Charging Current Compensation in Semiintegral Electroanalysis Steven C. Lamey, Roman D. Grypa, and J. T. Maloy' Department of Chemistry, West Virginia University, Morgantown, W. Va. 26506
Rapid evaluation of the current semiintegral [m( t ) ] is necessary for some kinetic studies and some types of electroanalysis. Preliminary experiments presented herein indicate that this is not posslble In the potential step experiment because non-faradaic charging currents contribute deleteriously to the analog m(f) signal obtained. To circumvent this, a current clipper circuit has been designed. Used in conjunction with an analog semiintegrator, this circuit selectively enhances the faradaic component of m ( t ) at the expense of components due to charging currents passed soon after the potential step. The utility of the circuit is supported theoretically and experlmentally. The theory predicts effectlve capacitive compensation at all times greater than 100 RC with judicious selection of the cilpping time. The reductions of aqueous Pb2+ and diethyl fumarate and diethyl maleate in DMF illustrate the experimental feasibility of the method, but the theory Is not completely verifled because of apparent instrumental ilmltations. Concentration studies with Fe(EDTA) indicate that the method is especially suitable for trace analysis.
Semiintegral electroanalysis has been proposed as a rapid method suitable for analysis of electroactive species at a solid electrode because the signal obtained is constant and proportional to concentration. Since the output signal obtained may be displayed as a function of electrode potential, an analogy has been drawn between potential sweep semiintegral electroanalysis and polarography (1). The technique provides a measurable quantity which gives a characteristic maximum constant value proportional to concentration when the potential of the electrode is such that the concentration of the electroactive species a t the electrode surface is zero. This maximum value has been proposed to be independent of the process by which this potential is reached ( 2 ) . I t has also been postulated ( 3 ) that semi'integration may be useful in the study of the kinetics of homogeneous chemical reactions following electron transfer a t the electrode; i.e., EC, ECE, dimerization, etc. In this work it has been suggested that semiintegral electroanalysis in the potential step experiment (dubbed chronoamplometry) may be useful in studies of this type. Working curves obtained through digital simulation are presented therein to show the variation of the kinetically perturbed current semiintegral in the potential step experiment. These working curves indicate that it would be possible to distinguish among the mechanisms presented using the semiintegral technique provided that the stepping frequency was faster than the kinetic perturbation; this would require that the semiintegral electroanalysis be performed over short time intervals in some cases. In addition, the working curves presented are valid only for the faradaic component of the current semiintegral; no attempt was made in that work to take non-faradaic contributions into account. Preliminary experimental investigations to verify the authenticity of these working curves have been conducted in conjunction Author to whom correspondence should be addressed. 610
ANALYTICAL CHEMISTRY, VOL. 4 7 , NO. 4 , APRIL 1975
with some low-temperature studies of electrochemical kinetics under way in this laboratory. In these studies, the recorded current-time curves have been digitized manually so that the semiintegral could be evaluated numerically using a previously published algorithm ( 3 ) . Shown in Figure 1 are the current semiintegrals ( m ( t ) ) obtained by numerical integration of recorded currenttime data for a double potential step experiment on a dimethylformamide solution of ethyl cinnamate. Curves a and b, respectively, represent experiments run a t 0 and -30 "C. Curve c shows the behavior expected in the absence of kinetic perturbation. Rate constants may be calculated by comparing the semiintegral obtained in the reverse step to that of the forward step ( 3 ) . As predicted, lowering the temperature reduces the rate constant so that the current semiintegral begins to approach zero after the second potential step. Oldham ( 4 ) has recently developed an analog device which will trace the semiintegral directly without the tedious data transcription required to obtain Figure 1. An apparatus of this type has been constructed and is being used in potential step studies of the current semiintegral. Initially, double potential step studies were attempted, but deviations from the results obtained using numerical semiintegration were evident immediately. These deviations are apparent even in the single potential step current semiintegral of a kinetically uncomplicated system like that of Pb2+ shown in curve a of Figure 2, obtained using analog semiintegration. Distortion of the semiintegral is evident, especially a t short times. Also, a comparison with m ( t )obtained using a slow ramp (trace 2 b ) reveals that the long time m ( t )value of a exceeds the constant value obtained in the sweep experiment. Similar behavior is observed following the second potential step also. This behavior is, of course, unsatisfactory either for potential step kinetic studies a t short times or for rapid analysis. Even trace 2b shows a slight distortion a t short times. I t seems likely that this effect can be attributed to the semiintegration of non-faradaic currents. These currents would be semiintegrated just like faradaic currents are; however, in the numerical semiintegration, non-faradaic currents occurring soon after the potential step (charging currents) are eliminated somewhat by the inability of the recorder to respond to the instantaneous current signal. Therefore, these currents are not included as points in the numerical semiintegration. However, non-faradaic currents are processed by the analog circuit, and their long time effects are incorporated and recorded in the semiintegral. These observations suggest that an electronic device might be constructed to deliberately limit the current signal passed to the semiintegrator a t the early stages of the experiment. (Ideally, one would like to separate the faradaic and non-faradaic components of the current signal. This is not possible. However, since one would expect charging currents to predominate immediately after the step, this alternate method for charging current compensation in rapid semiintegral electroanalysis is proposed.) Current limiting, in an electronic sense, may be achieved by removing the extremities of the signal that is proportional to the current by means of vacuum tubes or semiconductors.
