Second Harmonic Alternating Current Polarography. Experimental Observations with a System Involvinga Very Rapid Chemical Reaction Following Charge Transfer Thomas G. McCord1 and Donald E. Smith2 Department of Chemistry, Northwestern University, Evanston, Ill. 60201 Results are presented of second harmonic ac polarographic measurements with the electrode reaction [Anthracene]-
+ e + [AnthraceneI2--
2H +
Dihyd roanthracene in acetonitrile-tetraethylammonium perchlorate electrolyte. This electrode process is totally irreversible, even’on the ac polarographic time scale, due to the very rapid follow-up chemical reaction of the anthracene dianion. Experimental results are in excellent agreement with the relevant theory. This fact and the high quality of experimental data serve to further support the recently-revealed applicability of the ac polarographic method to the study of irreversible processes. SECONDHARMONIC ac polarographic measurements recently have been applied successfully to the measurement of charge transfer kinetic parameters (ks and a) with several simple quasi-reversible systems (1-3). These investigations were aided considerably by advantageous properties of the second harmonic response such as negligible double-layer charging current (background current) and high sensitivity to kinetic effects of heterogeneous charge transfer (4,5). The negligible double-layer charging current, combined with high-precision instrumental compensation of effects associated with ohmic potential drop (6, 7) enables direct theoretical analysis of instrument readout without the necessity of tedious corrections for nonfaradaic effects preliminary to analysis. The small charging current contribution attending second harmonic measurements has been frequently acknowledged (4,5, 8-12) as an advantage permitting measurements at much higher
frequencies than accessible to techniques characterized by a normal charging current contribution which becomes the predominant observable at sufficiently high frequencies. However, seldom-quoted advantages for moderate and low frequency measurements also arise by virtue of the low charging current. Because of this property, situations involving abnormally small ac responses-e.g., irreversible processes for systems with sparingly soluble electroactive componentsshould be accessible to second harmonic measurements where more conventional techniques may fail throughout the frequency spectrum because of inadequate signal level. We have been particularly interested in applications of second harmonic ac polarography in the latter type of situation involving relatively meager faradaic responses. The origin of our concern is found in the desire to apply the ac polarographic method to the study of irreversible electrode processes [once considered a virtually impossible application (5, 13-15) but recently shown to be otherwise (16-20)] and to electrode reactions of relatively insoluble species of biological interest. In order to evaluate the possibility of effecting reasonably precise quantitative second harmonic measurements with systems yielding unfavorably small faradaic responses, a study of a system involving a rapid electrode reaction coupled to a very rapid irreversible following chemical reaction (Mechanism R1) k
O+neeR-Y was undertaken.
(R1)
Under conditions where
k
>> w
(1)
= applied frequency), the system can be considered totally irreversible-i.e., electrochemical reoxidation of species R is precluded, even on the short time scale of the applied alternating potential, due to the much shorter half-life of species R with respect to chemical decomposition (16). Within the framework of Mechanism R1, such conditions represent a worse case in that the smallest possible wave is obtained. The system selected for this investigation was anthracene in acetonitrile-0.1 M tetraethylammonium perchlorate (TEAP). The mechanism of anthracene reduction in diox(W
1 NIH Graduate Fellow, 1967-68; present address, General Electric Corp., Materials and Processes Laboratory, Schenectady, N. Y., 12305. To whom correspondenceshould be addressed. f
-
~~
(1) J. E. B. Randles and D. R. Whitehouse, Trans. Faraday Soc. 64, 1376 (1968). (2) T. G. McCord and D. E. Smith, ANAL.CHEM., 41, 131 (1969). (3) T. G. McCord and D. E. Smith, ibid., 42, 126 (1970). (4) D. E. Smith in “Electroanalytical Chemistry,” Vol. 1, A. J. Bard, Ed., Marcel Dekker, Inc., New York, N. Y.,1966, Chapter 1. ( 5 ) B. Breyer and H. H. Bauer in “Chemical Analysis,” Vol. 13, P. J. Elving and I. M. Kolthoff, Eds., Interscience Publishers,
