1016
Anal. Chem. 1981, 53, 1016-1020
(6) Feidberg, S. W. In "Electroanalytical Chemistry"; Bard, A. J., Ed.; Marcel Dekker: New York, 1969;Vol. 3. (7) Feldberg, S. W. In "EiectrochemiStry. Calculatlons, Simulations and Instrumentatlons";Mattson, J. S., Mark, H. B., Jr., Mac Donald, H. C., Jr., Eds.; Marcel Dekker: New York, 1972;Vol. 2,Chapter 7. (8) Sandifer, J. R.; Buck, R. P. J . Electroanal. Chem. 1974, 49, 161-170. (9) RuiiE, I.; Feldberg, S. W. J . Nectroanal. Chem. 1974,50, 153-162. (IO)Crank, J. "The Mathematics of Diffusion", 2nd ed.; Ciarendon Press: Oxford, 1975;Chapter 8. (11) Smith, G.D. "Numerical Solution of Partlal Differential Equations: FinIte Difference Methods", 2nd ed.; Clarendon Press: Oxford, 1978. (12) Feidberg, S.W., private communication. (13) Oldham, K. B. Anal. Chem. 1973, 45, 39-47. (14) Parker, I. B.; Crank, J. Comput. J. 1964, 7 , 163-167. (15) Oppenheim, A. V.; Schafer, R. W. "Digital Signal Processing"; Prentice-Hall: Englewood Cliffs, NJ, 1975;Chapter 3.
(16) Walt, J. V. In "Active Filters: Lumped, Distributed, Integrated, Digital and Parametric";Hueisman, L. P.; Ed.; McGraw-HID: New York, 1970; Chapter 5. (17) Nicholson, R. S.; Shain, I. Anal. Chem. 1964,38,706-723. (18) Nlcholson, R. S.; Shain, I. Anal. Chem. 1965,37, 178-190. (19) Nlcholson, R. S. Anal. Chern. 1965, 37, 1351-1355. (20) Ryan, M. D. J. Electroanal. Chem. 1977, 79, 105-119. (21) Miaw Lee-Hua, L.; Boudreau, P. A,; Pichler, M. A,; Perone, S. P. Anal. Chem. 1978, 50, 1988-1996. (22) Whiting, L. F.; Carr, P. W. J. flecfroanal. Chem. 1977, 81, 1-20. (23) Speiser, B.; Rieker, A. J. Nectroanal. Chem. 1979, 102, 1-20. (24) Speiser, B. J . Electroanal. Chem. 1980, 110, 69-77.
RECEIVED for review June 13,1980. Accepted February 17, 1981.
Differential Pulse Polarography at the Static Mercury Drop Electrode J.
E. Anderson, A.
M..Bond," and R. D. Jones
Division of Chemical and Physical Sciences, Deakin University, Waurn Ponds 32 17, Victoria, Australia
The static mercury drop electrode, SMDE, is an Important new electrode for use In polarography. In this paper an approximafe theoretlcal treatment of a reverslble electrode process Is presented for the technlque of dlfferentlal pulse polarography. The considerably dlfferent nature of the DC response at the SMDE compared to that of the conventlonal dropplng mercury electrode (DME) leads to new factors whlch need to be carefully considered in analytlcal appllcations of dlfferential pulse polarography at the SMDE. For example, the DC time dependence of f-"*, SMDE, vs. f'/*, DME, for reverslble electrode processes can lead to a large negative dlstoitii term for reversible electrode processes at the SMDE which is of opposlte sign and far larger In magnltude than at the DME (reduction process assumed). Interestlngly, for irreversible electrode processes the DC dlstortlon term in dlfferential pulse polarography at the SMDE reverts to belng posltive. For a quasi-reversible electrode process the DC dlstortlon term In dlfferential pulse polarography at the SMDE can be negatlve, zero, or positive dependlng on the parameters chosen for the experlment. Differences in DC terms are also shown to be Important In comparing dlfferentlal pulse polarograms obtained at the SMDE and DME for electrode processes exhlbltlng phenomena related to adsorption or film formatlon.
