Differential Coulostatic Polarography J. M. Katzenberger and P. H. Daum Northern Illinois University, DeKalb, Ill. 60 1 15
An experimental study of a new method of electrochemlcal analysis, dlfferentlal coulostatlc polarography, has been undertaken. A slmpilfled theoretical approach has been presented which serves as a useful gulde to the evaluation of the parameters which affect the analytical utllRy of the technique. Instrumentation has been developed which controls or compensates for these parameters, lnciudlng a unlque capacltance compensation feedback network. Experimental results have been obtained which lndlcate that the detectlon llmlt surpasses 0.1pM and that supportlng electrolyte concentrations as low as 0.0001M can be tolerated.
The development of pulse methods in electrochemistry has been responsible for the resurgent use of polarographic techniques in trace analysis. The well known advantages of these methods stem from their ability to discriminate against capacitive charging currents which are responsible for the sensitivity limitations of normal polarography. This is accomplished by applying a voltage pulse to the electrode towards the end of drop life, waiting for the capacitive current to decay essentially to zero, and then measuring the faradaic current. This effectively maximizes the ratio of faradaic current to charging current, and extends the sensitivity of polarographic methods several orders of magnitude. We would like to report the development of the instrumentation for a new pulsed polarographic method which has the advantages of more conventional pulsed methods in that the polarograms are relatively free of the limitations imposed by charging processes, and is a t least potentially more sensitive in certain experimental situations. The theory of the method has been previously developed by Astruc and Bonastre (1,2) and development of an experimental system operating under computer control for a similar method has been reported by Enke and coworkers (3). The concept of the method is illustrated in Figure 1. A ramp voltage is applied to a conventional polarographic cell. Towards the end of drop life, when the change of area with time is minimal, the ramp voltage is disconnected from the cell and a coulostatic pulse is applied to the system. This abruptly changes the potential of the cell which is then allowed to decay a t open circuit for a predetermined period of time. A parameter related to the slope of the decay curve is measured and plotted as a function of the applied potential. The resulting curve is peak shaped with the peak occurring near the Ell2 of the electrode process. The peak height is proportional to the bulk concentration of the electroactive species. The technique owes its origins to the coulostatic methodology developed by Reinmuth and Delahay (4-20)in that a coulostatic perturbation is used to abruptly change the electrode potential and the rate of decay is then related to concentration. As a coulostatic method, it accrues the advantages of extreme sensitivity and the ability to operate in extremely high resistance solutions. However, the method retains the simplicity of operation and selectivity of normal polarographic techniques.
THEORY An approximate theory upon which discussion can be based can be easily derived from the equation developed by Reinmuth (10) for a small amplitude diffusion limited decay, Equation 1.
where AEi is the maximum potential excursion developed after injection of the charge to the electrode (i.e., at zero time in the decay), and AE is the potential excursion at any other time. Both excursions are measured with respect to the potential of the electrode just prior to the application of the charge. T d , the diffusional time constant is defined as
where C, is the double layer capacitance in yF/cm2. D oand D R are the diffusion coefficients of the oxidized and reduced species, respectively, and C, and CR are the concentrations. Other terms in the equation have their usual meaning. Although Equation 1does not rigorously apply to the experimental situation in the present case, it does serve as a very useful guide to the variables which are important to the method. A more rigorous model has been developed, and the reader is directed to the papers of Astruc and Bonastre for the details (1,2). Considerable simplification of Equation 1 can be accomplished when ( t / T d ) l / ’ is small, by expansion of the equation in a Taylor’s series and dropping all but the first two terms to give Equation 3.
(3) The approximation is valid for all of the experimental situations in which the method would be ordinarily used. The potential dependency of the decay, which should give the form of the polarographic curve, can be introduced via the dependence of C, and CR at the electrode surface on the ramp voltage. These concentrations turn out to be
, C OJ lostat I c
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Figure 1. Potential-time behavior of test electrode
ANALYTICAL CHEMISTRY, VOL. 47, NO. 12. OCTOBER 1975
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b
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Flgure 2. Timing circuit
c,
c *e
CO*Y = 0. CR=-
1+0’
1+8
(4)
where y = d m , 0 = exp (nF/RT)(E- E1/2),C,* is the concentration of the oxidized species in the bulk of the solution, and C , and C R are the concentrations in the neighborhood of the electrode surface at a given potential. Substitution of these concentrations into Equation 3 gives the decay as a function of potential, Equation 5 .