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Figure 1. Numerically evaluated current semiintegrals in a double potential step experiment Results are shown for the one-electron reduction of 1.43mM ethyl cinnamate in dimethyl formamide. Curve a was obtained at 0 OC; curve 6 was obtained at -30 OC; curve c shows the predicted behavior in the absence of kinetic complications
Diodes connected in parallel to a high impedance load can limit an input voltage to any desired positive or negative value by holding the proper diode electrode at that voltage by means of a battery or biasing resistor. This principle, called clipping, is used in the clipper circuit described below. The use of this clipper circuit for charging compensation in potential step semiintegral electroanalysis is substantiated theoretically also. This development predicts the optimum experimental conditions for its use. Presented herein, then, is a means to compensate for charging currents in semiintegral electroanalysis. This is achieved by using a clipper circuit to deliberately limit the current during the time immediately following the potential step. A theoretical development is presented to indicate that this method is feasible, and the circuit used to do this is described. Finally, the results of some preliminary experiments employing the circuit are reported to substantiate the theoretical development. A complete verification by experiment has proved difficult because of time delays introduced by instrumental electronics which cause measurements a t very short times to be unreliable.
THEORY T o give a mathematical foundation to the inferences drawn above, a model has been developed to predict the effect of capacitive currents on the current semiintegral in the potential step experiment. This was accomplished by assuming that the total current i(t) shown in Figure 3 is the sum of if(t) and i,(t) a faradaic component and a capacitive component, respectively. While the faradaic component in a potential step experiment is given by the Cottrell equation
the capacitive component is assumed exponential in nature
i,(t) = i,(0)e-t'T
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5
t (sec) Figure 2. Current semiintegrals obtained by analog methods. Results are shown for the reduction of 5mM Pb(N03)~in an aqueous solution of 0.1M KN03. Curve a was obtained from a potential step experiment while curve b was obtained using a potential sweep (0.28 to -0.45 V vs. SCE). Curves c, d, and e were obtained from a potential step experiment empioying current clips of 240-, 370-, and 620-msec duration, respectively
-r
AE/v
'0
-tFigure 3. A represenration of the current-time curves used in the theoretical development Definitions appear in the text.
is shown to be clipped a t the level io for the duration to; after this time, the current function becomes i(t), the unclipped current. At the time clipping is terminated, the current component ratio is given by (4)
This indicates that, regardless of /3 (the current ratio at T), the capacitive component of the current is small with respect to the faradaic component when t o is large with respect to T . Since i~ = i f ( t o ) i,,(to),substitution of Equation 4 yields
+
(2)
where T is the RC constant associated with the charging phenomenon. The magnitudes of the two components may be compared a t time T through the ratio p defined:
(3 1 The effect of current limitation with some sort of clipping device is illustrated in Figure 3 also. Here, the current
Equation 5 will be used in the following discussion in which the clipped current is subjected to the semiintegration operation to yield a current semiintegral that is a function of t , to, /3, and T . Inspection of this function provides a way to predict the effect of clipping on the current semiintegral. ANALYTICAL CHEMISTRY, VOL. 47, NO. 4, APRIL 1975
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log (tit,) Figure 4. Effect of current clipping on the faradaic current semiintegral in the absence of capacitive currents in the potential step experiment
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Figure 5. Effect of current clipping on the total current semiintegral in the potential step experiment
The current is clipped for the duration to
The current semiintegral m ( t )has been defined ( 3 )
The number associated with each line shows the value of b / T used in its fl = 0.10, (-) p = 1.0, (- - -) = 10.0 construction. (e
substitution of the clipped current function into this definition yields
for t
00
< to, and
a)
plications), the function given in Equation 6 will approach a value of 1.0 when these effects cause a minimum perturbation in the faradaic current semiintegral in the potential step experiment ( 3 ) . The effect of current clipping on the faradaic component may be investigated by setting /3 equal to zero in Equation 6; in the limit of small capacitive effects, the clipped current semiintegral represents only that due to the faradaic component (rnr(t))
and for t Ito Upon integration this becomes 172(t)
=
-$[io (i-i- :t-/O)
+
where daw x is Dawson's integral ( 2 , 5 ) . Elimination of io and i,(O) through Equations 3 and 5 and rearrangement yields the form used in this analysis
and
for t Ito. This equation gives the normalized current semiintegral in terms of three dimensionless parameters: /3 (which compares the magnitudes of current components a t a fixed time, T ) , tolr (which compares the duration of the current clip with the time constant of the capacitive current), and t / T (which compares the real time duration after the potential step with the capacitive time constant. Because m ( t ) has been rendered dimensionless by the Product .that it equals in the absence of capacitive effects or kinetic com612
ANALYTiCAL CHEMISTRY, VOL. 4 7 , NO. 4 , APRIL 1975
