Direct Measurement of E with Reversible and EC Electrode Processes by Second Harmonic Alternating Current Polarography and Voltammetry Alan M. Bond Department of Inorganic Chemistry, University of Melbourne, Parkville, Victoria 3052, Australia
Donald E. Smith Department of Chemistry, Northwestern University, Evanston, Ill. 6020 1
Certain characteristics of the second harmonic ac polarographic response, which have been well-established in the literature, suggest that this form of electrochemical readout has excellent possibilities for precise, direct determination of the thermodynamically-significant reversible half-wave potential, E '112. Specifically, the dc potential corresponding to the second harmonic polarographic wave's minimum (absolute value readout) or zero current point (phase-selective readout) appears to represent a superior index of than the commonly-employed dc polarographic halfwave potential or the fundamental harmonic peak potential. Theoretical arguments are discussed and experimental data are presented in support of the foregoing concept. Data with reversible redox couples at the dropping mercury electrode and a variety of stationary electrodes clearly show that higher precision is provided by the second harmonic approach. With several systems undergoing reductive EC mechanisms, the second harmonic approach is found to yield an excellent appraisal of E'112under conditions where the dc and fundamental harmonic ac polarographic estimates contain significant systematic error due to kinetic influence of the follow-up chemical reaction.
Being closely related to the standard redox potential, Eo, and therefore having thermodynamic significance, the reversible polarographic half-wave potential, Er1/2, is a parameter frequently required in electrochemical investigations. For example, calculation of stepwise stability constants and other equilibrium constants can be made from measurements of Er1/2, this representing a very common use of polarographic methodology (1-4). Similarly, kinetic investigations of electrode processes are greatly facilitated if E r l / z is known (I, 2, 5, 6). Finally, relationships between Erl12 and a wide range of physical chemical parameters have been examined extensively by chemists in efforts to acquire insights into the correlation between redox potentials and other molecular or ionic properties (1, 7-9). In dc polarography, the observed half-wave potential, Elpz, equals Er1/2 for a reversible (nernstian) electrode process of the type (1) R. S. Nicholson, Anal. Chem., 44, 478R (1972). (2) D. E. Smith, Crit. Rev. Anal. Chem., 2, 247 (1971). (3) S. C. Saraiya and A. K. Sundaram, "Review on the Study of Complexes by Polarography," India At. Energy Comm., Bhabha At. Res. Cent. (Rep), BARC-410 (1969). (4) H. Irving, Advan. Poiarogr., 1, 42-67 (1960). (5) D. E. Smith, Elecfroanal. Chem., 1, 1-155 (1966). (6) M. Siuyters-Rehbach and J. H. Sluyters, Elecfroanal. Chem., 4, 1-128 (1970). (7) G.J. Hoijtink, Advan. Nectrochem. Electrochem. Eng., 7, 221-81 (1970). (8) M. E. Peover, Hecfroanal. Chem. 2, 1-51 (1967). (9) P. Zuman, Ed., "Topics in Organic Polarography," Plenum Press, New York, N.Y., 1970.