Since what is measured with the present instrumentation is the difference between AEi and AE a t some predetermined time, the relationship between the measured parameter E , ( E , = AEi - AE),and the potential of the electrode as determined by the ramp voltage is Equation 6.
Though not rigorous, Equation 6 correctly predicts that the diffusion controlled differential coulostatic polarogram will be peak shaped, with the peak occurring a t a potential corresponding to the half-wave potential of the electrode reaction (i.e., a t 0 = 1).Furthermore, it predicts linear dependency bulk concentration of electroactive species and peak height. This can be easily seen by setting 6’ = 1 in Equation 6, and obtaining for the peak height
Em, =
A E i n 2 F 2 aC , * d 2& RTC,
(7)
The shortcomings of the model are the result of several causes. As originally derived, Equation 1 applies only to small voltage perturbations away from equilibrium. Therefore, the exact morphology of the decay curve and, more importantly, the linear relationship between E,, and AEi would be expected to break down for values of AEi greater than a few millivolts, However, in a more recent publication, Nicholson has shown that perturbations as large as 25/n mV can be tolerated a t the 2% error level (11). Thus 1888
while linear dependency between E,, and AEi is observed experimentally as predicted by Equation 7 , for a relatively wide range of values, the observed leveling off for large values is not predicted. The second shortcoming of the model results from the assumption that the concentrations of “0” and “R” established at the electrode surface by the ramp voltage, extend reasonably far out into the solution. Obviously this is not the case under conditions of the present experiments. Concentration profiles will tend to return to their original values during the open circuit decay. The process is aided by expansion of the drop into the diffusion layer during the relaxation time. The net result of both these factors is that the actual polarographic curves are somewhat higher and somewhat broader than predicted by Equation 6. In addition, the reader should be reminded that the preceding equations are derived for a diffusion-controlled process and more complex mechanistic schemes will alter the response properties which have been discussed. Nonetheless, despite these difficulties, Equation 6 is remarkably accurate considering the approximations. The real value of the model is not that it closely approximates a more elaborate one, but that it clearly shows the variables which must be controlled or accounted for if the method is to be useful. Reference to Equation 6 shows that E,, is dependent on AEi and C,. AEi in turn is a function of C, for a given quantity of charge, i.e., AEi = Q/C,. As the capacitance is known to be a function of potential, electrolyte, electrolyte concentration, and solvent, it would appear that gross distortions of the polarographic curves would result if, for example, the capacitance changed drastically in the region of the reduction wave as is the case for lead in KC1. Furthermore, the presence of trace quantities of surface active agents which are known to cause changes in capacitance, could cause different values of E,, for a given concentration of electroactive species in a given electrolyte, which would certainly limit the usefulness of the method. For the method to be useful, instrumentation must be devised so that the amount of charge used to perturb the electrode is changed as the capacitance changes to maintain AEi a t a predetermined level. In effect, the electrode
ANALYTICAL CHEMISTRY, VOL. 47. NO. 12, OCTOBER 1975
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Timing. The timing circuit is based on a Heath crystal oscillator and scaler card (EU-800-KC). The sequence of events occurring in the timing circuit will be described beginning at a time near the end of the drop life just prior to the application of the coulostatic pulse. At this time, decade counters DC-1 and DC-2 (Figure 2), which control the drop time, have almost reached the preset count. The count is set on front panel BCD switches, and is variable between 0.1 and 9.9 seconds in 0.1-second intervals. The switch output is OR’ed with the counter outputs and this is connected to Gate N-1, so that when the preset count is reached, N-1 undergoes a 1-0 transition. The following series of events which are shown on the timing pulse diagram (Figure 3) then occur. Gate N-1 triggers MS-1 (MS = monostable), which is used as an oscilloscope trigger. MS-1 in turn triggers MS-2 and MS-3. MS-3 performs several functions; it triggers the pulse generator, disconnects the potentiostat from the cell, causes OA-4 (OA = operational amplifier) to enter the hold mode, and at the end of its cycle (variable from 100-500 msec) it triggers MS-4, which activates a relay to knock the drop off the DME. MS-2 triggers the first measurement of the decay signal by triggering MS-5 which causes the output of Gate A-2 to go from 1 to 0. This triggers MS-2 and FF-1 (Figure 4), whose function will be explained in the discussion of the measurement circuit. MS-2 also resets all counters and the oscillator and the 0-1 transition at the end of its cycle causes DC-1, DC-2, and DC-3 to start counting. DC-3 controls the time at which the second measurement of the decay signal is made. This time is determined by a front panel BCD switch using the same circuitry as the drop timer. The time interval is variable between 1 and 9 times the oscilIator input, which is usually set at 100 Hz. When the preset count is reached, Gate N-2 undergoes a 1-0 transition as does Gate A-2 which triggers the second measurement of the decay signal. Pulse Generator and Potentiostat. Potential control is achieved using a conventional operational amplifier circuit for applying a variable initial potential and ramp voltage to a two electrode cell. The potentiostat is connected to the cell through FET-1 (FET = field effect transistor), Figure 4,which is always closed except during the decay measurement sequence.