for t
2
to (7b)
a function only of t h o . This function, shown in Figure 4, indicates clearly that the current semiintegral in the absence of capacitive effects approaches its expected constant value when t approaches 100 to. This result implies that a current clip may be applied (at least) over the first 1%of the time following a potential step with essentially no alteration in the value of the constant semiintegral obtained. (Since 100 data points were used to represent the current-time curves between successive potential steps in the numerical semiintegrations obtained previously, this observation illustrates why it is unnecessary to exceed this number of data points to obtain a constant value for m ( t ) ;sampling a t this interval corresponds to a current clip during the first 1%of the total time interval.) Strictly speaking, however, this result is valid only if there is no charging current effect on the semiintegral. If (3 has appreciable magnitude, a clipping interval larger than the first 1%of the total time interval may be used to eliminate the effect of capacitive currents. This is illustrated in Figure 5 which shows Equation 6 evaluated over the dimensionless time axis t / T for several different values of (3 and t o / 7 . The majority of these evaluations have been performed for the special case when the charging current equals the faradaic current a t time T (6 = 1.0); these are shown as solid lines in the figure. Associated with each line is the numerical value of t o / T used in its construction. Thus, it is clear that if p = 1.0, the potential step current semiintegral in the absence of a current clip (as ~ O / Tapproaches zero) deviates significantly from the constant value obtained in the long time limit. As the time of clip is increased, the deviation from faradaic behavior is decreased. The semiintegral still displays a component due
to charging currents if the time of current clip equals the time constant of the capacitive component. Adjustment of the clipping time so that t o / T = 5.0 completely eliminates the effect of the capacitive component upon the predicted faradaic behavior. This is quite reasonable because the positive deviation from faradaic behavior is attributable to the term involving Dawson's integral (which has a maximum value of 0.54) in Equation 6b; this term vanishes as the exponential quantity (1 - t o l r ) becomes negative. For @ < 10, this term may be eliminated if the current is clipped a t t o = 5 T . Of course, one may apply the current clip for too long a duration. This is illustrated for @ = 1.0 when t o / T = 100. For small values of @,the shape of this sort of curve resembles that shown in Figure 4. Thus, if @ is small, it would not be advisable to apply the current clip for more than 5% of the time following the potential step. Figure 5 also shows in a limited fashion the behavior one would expect with variations in @. A large capacitive component ( p = 10.0,dashed line) significantly increases the current semiintegral above that expected on the basis of pure faradaic behavior even if the current signal is clipped a t t o = T ; moreover, this increase would be manifested in the current semiintegral for more than 1000 capacitive lifetimes. In this case, clipping at t o = 55 eliminates the deleterious effect completely at any time greater than 1 0 ~ A . small capacitive component (6 = 0.10, dotted line) has virtually no effect on the predicted faradaic behavior even if the current is not clipped (to17 = 0.001). This analysis is somewhat incomplete. If one wished to study the effect of charging currents in the presence of faradaic processes using this technique, a more detailed description of the variation of the m ( t ) maximum as a function of /3 and T would be required. This could certainly be accomplished using Equation 6, but this is beyond the scope of this work. It is intended herein only to rationalize the m ( t ) waveform obtained experimentally in the potential step experiment and to justify the use of a current clip to eliminate the effect of charging currents on the current semiintegral. This development meets these objectives. In addition, it provides semiquantitative criteria that may be used to set the duration of the current clips: 1)to eliminate the effect of charging currents, one should apply the current clip for a t least 5 capacitive lifetimes; 2) to prevent the long time loss of the faradaic component of the semiintegral, one should clip no more than the first 5% of the total current-time curve. Thus, in theory, one may use a current clip to compensate for charging currents in m ( t ) if t is greater than 100 T. Finally, this analysis allows one to compare the magnitude of the capacitive component of the current semiintegral in a potential step experiment with current clipping (n, ( t ) )with the magnitude of the capacitive component of the current semiintegral in the potential sweep experiment ending in a capped ramp ( m r ( t ) )T. o do this, one must first subtract Equation 7 from Equation 6 to obtain an expression for m , ( t ) :
because it is proportional to dE/dt, a constant. Since the same total charge would be passed in either the potential step or the capped ramp experiment ic(0)e-t"dt =
LAE
ipt
so that i, = iC(O)7u l u . A comparison of m,(t) and m,(t) may be obtained by dividing Equation 8 by Equation 9. If one assumes throughout that t o E/u
This is simplified by noting that if t is large with respect to to, r, and AElu
mc(t)
N
e-t@lT
m,(t) Thus, if no clipping is applied, the two techniques produce an equal capacitive component in the semiintegral in the limit of long time. On the other hand, if t o is large with respect to T , the capacitive component in the potential step experiment may be decreased significantly.
