Anal. Chem. 1908, 60, 503-507
503
Chronopotentiometry by Measuring Current Transients Abul Hussam* a n d Gamini G u n a r a t n a Chemistry Department, George Mason Uniuersity, Fairfar, Virginia 22030
Chronopotentiograms in normal and differential mode are generated simultaneously by measuring the decay time of a transient current to a preset value after the application of potentlal pulses. I t Is shown that the excitation potential as a function of time Is a normal chronopotentlogram and the response time as a function of the applied potentlal is a differential chronopotentiogram. A general equation for voltammetry wtth stepfunctlonal potentlal changes Is applied to simulate the chronopotentiograms. Application of the technique in stripping analysis of metal amalgams Is outlined.
Constant current chronopotentiometry has been in existence for more than three decades ( I ) . Other variations of it, including chronopotentiometry with compensation for extraneous current (2), programmed current (3), chronopotentiometry in solution layers of finite thickness ( 4 , 5 ) chronopotentiometry under restricted diffusion for both oxidized and reduced species (6,7),and derivative technique (8), have been developed. These developments were motivated by three factors: to achieve a better current efficiency of the constant current applied with a galvanoatat, to measure transition time accurately, and to obtain a linear relationship between transition time and concentration. Analytically, it is necessary to measure transition time accurately, and preferably, the transition time should be directly proportional to the concentration of the analyte. All chronopotentiometric measurements and its variations have used a galvanostat as the constant current source. Since it is often inconvenient to change from the potentiostatic to the galvanostatic mode, particularly with dedicated computerized instruments (9) that perform a number of electrochemical techniques, one of the objectives of this paper is to investigate the possibility of generating both normal and differential chronopotentiograms by using a computer-controlled potentiostat. The technique is based on the principle of transient current measurement after the application of constant potential pulses. The time elapsed for the current to decay to a constant or threshold value is monitored and plotted as a function of the applied potential that generated the normal chronopotentiogram. We have also shown here that a general equation for pulse voltammetry can be applied to simulate the chronopotentiograms along with classical equations. Application of the technique in chronopotentiometric stripping of amalgamated metals is examined. EXPERIMENTAL SECTION Materials. Potassium ferrocyanide, potassium chloride, and potassium nitrate were reagent grade chemicals. Potassium ferrocyanide (4.98 mM in 1.0 M KC1) solution was thoroughly deaerated by bubbling nitrogen through it and stored under a nitrogen atmosphere. For stripping experiments, Pb and Cd (AA Standards by Fisher Scientific) were used. The glassy carbon electrode (IBM Instruments, Inc.) was first polished with a 600-grit silicon carbide powder (Buehler, Evanston, IL)on a wet polishing cloth and then polished again with a 0.3-pm alumina slurry until a mirror finish surface was obtained. It was thoroughly washed with distilled deionized water. The electrode was then conditioned in a solution of 4.98 mM potassium ferrocyanide in 1.0 M KC1 by cycling the potential between -200 mV 0003-2700/88/0360-0503$01.50/0
and 800 mV vs SCE (SCE = saturated calomel electrode). The result was a cyclic voltammogram with a peak potential difference = 210 mV v8 SCE, and a peak current ratio, i p / i w of 75 mV, = 1.08 at a scan rate of 30 mV/s. These values were comparable to the prescribed values (IO). The geometric area of the working electrode was 0.1963 cm2. A saturated calomel electrode (IBM Instruments, Inc.) was used as a reference electrode and a platinum coil was the counter electrode. For chronopotentiometric stripping analysis a hanging mercury drop electrode (Metrohm) was used. Experimental Setup. A schematic diagram of the experimental setup is shown in Figure 1. The potentiostat is a conventional unit with three operational amplifiers (Texas Instruments, Inc., Model TL 084 with FET inputs) without positive feedback iR compensation. The potentiostat is interfaced to the data acquisition and control board (ADALAB, IMI, State College, PA), located in a personal computer (Leading Edge, Model 3D). The ADALAB card has a 12-bitDAC (digital-to-analogconverter) and two 12-bit ADC's (analog-to-digital