1946
0
+
tze
R
where 0 and R are soluble species. The value of Er112, therefore, can be obtained directly from the dc polarogram under these circumstances. However, when extreme accuracy is demanded, as in stability constant studies, measurement of Er1/2 by the foregoing approach often represents a difficult and time-consuming task because subtraction of double layer charging current and evaluation of the limiting current, id, from a frequently far-from-ideal sigmoidal curve must be undertaken. This can even be a somewhat arbitrary task if the limiting current region is not extremely well-defined due to maxima, or onset of a second polarographic wave, for example. Evaluation of Erl/*from a plot of log ( i d - i)h, rather than the direct measurement of the potential a t half the limiting current, while more accurate, is an even more tedious and time-consuming procedure and suffers from similar limitations in the presence of ill-defined limiting currents. In small amplitude fundamental harmonic ac polarography, the reversible wave's peak potential, E,,, is equal to Er1/2 and the direct evaluation of E'llz from the ac polarographic i-E curve is attended by much simplification and less ambiguity compared with dc polarography (2, 10-16). The major limitation in the precision of the ac approach results from the fact that, a t potentials around the peak potential, changes in ac current are not particularly sharp. Table I provides some relevant data. Here the direct measurement of E , with an uncertainty much less than f 0 . 5 mV is difficult to obtain. Also, the background doublelayer charging current is a possible source of systematic error. However, in the second harmonic mode of ac polarography (2, 5, 6), Er1/2 corresponds to the potential where the second harmonic current, Z ( Z w t ) , is zero with reversible processes. Furthermore, a t potentials in this region an almost linear Z(2wt) us. E d c relationship exists (2), and relative changes in current per unit potential increment are extremely large as data in Table I show. Finally, measurement complications arising from double-layer charging current contributions are negligible in second harmonic ac polarography for concentration levels in excess of 10-jM. Consequently, extremely high precision in locating the potential where Z ( 2 w t ) = 0 should be possible, enabling correspondingly precise direct readout of Er1/2. Previously acknowledged difficulties (5, 17) related to the small magni(10) (11) (12) (13) (14) (15) (16) (17)
ANALYTICAL CHEMISTRY, VOL. 46. NO. 13, NOVEMBER 1974
A. M. Bond, J. Electroanal. Chem., 20, 109, 223 (1969). A. M. Bond, J. Elecfroanal. Chem., 23, 269, 277 (1969). A. M. Bond, J. Electroanal. Chem., 28, 433 (1970). A. M. Bond and R . J. Taylor, J. Electroanal. Chem., 28, 207 (1970). A. M. Bond and A. 5. Waugh, Electrochim. Acta, 15, 1471 (1970). A. M. Bond, J. Electrochem. Soc., 117, 1145 (1970). A. M . Bond, Anal. Chim. Acta, 53, 159 (1971). B. Breyer and H. H. Bauer, "Alternating Current Polarography and Tensammetry," Interscience, New York, N.Y., 1963.
Table I. Dependence of DC a n d AC Polarographic Currents on Applied D C Potential, E&, in the Vicinity of Er1,2for Nernstian Processes at 25 "C '1
r!
- E r < 2) i r \
5 00 4 00 3 00
2 (JO 100
0 00 100 -2.00
3.00 -4 00 - 5 00
Direct cturent,
'
'd
0.4515 0.4612 0.4708 0.4805 0.4903 0.5000 0.5097 0.5195 0.5292 0.5388 0.5485
Fundamental harmonic, I(Llf1l
ID(ilt)h
0.9906 0.9940 0.9966 0.9985 0.9996 1.0000 0.9996 0.9985 0.9966 0.9940 0.9906
Second harmonica I(2-t) I Ip(ZwtIb
0.2496 0.2006 0.1510 0.1009 0.0505
0.0000 -0,0505 -0.1009 -0,1510 -0.2006 -0.2496
a Phase-selective readout. I,(wt) and 1,(2wt) designate peak fundamental and second harmonic currents, respectively.