EXPERIMENTAL and
daw
431 T
for f
2
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T o obtain an expression for m,(t) one must note that I E l c (the potential change divided by the sweep rate as shown in Figure 3) is the time required to effect any charging processes. The charging current, then, is a constant (i,)
Circuit. Figure 6 shows the circuit constructed to carry out the operations previously discussed. It is possible to clip the current signal without all the operational amplifiers shown, but the configuration in Figure 6 combines versatility with ease of operation. The Princeton Applied Research Model 170 (PAR) instrument used in these studies is equipped with a monitor connector which may be used to detect a signal proportional to the current response of the electrochemical cell before this signal is processed by the instrument itself. The signal from this output may be displayed on an external recorder while the same signal is being processed and recorded by the PAR. The circuit employs five operational amplifiers; two of these (1 ANALYTICAL CHEMISTRY, VOL. 47, NO. 4, APRIL 1975
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namate (Eastman Organic Chemicals), and diethyl maleate (Aldrich Chemical Co.) were used as received. Iron EDTA was prepared by the method of Sawyer and McKinnie (9). The purification of the dimethylformamide and the techniques used in electrochemical experiments have been described previously (10).
RESULTS
Figure 6. The current clipping circuit showing the analog semiintegrator
The current signal originates at the PAR Model 170 (PAR), is semiintegrated by amplifier 5 having element M (developed by Oldham) in its feedback loop. and displayed on a recorder (Rec).R , = R 3 = 10 Kohm; R2 = 2.1 Mohm; PI = P2 = 100 Kohm, 10-turn. Other symbols explained in text and 3) are in the voltage follower mode to match impedances. The signal from the PAR passes through the first of the followers to amplifier 2 where it may be amplified up to a factor of ten with the resistance values shown. The amplified signal is then clipped by These diodes allow a signal t o pass only if its diodes DI and Dz. voltage is smaller than the sum of the potential applied from one of the voltage sources (VI, VZ, V3, and V,) and the bias voltage of the diode itself. Mercury batteries rated at 1.35 V are indicated by Va and Vq. Heathkit voltage reference sources, VI and V1, are continuously variable from 0 to 10 V. Either the batteries or reference sources may be employed by closing the proper switches. The two diodes in the configuration shown are necessary when clipping signals of opposite polarity such as those obtained in a double potential step experiment. These diodes will not allow any part of a signal to pass to amplifier 4 if it exceeds the preset potential of the voltage sources. With all switches in the open position, the diode clipper is out of the circuit, and the unclipped signal is allowed to pass to the remainder of the circuit. Amplifier 4 uses fixed and variable resistors identical t o those associated with amplifier 2 . However, the roles of these resistors are reversed; in amplifier 2 , the variable resistor PI is used in the input; in amplifier 4, PZis used in the feedback loop. Potentiometers 1 and 2 are mechanically coupled so that they may be simultaneously rotated at the same rate in opposite directions. Thus, the amplification factor of amplifier 4 is the reciprocal of that of amplifier 2. With bat,teries V3 and V 4 in the circuit, an increase in the amplification factor of amplifier 2 causes a greater fraction of the current signal to be clipped by the diodes. However, since there exists a reciprocal relationship between the amplification factors, the gain of the unclipped signal processed by both amplifiers is unchanged. This allows one t o record the resulting semiintegral at the same sensitivity, regardless of the fraction of the signal that is clipped by the circuit. The semiintegrating circuit itself, co?tained in the feedback loop of operational amplifier 5 is attributed to Oldham ( 4 ) . The original circuit (shown in Figure 10 of reference 4 ) required slight modification. An 8300-kilohm resistor was used in place of a resistor incorrectly labeled 830 kilohms (6). The semiintegrated signal is then passed directly to an X-Y recorder. Apparatus. The electrochemical cell and the cooling cryostat used for experiments involving nonaqueous solvents have been previously described (7, 8). The cell used for experiments in aqueous media consisted of a beaker fitted with a stopper drilled to accomodate three electrodes. A saturated calomel electrode served as a reference electrode; the auxiliary electrode was a platinum coil; the working electrode was either a platinum button or a hanging mercury drop. The Princton Applied Research Model 170 electrochemistry system was used in all electrochemical experiments. Operational amplifiers 1, 2, 3, and 4 were all Burr-Brown No. 3043/15; amplifier 5 was a Burr-Brown No. 3292/14 chopper stabilized model. The external recorder was a Hewlett-Packard Model 7005B. A Tektronix Type 531 oscilloscope was also used to measure the duration of the current clip. Reagents. Lead nitrate (J. T. Baker Chemical Co.), potassium nitrate (Fisher Scientific Co.), sodium sulfate (Fisher), ethyl cin614