New York, N. Y.,1963. (6) E. R. Brown, T. G. McCord, D. E. Smith, and D. D. DeFord, ANAL.CHEM., 38, 1119 (1966). (7) E. R. Brown, H. L. Hung, T. G. McCord, D. E. Smith, and G . L. Booman, ibid., 40, 1424 (1968). (8) J. Paynter, Ph.D. Thesis, Columbia University, New York, N. Y., 1964. (9) R. Neeb, Z . Anal. Chem., 188,401 (1962). (10) H. H. Bauer, J. Electroanal. Chem., 1,256 (1960). (11) H. H. Bauer and P. J. Elving, ANAL.CHEM., 30, 341 (1958). (12) D. E. Smith and W. H. Reinmuth, ibid., 33,482 (1961). 2
ANALYTICAL CHEMISTRY, VOL. 42, NO. 1, JANUARY 1970
(13) P. Delahay, “New Instrumental Methods in Electrochemistry,” Interscience Publishers, New York, N. Y., 1954, pp 173-175. (14) W. H. Reinmuth, ANAL.CHEM., 36, 211R (1964). (15) D. E. Smith, Ph.D. Thesis, Columbia University, New York, N. Y., 1962. (16) D. E. Smith and T. G. McCord, ANAL.CHEM., 40,474 (1968). (17) B. Timmer, M. Sluyters-Rehbach, and J. H. Sluyters, J. Electroanal. Chem., 14, 169 (1967). (18) B. Timmer, M. Sluyters-Rehbach, and J. H. Sluyters, ibid., 14, 181 (1967). (19) J. E. O’Reilly and P. J. Elving, J. Electroanal. Chem., 21, 169 (1969). (20) B. G. Dekker, M. Sluyters-Rehbach,and J. H. Sluyters, ibid. 21, 137 (1969).
ane-water solvents (21) and in nonaqueous dimethylformamide (DMF) (22, 23) has been shown to involve two oneelectron steps of the form R+e*RRZ(HS
=
+ 2HS
+
A
(a) (first wave)
+ e * Re
R-
I
RHz
+ 2s- (b)} (c)
(second wave)
(R2)
solvent)
The half-wave potentials of the two electron transfer steps are sufficiently separated that Steps b and c can be considered independent of step a, at least from the viewpoint of the ac polarographic experiment. Previous measurements (23) indicated that the follow-up chemical reaction (Step c) is essentially irreversible and sufficiently rapid that the condition of Equation 1 probably applies throughout the available frequency spectrum. The associated electron transfer step (Step b) is expected to be sufficiently rapid that nernstianconditions will apply over a reasonable frequency range (23). Thus, the mechanism of interest (Mechanism R1) with the desired kinetic properties is manifested in the second reduction step of anthracene in aprotic solvents. The first electron transfer step (Step a), an essentially diffusion-controlled process, was not of interest in this work. Acetonitrile was used in this investigation, rather than the previously employed solvents, because it was immediately available and because mechanistic and essential kinetic aspects of the anthracene reduction were found to be the same in acetonitrile as in DMF. It was decided to compare experimental results with previously untested theoretical predictions (16, 24) for Mechanism R1 in order to assess the fidelity of second harmonic measurements under the relatively demanding conditions in question. A successful match of theory and experiment could be taken as an indication that both theory and experimental data were satisfactory. A mismatch of theory and experiment would imply either a failure of theory, imprecise experimentation, and/or a reduction mechanism differing from Mechanism R1. Thus, only an affirmative result of the theory-experiment comparison would be definitive with regard to one's ability to effect accurate second harmonic measurements. Our studies have yielded an affirmative conclusion. The results are reported here. THEORY
The theory for the second harmonic ac polarographic current with electrode reactions following Mechanism R1 has been discussed in detail (16, 24). Of particular interest in the present work is the behavior of nernstian systems in the limit described by Equation 1. It has been pointed out (16) that an excellent approximation to the general theoretical formulation for the second harmonic response under such conditions may be written Z(2wt) = 2(2w)W(w)sin(2wt
+ 6)
(2)
where Z(2w) =
2.325 n2F2ACo*( ~ D O ) " ~ A E RTe-a(l e1.0g16)[I (1 Qze6)31'2
+
+ +
(3)
(21) G. J. Hoitink, J. Van Schooten, E. DeBoer, and W. Ij. Aalbersberg, Rec. Trau. Chim.,73, 355 (1954). (22) K. Umemoto, Bull. Chem. SOC.Jap., 40,1058 (1967). (23) A. C. Aten, C. Buthker, and G . J. Hoijtink, Trans. Faraday SOC.,55, 324 (1959). (24) T. G . McCord and D. E. Smith, ANAL.CHEM., 41,1423 (1969).