The static mercury drop electrode (ShfDE) is a new and important development in polarography (1). Data (2) indicate that at the SMDE, where area growth terms are absent, use of a constant potential technique (DC polarogrdphy) provides comparable detection limits to using time-dependent waveforms associated with normal and differential pulse polarography. In this paper a simple theoretical interpretation of differential pulse polarography at the SMDE is presented for a reversible electrode process. Results c o n f i i that differential pulse polarography when undertaken at a SMDE suffers from a distortion term ( I ) which for reversible electrode processes manifests itself as a negative offset of the base line at po-
tentids negative of the peak potential (for a reduction process). A related but considerably less severe positive offset is observed with conventional dropping mercury electrodes (DME) ( 3 , 4 ) . However, the absence of the atea growth terms with the SMDE causes the offset to be of opposite sign and substantially larger in magnitude than with a DME. Experimental results and implications of this work to reversible as well as other classes af electrode processes are considered. Interestingly, for irreversible electrode processes, the offset reverts to being negative as is the case at the DME (reduction process assumed).
EXPERIMENTAL SECTION Unless otherwise stated the polarographic experiments described here were performed using an EG&G Princeton Applied Research Corp. (PARC) Model 174 polarographic analyzer modified as described previously (5) to provide the output of the pulse and DC components while in the differential pulse mode. An EG&G PARC 374 microprocessor-controlledinstrument was used for some experiments. Such experiments are specifically designated as being performed with this instrumentation. The EG&G PAkC 174 instrumentwas equipped with an EG&G PARC Model 172 drop timer for experiments at the DME. A platinum auxiliary electrode and a Ag/AgC1(3 M KC1) reference electrode were used in conjunction with a conventionalDME or the EG&G PARC 303 Model SMDE.
REAGENTS AND PROCEDURES Analytical reagent grade chemicals were used throughout the experiments. Polarograms were recorded at ambient temperatures of (20 & 1)"C. A11 solutions were degassed with nitrogen for at least 5 min prior to undertakiig the experiments. Electrode areas were calculated by weighing 100 drops and assuming a spherical shape. The drops were grown in the supporting electrolyte at a potential of -0.4 V vs. AgIAgC1.
RESULTS AND DISCUSSION The SMDE, as does the DME, consists of a capillary through which mercury flows from a reservoir. However, a t the top of the capillary a solenoid activated plunger mediates the flow of mercury. The plunger normally prevents the flow of mercury into the capillary. When the solenoid is activated, the plunger rises from the end of the capillary allowing
0003-2700/8l /0353-1016$01.2510 0 1981 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 53, NO. 7, JUNE 1981
mercury to flow through the capillary. By controlling the time during which the plunger is raised, one may control the amount of mercury which flows through the capillary. Once the plunger drops and seals the top of the capillary, the mercury drop which has formed ceases to grow and becomes a hanging mercury drop. At the drop time selected, the mercury drop is mechanically dislodged from the capillary and a new drop is grown by activating the solenoid. Thus, during the drop life (time), there are two distinct periods: (1)the short time during which drop growth occurs, (2) the time during which the drop of constant area is held until mechanically dislodged. In this work three preselected growth times (50,100,200 ms) were used to provide three drop sizes of different area (0.010, 0.0150 and 0.0240 cm2). T o provide a simple theoretical treatment of differential pulse polarography at the SMDE for a reversible electrode process, we made four basic assumptions: (1)It was assumed that the mercury drop grows instantaneously. (2) It was assumed that as with any stationary electrode to which a pulsed potential is applied that the Cottrell equation can be used (use of this equation in its basic form also assumes that a shielded planar electrode and the absence af any hydrodynamic terms from the area growth period are adequate models). (3) The DC! component of the experiments is described by an area step experiment which is equivalent to a potential step experiment. (4) DC and pulse terms are additive for a reversible electrode process. It should be noted that the calculated “dic component” is identical with a pulse component since the Cottrell equation is used. However, for simplicity the term ’‘dc component” is still used to denote current resulting due to drop growth prior to the application of any potential perturbation. Given that these four assumptions may be applied, a simple theoretical treatment may be made in an analogous manner to that of Christie and Osteryoung for differentid pulse polarography at a DME (3). The obvious difference is that a model related to a stationary drop is being used for DC as well as pulse terms. Thus cpdse