ANALYTICAL CHEMISTRY, VOL. 47, NO. 4, APRIL 1975
Experiments have been conducted t o verify the 'proposals previously discussed. Initial work was directed toward substantiating the theoretical analysis. Parameters such as time of the experiment and the time of clip are experimentally controllable. These may be used t o estimate the lifetime of the charging process. Experimentally, this might be done by adjusting the time of clip ( t o ) t o a value which gives a semiintegral trace equal to that predicted for the faradaic response only. If only one non-faradaic process is occurring (e.g., the charging of the double layer), it should then be possible to estimate the value of p for the particular system under consideration. However, it is reasonable to assume that many systems exhibit more than one nonfaradaic current response. In addition t o double layer charging, these can be due t o adsorption of materials on the electrode surface. Because the theory developed above treats only one non-faradaic process, the presence of additional sources of charging currents will give results which would not be expected to agree with the theory presented previously. Each additional charging process would presumably introduce another semiintegrated maximum into the total response, provided that its lifetime differs significantly from that of other charging currents. Experimental work reported herein indicates one or more non-faradaic processes contributing t o the current semiintegral, but does not render conclusive evidence as to the specific origin of these processes. T h e results of experiments designed to investigate these ideas appear in Figure 2. This figure shows the semiintegral traces produced by the analog device during a potential step experiment. The solution was 5.00mM Pb(NO& in 0.10M KN03. Curve a shows the current semiintegral obtained during five seconds of electrolysis. This curve, as previously discussed, is obviously distorted at very short times. The distortion is not unlike that predicted theoretically. Curve b is the current semiintegral that results when a 50 mV/sec ramp is applied to this system. Because no convenient method to obtain a reference signal containing only the faradaic response has yet been devised, a slow ramp was employed here as the reference, subject t o the considerations discussed in the theoretical treatment. Curves c , d, and e were obtained under the same experimental conditions used t o obtain curve a except that the clipper circuit was used to clip out various amounts of the signal; the time of clip ( t o ) was 240 msec for curve c , 370 msec for curve d, and 620 msec for curve e. This time parameter may be obtained experimentally by passing the output of amplifier 4 before semiintegration, t o a triggered oscilloscope. The unclipped signal appears on the scope as a typical current-time curve. A clipped signal appears a t a constant level (io) for a measurable time duration (to); after this time, the response is the same as the unclipped signal. Curve c gives a signal of the same magnitude as the reference or slow ramp, so that curve c is assumed to have produced the ideal semiintegrated signal. Curves d and e, on the other hand, appear to have been clipped for too long a duration and consequently are of less magnitude than the reference. These results show that the circuit is capable of giving a semiintegrated signal free of the distortion in Figure 2a. It is significant that 240 milliseconds of clip are necessary to
give a trace which matches the reference. This indicates that the lifetime ( T ) of the compensated charging process is in the vicinity of 50 msec. One would expect the time required to charge the double layer to be about two orders of magnitude less than this. There are several plausible explanations for this discrepancy: 1) T h e time required to charge the double layer is much longer than previously thought. 2) There are other non-faradaic charging processes present in this system. 3) The various instruments and associated electronics (PAR, clipper, semiintegrator) are unable to properly process the electrochemical cell responses at very short times. This first explanation can probably be dismissed as the cause. Previous work (11, 12) in this area has shown that the time to charge the double layer does not approach 50 msec. Either the second or third explanations could be considered as likely possibilities. Experiments to determine if either of these, or both were the cause of this anomaly were carried out. The electrochemical system used was an aqueous solution of 5mM Fe(EDTA) with 1M Na2S04 as background electrolyte. A series of experiments was conducted on the system in the presence and absence of Fe(EDTA). In both cases, the current semiintegral obtained using a slow, capped potential ramp was recorded; then, potential step experiments were conducted with various amounts of clip applied. The magnitude of the clipped semiintegrated current response was compared to the ramp signal as explained previously. Results are shown in Table I. In the case when no Fe(EDTA) was present, the current semiintegral obtained using a capped ramp did not reach an apparent constant value as rapidly as it did when Fe(EDTA) was present. Its behavior, predictably, was