converter), one with a slow 30-Hz and the other with a fast 20-kHz sampling rate. The control software was written in BASICA (GW-Basic, Version 2 by Microsoft) with the exception of BASICA callable assembly language subroutines (supplied by IMI) which control the D/A (potential output) and the A/D (current sampling). Time measurements were accomplished by the TIMER command of BASICA. Measured time values were accurate to 0.01 S and were sufficient for the present purpose. Data analysis programs were written in TURBO-PASCAL (Version 2 by Borland International, CA). The data analysis program PLOT.COM was called from the main program by using a SHELL command. A full screen plot of the acquired data was analyzed by moving an on-screen cursor and transition time, transient potential, peak time, and peak potential were obtained. A moving average smoothing program was also included in the PLOT program to facilitate data plotting. Chronopotentiograms shown in this paper were plotted by the printer. On the basis of this instrument we have implemented a wide variety of electroanalytical techniques including some of the pulse techniques. All experiments were performed at room temperature (23-25 "C). Numerical simulation of the chronopotentiograms was carried out in real time by using the same TIMER command and processed by the same PLOT program. Principle and Procedure. The principle of the method is shown schematically in Figure 2. First, an initial potential is selected where no faradaic reaction takes place. After a predetermined delay period, potential pulse AE is applied (Figure la) and the decay current is monitored as a function of time. When the absolute value of the decay current reached a value smaller than or equal to the threshold current ith (within one count of the full scale A/D), the time elapsed after the pulse is monitored (Figure 2b). The threshold current is equivalent to a constant current in a galvanostatic method. The second potential pulse of the same magnitude is applied on El, and the time measurement procedure is repeated until a final potential is reached. Time values t l , t2,...,t , and the differences Ato, Atl, ..., Atn-l are stored as a function of the applied potential. In the absence of electroactive species, the potential will increase linearly with time due to the charging of the double-layer as shown by the broken lines of Figure 2c. In the presence of a redox couple, the transient potential will start to vary slowly at a characteristic overpotential until the reaction is diffusion controlled, after which the transient potential will regain the initial slope. The plot of electrode potential as a function of time is the normal chronopotentiogram and the plot of differential time as a function of electrode potential is the differential chronopotentiogram as shown in parts c and d of Figure 2, respectively. It should be noted that the pulse excitation as a function of time is the analytical signal and Figure 0 1988 Amerlcan Chemlcal Socletv
504
ANALYTICAL CHEMISTRY, VOL. 60, NO. 5, MARCH 1, 1988
560.4 h
W v)
; 373.6 5
AID
/
>
" 106.8 w
:
:
:
!
:
:
10.0
:
! 15.0
t (sec)
,. " av L1 l
"'"t
0.24
Figure 1. Block diagram of the experimental setup.
21 6 . 5
433.0
649.6
E (aV vs. SCE)
Flgure 3. Background of (a) normal and (b) differential chronopotentiograms of 1.0 M KCI. Conditions: AE = 12.2 mV; i,,, = 19.5 wA. A three-point moving average smoothing was used to plot b. t Uelay 0
tl
-, 0
t2
,'.
,
tI
t
tt
I
0
I \
. I . - - -L E Flgure 2. Schematic description of the principle.
2a is simply an exploded view of the first few points of Figure 2c. The current transient measurement procedure is illustrated in Figure 2b. After the application of the potential pulse, the total current (faradaic + charging) is allowed to decay, and during this decay, current is sampled at a rate of 30 Hz. A number of samples are then averaged and compared to ith. The time recorded was that when ith I imeard. Experience showed that the averaging procedure reduced noise. Because of the overhead time requirement of the software, the number of points averaged are kept to a minimum (between 2 and 5 points). As we know that the double-layer charging component of the total current decays much faster (exponentially) than the faradaic current after the potential pulse, i* is mostly due to the faradaic processes. This is particularly true for small ith and AE values. Therefore, by choosing
an appropriate ithand hE values, chronopotentiograms could be obtained with a high current efficiency on a constant background. Similar advantages cannot be realized by a conventional galvanostatic method.