nFAD1/2C = --
+ q)(1+ u2q)
(1)
1 + 6) = anFAD112C q 1 + 61) (7 + 6)1/2
(2)
(a6)1/2
idc(E1,r
(1-- a2)tl
idc(EiL,7)
(1
nFAD112C 1 T’I2(1+ €1) 71/2
(3)
where, El = potential prior to application of pulse, Ez = potential after application of pulse (zero scan rate assumed), 7 = time prior to appllication of pulse when current is measured, 6 = time after application of pulse when current is measured, (7 + 6) = drop life, u2 = exp(nP/RT)AE, el = exp(nF/R7‘)(El - E’,/z, AE = pulse amplitude = (E2-El), ipde= current arising from application of pulse, idc = current associated with DC potential at potential El, and n, F, A, C , D, and Er112= number of electrons, Faraday constant, area, concentration, diffusilon coefficient, and reversible half-wave potential, respectively. The equation for a reversible differential pulse polarogram is given by the expression
Ai = ipulse idc(E1,6+ 7) - idc(E1,7)
(4)
Ai = ipuLse 4- Aidc
(5)
or
where (Ai) is the differential pulse current. Thus the difference in the DC terms, Aidc, which leads to the distortion or offset mentioned in the introduction, is
1017
This may be compared to the offset term for the DME which is ( 3 )
The difference in the sign of the time exponents in these two equations leads to the difference in the sign of the offset. The presence of larger exponent of the time parameter in the SMDE equation (t-lI2,SMDE vs. t1/6,DME) leads to the prediction that the magnitude of the offset will be larger by a cubed fador at the SMDE and thus far more important than is the case with the DME. The equation8 presented predict that the offset will increase in magnitude as n, A, or C are increased. It i s important to note that n, A, and C will not change the ratio of the offset to the differential pulse peak current. However, whilst the pulse amplitude, AE, does not affect the magnitude of the offset, an increase in AE will increase the ratio of the differential pulse peak current to the offset, and from the analytical viewpoint this means the DC distortion term will be less significant with larger pulse amplitudes. A further interesting aspect of these equations is the drop time dependence of the DC distortion term. From eq 6 it is apparent that as the drop life (t = 7 + 6) is decreased, the offset should increase. However, the drop life should have little effect on the differential pulse peak current if 6 remains constant when decreasing t and the relative contribution of Ai& can therefore become considerable at short drop times. It is also clear that while short drop times offer little advantage with respect to sensitivity in differential pulse polarography, short drop times must provide the highest sensitivity (current per unit concentration) in constant potential sampled DC polarography at the SMDE where t = 7. Indeed, the theory presented provides the interesting result that the dc diffusion controlled limiting current at the SMDE is similar in magnitude to the pulse component and actually larger in magnitude than the resulting differential pulse peak current for drop times of 0.2 B (AE= -25 mV and 6 = 50) ms verifying many of the claims made by Bond and Jones (2) that for simple electrode processes performance of pulse and DC techniques do converge at the SMDE. A final important result to emerge from the approximate theory is that differential pulse polarography at the SMDE now has characteristics closely allied to those commonly associated with normal pulse polarography (potential step experiment). However, approximations have eliminated considerations associated with hydrodynamics, etc., and under appropriate conditions these neglected terms can be important as will be seen subsequently. The SMDE is in reality a combination of a DME and a stationary electrode and has features assQciated with both classes of electrode. At short times DME behavior dominates and at long times where the present theory is valid, stationary electrode behavior is predominant. Figure 1shows the theoretical and experimental components as well as the differential pulse response for 5 X M Cd(I1) at the SMDE under one set of conditions. Curve a is the dc component, curve b is the pulse component, and curve c is the difference component. The experimental curves (solid lines) were obtained on an EG&G PARC 174 instrument modified as described by Anderson and Bond (5) and using a -25 mV pulse amplitude with a drop area of 0.024 cm2. Although the theoretical amplitudes of the peak currents are slightly larger than those obtained experimentally, the peak
1018
ANALYTICAL CHEMISTRY, VOL. 53, NO. 7,JUNE 1981
Comparison of differential pulse theory and experiment for reduction of 5 X M Cd(I1) in 1.0 M KCI at the SMDE: (a) DC component, (-) theory, (0) experiment; (b) pulse component, (-) theory, (A)experiment; (c) dlfference component, (-) theory, ( 0 ) experiment. Electrode area was (0.0240 cm2,drop time was 0.5 s, diffusioncoefficient was 7.8 X lo-’ om2 s-’,and pulse amplitude was -25 mV. Note: Differencecomponent is translated along the potential axis for clarity.
