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(293) Tanaka, T., Yoshirnori, T., BUnSek/ Kagaku, 24 (lo),614 (1975); Cheni. Absfr.. 85. 102934e 119761. (294) Tarayan, V . M., Sarkisyan, A. A., Shaposhnikova, G. N.. Arm. Khim, Zh. 28 (6), 461 (1975); Chem. Absfr., 83, 201511e (1975). (295) Teske, K., Glaeser, W., Mikrochim. Acta, 1975 (5-6), 653; Chem. Abstr., 83, 157308t (1975). (296) Tkacheva, L. M., Usatenko. Yu. I., Izv. Vyssh. Uchebn. Zaved., Khim. Khlm. Tekhnol., 19 (51, 813 (1976); Chem. Absfr., 86, 25497f (1977). (297) Toelg. G., Werner, W., Ger. Offen, 2,534,773 (CI. GOIN27/44), 17 Feb 1977; Chem. Absfr., 86 199398q (1977). (298) Toibaev, E. I., Songina, 0. A., Zakharov, V. A,, Izv. Akad. NaukKaz. SSR, Ser. Khim., 27 (2), 55 (1977): Chem. Absfr., 87, 94932b (1977). (299) Tdtusheva, G. T., Zakharov, V. A., Rikl. Teor. Khim., 1974 (5). 50; Chem. Absfr., 84, 11985k (1976). (300) Tomcsanyi, L., Anal. Chim. Acta, 89 (2), 409 (1977). (301) Toth, K., Pungor, E.. Am. Lab., 8 (6), 9, 12 (1976). (302) Tserkovnitskaya, I. A,, Zhilina, T. 1.. Vesfn. Leningr, Univ., Fiz,$Khim.. 1975 (3),113; Chem. Absfr., 84, 53519s (1976). (303) Usatenko. Yu. I., D'yachenko, L. F., Kravtsova. V. I . , Zavod. Lab., 4 1 (6), 645 (1975); Chem. Absfr., 83, 201500a (1975). (304) Usatenko, Yu. I., Kryukova, L. V., D v . Vyssh. Uchebn. Zaved., Khim. Khim. Tekhnol., 20 (31, 466 (1977): Chem. Abstr., 87, 110850f (1977). (305) Usvyatsov, A. A., Sudakov, A. P., Krylov, Yu. A,, Agasyan, P. K., Zh. Anal. Khim., 31 (3), 602 (1976): Chem. Absfr., 85, 86832n (1976). (306) Vadimovna, Ch. T., Mater. Vses. Nauchn. Stud. Konf.: Khim., 131h, 1975, 13; Chem. Absfr., 86, 133007e (1977). (307) Vajgand, V. J., Nikolic, V., Antonijevic, V., Glas. Hem. Drus., Beograd, 40 (5-6), 347 (1975); Chem. Absfr., 85, 86680m (1976). (308) Vajgand, V. J., Pastor, T. J., Bjelica, L. J., Glas. Hem. Drus., Beograd, 39 (9-10), 629 (1975); Chem. Abstr., 84, 1 4 4 3 3 7 ~(1976). (309) Vandenbaick, J. L., Mairesse-Ducarmois, C. A,, Patriarche,G. J.. Anaiusis, 3 (9), 473 (1975); Chem. Absfr., 84, 6688911 (1976). (310) Van der Linden, W. E., A n d . C h m Acta, 77, 327 (1975). (311) Van Oort, W. J., Veenendaal, G., Buijsman, E., Griepink, B., Fresenius' Z . Anal. Chem., 284 (2), 125 (1977); Chem. Absfr., 87, 15454w (1977). (312) Velichko, V. V., Machul'skii, B. M., Usatenko, Yu, I , , Zavod. Lab.. 42 (a), 923 (1976); Chem. Absfr., 86, 64993) (1977). (313) Verhoef, J. C., Barendrecht. E., J . flecfroanai. Chem. Inferfaciai Electrochem., 7 1 (3), 305 (1976). (314) Verma, B. C., Kumar, S., Talanfa, 22 (10-ll), 921 (1975). (315) Vire, J. C., Patriarche, G. J., Christian, G. D., Mikrochim. Acta, I (1--2), 17 119771: Anal. Absfr.. 33. 3E29 11977). (316) Vultein, J., Sb , Vys: Sk. Chem'.- Tekhnol. Praze, Anal. Chem., H 11, 101 (1976); Chem. Absfr., 86, 1 5 0 1 2 9 ~(1977). (317) Vuiterin, J., Sb. Vys. Sk. Chem.-Tekhnol. Praze, Anal. Chem. H11, 115 (1976); Chem. Absfr., 86, 150008 (1977). (318) VuRerin, J., Straka, P., S k . Vys. Sk. Chem.-Tekhnol. maze. Anal Chem., H11, 189 (1976); Chem. Absfr., 86, 1501309 (1977).