n
-
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Figure 3. Timing diagram
capacitance must be measured by some means, and its value must be used to control the amount of charge injected into the electrode, Concurrently the capacitance must be used to correct the measured value of E , so that dependency of the decay rate on capacitance is normalized. Such instrumentation has been developed and will be discussed in the next section.
INSTRUMENTATION The instrumentation will be discussed in four sections; timing, pulse generator and potential control, measurement, and compensation.
fi7
i_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ MEASUREMENT
‘ m
Figure 4. Block diagram of
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instrumentation ANALYTICAL CHEMISTRY, VOL. 47, NO. 12, OCTOBER 1975
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Figure 5.
h
-A
-
4
E vs SCE
-5
6
Typical polarograms
(A) Uncompensated. (8) Fully compensated, A& = -100 mV. Conditions: 2 MM Cd2' in 0.01M NaF, flow rate = 1.29 mglsec, drop time = 5 sec, measurement time = 90 msec
The coulostatic pulse is supplied by OA-1 (Date1 AM302A) connected as a current source with grounded load. The input of OA-1 is normally grounded through FET-2 so that no current ordinarily flows from the current source. When a pulse is to be applied, MS-1 (Figure 4) is triggered by MS-3 (Figure 2), causing FET-2 to open and FET-3 to close for a predetermined time, t . This allows E l , the output of OA-2 to appear a t the input of OA-1. The amount of charge supplied to the cell is equal to -Elt/R1, provided RZIR1 = RdIR3. Diodes D-1 and D-2 prevent the cell from discharging through the pulse generator and must be reversed for anodic pulses. The operational amplifier for the current source was chosen for two reasons; it is very' fast (slew rate of 100 volts/psec) and has a high compliance voltage (f150volts). This is necessary so that the test electrode can be charged in a minimum amount of time regardless of the cell resistance. Measurement Circuit. The measurement circuit consists of a variable gain Instrumentation Amplifier (Heath EU-900-DA) and a differential sample and hold amplifier (DS/H). The instrumentation amplifier is used in the differential mode to amplify the voltage difference between the potential source and the cell voltage (i.e., only the decay signal is amplified). The output of the instrumentation amplifier is sent to the multiplier whose function will be explained in the discussion of the compensation circuit. The voltage output of the multiplier, which has the same form as the original decay signal, is then sampled alternately by the positive and negative inputs of the DS/H in the following manner. A short time after the application of the coulostatic pulse, a signal from Gate A-2 (Figure 2) triggers MS-2 and FF-1 (Q = 0 initially). This closes FET-6 and causes the positive input of the DS/H to sample the decay signal for the duration of the MS-2 pulse (variable). When the second measurement is to be made, Gate A-2 again triggers MS-2 and FF-1 closing FET-5, which then activates the negative input of the DS/H, again for the duration of the MS-2 pulse. The output of the DS/H is then plotted on the Y axis of an X-Y recorder vs. the voltage of the potential source. Compensation Circuit. The compensation circuit consists of a difference amplifier (OA-3), an integrator (OA-2), a sample and hold amplifier (OA-4))and the multiplier. As mentioned previously, the amount of charge must be varied as the capacitance changes so that AEi is maintained a t a predetermined level. Also, the relative value of the capacitance must be measured to normalize the effect of capacitance on the decay rate. The compensation is accomplished in two steps. The first step is to control AEi. As mentioned in the discussion of the pulse generator, Q, the amount of charge supplied to the electrode is -EltIR1 and since A E i = Q/C,, then AEi = -E1t/R1Cx. R1 and t are constants, so that in order for AEi t6 remain constant if C, changes, El must change. This is 1890
-
- ,100
Flgure 6.