tude of I ( 2 w t ) in small amplitude ac polarography no longer exist because of the advent of modern solid state instrumentation which enables convenient, automated implementation of the second harmonic ac polarographic method without the possibility of operator-induced bias (2, 18-21). In dc linear sweep voltammetry at stationary electrodes, e g , platinum, glassy carbon, graphite, hanging mercury drop, etc., calculation of Er1/2can be subject to even greater uncertainty than in dc polarography, as this parameter has to be obtained from a point which is 87.2% of the maximum current on an asymmetric peak-shaped curve (in the case of a reversible process) (22). However, with linear sweep ac voltammetry, equations describing the i-E curves for reversible electrode processes are essentially identical to those derived for ac polarography, (assuming AEw >> L', where AE and w are the amplitude and angular frequency of the alternating potential, respectively, and u is the dc potential scan rate (23, 24). Consequently, precision approaching that in ac polarography should be possible. For the EC electrode process, 0 + 1 i e = R - Y ( Un!ess noted otherwise, discussion is confined to the irreversible R + Y step) Ell2 # Er1/2 in dc polarography, nor is the 87.2% current point a measure of Er1/2 in dc linear sweep voltammetry. The two observables in question can be significantly shifted toward positive potentials, relative to Er1/2,by the kinetic influence of the follow-up chemical reaction (22, 25). If Erl/z is to be obtained from such dc responses, resort to fairly complex calculation procedures invoicing quantitative kinetic characterization of the chemical reaction's rate must be undertaken (22, 25, 26). Although a similar situation exists regarding the fundamental harmonic ac polarographic E,-value, the disparity between this observable and Er1/2 is less than in the dc polarographic c i i e (27, 28). This advantage of the ac polarographic IneLhoa, iihich arises from the shorter time scale associated (18) 3 E. Glover and 12. E. Smith, Anal. Chem., 43, 775 (1971). (19) D.E. Glover and D. E. Smith, Anal. Chem., 44, 1140 (1972). (20) D.E. Glover and D. E. Smith, Anal. Chem., 45, 1869 (1973). (21) H. Elutstein, A. M. Bond, and A. Norris, Anal. Chem.. 46, 1754 (1974). (22)R. S Nicholson and I. Shain, Anal. Chem.. 36,706 (1964). ( 2 3 ) W 1 Underkofler and I. Shain, Anal. Chem., 37, 218 (1965). (24) i. Ruzic. C. E. Smith, and A. M. Bond, unpublished work. (25) J. Koutecky, Collect. Czech. Chem. Commun., 18, 597 (1953). (26) 6. J. Hwebert and D. E. Smith, J. Electroanal. Chem., 31, 333 (1971). (27) T. G. McCord. H. L. Hung, and D. E. Smith, J . Nectroanal. Chem., 21, 5 (1969)
(28) T. G. McCord and D.E. Smith, Anal. Chem., 40, 474 (1968).
with the applied potentials ac perturbation, is even more profound in the second harmonic response. In the latter case, theoretical calculations have predicted, for example, that the second harmonic polarogram's absolute current magnitude minimum, or the phase-selective polarograms zero current point, occur precisely at Er1/2for k l w < 3, provided heterogeneous charge transfer kinetic effects are not serious (2, 29). On the basis of this result, McCord and Smith have suggested that simple, direct measurement of Er1/2 should be possible by the second harmonic ac polarographic approach even with an EC mechanism where the half-life of the electrode reaction product is in the sub-millisecond range (2, 29). The EC mechanism is one of the most commonly-encountered reaction schemes. In organic chemistry, the reaction following reductive electrolysis often is associated with loss of a reactive group, protonation, or some other solvent interaction (8, 30). In inorganic chemistry, an electron transfer step often produces a reactive entity in a less stable oxidation state than the starting material and a wide range oi' follow-up reactions are known to occur (31, 32). Thus, one can readily appreciate the importance of a possible direct determination of Er1/2from simple observation of a second harmonic polarogram's minimum or zero current point without the need for complete kinetic-mechanistic characterization of an EC electrode process. Little or no attention has been given the validation and/ or use of the second harmonic ac polarographic or voltammetric response in the contexts just described. The purpose of the present paper therefore is to show, first of all, the ease with which highly precise assessments of Er1/2 can be obtained from second harmonic measurements with reversible processes a t the dropping mercury