 150 mV anodic of the half-wave potential, the potential was stepped 300 mV cathodic. The output signal was the total current, I T . The total charging current corresponding to the nth data point was obtained by using a finite difference form of the differential Equation 13.
A t short times, the amount of the total charging current was different than the charging current observed with a blank electrolyte solution at the same potential. The difference was assigned to the induced charging current as shown in Equation 12. The faradaic current, iF, was extracted according t o Equation 11. A similar approach was utilized in the analysis of the measured
total current under the influence of a staircase potential function. Starting at 150 mV anodic of the half-wave potential, the voltage was scanned stepwise cathodically, with 20-mV steps. The step duration was either 2000 p s or 5000 ps, depending on whether the cell time constant was 143 ps or 335 ps. and corresponded to 14 RC or 15 RC, respectively.
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ANALYTICAL CHEMISTRY, VOL. 51, NO. 11, SEPTEMBER 1979
21 0
a
STEP hUY6ER
b
STEP NdPBER
Experimental current contributions to staircase voltammograms for larger cell time constant. (Fe(Ox):-) 6.05 X M; R = 465 9 , (C& = 0.722 pf, (RuC0JE,= 335 ps; A = 0.0182 cm'y Do = 3.11 X lo-' cm'/s; ( E ,- E,,*) = 150 mV; A € = -300 mV. Solid lines, theoretical results; dotted lines, experimental results; (A) total current (measured),(B) total charging (calculated),(C) faradaic current (calculated). (a) sampling time, 0.90 RC, (b) sampling time, 3.58 RC Figure 7.
EXPERIMENTAL RESULTS A Single-Step Experiment. The experiments were run as described in the Experimental section, and the total current was analyzed as described above. The cell-time constant a t the initial potential was 335 ps. The experimental results were compared with simulated predictions at short times as shown in Figure 6, where excellent agreement was observed. Because of the manner in which faradaic currents must be computed from raw data, it was found that good agreement at short times could be obtained only with a data density greater than about 20 points during the first two RC periods. Because the step charging current decreases to 1%of the total after 10 RC, the interference of charging current at longer times is due to the induced charging current. Thus, deviation from Cottrell behavior was observed up to 33 RC, or up to 20 RC if correction for the charging current interference was made, as predicted in Figure 3. The slope of the straight line which fits those corrected data points at times greater than 20 RC was then used to calculate the diffusion coefficient of Fe(0x):- ion. The coefficient thus obtained was 3.11 x IO4 cm2/s. This value was then used for both the oxidizing and the reducing species in the digital simulation of the experimental studies. SCV Experiment. Simulation of staircase voltammograms predicted that the contribution from the charging current to the total current measurement taken to construct the voltammogram is not constant throughout the entire voltammogram. If the current was sampled at earlier times, then minimum contribution around the peak was predicted; while with a later sampling time, maximum contributions around the peak were predicted (Figure 5). Experimentally, we observed exactly the same phenomenon, as shown in Figure 7. The plots in Figure 7 were constructed from the currents, iT, iF, and ic(total),in a ferrioxalate system with R,CDL = 335 ws. Data used in Figure 7a were collected a t 0.9 RC, and in Figure 7b at 3.58 RC. CONCLUSIONS The results of experimental studies with ferric oxalate have demonstrated the validity of simulated predictions of the effects of potential-step and induced charging currents on faradaic and total currents. Agreement was observed for both single-step and SCV experiments. Thus, the implications of these studies should be considered at this point. First of all, it is clear that the usual assumption made in potential-step experiments that the interference due to charging current could be ignored after about 4 RC is not valid. Results here show that, in a potential-step experiment, there