that associated with the semiintegration of charging currents rather than faradaic currents. In either case, the value for m ( t ) using the capped ramp was taken after 5 sec; this had reached a constant value when Fe(EDTA) was present, but it had not with Fe(EDTA) absent. Thus, not as much significance may be associated with the actual magnitude of the semiintegral ratio in the latter case. With the iron in the system, the time of clip required to give a current semiintegral signal equivalent to that obtained using a slow ramp can be varied over an extended range without producing a significant change in the desired results. This is important for it verifies the theoretical prediction that the careful adjustment of the clipping time is unnecessary. The unclipped traces of the semiintegrated signals exhibited slightly different shapes with and without the iron present. With iron in solution, the trace was similar to that of the unclipped signal obtained for lead as shown in Figure 2; two distinct maxima were recorded. However, in the absence of iron, only the first spike at short times was observed, and the second somewhat drawn out peak (appearing between 0.5 and 2.0 seconds in Figure 2) was not present. This behavior may be due to differences in electronics response a t the widely varying current sensitivities required with and without Fe(EDTA). With the Fe(EDTA) present, 10 to 20 times less sensitivity was required to achieve a signal of equivalent magnitude to that with only electrolyte present. Of course, this behavior may also be attributed to some process directly associated with the presence of the Fe(EDTA). A comparison of the times of clip required to match the ramp signal with and without Fe(EDTA) present shows that a t least as much clip is required for the background alone as is needed when the iron is present. This tends to minimize the plausibility of adsorption of electroactive species as the reason for the long clipping times in this system. This does not mean to imply that adsorption cannot
Table I. Effect of Clipping Time Variation on the Current Semiintegral in the Potential Step Experiment Relative to T h a t Obtained Using a Capped Potential Rampa 5m.W Fe(EDTA) present T i m e of clip, msec
... 35 65 140 170 220 250 310 410 580 800 1150 1800
Relative c m e n t semiintegral
1.10 1.05 1.03 1.02 1 .oo 0.98 0.98 0.98 0.97 0.95 0.93 0.90 0.87
Fe(EDTA) absent T i m e of clip, msec
... 30 70 120 140 160 170 180 250 280 300 360 380
-
Relative c u n e n t semiintegral
1.86 1.65 1.62 1.20 1.14 1 .ll 1.09 1.01 0.97 0.90 0.87 0.78 0.73
a Time of experiment: 5 sec. Supporting electrolyte: 1M Na&04. Potential Step: 0.135 V to -0.150 V us. SCE.
cause longer clip times in other systems, only that it is probably not the cause of the long times observed here. The third possibility, instrumental limitations, was explored through further experiments performed with the Fe(EDTA) system. An immediate observation is that the PAR itself acts as a clipper. Oscilloscope traces show that the input to the clipper-semiintegrator is inherently clipped at very short times by the PAR electronics. The time of clip depends upon the current sensitivity employed; as the sensitivity becomes less, the amount of clip is smaller. However, this inherent clip time was never less than 4 msec and was usually about 10 msec with only electrolyte present. It therefore proves impossible to separate the faradaic current from charging currents and instrumental anomalies a t short times. This slow response can most likely be attributed to operational amplifier saturation due to very large initial cell currents. The apparent lifetime of the current-time response from the electrolyte alone as monitored by oscilloscope directly from the PAR was normally 15 msec (measured after the initial inherent clip); when measured after passing unclipped through the clipper circuit but before semiintegration, this lifetime was typically 80 msec. Thus, clipper circuit electronics may contribute to this effect also. These long lifetimes observed in the absence of Fe(EDTA) indicate that the probable cause for the large clipping times in this system is slow instrumental reresponse. The use of semiintegral electroanalysis for rapid analysis appears to be a likely application in the future; the constant response obtained appears inviting for analysis of slowly flowing streams (such as the effluent from a liquid chromatograph). The application of the current clip technique may make analyses of this type feasible; certainly, it should reduce the time required to acquire a constant current semiintegral, an important consideration in flowing systems. In addition, when one is considering a method for routine analysis, the limit of detection warrants consideration. With this in mind, a series of experiments designed to explore this area was carried out. In conjunction with this, the effect of non-faradaic signals near the limit of detection is pertinent, for a t low concentrations, the ratio of non-faradaic currents to faradaic currents ( p ) would be exANALYTICAL CHEMISTRY, VOL. 4 7 , NO. 4 . APRIL 1975
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C/C,,X Current semiintegral calibration curves for potential step &dies of Fe(lll)(EDTA) in 1M Na2S04
Figure 7.