-.500
E vs.
SCE
Effect of electrode capacitance on polarograms
(A) Full compensation. (B) Partial compensation. Conditions: All polarograms of 4.76 fiM Pb2+ in 0.01M of indicated electrolyte. Flow rate = 0.716 mg/ sec, drop time = 9.0 sec, measurement time = 50 msec, A€, = -100 mV
accomplished with a feedback network using OA-2 and OA-3. OA-3 measures and amplifies the difference between A& and a reference voltage, which represents the desired A E i . This difference is connected to the integrator (OA-2) through FET-7 during the measurement of the first point of the decay voltage. The difference is then integrated and the output of the integrator changes so that the next coulostatic pulse is of the appropriate magnitude to give the desired AEi. This method of compensation assumes that the capacitance of each successive drop will be virtually the same as on the previous drop which is not'necessarily true. However, as long as the change in capacitance is not discontinuous, virtual compensation will be achieved. As can be seen from the previous argument, if A& is a constant then E l , the output of the integrator, equals KC,; in effect, E1 is a measure of C,. This relationship is used to compensate the decay for the effect of capacitance on the slope by multiplying the decay signal by E1 with the multiplier. OA-4 is used to hold the output of OA-2 ( E l )during the measurement of the decay signal. This is necessary because the value of E1 changes during the decay measurement sequence.
RESULTS A N D DISCUSSION There are three ways in which differential coulostatic polarograms can be obtained. l) A constant charge can be applied to each successive drop as the potential is scanned through a reduction wave and A E i allowed to vary according to changes in capacitance and E , measured. 2) The charge can be varied as the capacitance changes in order to maintain AEi a t a predetermined level and E , measured. 3) AEi can be maintained at a constant value and E , can be corrected for capacitance changes. These three methods correspond to totally uncompensated, partially compensated, and fully compensated polarograms. The first method is almost totally useless for either quantitative or qualitative purposes as demonstrated in Figure 5. The peak height and position are determined by the changes in C, as the potential changes. Gross distortion of the experimental curve can result as demonstrated. The reason is that E , is a function of C, and A E i , which in turn is also a function of C, or in effect E , = f ( l / C X z )and obviously large changes in capacitance will cause gross distortions of the polarographic curves if the capacitance changes as a function of potential so that neither quantitative or qualitative work is possible.
ANALYTICAL CHEMISTRY, VOL. 47, NO. 12, OCTOBER 1975
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A€, (mv)
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Flgurr 7. Integrator output vs. potential for 0.01M soiutlons of electrolyte Conditions: Flow rate = 0.716 mg/sec, drop tlme = 9.0 sec, A€, = -100
Flgurs 8. A 6 vs. peak height ( A ) Partial compensation. (B) Full compensation, Conditions: 4.78gM Cd2+ in 0.01M KCI, flow rate = 0.716 mg/sec, drop time = 8.0 sec, measurement tlme = 50 msec
mV
Differences between the second and third methods are illustrated in Figure 6. Polarograms of 4 . 7 6 ~ MP b are shown in three different electrolytes, 0.01M KF, 0.01M KC1, and 0.01M KBr. Curve B in each case is a partially compensated polarogram where Mi is controlled to be 100 mV. As can be seen, the peak height (measured with respect to zero) for the electrolytes varies by a factor of about 2.5, between KF and KBr with that for KC1 being of an intermediate value. This difference is primarily due to changes in the differential double layer capacitance brought about by the change in electrolyte. Curve A in each case is a totally compensated polarogram with a AEi of 100 mV. The decay curves were multiplied by the integrator output voltage in order to compensate the decay for the effects of capacitance. The resulting peaks are greater in magnitude than the corresponding peaks with partial compensation because the multiplier voltage is normally greater than one. The integrator output voltage as a function of potential for the various electrolytes is shown in Figure 7. The form of the integrator voltage vs. potential curves traces out a typical differential capacitance curve for the three