electrode (DME), as well as at stationary electrodes. Second, data will be presented demonstrating that the presence of a follow-up chemical reaction does not preclude the possibility of direct measurement of Erl:2 with the second harmonic approach under conditions where the mechanistic complication in question introduces significant error into the corresponding dc and fundamental harmonic ac measurement approaches. Experimental methods for determining when the correct value of Er1/2 is being obtained are considered with respect to both polarographic and voltammetric methods. Results demonstrate the considerable value of the second harmonic approach in this area of investigation. EXPERIMENTAL Chemicals and Apparatus. All chemicals used were of reagent grade purity. Some compounds (see Tables 111 and IV) were prepared as described in the literature (33-25). Working electrodes used include t h e DME, the hanging mercury drop (HMDE, Metrohm BM-503), platinum, wax impregnated graphite, and glassy carbon electrodes. Saturated calomel and Ag/AgCl (0.lM LiC1; acetone) reference electrodes were employed in aqueous and acetone media, respectively. A piatiriiim wire was used as the auxiliary electrode in all experiments. Soiutions were thermostated and degassed with argon or nitrogen prior to rrc:)rding polarcgrams and voltammograms. Instrumentation. %me (Jt the dats presented here were obtained using ac polarography in the harmonic multiplex mode (19, 20). T b e instrument emplc~yec! for this purpose featured on-line
(29) T.G. McCord and D. E. Smith, Anal. Chem..41, 1423 (1969). (30) R. N. Adams, "Electrochemistry at Solid Electrodes," M. Cekker, New York, N.Y., 1969. (31) A. A. Vlcek, Progr. lnorg. Chern., 5 , 21 1-384 (1963). (32) J. B. Headridge, "Electrochemical Techniques for Inorganic Chemists," Academic Press, New York. N.Y., 1969 (33) C. G. Earraclough. R . L. Martin, and I. M. Stewart, Aust. J, Chem., 22 891 (1969). (34) A. R. Hendrickson and R. L. Martin, Ausf. J. Chm?.,25, 257 (1972). (35) A. T. Casey and J. R . Thackeray, Aust. J . Chern.,25, 2085 (1972).
ANALYTICAL CHEMISTRY, VOL. 46, NO. 13, NOVEMBER 1974
1947
Table 11. Evaluation o f E l , z for the Electrode Process, Pb(I1) + 2e F! Pb(amalgam), in 1M NaC104: pH = 3, T = 25"C, [Pb(II)]= 2.0 x 10-4M, AE = 5 mv, f = 228 HzO - E '112 (volts u s . SCE)b
Fundamental harmonic results
Second liarnionic resd:s
Data v i a analog approach d
Run No.
In-phase
Quadrature
Total
In-phase
1 2
0.3320 0.3325 0.3325 0.3325 0.3329
0.3320 0.3329 0.3320 0.3325 0.3325
0.3320 0.3325 0.3325 0.3325 0.3329
0.3324 0.3326 0.3328 0.3326 0.3326
3 4 5
In-phase
0.3325 0.3325 0.3325 0.3325 0.3325
Quadrature
0.3325 0.3325 0.3325 0.3325 0.3325
Total
In-phase
Quadrature
0.3325 0.3325 0.3325 0.3325 0.3325
0.3326 0.3326 0.3326 0.3328 0.3326
0.3328 0.3326 0.3328 0.3328 0.3326
AI3 and f represent applied ac potential amplitude and frequency, respectively. DC polarographic E', 2-value = 0.3328 f 0.0008 volt SCE (5 replicate measurements). cDigital readout, 3 drops averaged at each dc potential, dc potentia; incrf-rnect = O.OOU48 vo!t, E'1 2-values read directly without interpolation between potential increments, twin cell used to subtract charging current. tl Values read directly from graph. No subtraction of charging current undertaken. us.
computerized digital data acquisition and digital Fourier transform analysis of the waveform components to obtain simultaneously the dc, fundamental harmonic, and second harmonic polarographic responses. Full details of this instrument and attendant data processing procedures have been published (20). Data furnished by this digital approach were obtained by ensemble averaging the responses from three replicate measurements a t each dc potential and subsequently applying the Fourier transform smoothing technique (36) to the resultant polarograms. Also used in this work was an analog instrument featuring conventional X-Y recorder readout. Maximum expansion of the potential axis (0.01 V/in.) was used. The instrument was based on a PAR Model 170 Electrochemistry System, modified as described in the literature (21) to perform second harmonic experiments. Controlled drop times down to 50 msec were obtained L J ~ Qa digital drop timer system which will be reported elsewhere. In all ac work, an applied alternating potential amplitude of 5 or 10 mV peak-to-peak a t frequencies stated in the text and tables was used. At the DME, current sampled readout near the end of the drop life was used. In linear dc sweep experiments a t stationary electrodes, scan rates up to 50 mVlsec were employed.