Values of &,, are indicated in the figure. Open points were obtained with no current clipping; closed points were obtained using a 470-msec clip. The semiintegral signal was measured at t = 2.0 sec. The potential step was from +0.135 V to -0.150 V vs. SCE.
pected to assume a large value. Thus, it was anticipated that current clipping would significantly reduce the limit of detection by compensating for the relatively large fraction of charging currents a t low concentrations. The results obtained in Figure 6 indicate that this is true. This series of experiments was carried out using the iron system previously mentioned but employing widely varying concentrations of Fe(EDTA). For solutions of each concentration, the current semiintegral was recorded both in the absence of current clipping and in the presence of a 430-msec clip. This amount is slightly more than that required to match the slow ramp reference (Table I). This was done deliberately to ensure that only faradaic response was present, since the slow ramp itself appears to be slightly distorted by a non-faradaic contribution. Shown in Figure 6 is the relative current semiintegral after two seconds as a function of relative concentration. Figure 6 indicates that, a t lower concentration levels, it becomes increasingly difficult to obtain a linear response with the unclipped signal; however, the clipped signals are linear with concentration. In addition, without clipping, these calibration curves exhibit a non-zero intercept. One would assume that if the faradaic current is the only signal being recorded, the lines should pass through the origin, for when no faradaic component is present, no signal should be produced. Figure 7 indicates that this is achieved a t high concentrations but a greater proportion of non-faradaic response is observed a t lower concentrations. The conclusion drawn is that nonfaradaic currents cause deleterious effects a t low concentrations, thereby increasing the desirability of the current clip in trace analysis. I t would appear that rapid trace analysis by chronoamplometry should prove feasible if the signal is clipped before display; otherwise, non-faradaic responses will cause inconsistent results. The current clipper circuit also appears to be useful (if not necessary) in the semiintegral electroanalysis of organic compounds dissolved in nonaqueous media using the potential step technique. This is illustrated in Figure 8 which shows the clipped and unclipped current semiintegral obtained following a potential step into the one-electron reduction of 12mM diethyl maleate in dimethyl formamide solution. [A description of the typical experimental conditions employed appears elsewhere (7, S)]. Upon semiintegration, the unclipped current signal exhibits the two re616
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4
5
t (sec) Figure 8. The analog current semiintegral obtained following a potential step into the one-electron reduction of diethyl maleate Curve a shows the unclipped behavior: curve b shows the behavior obtained using a 430-msec current clip. The dimethyl formamide solution used was 12mM in diethyl maleate. The potential step employed was from -0.40 V to 1.55 V vs. SCE
-
cordable maxima shown in curve a; the application of a 430-msec clip results in curve b. At short times, the disparity between the clipped and unclipped signal is even more pronounced than that observed for an aqueous inorganic system in Figure 2. At longer times, the clipped and unclipped current semiintegrals approach identical values; this is illustrated in Table I1 which shows the value of the unclipped semiintegral relative to the clipped semiintegral as a function of electrolysis time for four different temperature-concentration combinations. The agreement a t longer times is exhibited in all cases. These data indicate that the capacitive component of the current semiintegral in the case of diethyl maleate is much larger than that associated with the reduction of Pb2+; with current clipping, the time required for analysis or kinetic studies is reduced by more than one order of magnitude. This long clipping time may again be due to instrumental artifacts. However, one would expect adsorption to play a much greater role in the electrochemical behavior of organic systems of this type than in the lead and iron systems previously discussed. I t is reasonable to assume that non-faradaic responses associated with the adsorption process would exhibit behavior similar to that shown here. If this is so, data like those in Table I1 might be used to study the extent of adsorption as a function of concentration and temperature. At this writing, insufficient data have been obtained to substantiate this conjecture, but further experimentation along these lines is anticipated.