RESULTS AND DISCUSSION General Features. The background chronopotentiogram (CP) and the differential CP of a 1M KC1 solution are shown in parts a and b of Figure 3, respectively. As expected, the background is a linear potential ramp with a calculated slope of 60 mV/s for the CP. For the differential CP, the average At is 0.16 s with almost a flat profile. Parts a and b of Figure 4 show typical CP and the differential CP for the oxidation of ferrocyanide. The average At of the differential CP background is 0.18 a, which is slightly higher than that in the supporting electrolyte alone. Transition times in constant current chronopotentiometry for a reversible system can be expressed by the following equations (11):
K = nFADo1/2.n1/2/2 = 85.5nADo1/' ((mA s1l2)/( cm2 mM))
B = icr (mA s)
(2)
(3) where C is the bulk concentration of the analyte, T is the transition time, A is the area of the electrode, Dois the diffusion coefficient of the analyte, ith is the total current (constant in the galvanostatic mode and threshold current in the present technique), and i, is the charging component of the total current. The last term in eq 1 is the total number of coulombs needed to charge an average double-layer capacitance from the initial potential to the potential a t which r is measured. It represents a correction factor in constant current chronopotentiometry. Table I shows the i t h and 7 values a t a constant potential pulse for the oxidation of ferrocyanide. According to eq 1,the best fit values of the slope and intercept are 0.2138 f 0.006 and -0.0715 f 0.043, respectively, with a
ANALYTICAL CHEMISTRY, VOL. 60, NO. 5, MARCH 1, 1988
IL
(a)
Table 11. Effects of Pulse-Step Size on Normal and Differential Chronopotentiogramsa
I
-
628.8
Y
t
505
AE,mV 2.4 6.1 12.2 18.3 24.4 48.8
(rec)
At,* E
E,/, (mV VB SCE)
Ep,k (mV
B
vs SCE)
fwhm,'mV
130.9 122.3 112.8 106.3 100.0 90.0
3.4 8.0 13.7 18.7 24.7 36.1
227 227 231 243 248 214
231 233 243 262 273 323
83 85 84 90 93 99
7,
The same solution a8 in Table I; ith = 19.5 @A. Peak time for the differential chronopotentiograms. Full width at half-maximum peak value of differential chronopotentiograms.
. o
E (mV
729.0
486.0
243.0 SCE)
VS.
Figure 4. Normal (a) and differential (b) chronopotentiograms of 4.98 mM K,Fe(CN), in 1.0 M KCI. Conditions are same as those given for Figure 3.
Table I. Effects of Threshold Current on Normal and Differential Chronopotentiogramsa it,,, @A
T , ~
E,,t
19.5 29.3 39.1 48.8 58.6 78.1
112.8 47.6 25.7 15.3 11.0 5.3
230 231 232 232 235 233
s
E,&'
slope: mV slope ratid
243 246 243 247 246 245
66 65 64 66 61 66
2.82 1.00 1.06 1.10 1.07
0.95
a Experimental conditions: 4.98 mM of potassium ferrocyanide in 1.0 M KC1; AE = 12.2mV. Initial and final potentials are -200 and 600 mV vs SCE, respectively. bAverageof at least three measurements. Quarter-wave potential (mV vs SCE) obtained from the plot of eq 4. Estimated experimental uncertainity is *2 mV. Peak potential (mV vs SCE) of differential chronopotentiograms. 'Slope of eq 4. fRatio of slopes between initial and final transients (see Figure 2c).