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(319) Vukerin, J., Straka, P., Sk. Vys. Sk. Chem.-Teknnoi. Raze, Anal. C k m , H11, 257 (1976); Chem. Absfr , 86, 1 3 3 1 5 1 ~(1977). (320) Vulterin, J., Straka, P., Chem. Prum., 26 (5), 242 (1976); Chem. Abstr.. 85, 116331t (1976). (321) Weingartner, C. E., Robertson, D. A,, J . Chem. Educ., 54 (a), 484 (1977). (322) Weisz, H., Pantel. S.,Anal. Chim. Acta, 76 (2), 487 (1975). (323) Werner, W., Toelg, G., Fresenius' 2. Anal. Chem., 276 (2), 103 (1975); Chem. Absfr., 84, 11923p (1976). (324) White, D. C., Anal. Chem., 49 ( l l ) , 1615 (1977). (325) Wilson, C. L., Wilson, D. W., Ed., "Comprehensive Analytical Chemistry", Voi. 2D: Coulometric Analysis, Elsevier, London, 1975. (326) Wolff, C. M., Schwing, J. P., Bull. SOC. Chim. Fr., 1976 (5-6, Pt. l ) , 675; Chem. Absfr., 85, 1 0 3 4 2 2 ~(1976). (327) Wolff, C. M., Schwing. J. P., Bull. Soc. Chim. F r . , 1976 (5-6, Pt. l ) , 679; Chem. Absfr., 85, 1034232 (1976). (328) Yakovlev, P. P., Nichugovskii, G. F., Zozulya, A. P., Sergeev, Yu. Yu., Rybkin, B. I., Strozhkov, A. I., Sidorenko, E. M., U.S.S.R. Patent, 525,014 (CI. GOlN27/42), 15 Aug 1976; Chem. Abstr., 86, 502921 (1977). (329) Yamasaki, S., Ohura, H., Nakamori. I., Bunseki Kagaku, 24 (12), 767 (1975); Chem. Absfr., 85, 171126e (1976). (330) Yamnova, T. P., Suprunovich, V. I., Usatenko, Yu. I., Vopr. KhimiiKhim. Tekhnol. Resp. Mezhved Temaf. Nauch.-fekhn. Sb., 1978 (44),71; Chem. Abstr., 87, 1 2 6 6 1 6 ~(1977). (331) Yoshimori, T., Taianfa, 22 (10-ll), 827 (1975). (332) Zakharov, V. A., Gavva, N. F., Songina, 0. A., Zh. Anal. Khim., 31 (4), 746 (1976); Chem. Absfr., 85, 171139m (1976). (333) Zakharov, V. A., Songina, 0. A., Aitkhozhaeva, T. A . , Zh. Anal. Khim.. 30 (7), 1430 (1975); Chem. Absfr., 84, 11854s (1976). (334) Zaul. L., Agasyan, P. K.,Veiss, A., Lafv. PSRZinaf. Akad. Vesfis, Kim. Ser., 1975 (3), 336; Chem. Absfr., 83, 1 8 8 0 2 5 ~(1975). (335) Zetlmeisl, M. J., Laurence, D. F., Anal. Chem., 49 ( l l ) , 1557 (1977). (336) Zhdanov, A. K., Akent'eva, N. A., Adrianova, 2 . V., Doki. Akad. Nauk Uzb. SSR, 32 (5). 38 (1975); Chem. Absfr., 85, 71625y (1976). (337) Zhdanov, A. K., Barkhudar'yan, A. A , , Doki. Akad. NaukUzb. SSR, 33, (2), 56 (1976); Chem. Absfr., 87, 15462x (1977). (338) Zhdanov, A. K., Barkhudar'yan, A. A,, Uzb. Khim. Zh., 1976 (6), 6 (1976); Chem. Absfr.. 87, 126570a (1977). (339) Zhdanov, A. K., Barkhudar'yan, A. A., Zh. Anal. Khim., 30 ( l o ) ,2045 (1975); Chem. Absfr., 85, 13319r (1976). (340) Zhdanov, A. K., Barkhudar'yan, A. A,, Zh. Anal. Khim., 32 (l), 92 (1977); Chem. Absfr., 87, 94876rn (1977). (341) Zhdanov, A. K., Markhabaev, I . A,, Murninov. N. P., Zh. Vses. Khim. Obshch. 20 (2), 238 (1975); Anal. Absb., 30, 1B66 (1976). (342) Zhdanov, A. K., Muminov, N. P., I z v . Vyssh. Uchebri. Zaved., Khim. Khim. Tekhnol, 19 (3), 478 (1976); Chem. Absfr., 85, 1161371 (1976). (343) Zhdanov, A. K., Muminov, N. P.. Uzb. Khim. Zh., 1978 (5), 8 (1976); Chem. Absfr., 86. 502479 (1977).
Analytical Electrochemistry: Theory and Instrumentation of Dynamic Techniques David K. Roe Department
of Chemistry, P o r t h n d State University, Portland, Oregon 9 7 2 0 7
Following the plan started tour years ago, the present review was prepared to complement t h e applications and methodology review by Kissinger in this issue. Again, the literature was based upon that cited in Chemical Abstracts, Volume 83, No. 22, to Volume 87, No. 22. With few exceptions, articles in November 1977 issues of most journals were reviewed. The format is t h e same as the previous review ( 2 6 A ) with six sections. Within each section, publications are grouped according t o apparent commonality; lead sentences help to identify the subclassifications. .4rticles were selected to provide a n overview of progress in the title areas; no concentrated effort was made t o be critical since the range of topics is too broad for the availahle preparation time. T o generalize a bit, the literature of relaxation techniques in electrochemistry has matured noticeably since 1968. Fewer articles appear each biennium and the theoretical methods have achieved increased sophistication. According to a bibliometric study b y Hawkins ( I S A ) ,there are 3500 journals which publish electrochemical articles, but the core consists of only 11 journals. In contrast, by an overwhelming margin, only one journal is the main repository for publications that are encompassed by the title of this review. The language of 0003-2700/78/0350-009RSOl 0010
electrochemistry is now almost exclusively English in t h e western world, a trend started a decade ago and essentially completed when the Journal of Electroanalytical Chemistq recently became monolingual.