electrolytes showing that the integrator voltage does indeed track the capacitance of the electrode as a function of potential. Calculations checking the values of electrode capacitance determined from the integrator voltage, with published values, yield good agreement. Although the fully compensated curves’ do not coincide, the differences between them are much smaller than the differences between the curves without compensation. Furthermore, not all of the differences can be ascribed to capacitance effects. The peak height as shown in Equation 6 is directly proportional to DO1l2,and it would not be expected to be the same for all three electrolytes although its value should not change more than about 10%. I t should also be pointed out that the above compensation circuits do not correct for capacitance effects which result from the small change in the area of the drop during the decay time. These residual capacitance effects are different for the three electrolytes and lead to somewhat different curve shapes particularly near the base line. It should be recognized that the preceding demonstration of the utility of the compensation system was done in a “worst case” situation. The reduction wave for lead occurs
in the region of the electrocapillary maximum for all of the electrolytes which were used as can be seen from Figure 7 . The capacitance changes more rapidly in this region as a function of potential and is more sensitive to the kind and concentration of electrolyte used than a t more cathodic potentials. The approximate difference for capacitances a t the peak potential for lead for the three electrolytes is about 2.5. This difference is much greater than that which is likely to be encountered in ordinary analytical work, and we feel that the compensation circuitry is adequate for all practical situations. Effect of A& Equation 6 predicts that the peak height should be a linear function of mi. Figure 8 shows experimentally determined plots of E,, vs. A E i for a solution of 4.76wM cadmium in 0.01M KC1. Curve 8A was obtained using partial compensation, holding Mi constant but not compensating for the effect of capacitance. Curve 8B was obtained using total compensation. The slopes of the two curves are obviously not the same. E m , increases much more rapidly as a function of AEi for the totally compensated polarograms than the partially compensated polarograms. This is due to the way in which capacitance compensation is made. The decay curve is multiplied by the integrator output voltage. However, the integrator output voltage also determines Mi because it is the control voltage for the current pulse generator. When larger values of AEi are required, the integrator output voltage is increased so that a larger current pulse is applied to the electrode. Hence, the decay curve will be multiplied by a larger value. The Em, for the totally compensated polarograms is thus increased for two reasons: 1) because AEi is increased, and 2) because it is multiplied by a larger voltage. The plot which should be compared with theory then is curve 8A, because the only variation in E,, is due to the variation in AEi. The curve is linear over a relatively large range of Mi values but tails off rapidly as Mi approaches 120 mV. The reason for this is that the maximum decay rate occurs when the value of mi is sufficiently large to perturb the electrode from the foot of the polarographic wave to the diffusion limited region. Increases beyond this value result in no further increase in peak height. The leveling off effect is not predicted by the simple theory because Equation l applies only for small perturbations away from equilibrium.
ANALYTICAL CHEMISTRY, VOL. 47, NO. 12, OCTOBER 1975
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t L
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Figure 9.
-4
-5 -6 E v s SCE
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Effect of Ah on peak shape E vs SCE
Curves 1-8, - A 6 = 20, 40, 60, 80, 100, 120, 140, 160 mV, respectively. Conditions: Same as Figure 8
Figure 11.
Effect of flow rate on peak shape
(A) (1) flow rate = 0.716 mg/sec, drop time = 9.0 sec. (2) flow rate = 1.24 mglsec. drop time = 5.2 sec. (8) (1) flow rate = 0.716 mg/sec, drop time = 4.5 sec. (2) flow rate = 1.24 mg/sec, drop time = 2.6 sec r
t
c
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Figure 12.
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-*
-5 *
-6
-7
EvsSCE
Figure 10.