correlation coefficient of 0.999 72. The diffusion coefficient calculated according to eq 2 is 6.53 X lo4 cm2/s,which is in good agreement with the literature value 6.32 X lo4 cm2/s (4.0 mM of potassium ferrocyanide in 1.0 M KC1) (12). The values of ith7lI2calculated from Table I reveal that the longer transition times obtained a t low ith values are affected by convection and edge-diffusion while the shortest transition time (at ith = 78.1 PA) is affected significantly by the contribution from the charging current. It caused a premature detection of At values of individual current transients before the next pulse was applied and thus a shorter transition time. Although we have used a high analyte concentration and the transition times are relatively long, clearly the charging contribution cannot be neglected a t high ith values. Excluding the i t h W at ith = 78.1 PA, the mean ithr112 is 198.5 f 7.3 at 95 % confidence interval, well within experimental values. Transient potential in constant current chronopotentiometry for a reversible oxidation is expressed by the equation
E, = E,,, - (RT/nF) In
-
[ ( ~ / t ) l 11 / ~
(4)
where E, is the measured transient potential, Ell1 is the
quarter-wave potentid, which is related by the polarographic half-wave potential, and all other terms have their usual meaning. The slope and intercept values according to eq 4 are listed in Table I. The slope values (RT/nF)show that the system is quasi-reversible in agreement with other workers (13). The intercept values are lower by the step potential value (12.21 mV in this case) in comparison to the literature value (13) for the redox couple. The peak potential of the differential CP, on the other hand, is in better agreement with the literature value for the quarter-wave potential. The results above indicate that the transition times and the shape of the transient potential are adequately described by the conventional chronopotentiometric equations, but not the quarterwave potential. Chronopotentiometric theory is based on the fundamental assumption that all of the electrolysis current advances the reaction of the electroactive species of interest and the mass transport is controlled by a semiinfiiite linear diffusion of the analyte (as in eq 1). In constant current CP, the double-layer charging causes the current efficiency to be less than unity. This causes the applied current to vary during the experiment and is highest at the beginning and near the end of the transient potential. It has been shown (14,15)(Figure 4 of ref 14) that at the start of the chronopotentiogram the constant current is wholly consumed in the charging of the double layer, and near the end of the transient potential the capacity current increases rather gradually. Diagnostically, it means that the slope of E,-t curve at the end and at the beginning are different and their ratio will be greater than unity. In Table I we have listed the slope ratios for different ith values while AE remained constant. It is observed that for a long transition time the ratio is greater than unity. This is probably due to the fact that the diffusion of the analyte is linear in the beginning and nonlinear at the end of the transition time. For the rest of the data, the ratio is close to unity even for high ithvalues. This is probably because the threshold current is sampled when dE/dt = 0. Generally, it takes a few milliseconds for the charging current to decay 95% of its initial value for a small potential pulse and for a small double-layer capacity (e.g., 20 pF/cm2 for a mercury electrode). The double-layer capacity is usually much higher at a carbon electrode and the charging transient decay will be slower. This is one of the reasons for a large background (0.16 s) in the differential CP. Conceptually, the present technique shows a way to eliminate the charging component of the total current to achieve a better current efficiency compared to that of the constant current chronopotentiometry. Future experiments are planned in this direction, using low analyte concentration. Effect of Pulse-Step Size and Simulation of Chronopotentiograms. Table I1 illustrates the effect of pulse-step size on the transition time (normal and differential), quarter-wave potential, peak potential, and the peak dispersion at a fixed ith value. While the transition time is decreased with increasing pulse-step size, the differential transition time
506
ANALYTICAL CHEMISTRY, VOL. 60,NO. 5, MARCH 1, 1988
-.h
(a)
1 140.8
500
158.2
316.4
474.6
632.8 v
t
(net)
c
a
(b)
.I:.' Current Ocnsit~(uA/crn-Z)
,.
Flgure 6. At vs threshold current density according to eq 5 at A€ = 5 (O), 10 (+), and 20 (0)mV. Parameters: Eo = -200 mV; E o = 230 mV; C = 5 mM; D = 6.32X 10" cm2/s;A = 0.1963 cm2:final potential = 600 mV.
u
v
1
Y
Q .---
_.
...d____..*
-217.6
:
.
L . 7
I
(a)
-: ''..:-
0
-108.8 E (nY
VS.
-_1oB.8 t
:
:
t (set)
I
217.6
SCE)
Figwe 5. Simulated (a)normal and (b) dtfferential chronopotentiograms according to eq 5. Parameters: im = 0.05 MA, A€ = 1.0 mV, E o = 230 mV, and C = 5.0 mM. Starting potential was 0 mV and final potential was 400 mV.
is increased. The increase in differential transition time with pulse-step size is analogous to the increase in the differential current with modulation amplitude in differential pulse polarography. The peak potential in the differential CP is shifted approximately by the size of the pulse with respect to the quarter-wave potential of the normal CP. A similar effect has been observed in window-sweep chronopotentiometry (16). The peak dispersion (full width at half-maximum of the peak) is increased with increasing pulse-step size. Similar peak broadening has been observed in differential pulse polarography (17) and square-wave polarography (18). Differential CP is observed to be noisier with large pulse sizes and less suitable for analytical purposes. Conventional chronopotentiometric equations described above do not show the effects of pulse amplitude on the transition time, transient potential, and the peak potential because they are derived specifically for constant current chronopotentiometry. To simulate chronopotentiograms based on the transient current approach, we used a general equation for voltammetry with step-functional potential change ( 1 7 ) . For a reversible oxidation the equations are
. Ith
A$j = (eo
=
nFAD112C *J/, # jE-5 1 tj'P
+ ~)l'ej-,/C0j-i + Y) - e j / ( s j + 711 Y =
(5)
(6) (7)
(9)
where ti is the total time required to reach the threshold current at the j t h pulse (see Figure lb), y is the ratio of the diffusion coefficients of oxidized and reduced species (for all
(b)
-1 3 . 2 n
1.6
u "
;1
-
E (mV
VS.