BOOKS AND REVIEWS Increased range of applications as well as new developments in electroanalytical techniques make two recent hooks especially relevant; t h e one by Galus (13'4) includes most methods of electroanalysis while the other ( 3 3 A )is devoted t o stripping analysis. Adsorption in ac polarography is the subject of the book by Jehring ( 2 I A ) ,published in German, as were two texts on electrode kinetics (ZOA, 32A). Albery ( I A ) has also prepared a n up-to-date review of electrode kinetics in a form suitable for use a s a textbook. A compilation of data on kinetic parameters, previously published as a review, has been expanded and prepared as a reference book (30A). A data book of interest to electrochemists (9.4) and a dictionary of electrochemistry ( 8 A ) have also appeared. A new series of reviews edited by Rangarajan has a number of articles of importance to electrochemistry and its applications. T h e review of techniques for the study of faradaic C_
1978 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL 50, NO 5, APRIL 1978
processes by Sluyter (29’4) is representative and will serve to identify this interesting volume. “Trends in Electrochemistry” is the title of the conference proceedings edited by Bockris et al. (3A);Bockris (4A) has also co-edited the electrochemistry volume in the second series of the International Reczeu) of Science. Pulse polarography was reviewed by Osterb oung and Hasebe (23A),and Jain et al. (20A) have summarized the theory of chronopotentiometry. An extensive review of rotating disk electrodes was prepared by Opekar and Beran (22’4). Judging from t h e list of references, nothing was omitted. A useful but brief summary of mechanisms of electrode reactions of analytical interest was authored by Tanaka ( 3 I A ) ,and Evans ( I I A ) has emphasized the study of reactions of intermediates in organic electrochemistry using linear potential scan techniques. Bruckenstein and Miller (5A) have outlined the utility of rotating electrodes in the study of reactions. Homogeneous reactions subject to a kariety of electrochemical techniques have been reviewed by Pletcher (25A) and by Ruzic et al. (27A) for dc and ac polarography. Surface studies by electrochemical methods were reviewed by Conway (6A, 7 A ) and the second citation includes other review articles on electrochemistry. Theories of charge transfer was the focus of the electrochemistry chapter in the 1975 Annual Revieu of Physical Chemlstrj (28A). Reports from the Analytical Chemistry Division and the Commission on Electrochemistrb of the IUPAC include recommendations for sign conventions and plotting of electrochemical data (16A),classification and nomenclature of electroanalytical techniques (17 A ) , proposed nomenclature for transport phenomena in electrolytic systems ( I # A ) , publication of reaction orders, transfer coefficients, and rate constants (19A). Frumkin and Krishtalik (12A) commented on the earlier recommendations for nomenclature in electrochemistry. Also of a review nature, but in the sense of basics, two publications appeared on the puzzle of different standard potentials for the same net cell reaction. The first article (14A) was in error and not a credit to the review system of the journal involved; Parsons (24A) responded with a correction. In the second, independent article 12.4), the solution was realistically presented, as it has been in several well-established textbooks. I t comes as no surprise, then. that students continue to hake difficulty with the mechanics of basic electrochemistry.
MASS TRANSFER The growing use of pulse voltammetry and its many possible variations prompted Rufkin and Evans (24B) to search for a general diffusion-controlled mass transfer solution to a current-time function applicable to any arbitrary sequence of potential steps. They found the solution in some unpublished derivations of Shain, dating from 1961. By appropriate choice of potential-time functions, curves may be calculated for staircase square wave and differential pulse voltammetry from the series solution equation. An interesting consequence of their computations for the latter technique is t h a t conditions were found for optimizing response of reversible over irreversible electrode reactions. Two variations on pulse polarography, specifically directed toward improving the faradaic to charging current ratio were described theoretically and experimentally tested by Christie et al. (5B, 6 B ) . The first makes use of the difference current between alternate mercury drops; the first drop is pulsed near the end of its growth as in normal or differential pulse methods, and the second drop experiences constant potential during its entire growth. By making the potential applied to the second drop equal to that applied to the first drop (Le., a long pulse), the capacitive currents a t the same time in drop growth are equal and therefore cancel. Faradaic currents are different, however, and taking the difference results in a diminution of signal level of up to 50%; a small sacrifice for elimination of charging current. Unfortunately, the baseline was not substantially flatter than in normal or differential pulse polarography; this was identified as being due to the presence of a “capillary response” current previously noted by Barker who ascribed the cause to capillary imperfections, specifically creeping of solution u p the wall of the lumen. The second variation (6B) was termed “constant potential pulse polarography” and was conceived to provide a constant value of capacitive current.