I \
Flgure 1.
potentials and general shape of the curves are in excellent agreement. Table I summarizes the comparison between theory and experiment for a number of drop times (0.5,1.0, 2.0 s), pulse amplitudes (-10, -25, -50 mV), and drop sizes (0.0100,0.0150,0.0240 cm2). As was the case with data provided in Figure 1,Table I indicates that although the shape and position of the theoretical curves match the experimental data, the amplitude or currents predicted are all too high. Although there are several reasons why deviations between theory and experiment may be expected with the SMDE, the assumption of instantaneous drop growth is one of the most suspect. The assumption of instantaneous drop growth basically attempts to equate the potential step experiment for which the Cottrell equation was derived with the corresponding “area step” experiment ( A = 0 at t = 0, A = x at t > 0). Theoretically, if a drop could be grown (or more realistically appear) instantaneously, the “area step” experiment would give the same results as the potential step experiment. With the existence of a finite drop growth period, one not only has difficulty in the assignment of a point in the drop growth at which to call t = 0 but depletion and hydrodynamics ,of the solution caused by drop growth must be considered. More detailed work is continuing in our laboratory to understand the “area step” experiment,introduced by the advent of the ShfDE; the present theory is adequate to investigate the analytical implications of applying differential pulse polarography at the SMDE. Implications of the DC Distortion Term in Practical Applications. The DC distortion, apart from the influencing the wave shape, has the effect of offsetting the base line at the more negative potential region (reduction assumed) of the differential pulse polarogram. This offset base line may have to be allowed for in the measurement of the peak height in analytical applications. In particular the presence of a more positively reduced compound will lower the base line on which a peak of interest is observed. This effect can be very severe when the more positvely reduced compound is in large excess and can cause problems in data acquisition when using computerized instrumentation to measure peak height if traditional and simple measurement routines using the solvent/ electrolyte base line are used. The peak of interest occurring at negative potentials can be correctly measured via reference to the lowered base line. However, a first generation computerized instrument such as the EG&G PARC Model 374 microprocessor-controlled instrument gives anomalous results
0.14pa
Flgure 2. Differential pulse polarogram for reduction of 1.0 X lo-‘ M zlnc(I1)in the presence of 1.1 X M cadmium(I1)in 1 M NaCl using the EG&G PARC 374 microprocessor-controlled instrument and an SMDE. Electrode area was 0.0100 cm2,drop time was 0.5 s, and pulse amplitude was -50 mV. Instrumental peak current reported = 0.14 PA. True peak current = 0.33 PA. Instrumental peak current reported in the presence of 1 X M Cd(I1) is -1.68 PA.
09
11
10
1.2
1
1
1.3
0.9
1.0
1.1
12
1.3
-01
-08
-09
-10
-11
1
1
1
1
1
1
1
1
c
I
-01
,
,
-08
,
I
-09
#
I
-10
.
I
,
-11
E
VI A
~ A ~ C I
Figure 3. Comparison of differential pulse polarograms at a DME (a and c) and an SMDE (b and d). Curves a and b are for reduction 5 X M Ni(I1) in 1.0 M KCI while curves c and d are for reduction of 1 X M Cr(II1) in 1.0 M NaC104/0.02M HC104. Electrode area of 0.0100 cm2 used In SMDE Cr(II1) experiment. Electrode area of 0.0150 cm2used in SMDE Ni(I1) experiment. Pulse amplltude was -25 mV. Drop time was 1.0 s.