RESULTS AND DISCUSSION Amalgam-Forming System at the DME. Probably the most common class of electrode processes used t o polarographically determine stability constants uia measurement of E'llz involves the reduction of metal ion complexes to an amalgam. The reduction process Pb(I1)
+
2e
====
Pb(ama1gam)
in 1M NaC104 was therefore chosen to evaluate the reproducibility with which the second harmonic potential where Z(2wt) = 0 could be located with this more-or-less ideal, reversible case. With total second harmonic current measurements (absolute value), the minimum value of Z(2wt) was used in instances where the current did not exactly attain a zero value, due to instrumental imperfections (e.g., incomplete rejection of the larger fundamental harmonic response and/or failure to take a data sample precisely a t the potential of zero current can lead to non-zero minimum currents which amount to 1-2% of the peak current). With phase-sensitive detection, the observed response always crosses zero (18) and the potential where I ( 2 w t ) = 0 could be readily and accurately located. Both the in-phase and quadrature second harmonic current components were recorded when phase-sensitive detection was used and, in (36)J. W.Hayes, D. E. Glover, D. E. Smith, and M. W. Overton. Anal. Chem., 45,277 (1973). 1948
each case, this apparent value of Erlpl was recorded. Numerical results of dc, fundamental, and second harmonic polarographic measurement of Er1/2 with the Pb2+/Pb(Hg) system are tabulated in Table 11. Figure 1 shows the quadrature component of the second harmonic polarogram. The unequal peak heights in Figure 1 are attributable to spherical diffusion effects (37). In the second harmonic mode, direct readout of the potential where Z ( 2 ~ t = ) 0 to ~tO.2mV is possible, so high-precision Erl,z data of the kind required for determining stability constants is readily available through this measurement approach. Direct Measurement of Er1/2 at Stationary Electrodes. The electrode process [Cp,V(rV)dBdtc]'
+
e === [Cp?V(III)dBdtc]
(Cp = cyclopentadienyl, dBdtc = dibutyldithiocarbamate) has been shown to be very fast in non-aqueous solvents, such as acetone (38).Thus, under ac polarographic conditions, a plot of peak height, I,, us. is linear up to a t least 600 Hz. This system is therefore ideal to test the equivalence of Er1k2 measured at stationary electrodes and the DME by the various techniques under consideration. Results a t a variety of electrodes are presented in Table 111. An uncertainty of h0.003 volt was found in measurement of Er1/2 from linear sweep dc voltammetry. Under ac conditions, identical curves to those found in ac polarography are obtained and extremely precise direct measurement of Er1/2is possible, as shown in Tabit 111. The uncertainty of less than 1 mV found in the second harmonic mode uia direct measurement forms a marked contrast to the linear sweep dc approach regircliag h : h precision and convenience. Also noteworthy is the independence of E r l / 2 on electrode material a t the submillivolt level shown in the second harmonic data. The EC Mechanism. ( a ) Polarography. Consideration of the theory for reversible charge transfer with a follow-up irreversible first-order chemical reaction leads t o the conclusions given below (27-29). Reductive electrolysis only is considered. Similar conclusions apply to oxidative processes and systems with second-order follow-up chemical reactions. For the reaction scheme (37)T. G. McCord, E. R. Brown, and D. E . Smith, Ana/. Chem.. 38, 1615 (1966). (38)A. M. Bond, A . T. Casey. and J. R. Thackeray, inorg. Chem., 12, 887 (1973).
ANALYTICAL CHEMISTRY, VOL. 46, NO. 13, NOVEMBER 1974
Table 111. Values of Erl12Obtained by Linear Sweep Fundamental and Second Harmonic Voltammetry at a Variety of Stationary Electrodes: Electrode Process is, [Cp2V(IV)dBtc]++ e s [Cp2V(III)dBtc]; T = 20.0 f 0.1 "C in Acetone, O.1M Tetraethylammonium Perchlorate -Er1/2(volts
LS.