This solution results from making the potential of each pulse have the same value vs. the reference electrode while the potential between pulses is scanned rather normally. The technique agrees well with theoretical expectations but nonideality of the capillary thwarted the full realization of the goal. Another approach (29B) toward decreasing the changing current in pulse polarography was based upon sampling the current twice during the pulse. Equations were given that show that the differences in charging current due to drop expansion a t the two sampling times are related by a simple constant, so t h a t subtraction of appropriately weighted currents cancels the charging component. In spite of the ingenuity shown in these papers, it appears t h a t improvement in the only remaining part of Heyrovsky’s original apparatus will be needed before these techniques can be effectively used to study the chemistry of trace metals. Other theoretical developments in pulse methods include the derivation (13B) of the current-potential response including the effect of the ramp potential on the concentration gradient just before the pulse, and a revised equation (12B) for the diffusion current which includes a correction for spherical effects at the DME. Such efforts are not significant in most applications of pulse polarography as has been clearly shown by a comparative calculation using digital simulation (11B). Bolzan (3B) suggested a pulse polarographic current constant following the earlier ideas of Lingane and Loveridge for classical polarography. I n the interest of faster potential scans than are practical with pulse polarography, Christie e t al. (8B)have examined the theory of square wave voltammetry in a generalized way. Numerical solutions were given for a staircase scan with superimposed square wave which may be unsymmetrical. I t is anticipated that the technique, in polarographic use, will allow a complete scan during the growth of a single mercury drop. From the same laboratory (7B),mass transfer solutions were calculated for staircase voltammetry applied to anodic stripping from thin mercury film electrodes. Maximum sensitivity is predicted for small step times and as large a step potential as is consistent with resolution requirements. Another useful application of fractional calculus to voltammetry is the derivative neopolarogram, obtained by taking a normal derivative of a semi-integrated current-time curve, or vice versa, as was first suggested by Goto. The theory for reversible and irreversible electrode reactions has been further amplified and corrections for spherical diffusion were applied (9B).Experimental studies (IOB) revealed an impressive detection limit of 50 n M for lead ions. A method of semiintegrating steady-state cyclic voltammograms was presented for both diffusion and charge transfer control (20B). Use of cyclic conditions has not been common, but it does allow improved precision through decreased noise. Nadjo and Saveant (19B) have used their version of convolution methods to correct chronopotentiometric curves for variations in faradaic current due to double-layer charging. The results were good and applications to kinetically-complicated systems were discussed. Large amplitude ac voltammetry with mass transport by diffusion has been derived for response to the sixth harmonic (1813);the equations also are applicable or reducible to those previously derived for intermediate and small amplitudes. Distortions of the dc polarogram by a large amplitude ac potential has been described generally for stationary and expanding plane diffusion models (22B). These distorted curves were first observed by Fournier and are of little more than academic value at this time. Mass transfer to rotating electrodes has been modelled to include simultaneous reactions (30B);nonuniformity of the ohmic drop across the disk may produce unequal reaction rates and distortion of the current plateau. Differences in the time necessary to reach a steady-state current at rotating electrodes, as well as under free convection, were noted for current ramp and potential ramp conditions (25B). A model for the decrease in the current at a disk electrode due to inhibition of electron transfer over part of the surface was described (15B). Nonlinear diffusion was included in the theory. In an analysis (27B)of the ac response of a rotating disk electrode, it was shown t h a t at rather moderate frequencies, the coupling of a hydrodynamic mass transport with that due to the ac potential could be negligible. Three wave forms-sinusoidal, square, and triangular-were used in the models.
ANALYTICAL CHEMISTRY, VOL. 50, NO. 5, APRIL 1975 David K. Roe is professor at Portland State University, Portland, Ore He received his A B degree from Pacific Ltheran Unrversw in 1954, the S M degree from Washington State University in 1956, and the Ph D degree from the University of Illinois in 1959 After a postdoctwal year in SMtgart Germany, he was with the Corrosion Department of Shell Development. Emeryville Calif for two years and then was an assistant professor in the Chemistry Department at MIT and associate professor at the Oregon Graduate Center His research interests are in electrochemistry and its analytical applications and in electronic instrument design
A general series solution for the current at a ring electrode resulting from any periodic forcing function applied to the disk electrode was derived ( 4 8 ) . Verification was shown by experiments using a square-wave current applied to the disk. Below the limiting current, there is nonuniformity of the current distribution across a disk electrode; theory was extended to include a ring electrode ( 2 1 8 ) under potential control, Also a comparison was made (14B)by digital simulation of the response of ring-disk and double ring electrode geometries for an imposed step change in current to the inner electrode. A theoretical description ( 1 4 8 ) of the limiting current a t a rotating cone electrode was prompted by the ideas t h a t a gas bubble cannot be stable on such a geometry. This allows smooth mass transport in the presence of gas evolution. Other electrode geometries that have been described theoretically for flow conditions include two- and three-dimensional convergent flow electrodes ( 2 6 8 ) . The electrode is positioned in the wall of a wedged-shaped or conical chamber. These electrodes differ from those in other flow geometries in that there is a high current density a t both the leading and trailing edges. The treatment was extended to include a preceding chemical reaction. Current distributions along a tubular electrode were calculated for one ( 1 8 )and two (2B) reactions; charge transfer kinetics were included. Experimental verification was possible by using sectioned electrodes. Axial diffusion was predicted to make a significant contribution to current distribution along the surface of a flow-through electrode (233). Porous electrodes, represented as a bundle of tubes, were also modelled for two electrode reactions under several conditions ( 2 S B ) . Application was made to the removal of metal ions, an area of interest in both analysis and industry. McCallum and Pletcher ( I 7 B ) described the transient response of a metallized membrane electrode permeable to oxygen under conditions of a potential step and a sudden change in gas pressure. This configuration has a faster response than does the classical Clark cell because there is no intermediate solution layer between the electrode and the membrane. CHARGE TRANSFER There is a clear need to know the role of nondiffusional rate control in a variety of electrochemical measurements applied to analysis. Many years of involvement with charge transfer rates per se now provide the background to examine theoretically the response functions of electroanalytical methods in trace analysis and speciation studies. Until a few years ago. t h e capability of pulse voltammetry to simply provide concentration information a t trace levels was satisfying enough. Now attention is turning to the study of the trace chemical species itself and it would be folly to limit the work to diffusion controlled reactions. With these thoughts in mind, Dillard and Hanck (,5C) have shown through digital simulation how the peak current in differential pulse polarography is decreased as a function of the value of the heterogeneous charge transfer constant. T h e latter may be measured by comparison with a diffusion controlled reaction. Data analysis methods for potentiostatic current-time transients have usually been restricted to short or long time approximations. A new approach by Kruse ( I 2 C ) makes use of a transformation of the i-t points t o include the derivative d i l d t . Graphical display allows rather unambiguous identification of single
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charge transfer, charging currents, and two-charge transfer steps over a wide time range. This type of data processing would be an interesting addition to pulse voltammetry. In square-wave voltammetry, there is the possibility of extracting kinetic data by measuring the current at the middle of each half cycle, according to a recent analysis ( 2 3 3 of Matsuda’s original equations. This allows, in principle, t h e use of very dilute solutions because of the high sensitivity of the method. Charging currents were discriminated against by time delay only; improvements are possible, as seen in other techniques. Ruzic ( I 6 C )has addressed the theorb of pulse polarography and related chronocoulometric techniques, including pulsed ac methods. The influence of heterogeneous rate constants on the measured quantity was derived for these techniques. Semi-integration of linear scan voltammograms of irreversible systems have several features useful in kinetic measurements (8C).The resulting curves are shifted along the potential axis with increasing scan rate but maintain the same shape and final height. Transfer coefficients were obtained from the shift of the curve along the potential axis with scan rate; rate constants were not determined. Goto (9C) has recently described semi-integration of pulse polarographic currents for diffusion, charge transfer, and mixed control; the paper was published in Japanese. The effects of adsorption and passivation were included in calculations of linear potential scans of reactions with charge transfer kinetic control (4C).