(Ed,C: 1;)
(VOLTS)
Figure 1. Theoretical second harmonic ac polarogram
Polarogram calculated from Equations 2-10 with C.* = 2 X lO-SM, T = 298 "K, AE = 15 mV, = 0.53 X 10-4 cm* sec-1/2, t = 2.3sec, w = 144radsec-1, k = 5.0 X 106sec-1
(4)
(7)
RT
Edo -
-
In (1.349k1'2t1'2) nF
Notation definitions are given below. Among the most s i p nificant aspects of the predictions of Equations 2-10 is that the second harmonic wave shape and magnitude will be independent of the chemical rate parameter, k. The predicted wave shape is characterized by a single peak with a shoulder located on the cathodic side of the wave (see Figure l), a unique departure from the wave characteristics found in more reversible situations ( 4 5 , 12). Other noteworthy predictions include a general broadening of the second harmonic wave with increasing frequency, a small, not noticeable, current magnitude frequency dependence of positive slope and a substantial mercury drop life dependence of negative slope (16). The foregoing theoretical relationships are based on the expanding plane electrode model. The attendant neglect of spherical diffusion effects is expected to give rise to slight inaccuracies in the theoretical predictions ( 2 , 3 , 25), particularly over the cathodic portion of the wave. The foregoing theoretical formulation was derived using the assumption that the reducible species was initially present in the bulk of the solution (initially uniform concentration profile). However, the theory is not invalidated by the fact that with the system studied here the reducible species (an(25) T. G. McCord, E. R. Brown, and D. E. Smith, ibid.,38, 1615 (1966). ANALYTICAL CHEMISTRY, VOL. 42, NO. 1, JANUARY 1970
3
7
FIRST W A V E
SCCCN3 WAVE
i ” -1.40
-1 .6 0 0.0.
PCTlNTlAL
-1.80 (VOLTS)
7
.
Figure 2. DC polarogram of anthracene
Figure 3. Second harmonic ac polarogram of anthracene
System: 2.0 X lOPM anthracene in 0.10M TEAP-acetonitrile at 25 “C Applied : de scan rate = 50 mV per minute Measured : instantaneous direct current
System: sameas Figure2 Applied: 1110 Hz, 20 mV peak-to-peak sine wave; de scan rate = 50 mV per minute Measured : instantaneous faradaic component at 2220 Hz (ordinate uncalibrated)
thracene radical anion) is generated in situ by the reversible electrode reaction associated with the first polarographic wave (yielding a nonuniform concentration profile). It has been shown (26) that in such situations the ac polarographic behavior is independent of whether the depolarizer is initially present in the solution bulk or is generated in situ by a polarographic process. EXPERIMENTAL
Details of instrumentation and second harmonic measurement procedures are given elsewhere (2, 6, 7). Supporting electrolyte and solvent purification employed previously described methods (7). Eastman anthracene was used without further purification. Second harmonic polarograms were run at 23, 332, and 11 10 Hz using the sample-and-hold readout mode with mechanically controlled drop life (2.3 seconds). In order to check time-dependence, natural drop-life polarograms were run with two column heights at 23 and 1110 Hz. Some preliminary dc and ac polarograms were also run using natural drop lives. DATA TREATMENT
tenstics is attended by comparable error (capillary shielding) and, finally, because the evaluation of Doliz would have relied on the dc limiting current giving rise to the same 2rror sources. Explicit determination of Eliz‘and k individually was not possible under the conditions of this work. Rather, the quantity
+ RT In (1.349 kt”*) nF -
was determined from the observed dc polarographic halfwave potential using the Koutecky expression (27, 28). This enabled calculation of the potential-dependent parameter, 6 (Equation 9), the only quantity in the theoretical formulation which is dependent on Ell2’ and k . By this procedure one tests the ability of the theory to locate the position of the second harmonic wave relative to the actual dc polarographic half-wave potential, rather than in relation to El,; (or Eo). By using the foregoing quantities evaluated from dc polarographic measurements and known values of all other parameters, theoretical polarograms were calculated from Equations 2-10 and compared directly to experimental polarograms obtained using the sample-and-hold readout mode.