Effect of measurement time on peak shape
Measurement times: (1) 30 msec, (2) 50 msec, (3) 70 msec, (4) 100 msec. Conditions: 3.85fiMCd2+ in O.OlMKCi, flow rate = 0.716 mg/sec, drop time = 9.0 sec, A€, = -100 mV
Variations in Mi also cause variations in the peak potential and in the broadness of the polarographic curves as shown in Figure 9. The peak potential shifts in the anodic direction as A E i is increased. Part of this variation is an artifact resulting from the way in which the data are plotted. The slope is plotted as a function of the potential before the coulostatic perturbation is applied and therefore E,, is always in error by at least the M i / 2 . The remainder of the variation is due to changes in the characteristics of the decay curve as AEi changes. Broadening of the curve occurs on an absolute scale, and results from the fact that the slope of the decay curve at any point on the reduction wave is a function of Mi. If AEi is very large, the polarogram will exhibit a very broad, rather flat peak. This occurs because the magnitude of a E i is such that the diffusion limiting region where maximum decay rate occurs is reached over a large range of ramp voltages. Effect of Measurement Time. Equation 6 predicts that the peak height of the polarographic wave should increase with the square root of the time between the two measurements of decay voltage. A least squares plot of recorder response y , in millivolts vs. t 1 I 2in secl/* gave the following relationship. y = -69 2449 t1/2with a standard deviation of f 3 . The obvious conclusion which might be drawn from this result is that a long measurement time ought to be used because of the increase in peak height which results. However, one must be careful in drawing this conclusion.
+
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Typical polarogram of 0.359~uM Cd2+
Conditions: Flow rate = 0.716 mg/sec, drop time = 9.0 sec, measurement time = 50 msec, AE, = -100 mV, 0.01 M KCi supporting electrolyte
As can be seen from the curves in Figure 10,the base line for the polarograms also increases as the measurement time increases. This results from two factors. The concentration distribution of the oxidized and reduced species with respect to distance from the electrode surface is primarily determined by the voltage applied to the DME prior to the application of the coulostatic pulse. The decay, however, occurs a t open circuit. In the absence of a driving force, the concentration distribution will change as a function of time, as the concentrations try to approach their equilibrium values. This causes the decay rate to be somewhat faster than predicted, particularly a t voltages cathodic of the peak maximum where concentration differences between the electrode surface and the bulk concentration are at their greatest. As measurement times increase, this factor becomes increasingly important causing the apparent base line, particularly on the cathodic branch, to be higher. The other factor results from residual charging effects due to the increasing area of the drop during the open circuit decay. This effect also increases as the measurement time increases. Both of these factors can be minimized by use of a stationary electrode. In this case, concentration profiles extend further into the bulk of the solution, minimizing the first factor, and the area does not change as a function of time eliminating the second. Effect of Drop Time and Flow Rate. Figure 11A shows polarograms of 3.85kM Cd in 0.01M KC1 at two different flow rates. Decay curves were taken a t the end of natural drop life so that the areas of the two drops were virtually identical when the measurements were made. The two curves are very similar, the only substantial difference being the increase in the apparent base line cathodic of the
ANALYTICAL CHEMISTRY, VOL. 47, NO. 12, OCTOBER 1975
peak for the curve taken a t the higher flow rate. This is caused by relaxation of the concentrations towards the electrode and would naturally be greater for a faster flow rate because the diffusion layer does not extend as far into the solution. Figure 11B is the same as Figure 11A except that the drop has been knocked off prematurely so that the electrode areas are less than in the previous case. The corresponding peak heights are reduced; however, this reduction is an artifact of the measurement technique. Reference to Equation 6 reveals that the decay rate is independent of the electrode area; however, since the decay curve is multiplied by a signal proportional to the electrode capacitance and this is a function of electrode area, the peak height is decreased. Concentration Dependence and Sensitivity. A least squares plot of a typical calibration curve for Cd2+ in the concentration region. 0.1 to l p M gave the relationship, y (mV) = 1.30 X 108C - 4.0, with a standard deviation of 0.5. A typical low concentration polarogram is shown in Figure 12. It is estimated that the detection limit of the present system using the instrumentation and techniques described, is about 10-8M for Cd. This compares favorably with the most sensitive electrochemical methods which have been developed (12).