Galvanostatic techniques have not received much attention in terms of theory, but applications continue to be reported, especially of the double pulse version. An extension ( I 9 C ) of theory to include consecutive charge transfer steps with an adsorbed intermediate was the only development noted in the period of this review. The method was tested with the C U ? tI Cu system. After using the double pulse method in a stud> of charge transfer rates of substituted nitrobenzene species, Koizumi et al. (IZC)expressed doubt about the rate constants reported for the same systems as measured by faradaic rectification; the values were ahout 10 c m j s whereas they found rate constants betmeen 0.3 and 0.6 cm s Further, they expressed doubt about any system actua ly having a charge transfer rate as high as that predicted by Marcus‘ theory, again about 10 cm/s. Some years ago, superposition of a small amplitude ac potential on a linear potential scan was described theoretically and tested experimentally. Perhaps because of the unavailability of digital simulation, as well as the overshadowing success and interest in linear scan voltammetrk, the full potentialities of the technique were not realized. The advantages are apparent in the recent revival of the technique by Bond et al. (2C);they accrue from the inherent dual time domain properties of the excitation signal. Sample curves were given for both fundamental and second harmonic response during cyclic sweeps. Transfer coefficients and rate constants can be obtained from working curves, as was done by Nickelson and Shain for linear scan voltammetry. Considerable qualitative and quantitative information was apparent in curves without using all of the available data the method provides. The authors pointed out that phase shifts were measured as well and their utilization will be described later, probably in the context of coupled homogeneous reactions and adsorption. In two articles in the Instrumentation column of this Journal, Smith (20C, 21C) has described Fast Fourier Transforms ( F F T ) and particularly their application to electrochemical relaxation measurements. The point that he stresses that is relevant to this section is that a change in the charge transfer rate of an anal-ytical electrode reaction can be readily noted from FFT processed data obtained by a relaxation measurement. If not detected, an erroneous interpretation of concentration might follow. His arguments in favor of making full use of all the information available in ac voltammetric measurements are compelling and in fact realizable with present instrumentation, as was demonstrated ( I S C ) for cadmium analysis in the presence of various concentrations of butanol. Judgment on the practicality of the approach, within the full scope of analytical chemistry, should be reserved until results from challenging, real analysis problems are published. Two observations, however, beg to be made: the technique is self-testing in a more-extensive-
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than-usual way, and similar validation can be made by the very simple technique of standard addition. Temperature perturbation methods, which have been frequently used to study homogeneous reactive kinetics, were proposed by Barker and Gardner ( I C ) to be adaptable to heterogeneous reactions. Time-dependent heating was proposed by modulation of the output of laser diodes; no results were given, but equivalent circuits were discussed. Harima and Aoyagui (1OC) implemented temperature jump methods by electrical heating of their electrodes and were successful in verifying their equation relating potential and time in terms of double layer capacity and the heterogeneous rate constant. Rather small changes in temperature were used. In the context of temperature effects, Weaver ( 2 4 0 has expressed the view t h a t activation parameters of simple electrode reactions do have significance and that the uninterpretability of standard heterogeneous rate constants as a function of temperature was an unnecessarily narrow conclusion. H e based his arguments on the similarity of the real enthalpy of activation and the Marcus’ reorganization factor and t h a t the real values are equal to the mean of the ideal (constant Galvani potential) values when the transfer coefficient is one half. Innovations in data processing and in seeking approximate solutions to hydrodynamic problems have been reported. In the first case, nonlinear regression analysis of rotating electrode data was made possible by orthogonal collocation ( 3 C ) ;t h e goal was to obtain kinetic information simultaneous for a wide range of practical conditions in copper deposition (see also the Homogeneous Reaction section). Glarum (7C) applied variational analysis to obtain solutions to the current distribution across a rotating disk electrode; directness and relative simplicity are claimed for the method. Porous electrodes can be used to obtain direct measurements of the rates of charge transfer reactions, according to a scheme adopted from gas phase kinetics by Stonehart and Ross (22C). I t is necessary t o make current density measurements with and without mass transport limitations; for the latter the authors proposed a rotating porous disk electrode. Lorenz ( 1 3 2 ) has examined some of the implications of electrochemical kinetics without a supporting electrolyte. Similarities to the space charge layer in semiconductor electrodes were predicted. Charge transfer rates of redox couples that interact only weakly with the electrode should be independent of the type of electrode material. Schmickler ( I 7C) has suggested t h a t even so, non-Franck--Condon contributions may be present. In this connection, Rosanske and Evans ( I 5 C ) have reported rate constants of several quinones a t different electrodes; no clear conclusion on the role of the electrode could be made but the rates were nearly two orders of magnitude higher than previously reported. According to Dogonadge and Kuznetsov ( 6 C ) ,the ionic atmosphere of a charge transfer reaction changes during the reaction and assumes states corresponding to intermediate charges of the reacting species. Overpotentials have been defined by Nagy ( 1 4 C ) in terms of the entropy production of the process. From his nonequilibrium thermodynamic viewpoint, he attempted to show how the three sources of overpotential may be separated.