SCE)
Optimized (a)nwmal and (b) differential chronopotentiograms for the reduction of 8.9 X lo-' M Cd(I1) In 1.0 M KCI at a HMDE. Conditions are i, = 0.11 PA and A€ = -7.2 mV. Observed peak potential is -598 mV vs SCE. Flgure 7.
practical purposes y is assumed to be unity), Eo is the initial potential, Eo is the standard redox potential, and all other terms have their usual meaning. Equation 5 reduces to the specialized forms applicable to square-wave voltammetry (18) and staircase voltammetry (19,20) by inserting appropriate values for sampling time. For the purpose of simulating chronopotentiograms we calculated the time required for the current to decay to a fixed ith value after the application of a potential pulse. To be realistic, we used the same TIMER command of the experiment in the program. Simulated normal and differential chronopotentiograms are shown in parts a and b Figure 5, respectively, using 1-mV potential pulses. It is clear from the plot that the standard redox potential is the half-wave potential in the normal CP and the peak potential in the differential CP. The actual resolution of At of the differential CP at low At values shows the imprecision of the TIMER command. Equation 5 does not yield
ANALYTICAL CHEMISTRY, VOL. 60, NO. 5, MARCH 1, 1988
-
E (mV
VS.
SCE)
Figwe 8. Normal (a) and differential (b) stripping chronopotentiograms of 1.78 X lo-' M Cd(I1) and 9.66 X lo-' M Pb(I1) in 0.1 M KNO, at a HMDE. Experimental condttbns: i, = 3.42 pLA; A€ = 12.2 m V 30-s deposition time in a stationary solution at -800 mV vs SCE. A twopoint moving average smoothing was used to plot b.
a simpler form for transition time and peak potential because the calculated time value a t any point on the chronopotentiogram depends on the previous steps. The dependence on the pulse-step size is hidden in the A$j term. Figure 6 shows the nonlinear response to At as a function of current density at different pulse-step size. It is also noted that At increases nonlinearly with increasing AE at a constant current density. Since the theoretical simulation does not contain the charging current component, the observed effect in Table I1 is qualitatively similar. Examination of eq 5 and Tables I and I1 suggests that by optimizing hE and ith values a longest transition time can be obtained for a particular concentration of the analyte. This increase in sensitivity in differential CP is generally obtained by using a large hE and small ith values. Figure 7 shows chronopotentiograme obtained by using one such value for the reduction of cadmium ions on a hanging mercury drop electrode. When the value of the transition time (31.6 s) is used, the calculated concentration for an assumed transition time of 0.1 s is found to be 5 X lo-' M; the shortest transition time reached with feedback compensation of the double-layer charging current is of the order of 0.1 s (21). Similar chronopotentiograms are indeed very difficult to obtain by galvanostatic means. In both cases, however, care should be taken not to use very small current values with unshielded electrodes (22). Stripping of Lead and Cadmium. Chronopotentiometric stripping of 1.78 X M Cd(I1) and 9.66 X 10" Pb(I1) from a hanging mercury drop electrode in a stationary solution is shown in Figure 8. The distinction between two waves is excellent compared to that obtained by using a galvanostatic method with similar concentrations at a thin mercury film on a glassy carbon electrode (23). It may be noted from Figure
507