when the base line is distorted from the instrumental zero or solvent blank because it uses an erroneous background solvent or electronic zero point as a reference and not the offset base line. The use of more sophisticated software would of course eliminate this problem. Use of long drop times and large pulse amplitudes will minimize the problem as the work of Peterson (I), our theory, and data in Table I demonstrate. Figure 2 experimentally shows how the base line lowering due to an excess of cadmium(I1) can effect the peak current measured for zinc(I1). Indeed, in the presence of sufficient cadmium the EG&G PARC Model 374 instrument will produce apparently negative peak currents (concentration) for zinc. An improved peak measuring routine of the kind described elsewhere (6)circumvents this problem, and indeed the second generation EG&G PARC Model 384 microprocessor instrument may be able to more adequately cope with the difficulty created by the distortion term. However, without due care it is clear that the distortion term could lead to problems in routine analysis particularly when using automated instrumentation, and the user needs to verify that the software is appropriate for the measurement being undertaken. Other nonreversible electode processes were also investigated with the SMDE to determine the more general nature
ANALYTICAL CHEMISTRY, VOL. 53, NO. 7, JUNE 1981
Table I. Comparison of Theory and Experiment at the SMDE" drop size, cma 0.010
-AE,
mV 50 25 10 50 25 10 50 25 10
0.015
5o
25 10 50 25 10 50 25 10 0.024
5o
25 10 50 25 10 50 25 10
differential pulse component E,, v (-0.632) -0.634 (-0.643) -0.646 (-0.6 50) -0.652 (-0.633) -0.634 (-0.645) -0.646) (-0.6 52) -0.652 (-0.633) -0.634 (-0.646) -0.646 (-0.653) -0.652 (- 0.6 38) -0.634 (-0.6 50) -0.646 (-0.6 57) -0.652 (-0.63 7) -0.634 (-0.6 50) -0.646 (-0.6 57) -0.652 (- 0.6 38) -0.634 (-0.651) -0.646 (-0.657) -0.652 (-0.632) -0.634 (- 0.64 5) -0.646 (-0.653) -0.652 (-0.635) -0.634 (- 0.64 8) -0.646 (-0.6 55) -0.652 (-0.637) -0.634 (-0.648) -0.646 (-0.6 56) -0.652
Ai,, PA
(4.38) 4.82 (2.70) 2.93 (1.08) 1.19 (4.62) 4.83 (2.85) 2.91 (1.20) 1.23 (4.61) 4.83 (2.90) 2.92 (1.25) 1.24 (7.23) 7.23 (4.20) 4.33 (1.68) 1.79 (7.65) 7.24 (4.55) 4.37 (1.93) 1.84 (7.76) 7.24 (4.78) 4.38 (2.03) 1.86 (12.10) 11.56 (7.1) 6.94 (2.87) 2.87 ( 12.35) 11.58 (7.45) 6.99 (3.15) 2.95 (12.35) 11.59 (7.55) 7.01 (3.25) 2.98
w,,, (0.061) 0.06 2 (0.050) 0.04 8 (0.044) 0.044 (0.062) 0.062 (0.050) 0.048 (0.046) 0.044 (0.062) 0.062 (0.050) 0.04 8 (0.044) 0.046 (0.060) 0.06 2 (0.050) 0.046 (0.044) 0.044 (0.061) 0.062 (0.049) 0.04 9 (0.044) 0.046 (0.061) 0.06 2 (0.050) 0.04 8 (0.044) 0.042 (0.061) 0.06 2 (0.048) 0.048 (0.042) 0.044 (0.062) 0.062 (0.050) 0.048 (0.045) 0.044 (0.062) 0.06 2 (0.050) 0.04 8 (0.046) 0.046
pulse component E,,
v
(-0.635) -0.636 (-0.650) -0.652 (-0.668) -0.668 (-0.635) -0.636 (-0.650) -0.650 (-0.664) -0.662 (-0.63 5) -0.634 (-0.648) -0.648 (-0.660) -0.660 (-0.640) -0.636 (-0.656) -0.652 (- 0.6 70) -0.668 (- 0.64 1) -0.636 (- 0.655) -0.650 (-0.680) 0.662 (- 0.641 ) 0.634 (-0.654) -0.648 (-0.675) -0.660 (-0.640) -0.636 (-0.653) -0.652 (- 0.6 72) -0.668 (- 0.640) -0.636 (-0.6 52) -0.650 (-0.665) -0.662 (-0.638) -0.634 (-0.651) -0.648 (-0.663) -0.660