SURFACE EFFECTS Conceptual separation of the solution side of the interfacial region of an electrode into two parts, inner Helmholtz plane and a diffuse region, provided a theoretical model for Grahame and others in general agreement with differential double layer capacity measurements. Further measurements have led to the calculation of the entropy of formation of the inner layer as a function of charge density; strangely, the maximum in entropy does not coincide with the maximum in the differential capacity curve. Previously, it was thought that the capacity “hump” was a result of oriented wat,er molecules. Cooper and Harrison ( 8 0 )have examined a model of the inner layer in which water dipoles are allowed two orientations and then calculated the entropy as a function of electron field. No agreement was found with the experiment, suggesting that the cause of the capacity hump is more complex than suggested. Oldham and Parsons ( 2 5 0 ) ,reversing the trend to use the English language in scientific publications, have expressed their views of the capacity hump in Russian. With their refined dipole model, qualitative agreement was claimed
but only limiting cases could be solved numerically. Mohilner et al. ( 2 4 0 ) have proposed further details of the inner Helmholtz plane in order to interpret their results of 2-butanol adsorption on mercury. A surface solution is described which is composed of water and alcohol; Raoult’s law was applied to the mixture, with due inclusion of charge density, to obtain an electrosorption isotherm. Blum ( 4 0 ) has employed a hard sphere model of ions in describing the differential capacity of electrified interfaces. An interesting, physically realizable situation is a very thin layer cell in which the diffuse layers of opposing electrodes overlap. From the mathematical model, it was predicted ( 1 1 0 ) that the redistribution of ions under charge flow would result in an increase of ohmic resistance of dilute electrolyte solutions. Fawcett and Gardner ( 1 3 0 ) have proposed that dipolar reactants and products of electron transfer are subject to an addition work term that should be included in the general class of double layer effects. Corrections for apparent transfer coefficients were derived; the discussion included a review of recent experimental work, including charged species, and the problem of distinguishing between inner and outer sphere mechanisms. An earlier paper ( 1 2 0 ) by Fawcett and Levine addressed the accelerating effect of certain ions on charge transfer reactions in terms of ion pair formation. Kravtsov ( 2 1 0 )has reviewed criteria upon which mechanistic distinction has or could be made between inner and outer sphere mechanisms. Weaver and Anson ( 3 2 0 ) , in presenting experimental results on the nondependence of the transfer coefficient on potential for an outer sphere reaction, pointed out that two definitions of transfer coefficients have appeared in the literature and a relation between them was given to avoid confusion. In the last review period, a number of publications appeared on the subject of partial charge transfer, that microscope mechanistic model proposed by Lorenz and Pleith in which the product of charge transfer is adsorbed and possesses a partial charge. I t was noted that variations on the model, terminology, and question of measurability arose. T h e situation now is rather the same, as evidenced by recent papers ( 7 0 , lOD, 160, 2 0 0 , 2 7 0 ) . However, Lorenz and Salie ( 2 2 0 ) have carefully reviewed the theoretical foundations and devoted much space to substantiate the measurability of the effect by a variety of methods. A summary of experimental results was included, although what the section included was a listing of systems in which partial charge transfer might be expected. Guidelli ( 17 0 ) in a broad sweep through double layer effects included a reaffirmation of the immeasurability of partial charge transfer. Lorenz and Sahlie’s paper may promote the experimentalists to provide the major missing ingredient: data. Adsorbed species in charge transfer reactions have been examined from several new viewpoints in terms of the many possible mechanisms. Some form of interaction between adsorbed products, attractive or repulsion, should be included and such effects have been shown in calculated ( I D ,2 0 ) linear potential scan curves, but only where the rate of the charge transfer step was significant. Several different microscopic mechanisms were characterized in the calculations; strictly whole-number faradaic processes were considered. An interesting comparison would be to allow partial charge transfer and double layer reorganization in the calculations. Similar calculations were reported ( 9 0 ) for monolayer films under so-called triangular modulated linear potential sweep conditions. The curves provide a useful qualitative view of a complex process but the name given to the technique is ambiguous. Schuhmann ( 2 6 0 ) discussed the use of a linear potential sweep with a superimposed ac signal and correlated the admittance with light reflectivity due to an adsorbed product. (There is an error in the journal abstract and in Chemical Abstracts in that chronopotentiometry was substituted for chronoamperometry in reference to Schuhmann’s article.) An additional variation in the mechanism of adsorbed reaction products is t o allow the charge transfer product to undergo an irreversible chemical reaction and then be adsorbed. Such a case was described for controlled current conditions ( 1 4 0 ) . A somewhat more general treatment was also described ( 3 1 0 ) and included adsorption of all three species in an EC mechanism. Conditions were double potential step with monitoring of optical absorption as a function of time. The latter measurement of the chemical reaction
ANALYTICAL CHEMISTRY, VOL. 50, NO. 5, APRIL 1978