A g / A g C l , 0 . 1 Lic1, ~ acetone)'
: 11ectrod e
Fundamental armonic results$
Hanging mercury drop electrode Platinum electrode Glassy carbon electrode Wax impregnated graphite electrode
resultr~onic
0.4225
0.422 0.423
0.4228 + 0.0004 0.4221 f 0.0005
0.001
* 0.001
0.421
i
0.4220 + 0.0008
0.001
DC ~oltammetricErl 2-value = 0.422
0
+ ne
,I
r
I
-A -
F==
R
f
-
~
2
" 3
\LLT
0.003 volt. Results obtained using dc scan rate of 20 mV/sec. applied ac sine wave of 10-mV amplitude at 280 Hz.; uncertainties indicate average deviation from the mean of 10 replicate measurements. Analog instrument employed. a
f - r
+ 0.0006
0.422 i 0.001 L
I
Second ha
1
44
rF
Figure 1. Phase-selective second harmonic ac polarogram of Pb(ll) System 2 0 X 10-4M Pb2+ in aqueous 1M NaCIO.,, pH 3 T = 25 O C Applied 228 Hz 10 mV peak-to-peak sine wave, dc scan rate of 50 mV per minute Measured Quadrature 456-Hz faradaic current signal at end of mechanically-controlled drop life (5 sec),using analog instrument
1-
Y I ,L
the most important advantage of using the second harmonic approach is derived from the previously-mentioned fact that the minimum on the second harmonic polarogram is relatively much less sensitive to the effects of the follow-up chemical reaction than the corresponding dc and fundamental harmonic indices of E'llz. Two effects combine to yield this result. First, for nernstian and near-nernstian conditions, the point of minimum faradaic nonlinearity is located a t E r 1 / 2 , as long as k does not significantly exceed w . T h e latter qualification identifies the second contributing effect which is the shorter time scale of the ac experiment (approximately the period of the ac signal). The latter reduces the influences of the follow-up reaction relative t o the d c case-Le., the ac perturbation can "outrun" the chemical step. The fundamental harmonic approach shares the advantage of the shorter time scale, but not that of the advantageous location of the faradaic nonlinearity minimum. Thus, the effects of the follow-up chemical reaction on the relevant polarographic responses decrease in the order d c > fundamental harmonic > second harmonic. The key effect of the follow-up reaction regarding E r 1 / 2 evaluation is t o shift waves t o more positive potentials. This is illustrated in Figure 2 for the case of' the polarographic observables which are relevant t o Er1/2 evaluation. I t is evident that the second harmonic observation will be much less perturbed by the follow-up reaction than the d c and fundamental harmonic counterparts, while the effect on the fundamental harmonic observable is intermediate. Also notable is the fact that the second harmonic minimum disappears when perturbations of the follow-up reaction take on significant proportions. Consequently, use of this second harmonic observable when it is not a n accurate direct measure of' E',/? is not possible, whereas the d c El/? and fundamental harmonic E,-values are subject to such misuse if care is not taken. A word of caution is appropriate in the evaluation of the foregoing conclusions. Specifically, it must be recognized t h a t they are applicable when heterogeneous charge transfer is reasonably facile, which is the case for many systems following the EC mechanism. However, a more complex and less ideal situation obtains when heterogeneous charge transfer is slow (29), although, even in this
IO
-1,
8,
u
I
I
1.
2 1 "L
'
, ,>
1
I,
~
Figure 2. Example of chemical rate constant effect on location of dc and ac polarographic observables used to estimate Firstorder EC mechanism with nernstian charge transfer k = first-order homogeneous chemical rate constant (sec-'). E , / 2 = dc POlarographic half-wave potential. E, = fundamental harmonic ac polarographic peak potential. E c2 = potential where second harmonic quadrature (outof-phase)component equals zero. € r2 = potential where second harmonic resistive component equals zero. E m2 = potential of total second harmonic current minimum. Calculated using theory based on expanding plane electrode model (27-29) for the special case where frequency = 1590 Hz, A €
= 5.0mV, Do = DR = 1.0 X
k, = -, f = 6.00 sec, n = 1.00
case, the second harmonic approach is often the preferable one. The advantages of the second harmonic approach can be substantially accentuated by employing a second strategy which recognizes t h a t the time scale of the ac experiment is dually governed by d c terms (drop time) and ac terms (frequency) (2, 5, 27, 29). Thus, in addition t o raising the frequency, shortening the drop life also effects reduction of one of the relevant time scales, which will lessen the influence of the follow-up reaction. In dc polarography, it has
ANALYTICAL
CHEMISTRY, VOL.