is still a significant amount of charging current after 4 RC (1150/~).After 7 RC most of the charging current (>95%) is induced by the flow of the faradaic current. Moreover, the interference decays very slowly with time, reaching 1% of the total current at 50 RC. Thus, if an interpretation of current-time behavior at short times based on theoretical predictions of simple kineticdiffusion Fick's law expressions is desired, the data analysis will be inappropriate and perhaps significantly inaccurate. In fact, whenever coupled chemical reactions affect the faradaic current, it is likely that induced charging currents will be greater than for diffusion-only processes (12). Unfortunately, the predictions of total and faradaic current cannot be done analytically, and digital simulation is required to predict behavior. However, it is always possible to calculate the total charging current contributions to measured current by the derivative method described here and elsewhere (13). A comparison of experimentally observed faradaic currents to a simulated family of curves might allow the extraction of fundamental information even at very short times. At the very least, simulation studies could define the time domain in which undistorted faradaic currents might be obtained for fundamental studies of kinetic-diffusion processes. The implications of the work for analytical measurements with SCV are significant. Firstly, the analytical advantages of very short sampling times suggested by previous theoretical work (14,15) cannot be achieved when T' 5 20 RC. Because ratios of step time to sampling time ( T / T') greater than lo4 would be required to achieve substantially improved peak enhancement and resolution in SCV, total required analysis time would be prohibitively long unless RC 5 10 p s . The above observations lead ultimately to the recommendation that experimental studies in potential-step chronoamperometry and voltammetry should employ cells with short time constants (IO)and/or potentiostatic correction for uncompensated ohmic distortion. It should be noted, however, that even with potentiostatic compensation, there will still be an effective residual time constant for double-layer charging which effects short-time distortions as described in this work. T h a t is, using IR compensation only pushes the problems to shorter times for any given cell, but the distortions still exist, and the time-scale may be substantial, as for example, with nonaqueous solutions. Thus, the work presented here describes quantitatively how the short time data can be interpreted, regardless of the magnitude of the actual or effective cell-time constant.
LITERATURE CITED (1) Fratoni, S. S.,Jr.; Perone. S. P. Anal. Chem. 1976, 48, 287-295. (2) Dahnke. K. F.; Fratoni, S.S., Jr.; Perone, S. P. Anal. Chem. 1976, 48, 296-303. (3) Delahay, P. J. Phys. Chem. 1966, 70, 2373. (4) Delahay, P.; Susbielles, G. G. J. Phys. Chem. 1966, 70,3150. (5) Holub, K.; Tessari, G.; Delahay, P. J. Phys. Chem. 1967, 77,2612. (6) Rlh. A. A. "Electrochemisw, C a l c u h h , Simuhtbn, and Instrumentah"; Mattson, Mark, and McDonald. Ed.; Marcel Dekker: New York, 1972. (7) Berntsen, J. H. R.D. Thesis, University of Wisconsin, Madison, Wis.. 1974. (8) Feldberg. S.W. "Electroanalytical Chemistry"; Bard, A. J.. Ed., Marcel Dekker, New York, 1966; Vol. 3. (9) Mew, L. H. L. R.D. Thesis, Purdue University, West Lafayette, Ind., 1978. (10) Mumby, J. E.; Perone, S.P. Chem. Instrum. 1971, 3 , 191-227. (1 1) Kolthoff, I.M.;Sandell, E. B.; Meehan, E. J.; Bruckenstein, S."Quantitative Chemical Analyses", 4th ed.; The Macmillan Co.: New York; Chapter 61. (12) Fratoni, S. S.,Jr.; Perone, S. P. J . Electrochem. SOC. 1978, 123, 1672-1676. (13) Eahnke. K. F.;Perone, S.P. J. €A?cb.ochem. SOC. 1976, 723,1677-1683. (14) Zipper, J. J.; Perone, S.P. Anal. Chem. 1973, 4 5 , 452-458. (15) Miaw, L. H. L.; Botidreau, P. A.; Pichler. M. A.; Perone, S.P. Anal. Chem. 1978, 50, 1988-1996.
RECEIVED for review May 30, 1978. Accepted May 24, 1979. The financial support of the Office of Naval Research and the Department of Energy, contract EG-77-S-02-4263is gratefully acknowledged.