The only unknown quantities required to calculate theoretical polarograms from Equations 2-10 are the parameters A , Do1/2, Eli;, and k . The product ADo1/2was determined from the limiting current of the second dc polarographic wave with the aid of the Ilkovic Equation. In a few instances involving comparison of measurements performed at different mercury drop lives, the relevant observables were normalized to the same drop life. One should recognize that the well-known difficulties in estimating the magnitude of a dc polarographic wave whose background current comprises the contribution from an earlier wave influences the accuracy of this evaluation of Because of this problem, together with other sources of error-e.g., the Ilkovic Equation-one should anticipate uncertainties of a few per cent in comparisons of absolute second harmonic current magnitudes to theory. We did not attempt individual determination of A and because of the convenience of the method employed, because determination of A from capillary charac-
Figure 2 shows a conventional dc polarogram (natural drop life) of the anthracene system. Figure 3 gives the corresponding second harmonic ac polarogram. It is the second (more cathodic) of the polarographic waves which is of concern in the measurements described here. Figure 3 provides an excellent frame of reference with regard to the magnitude of the irreversible wave of interest relative to a near-reversible wave (first wave-Figure 3). However, in this regard one should recognize that a small part of the difference in magnitude of the two waves in Figure 3 is due to the much shorter drop life at potentials of the second wave, relative to the first. This attenuation of drop life at cathodic potentials is characteristic
(26) H. L. Hung and D. E. Smith, J. Electroanal. Chem., 11, 237 (1966).
(27) J. Koutecky, Collect. Czech. Chem. Commwz., 18, 597 (1953). (28) J. Koutecky, ibid., 20, 116 (1955).
4
ANALYTICAL CHEMISTRY, VOL. 42, NO. 1, JANUARY 1970
RESULTS AND DISCUSSION
'. .. _. -. 0
z
p 0' Y u
-. ._ . i.
0.1:
I CI
.
I '
b
/-'
I
I
.
~>--
*;/
*-
.(
-SI.. -1.80
. "
,
-1.30
-2.00
-
O.C. P O T E Y T I A L ( V O L T S )
Figure 5. Absolute comparison of theoretical and experimental second harmonic ac polarograms of anthracene -1 . R 5
System : same as Figure 2 Applied: 1110 Hz 30 mV peak-to-peak sine wave; dc scan rate = 25 mV per minute Measured: 2220 Hz faradaic component at end of mechanically controlleddrop life using sample-and-holdreadout mode 0 = theoretical points calculated using parameters listed in Figure 1, except k was not specified: 6 value was obtained from dc polarographic half-wave potential as described in text
-1.95
O.C. P O T E N T I A L (VOLTS)
Figure 4. Second harmonic ac polarogram of anthracene: second reduction step All conditions same as Figure 3 except ordinate at higher sensitivity
of aprotic solvent polarograms and is the primary cause for the apparent magnitude difference in the two dc polarographic waves (Figure 2). Figure 4 shows the more cathodic second harmonic wave at higher sensitivity (ordinate) than Figure 3. Figure 4 provides verification of one important qualitative aspect of the theoretical predictions (Figure l), namely, the peak-shoulder character of the second harmonic wave form. Figure 5 illustrates a comparison of theory and experiment in which the predicted theoretical response (solid points, Figure 5) is superimposed directly on a second harmonic
polarogram obtained using sample-and-hold readout (staircase curve-Figure 5). Deviations between theory and experiment shown in Figure 5 manifest mismatch in both shape and magnitude of the wave. Because of the above-mentioned problems in experimentally determining certain parameters influencing wave magnitude, it was of interest to examine more closely the success of Equations 2-10 in predicting wave shape, an observation much less susceptible to experimental error (provided instrumental compensation of ohmic potential drop is operative). This was done by matching theoretical and experimental second harmonic peak magnitudes so that the subsequent theory-experiment comparison would manifest primarily disparities related to wave shape. A typical result is shown in Figure 6. Finally, comparisons of theory and experiment for certain key aspects of the second harmonic wave are given in Table I.