product was especially diagnostic for the study of the reaction scheme. Shapes of dc polarograms reflect adsorption of products and reactants, but the situation may not be as simple as has been described by pre- and postwaves, according to a review by Sluyters-Rehbach and Sluyters ( 2 8 0 ) . Curves were calculated for a diffusion layer model and a Langmuir isotherm; it was concluded ( 2 9 0 )that analysis of the polarograms was possible if only one component adsorbed. To aid in further calculations of this type, a series expansion ( 3 0 0 ) was found which overcame the nonconvergences of the series obtained by Reinmuth under certain conditions of electrode coverage. In differential pulse polarography, enhancement of peak currents was found ( 3 0 ) due t o reactant adsorption. An equation was derived which included a linear isotherm for either reactant or product, and was later extended ( 1 5 0 ) to included depletion of the reactant, the Frumkin isotherm and uncompensated cell resistance. Digital simulation was used for the extended model. Several methods have been recently described to chemically attach reactants to the electrode surface. These include adsorbed olefinic chelates, strongly bound aromatic compounds, and covalently bonded silyl groups. Linear scan and differential pulse voltammetric curves were calculated for such situations and compared with experimental results ( 5 0 ) . Uncompensated resistance was used as an experimental variable leading t o determination of the adsorbate surface concentration. Theory has generally outstripped experiment in surface effects related to metal deposition. However, during the past biennium, some very impressive experimental studies have been reported which will help to refine the theoretical developments. In electrocrystallization, there was reexamination ( 6 0 , 1 8 0 ) of the model of overlapping growth of two-dimensional nuclei. The conclusion was reached that the new model, which includes fluctuations in growth, does not predict damped current oscillations leading to a steady current (or potential for galvanostatic conditions). This is surprising because experimental confirmation of the damped oscillation has been reported. Kashchiev ( 1 9 D ) has discussed kinetic models of the initial stages of nuclei formation under galvanastatic conditions. Deduction of first principles in the quantitative description of surface effects is the most difficult task of the work included in this review. Verification of each assumption and selection of significant details in the model taxes the imagination of the theorist and the ingenuity of the experimentalist alike. Progress is not rapid. The alternate pathway, by induction, has been explored only infrequently. For example, the energetics of ad-atom positions on a crystal lattice were based upon subdivision of bulk properties, e.g. lattice energy. However, application of molecular orbital calculations ( 2 2 0 ) to establish first principles about the electrode-solution interface is the turning of a new page in electrochemistry. From these calculations of Leban and Hubbard, the minimum energy positions of Pt, H, H20, OH-, and halides on a platinum crystal surface were found. With further results, and perhaps some refinements such as the inclusion of an electric field, a model of the compact double layer will evolve which has a validity equal to the sum of all of its parts.
HOMOGENEOUS REACTIONS Electrochemical tools for the investigation of homogeneous chemical reactions continue t o be a popular and useful subject of research. New approaches have been proposed and old ones have been improved since the last review. Mathematical complexities vary considerably with the different techniques and any short cuts in this area are always welcome. Orthogonal collocation, mentioned in the section on charge transfer, was introduced by Whiting and Carr (34E) to shorn its advantages in obtaining numerical solutions to coupled reactions. Briefly, the partial differential equations are solved by fitting an orthogonal polynomial through adjustment of its coefficients so that the average residuals are zero as calculated at selected collocation points. Major savings in computer time result if the selected points are also roots of the polynomial. Accurate working curves were calculated for chronoamperometry applied to ECE and to first- and second-order disproportionation reactions a t planar electrodes. Only a few seconds of CPU time were required for each case and programs were stated to be easily modified to accom-
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modate different mechanisms and conditions. Potential step and pulse methods have received the most attention during the past two years, probably because of the apparent ease with which the changing current is avoided and because of applicability to low concentration conditions. Ryan (30E) selected staircase scan voltammetry because of these advantages and solved numerically the cases of charge transfer followed by a chemical reaction and followed by a regeneration (catalytic) step. Normal pulse polarography response in the presence of a preceding chemical reaction (CE) and a catalytic step have been re-examined (12E, 13E) t o remove the limitations on pulse drop time ratio of previous derivations. Difficulties with t e precision of numerical solutions involving pulse polarography and kinetic currents were shown (29E)to be due to a double summation in the equations. In the single potential step technique, response curves were calculated (33E) for reactant regeneration under fractional stoichiometric ratios. In contrast to these mathematically involved articles, Gross and Jordan (15E) have provided a simple diagnostic measurement by modification of the sampling time, or window, in normal pulse polarography. By moving the sampling window across the pulse period, a t constant potential, the recorded current was shown to have a characteristic slope vs. the sampling time on a log-lot plot. Diffusion controlled reactions, for example, had the expected slope of while preceding chemical reactions gave a slope of zero w en rate determining. Double potential steps are especially useful in the study of chemical reactions following charge transfer because the charging current can be made to decay rapidly, revealing electroactive intermediates. Solutions for current, charge, and optical absorbance as a function of time were reported by Ridgeway et al. ( B E )for a regeneration sequence of half-order. Holub (16E) proposed a variation in which the equations were solved for a constant, final value of charge a t the end of the second pulse. Several additional reaction sequences were added later ( I 7E). Analytic solutions for the semi-integral of current during the second pulse were obtained by Bess et al. (5E) for five different reaction schemes. A small, unexplained deviation from numerical solutions previously reported for the EC and ECEC mechanisms was noted. Use of a light pulse instead of a potential pulse allows the study of photochemically produced products and their reactions under controlled potential conditions. However, Frantoni and Perone (IOE) noted that the charging current was not zero following the light pulse, as would be expected for an electrode a t constant potential. This “induced