DISCUSSION These experiments have served to demonstrate the utility of current clipping in potential step semiintegral electroanalysis. This appears to be necessary if one wishes to use the potential step technique in either rapid analysis or kinetic studies of rapidly reacting systems. Since fast (capped) potential sweeps approach potential steps in the limit of high sweep velocity, the fast potential sweep experiment suffers from the same drawbacks as the potential step experiment. (In fact, experiments conducted in this laboratory, but not reported above, indicate that current clipping in the fast potential sweep experiment may be used to reduce the contribution of capacitive currents in semiintegral neopolarograms.) Thus, this technique may be generally useful in rapid semiintegral electroanalysis. The conventional electrochemical techniques such as
Table 11. Comparison of m ( t )Relative to m ( t )with Current Clipping=in the Potential S t e p Electrolysis of Diethyl Maleate Concentrat i o n , m.M
8 .O 11.9
a
Tempera-
turf,
Electrolbsis t i m e ( t ) , sec
Oh:
2 .o
5 .O
295 218 295
1.23 1.25 1.25
218
1.14
10.0
25.0
1.14 1.15 1.20
1.12
1.03 1.04 1.02
1.03
1.01
1.11 1.12
...
Clipping time was 430 msec throughout. -
chronoamperometry and chronocoulometry are subject to the effects of capacitive currents also. In neither of these techniques is charging current compensation an easy operation without considerable data manipulation. In chronoamperometry, the current is small and rapidly changing by the time that the charging current has become insignificant. Deviations from a plot of i us. t-1/2a t short times may be attributed to charging currents, but these deviations are measured from an extrapolation through points that are difficult to measure experimentally. In chronocoulometry, the charging current is incorporated into the integrated current from the onset of electrolysis. The integral of the charging current may be estimated from the intercept of a plot of Q us. t1/2;this, too, requires an extrapolation of data points obtained et long times from a non-constant chargetime curve. Current clipping combined with semiintegral electroanalysis permits charging current compensation without the need for tedious data transcription, but current clipping must be combined with the semiintegral operation to be effective. In the chronoamperometric experiment, current clipping would have no beneficial effect other than damping the recorder response. In chronocoulometry, charging current compensation could be achieved a t long times through current clipping, but a unique time of clip would be necessary to compensate for the charging current associated with every concentration studied. Thus, the analytical utility of current clipping in chronocoulometry is dubious. Semiintegral electroanalysis, which emphasizes the effect of long time currents a t the expense of short time behavior, is uniquely capable of employing the clipping
technique advantageously over a wide range of clipping times. I t is somewhat disconcerting that clipping times of the order of 0.25 second are required to bring about a constant current semiintegral, even if the constant value is recorded approximately one second later. This appears to establish a low upper frequency limit for kinetic studies using double potential step chromoamplometry. These long clipping times have been shown to be due primarily to instrumental limitations. It is not known whether charging currents associated with an adsorption phenomenon also contribute to the recorded semiintegral. These processes may take place more rapidly than the observed response time of the instruments employed. The data obtained above do indicate that clipping times of this magnitude are necessary to produce significantly improved m ( t )curves if the clipper circuit and the PAR are employed in the configuration specified. Further investigations of other instrumental configurations are under way to determine whether the time of clip can be significantly reduced. ACKNOWLEDGMENT The authors thank Robert Smith for his assistance in construction of the electronics described herein. LITERATURE CITED (1) (2) (3) (4)
K. B. Oldham, Anal. Chem., 44, 196(1972). M. Grenness and K. B. Oldham, Anal. Chem., 44, 1121 (1972). R . J. Lawson and J. T. Maloy, Anal. Chem., 46, 559 (1974). K. B. Oldham, Anal. Chem., 45, 39 (1973). (5) "Handbook of Mathematical Functions," M. Abramowitz and I. A. Segun, Ed.. Dover Publications, Inc.. New York, N.Y., 1965, pp 297319. (6) K. B. Oldham. personal communication. (7) R. D. Grypa, M.S. Thesis, West Virginia University, Morgantown, W. Va.. 1974. (8) R. D. Grypa and J. T. Maloy, J. Nectrochem. Soc., in press. (9) D. T. Sawyer and J. M. McKinnie, J. Amer. Chem. Soc., 82, 4191 (1960). (10) T. M. Huret and J. T. Maloy, J. Elecfrochem. Soc., 121, 1178 (1974). (11) A . T. Hubbard, R. A. Osteryoung, and F. C. Anson, Anal. Chem., 38, 692 (1966). (12) G. Lauer and R. A. Osteryoung, Anal. Chem., 38, 1106 (1966).
RECEIVEDfor review July 12, 1974. Accepted November 27,1974. This research was supported in part by the donors of the Petroleum Research Fund administered by the American Chemical Society. We are also indebted to the W.V.U. Senate Committee on Research for partial support. We are grateful for the support of an N.S.F. Traineeship to S.C.L.
ANALYTICAL CHEMISTRY, VOL. 47, NO. 4 , A P R I L 1975
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