3
Y
Figure 6. Comparison of theoretical and experimental second harmonic ac polarographic wave shape for anthracene System: same as Figure 2 Applied: 332 Hz, 30 mV peak-to-peak sine wave; dc scan rate = 25 mV per minute Measured: 664 Hz faradaic component at end of mechanically controlled drop life using sample-and-hold readout mode = theoretical points calculated as described in Figure 5, except peak current was matched to experimental value by introduction of appropriate scalingfactor
Table I. Theory-Experiment Comparison of Various Second Harmonic Observables Second harmonic Frequency Experimental Theoretical W) value value observable E11rEp 23 45 46 (millivolts) 332 63 65 1110 72 71 WliZ 23 96 90 (millivolts) 332 110 109 1110 127 122 Ep-Eshoulder 23 66 63 (millivolts) 332 77 77 1110 85 87 2.3 23 2.6 332 2.9 3.3 2.9 3.3 1110 I p relative 23 1 1 to I p at 332 1.5 1.3 23 Hz 1110 1.8 1.4
ANALYTICAL CHEMISTRY, VOL. 42, NO. 1, JANUARY 1970
5
The agreement between theory and experiment shown in Figures 5-6 and Table I must be considered as generally good-to-excellent, particularly in view of the unfavorably small ac response and other previously acknowledged measurement problems. Predictions regarding wave position (E,-Ell~--Table I), and shape ( W w , E p - E s h o u l d e r IpllshoulderTable I, Figure 6) were most satisfactory. Slight deviations between predicted and observed wave shape (Figure 6) could easily arise from spherical diffusion or depletion effects which are not incorporated in the predictions. Agreement between theory and experiment with regard to current magnitudes (Figure 5 ) is within probable experimental error and must be considered good. The observed peak current frequency dependence is slightly larger than predicted. This might be due to the fact that the condition for total irreversibility (k >> w ) is not precisely realized at the higher frequencies, an effect which could enhance the frequency dependence slightly without appreciably altering wave shape (24). The frequency profile’s sensitivity to minor deviations from total irreversibility is readily recognized if one recalls that a nearly seven-fold increase in I p would accompany an increase in frequency from 23 to 11 10 Hz with a totally reversible process. Measurements of the mercury drop life dependence of second harmonic current magnitudes exhibited the predicted decrease in current magnitude with increasing drop life (16,24). Because the instrumentation employed compensates precisely for ohmic potential drop only at a single point in drop life (6,7) and, thus, only the sample-and-hold readout procedure is quantitatively precise, no attempts were made to quantitatively compare theory and experiment with regard to the detailed I(2ot)-t profile. It should be recognized that the match of theoretical and experimental current magnitudes (Figure 5) implicitly depends on the accuracy of the timedependent term so that a theory-experiment comparison of the I(2wt)-t profile would be somewhat redundant. The success realized in obtaining satisfactory quantitative agreement between theory and experiment in this work strongly supports the validity of the relevant theory and one’s ability to perform precise second harmonic measurements under the circumstances in question. Although validation of the theory involves only a kinetically-uninteresting limiting case of the general theory for Mechanism R1, nevertheless, it represents a nontrivial step toward a more extensive test of the general theoretical framework. The apparent fidelity of the experimental measurements is of more far-reaching significance. The noise-free, well-defined, theoretically-interpretable second harmonic polarograms obtained in this work carry favorable implications, not only with regard to investigations oriented toward kinetic-mechanistic measure-
6
ANALYTICAL CHEMISTRY, VOL. 42, NO. 1, JANUARY 1970
ments, but also for strictly analytical applications. For example, the background currents associated with the experimental polarograms of Figures 5 and 6 were essentially undetectable at the sensitivities employed, Consequently, one could conservatively conclude that quantitative analysis of electroactive components exhibiting irreversible ac responses should be possible with concentrations at least two-orders of magnitude smaller than in this investigation-ie., 10-5Musing second harmonic ac polarography. Clearly these results emphasize previous findings (16-20) which suggested the necessity of re-evaluating the role of the ac polarographic method for the study of irreversible processes. NOTATION DEFIhITIONS = electrode area
= diffusion coefficient of Species i = activity coefficient of Species i =
initial concentration of oxidized form
= standard redox potential in European convention =
dc component of applied potential
= amplitude of applied alternating potential = reversible dc polarographic half-wave potential
observed dc polarographic half-wave potential second harmonic -peak -potential Eshoulder = potential at shoulder (inflection point) of second harmonic wave F = Faraday’s constant R = ideal gas constant T = absolute temperature = number of electrons transferred in heterogeneous n charge transfer step w = angular frequency t = time = heterogeneous charge transfer rate constant at Eo ka a = charge transfer coefficient = rate constant for irreversible homogeneous chemk ical reaction following charge transfer I(2wr) = second harmonic faradaic alternating current = phase angle of second harmonic faradaic alternat6 ing current relative to applied alternating potential = second harmonic peak current amplitude IP Ishoulder = second harmonic current amplitude at shoulder (inflection point) W l I z = width of second harmonic wave at half-height =
=
RECEIVED for review August 18, 1969. Accepted October 20, 1969. Work supported by National Science Foundation Grant GP-7985.