8 that the slopes in the beginning and at the end of each transition time are approximately equal (the calculated ratio was 1.02). As described earlier, this means a better current efficiency due to the screening of the charging current. We made no attempts to optimize the stripping chronopotentiograms by choosing appropriate values of i t h and AE. These studies will be discussed elsewhere. One of the major disadvantages of chronopotentiometry at a macroelectrode is that the transition time has a squared dependence on the analyte Concentration. This dependency may be linearized by using ultramicroelectrodes (e.g., fiber or dot) where a steady-state concentration gradient is reached almost instantaneously (24). It has been noted (22),however, that there was no difference between the chronopotentiograms of oxidation and reduction from a mercury pool electrode for multicomponent samples, but stripping of metals from a mercury-film amalgam has shown a linear relationship between transition time and concentration without an enhancement effect. In conclusion, the technique presented in this paper for generating chronopotentiograms is suitable for a computercontrolled potentiostat. The peak-shaped differential chronopotentiogram which resembles, in many ways, that of differential pulse polarography is particularly suitable for analytical purpose. To obtain the best possible signal, it may be possible to find the optimum threshold current and pulse size either by performing a few initial experiments or by using a simplex optimization technique guided by the theoretical equations. ACKNOWLEDGMENT We thank Edward Johnson of this department for valuable discussions. Registry No. Pb, 7439-92-1;Cd, 7440-43-9; potassium ferrocyanide, 13943-58-3. LITERATURE CITED (1) Delahay, P.; Berzin, T. J . Am. Chem. SOC. 1953, 7 5 , 2486. (2) Shults, W. D.; Haga, F. E.; Mueller, T. R.; Jones, H. C. Anal. Chem. 1965, 3 7 , 1415. (3) Hurwitz, H.; Gierst, L. J . flectroanal. Chem. 1961, 2 , 128. (4) Perone, S.P.; Davenport, K. K. J. flectroanal. Chem. 1966, 12, 269. (5) Perone, S.P.; Brumfield, A. J. flectroanal. Chem. Interfackl Nectrochem. 1967, 13, 124. (6) Christenson, C. R.; Anson, F. C. Anal. Chem. 1963, 3 5 , 205. (7) Oglesby, D. M.; Omang, S.V.; Reiiley, C. N. Anal. Chem. 1965, 3 7 , 1312. (8) Peters, D. G.; Burden, S. L. Anal. Chem. 1966, 38, 530. (9) He, P.; Awry, J. P.; Faulkner, L. R. Anal. Chem. 1962, 5 4 , 1313A. (IO) Thornton, D. C.; Corby, K. T.; Dube, D. G.; Spendel, V. A.; Jordan, J.; Robbat, A., Jr.; Rutstrom, D. J.; Gross, M.; Ritzier, G. Anal. Chem. 1985, 5 7 , 150. (11) Bard, A. J.; Faulkner, L. R. €/echochemical Methods : Fundamentals and Methods; Wiiey: New York, 1980; p 261. (12) Sawyer, D. T.; Roberts, J. L., Jr. Experimental Electrochemistry for Chemists; Wiley: New York, 1974; p 77. (13) Delahay, P.; Mattax, C. C. J . Am. Chem. SOC.1954, 7 6 , 874. (14) DeVries, W. T. J . flectroanal. Chem. Interfacial flectrochem. 1966, 17, 31. (15) Reinmuth, W. H. Anal. Chem. 1961, 33, 485. (16) Kato, Y.; Yamada, A,; Yoshida, N.; Unoura, K.; Tanaka, N. Bull. Chem. Soc. Jpn. 1961, 5 4 , 175. (17) Rifkins, S. C.; Evans, D. H. Anal. Chem. 1976, 4 8 , 1818. (18) Ramaley, L.; Kraus, M. S.,Jr. Anal. Chem. 1969, 4 1 , 1362. (19) Christie, J. H.; Llngane, P. J. J . Nectroanal. Chem. 1965, IO, 176. (20) Ferrier, D. R.; Schroeder, R. R. J . Electroanal. Chem. Interfackl flectrochem. 1973, 4 5 , 343. (21) Bos, P.; Dalen, E. Van. J . Nectroanal. Chem. Interfacial flectrochem. 1973, 45. 165. (22) Bard, A. J. Anal. Chem. 1961, 3 3 , 11. (23) Bos, P. J . flectroanal. Chem. Interfacial flectrochem. 1972, 3 4 , 475. (24) Wightman, R. M. Anal. Chem. 1981, 53, 1125A.
RECEIVED for review December 5, 1986. Resubmitted September 9, 1987. Accepted November 17, 1987.