ip, PA (4.85) 5.13 (3.30) 3.60 ( 2.23) 2.38 (4.70) 5.03 (3.35) 3.38
(1.99) 1.98 (4.99) 4.97 (3.27) 3.24 (1.76) 1.74 (7.70) 7.69 ( 5.50) 5.40 (3.65) 3.57 (7.80) 7.55 (5.30) 5.07 (3.12) 2.98 (7.95) 7.46 (5.12) 4.83 (2.85) 2.61 (13.10) 12.31 (9.35) 8.64 (6.50) 5.72 (12.90) 12.04 (8.75) 8.12 (5.12) 4.77 (12.65) 11.93 (8.35) 7.77 (4.50) 4.17
1019
dc component id, P A (2.60) 2.29 (2.60) 2.29 (2.60) 2.29 (1.55) 1.56 (1.55) 1.56 (1.55) 1.56 (1.15)
1.33
(1.15) 1.33
(1.15) 1.33 (3.60) 3.43 (3.60) 3.43 (3.60) 3.43 (2.53) 2.35 (2.53) 2.35 (2.53) 2.35 (1.80) 1.64 (1.80) 1.64 (1.80) 1.64 (6.70) 5.48 (6.70) 5.48 (6.70) 5.48 (4.20) 3.76 (4.20) 3.76 (4.20) 3.76 (2.85) 2.62 ( 2.85) 2.62 ( 2.85) 2.62
ioff, PA
td, s
(-0.20) -0.17
0.5
(-0.07) -0.06
1.0
(-0.05) -0.04
2.0
(- 0.36)
-0.25
(- 0.17)
0.5
-0.08
1.0
(-0.10) -0.03
2.0
(-0.55) -0.40
0.5
(-0.17) -0.14
1.0
(- 0.0 7)
-0.05
2.0
a System studied is reduction of 5 x l o v 4M Cd(I1) in 1.0 M KC1, diffusion coefficient 7.8 X cm2/s. AE = pulse amplitude, E , = peak potential, a i = differential peak current, i, = pulse peak current, W,,, = peak width at half-height, id = DC diffusion current, i,ff = offset in base line, and td = drop time. Experimental data are in parentheses.
of differential pulse polarography and any analytical implications. With irreversible systems such as the reduction of Ni(I1) in 1M KC1, NI(I1) 2e-- Ni(O), the normal positive offset which occurs at a conventional DME as a result of the differential pulse mode operation is considerably enhanced relative to a reversible electrode process (Figure 3a). At the SMDE it was found that the reduction of Ni(I1) yields a differential pulse polarogram with a net positive offset (Figure 3b). This net positive offset is in contrast to the negative offset observed in the case a9 the reversible Cd(I1) reduction and appears to be the result of the summation of two opposing offsets, i.e., the positive offset due to irreversible nature of electrode process is partially nulled by the negative offset of
+
SMDE as described when considering the reversible cadmium reduction. Indeed, by using conditions which increase the magnitude of the negative offset resulting from the use of the SMDE (short drop time) and conditions which decrease the apparent positive offset for the irreversible reduction of Ni(I1) (small pulse amplitude), the net offset (positive) could be reduced to nearly zero. For the irreversible reduction, Cr(II1) + e- Cr(II), in 1 M NaC104/0.02 M HC104, involving a solution soluble product, a positive offset is also observed at the DME and SMDE, but as for the nickel case it is less important at the SMDE where the negative term causes some nulling (Figure 3). Simple theory based on stationary electrode concepts could not completely explain the above results. The
-
1020
-08
ANALYTICAL CHEMISTRY, VOL. 53, NO. 7, JUNE 1981
-01
-06
-08
-05
-01
-06
-05
E VIAg/AgCI
Flgure 4. Oxidation of mercury in the presence of sulfide (5 X lo-‘ M) in 0.1 M NaOH at (I) a DME and (11) an SMDE: (a)DC component, (b) pulse component, (c) difference component. Drop time was 1.0 s, pulse amplitude was -25 mV, and DME flow rate was 0.937 mg/s. SMDE electrode area was 0.0150 cm2.