46, NO. 13,
NOVEMBER
1974
1949
Table IV. Direct Measurement of Erl 2 by Second Harmonic AC Polarography with EC Mechansim. Comparison with DC Polarographic E?I 2-Values and Fundamental Harmonic Eu-Values (Apparent E': 2's ); T = (20.0 f 0.1) "Cin Acetone, 0.lM Tetraethylammonium Perchlorate St
Drop time sec
Compoundn
DC-E1
,-\slue
u3.
Ay/A+Ij
1
P
-*'I1uae
(753 H z ) (553 Hz) (443 Hz) (268 Hz) (73 Hz)
(volt
L6.
&y/AgClj
*
-0.960 0.001 over frequency range 20 to 1000 Hz, d r o p t i m e s 0.16 to 10 s e c . 40 individual measurements E r i / 2 = -0.979 0.002 over frequency range 100 to 1000 Hz, d r o p t i m e s 0.16 to 10 s e c , 32 individual measure!?1 ent s fi,"i/2 = -1.074 0.001 over frequency range 100 to 1000 Hz, d r o p t i m e s 0.16 to 10 s e c , 32 individual measurements - 1.159 (753 Hz) -~1.160 (553 Hz) - 1.160 (443 Hz) -- 1.160 (268 Hz) --1.159 (73 Hz) Er1/2 =
*
*
SacSac = dithioacetylacetonate, Sacac = monothioacetylacetonate, OEt -Sacsac = 0 - e t h y l thioacetorhl(incer3le. Zlectrode process
+
- k
in each case is, ML2 e - 2 ML2 - * products, bee References -10 and -li for further details. Data obtained with analog instrument for Ni(SacSac)a, Xi(SacSac)(Sacac), Ni(Sacac)2, and uia the harmonic multiplex mode with on-line digital data acqiilbitiun and FFT processing for Zn(OEt-SacSac)z. ~
been shown (39) that use of short drop times may sometimes be used to outrun the kinetic influence of the followup chemical step. That is, on decreasing the drop time, E1p2 becomes more negative until, a t sufficiently short drop time, the value becomes independent of drop time, indicating that it is equal to E'llz. Similar considerations apply in ac polarography where drop time reduction combined with the use of high frequency represents strategies designed to minimize effects of the chemical step on both time scales which are relevant in ac polarography. Of course, it should be recognized that drop life independence is an excellent indication that valid Er1/2 has been obtained. Many polarographically-reducible organometallics give unstable reduction products which undergo rearrangement, reaction with the solvent, or the like, so that the EC scheme is very common. A t the same time, in many of these studies, the primary parameter of interest is the Eo-value attending the charge transfer step. For these reasons. we considered reductions of some organometallic species as appropriate examples with which to test the fidelity of the foregoing concepts concerning Erl'2 measurements with the EC mechanism. Table IV shows the feasibility of' direct measurement of Er1/2for some sulfur chelate systems. The detailed electrochemistry of these systems has h e i i reported previously (40, 41 ). For the Ni(SacSac): complex, the dc polarographic Erl/yvalue is obviously drop time de(39) A. M. Bond, J. Necfrochem. Soc.. 118, 1588 (1971). (40) A. M. Bond, G. A. Heath, and R. L. Martin, Inorg. Chem., 10, 2026 (1971). (41) A. M. Bond, A. R. Hendrickson, and R. L. Martin, J. Amer. Chem Soc..
95, 1449 (1973).