CONCLUSIONS Differential coulostatic polarography is a highly sensitive electrochemical method which should complement other sensitive and useful methods which have been previously developed. While the method has some advantages, it suffers from the same limitations as more widely known methods such as differential pulse polarography-the major limitation being the residual capacitance effects which result from the changing area of the drop during measurement of the decay. While not a serious problem for most applications, this factor is ultimately responsible for the sensitivity limitations of the method. Whether the limitations are inherently greater for this method than others, remains to be determined. We are currently working on a mathematical analysis of the method to determine this factor, similar to the analysis done by Christie and Osteryoung ( 1 3 ) for differential pulse polarography. There are several additional comments to be made, however, regarding the sensitivity of the method. This is best explained with reference to a stationary electrode where sensitivity limitations due to area changes are eliminated. Voltage pulse methods measure the faradaic current a t a certain time after application of the voltage pulse. As concentrations decrease to extremely small values, the current becomes vanishingly small. The obvious solution is to make the measurement sooner in time so as to be able to measure a finite current. However, the separation of faradaic and charging currents may then be no longer complete, and the principle of the method is defeated. In coulostatic polarography, as the concentration decreases, the time between the two measurements of the decay voltage can be increased with no complication arising from capacitance effects-the principle heing that ultimately the voltage perturbation must return to zero. Thus, a measurable decay can be obtained in principle, from any concentration, provided that other unforeseen factors do not intervene. With the use of the DME, t,his advantage is not realized because of the necessity that measurement of the decay must be done at the end of drop life to minimize area changes.
Therefore, only a finite amount of time is available to make the measurement. This sensitivity advantage can obviously be put to good use if the method is applied to anodic stripping analysis. The sensitivity may be such that deposition times can be significantly decreased, thus increasing the usefulness of the method for routine analysis. In fact, sensitivities may be high enough to directly measure concentrations which would ordinarily be done by stripping methods. The application of this method to these problems is currently under study in this laboratory. Finally, one of the advantages to be expected from application of coulostatic methodology is relative freedom from the effects of solution resistance on the polarographic curves. The advantages to be accrued from being able to operate in solutions of high resistance are obvious. Electrochemical analysis can be run in solutions of low concentrations of inert salt, thus eliminating many of the purification procedures involved with other methods. Determinations can be made in various organic solvents in which high concentrations of salts are not soluble and so forth. These expectations have not been fully realized with present instrumentation. While we have been able to obtain respectable polarograms a t ionic strengths as low as 0.0001M, which are linear in concentration and appear normal in shape, several difficulties have been noted. The capacitance a t very low electrolyte concentrations changes much more rapidly both as a function of electrolyte and electrolyte concentration than a t higher concentrations. This results in higher base lines than are normally observed, and we have also had some difficulty in correcting for capacitance effects. Some distortion of the polarographic curve is also observed which results from the use of a conventional potentiostatic circuit to apply the ramp voltage to the test electrode. This circuitry is not immune to the effects of solution resistance as no compensation for IR drop is made. These problems, however, are not inherent in the method; they are the result of instrumentation problems for which solutions can be found. It is expected that further development of the instrumentation will lead to their resolution. NOTE ADDED IN PROOF:We have recently become aware of a publication, M. Astruc, F. Del Rey, and J. Bonastre, J. Electroanal. Chem., 43, 125 (1973), briefly describing instrumentation which will perform Differential Coulostatic Polarography. However, the design concept and experimental implementation of the instrumentation of the present publication is considerably different, and we believe presents significant experimental advantages.
LITERATURE CITED (1) M. Astruc, J. Bonastre, and R. Royer, J. Electroanal. Chem., 34, 211 (1972). (2) M. Astruc and J. Bonastre, J. Nectroanal. Chem., 40, 31 1 (1972). (3) J. M. Kudirka, R. Abel, and C. G. Enke, Anal. Chem., 44, 425 (1972). (4) P. Delahay, Anal. Chim. Acta, 27, 400 (1962). (5) Ref. 4, p 400. (6) P. Delahay and Y. Ide. Anal. Chem., 34, 1560 (1962). (7) P. Delahay. Anal. Chem.. 34, 1267 (1962). (8) Ref. 7, p 1662. (9)P. Delahay and Y. Ide, Anal. Chem., 34, 1119 (1962). (10) W. Reinmuth, Anal. Chem., 34, 1273 (1962). (1 1) R. S.Nicholson, Anal. Chem., 37, 667 (1965). (12) B. Miller and S.Bruckenstein, Anal. Chem., 46, 2027 (1974). (13) J. Christie and R. A. Osteryoung, J. Electroanal. Chem., 49, 301 11974).
RECEIVEDfor review March 17, 1975. Accepted June 16, 1975. Work supported by the Donors of the Petroleum Research Fund administered by the American Chemical Society.
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