fact that the SMDE is exactly a DME in its early stage will need to be considered in rigorous theoretical treatments. Departures from the stationary electrode approximation are more obvious in the above situation where irreversible reactions are being considered. In the case of the quasi-reversible reduction of Zn(I1) in 1 M KCl M HCl), Zn + 2e- + Zn(0) the net offset at the SMDE could be made positive or negative by varying the experimental parameters. At a pulse amplitude of -25 mV and a drop time of 1.0 s the offset is negligible. It appears that for systems exhibiting other than reversible behavior, the selection of appropriate drop times (and pulse amplitudes) may make the evaluation of background (or base line) somewhat easier (no offset). It is well established that the offset in differential pulse polarography should be independent of the standard rate of electron transfer. This is clearly shown in the theoretical treatment given by Aoki, Osteryoung, and Osteryoung (7). The deviation observed in this work for other than reversible systems are most likely due to hydrodynamics and/or mechanistic nuances of the electrode processes studied. Another system, which was briefly investigated was the oxidation of mercury in the presence of sulfide Hg + S2-+ HgS 2e-. Figure 4 compares the responses obtained at a DME and the SMDE of 5 X M sulfide in 0.1 M NaOH with a drop time of 1.0 s. Curves a and b are the DC and pulse components, respectively, and curves c the difference component or differential pulse polarogram. Several waves have been reported for this system with the DME (8-10). They are believed to originate from the formation of insoluble films of mercury sulfide, and the number of waves observed is dependent on the concentration of sulfide and drop time. It is apparent from Figure 4 that with the DME only two waves
+
are present at the drop time (1.0 s) and concentration shown and three with the SMDE. Presumably at this drop time with the SMDE, an additional layer of insoluble film has had sufficient time to form due to the nonexpanding area of this electrode for most of the drop life. This suggests that adsorption and related surface phenomena may play a more important role in the response obtained with the SMDE than with a DME. As expected (11)normal pulse type measurements simplify the sulfide electrochemical responses at the SMDE and for this kind of mechanism previously mentioned parallels between the DC, differential, and normal pulse experiments need to be treated with care. At the SMDE, use of the normal pulse waveform is considerably superior to use of the differential pulse one for determining sulfide. By contrast differential pulse responses are inferior to that obtained at the DME with the same waveforms. For practical analytical purposes, ways of minimizing deleterious effects assocated with adsorption and use of the SMDE must be investigated fully.
CONCLUSIONS From the above it is clear that whilst differential pulse curves at the SMDE may frequently appear to be superficially similar to those obtained at the DME, they can in fact be significantly different because of differences having their origin in the different form of the DC terms applicable to the electrodes. In particular in this work the DC offset term a t the SMDE in differential pulse polarography is demonstrated to be considerablydifferent to that at the DME and similarly systems exhibiting characteristics of adsorption or film formation are likely to be quite different at the two electrodes.
LITERATURE CITED (1) (2) (3) (4) (5) (6) (7) . ,
(8)
(9) (10) (11)
Peterson, W. M. Am. Lab. (Fairflekf, Conn.) 1979, 1 1 (12), 69-78. Bond, A. M.; Jones, R. D. Anal. C h h . Acta 1980, 121, 1-11, Christie, J. H.; Osteryoung, R. A. J. Electroanal. Chem. 1974, 49, 301-311. Grabaric, 8. S.; Bond, A. M. Anal. Chlm. Acta 1977, 88, 227-236. Anderson, J. E.; Bond, A. M. Anal. Chem. 1980, 52, 1439-1445. Bond, A. M.; Grabaric, B. S. Anal. Chem. 1979, 51, 337-341. Aoki, K.: Ostewouna, J.; Ostewouns, . - R. A. J . Nectroanal. Chem. 1980, 110, I-is. Heyrovsky, J.; Kuta, J. “Principles of Polarography”; Academic Press: New York and London, 1966; p 174. Bond, A. M. “Modern Polarographic Methods in Analytical Chemistry”; Marcel Dekker: New York and Basel, 1980; p 112. Zhdanov, S. I. In “Encyclopedia of Electrochemistry of the Elements”; Marcel Dekker: New York, 1975; Vol. IV, p 282. Turner, J. A.; Abel, R. H.; Osteryoung, R. A. Anal. Chem. 1975, 47, 13. 43-47.
RECEIVED for review July 11,1980. Accepted February 9,1981. The financial assistance of the Australian Research Grants Committee in support of this work is gratefully acknowledged by the authors.