1950
pendent down to approximately 1 sec, but Erlirstill can be measured directly by fundamental and second harmonic ac polarography over the entire drop time range considered because of the absence of the drop life dependence of the relevant ac parameters. For Ni(SacSac)(Sacac). the drop life dependence of the dc El/n-value is severe and a noticeable effect is apparent on the fundamental harmonic E ,. These observables give valid, direct measixes of Erl;2 only with the shorter drop lives employed. Nevertheless, the second harmonic technique gives a valid. drop life independent appraisal of over the entire drop time range, as well as over a decade range of frequency. Similar results are obtained with the Ni(Sacac12 species, while measurements on the Zn(OEt-SacSac):! compound at a single drop life indicate that good estimates of E r I a are 2 yielded by hoth ac methods, while [he cic positive by virtue 0:' surnmary, the data i n Tdiiie I\' >I,:,\',. 1:i theory (29), i i i a ~the 1.1 sensitive to the presen . mstances used for direcr. mci+..iure~nti:i o!' Lr :.. where other method> I despite significant inf11it.r:~~ 01' ;!>e !'o!It 9n.i:iX re:iczi:)n on the .\/zapt, of the , e c ~ n d iiarmonic, ivave. Regarding the data In T2tJkI\.. one follow-up rmction: a.ssociatt=d7.vith :hi. not represent the m o 5 t demandiny c';ii:es t o a h i c h :he second harmctnic apprcizch can he su -s!'ti 1!:; ;i ;ipIi eti . T h e fastest chemical reaction is associcted \vii h Sacac) system and is characterized by a w t e comtant of ap-
ANALYTICAL CHEMISTRY, VOL. 46, NO. 13, NOVEMBER 1974
proximately 10 sec-l; calculated on the basis of the data in Table IV, together with dc and ac polarographic theory for the EC mechanism. Systems with follow-up reaction rates much faster than this are within the capability of the second harmonic approach (2,29).Somewhat moderate examples were selected for the present study so that valid Er1/2 appraisals could be made a t the shortest available drop lives with all techniques, allowing the opportunity to compare the best estimates from each technique. Table IV shows that such comparison indicates excellent agreement, further validating the second harmonic method's applicability under all conditions invoked. ( b ) Voltammetry. Although a rigorous quantitative theory has not been published for the ac cases, the basic picture for linear sweep ac and dc voltammetry with the EC mechanism is the same as discussed above for polarography, except that the scan rate (or its reciprocal) replaces the drop time as the relevant index of the dc time scale. This is confirmed by experimental measurements which yield results similar to those shown in Table IV. For example, the same values of Er1/2as those in Table IV were obtained from second harmonic linear sweep voltammetry a t platinum electrodes, using the point where Z(2ot) = 0, as before. Measurements encompassed scan rates of 5 to 50 mV sec-l and frequencies from 100 to 1000 Hz. At the same time, the dc and fundamental harmonic estimates of Er1/2 were influenced by the follow-up reaction in many cases.
CONCLUSIONS Data presented here support the theoretical suggestion that second harmonic ac polarograms or voltammograms provide a superior approach to directly evaluating the thermodynamically-important E '1/2-value, relative to the better-known dc and fundamental harmonic ac methods. Random error sources are minimized because the relevant second harmonic observable is locatable with less ambiguity and greater precision. Systematic error sources associated with background double layer charging currents and mechanistic complications are much less troublesome in the second harmonic case. In acknowledging these advantages, one should recognize that they are relative, not absolute. Thus, although generally less likely, the second harmonic measurement approach is subject to the kind of misapplications that occasionally arise with the dc and fundamental harmonic ac methods. Mechanistic complications not addressed in this report, such as a reversible follow-up chemical reaction (29), preceding chemical reactions (42), slow heterogeneous charge transfer (29), adsorption ( 4 3 ) , etc., under appropriate conditions can invalidate the use of the second harmonic minimum or zero-current crossing points as estimates of E'llz. One must always recognize that all electrochemical observables obtained with finite cell current are (42) T. G. McCord and D.E. Smith, J. Elecfroanal. Chem., 26, 61 (1970). (43) A. M. Bond and G.Hefter, J. Hecfroanal. Chern., 42, 1 (1973).
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