charging current” was due t o nonpotentiostatic conditions at the electrode since a finite, uncompensated resistance remained in the circuit. A rather detailed analysis allowed a correction to be made for the charging current in simple as well as complicated following reaction schemes ( I I E ) . In this connection, it would be preferable to use the term “potentiostated cell” to indicate the presence of residual resistance and “potentiostated electrode” when true controlled potential conditions exist. In the linear potential scan domain, Carney (6E) presented an analytic solution for a chemical reaction preceding charge transfer with semi-integration of the current. Rate and equilibrium constants were calculated by a successive approximation method instead of working curves. An improved equation for the approximation of Koutecky’s function for CE mechanisms was reported (25E) and a method to obtain the rate constant of a preceding chemical reaction from linear scan curves without prior knowledge of the half-wave potential was proposed (24E). Within the experimental limitations of thin layer cells, there is room to solve rather detailed reaction schemes, as Plichon and Laviron (27E) have shown. A two-step charge transfer sequence was allowed first order, dimerization and coupling followup reactions involving reactant, product, and intermediate. Later, solutions were given (23E) for ECE with several types of chemical steps. Karbainov and co-workers (19E-2IE) have examined the consequences of homogeneous reactions in anodic stripping voltammetry. Potential-time functions for controlled current conditions have been obtained by Kontturi et al. (22E)for ECE scheme using an arbitrary power of time current function in the model. Linear ramp and ac currents were used by Jain and Gaur (1823)in deriving equations for a catalytic follow-up reaction. A variety of reaction schemes has been treated by Dracka
h
-‘k,
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 5, APRIL 1978
(7E-9E) using current reversal, including adsorbed or soluble products undergoing reactions. Gibson and Sturrock ( I 4 E ) employed derivative techniques in chronopotentiometry to decrease the influence of charging current in the determination of the rate of a preceding chemical reaction. They noted that the resulting equations were restricted to reversible charge transfer. A new technique for the study of photochemically produced species was devised and described by Albery et al. ( 2 E ) . A semitransparent rotating disk electrode allows both the generation of intermediates by impinging light and their detection on the disk electrode. Numerical solutions (26E) were obtained for t h e rate of a first-order chemical reaction between two charge transfer steps at a rotating disk electrode. Multiple reactions, both simultaneous and sequential (ECE) were described by Alkire and Gould (3E) for flow-through electrodes. The current a t an electrode in the wall of a flow channel was derived for the condition of a preceding chemical reaction (32E). By locating a second channel electrode downstream, follow-up reactions have been studied but a rigorous mathematical treatment was only recently published for this case (4E),which is similar to the ring disk electrode. Generation of radicals in flowing systems provides a means to rapidly transport unstable species into an ESR cavity. Decomposition by second-order kinetics during transit was treated ( I E ) t o allow interpretation of the ESR signal with flow rate. Finally, an electrochemically triggered reaction wave was described ( 3 I E )that travelled several centimeters in solution and was detected by another electrode.
INSTRUMENTATION Computerized systems, consisting of a laboratory or minicomputer and various input-output modules, provide more than just data acquisition and processing, as described in several articles. Essentially complete automation of anodic strippin was achieved by a system developed by Kryger and Jagner f24F), including flow of the purging gas, control of stirrers, and addition of standard reagents. However, the real improvement was the use of rapid, multiple scans with digital signal summing followed by recording of multiple background scans. This provided signal averaging and excellent correction for background currents. Their measurements equal the best published thus far, even though a simple linear potential scan was used, not a pulse method. Turner et al. (41F) compared anodic stripping curves obtained by computer-generated waveforms-staircase, differential pulse, and square wave. T h e latter two gave t h e best results, with the edge going t o the square-wave method. They also used background subtraction, but of single scans. An interactive program that optimized the sensitivity-analysis time trade-off in linear scan anodic stripping was described by Thomas et al. (40F). Improvements of over tenfold in signal to background were shown to be possible. For on-line processing of anodic stripping data, the Kalman filter was suggested (34F). This is not a discrete component filter but a numerical method for optimizing t h e information content of noisy transients. Random noise has not been the limitation, thus far, in anodic strippin so it is unlikely that much improvement will be obtainef with real measurements. Use of computers in data analysis of ac measurements has been summarized by Smith (36F), and t h e inclusion of a minicomputer in the negative feedback loop of a potentiostat was achieved by Pomernacki and Harrar (30F). Interpretation of overlapping current-potential curves by computer analysis has been generally successful by two methods: pattern recognition (30F, 39F) applied to linear potential scan curves, and for dc polarograms an algorithm using logorithmic current functions (I2F). An experimental approach using the background recording memory of the PAR Model 374 was also demonstrated ( 9 9 , but the same results could have been obtained with two cells and a difference amplifier. Performance characteristics of the Model 374, which is microprocessor controlled, was described recently ( I O F ) , but most of the details were concerned with the consequences of the short drop times available from the pressurized dropping mercury electrode system. A considerable sacrifice in sensitivity was noted, but fast analysis times were possible. An improved pulse polarograph providing a wide range of op-
erating parameters was constructed and tested (42F);discrete digital circuitry provided the signal which was based upon a staircase scan. Methods to shorten the rise time of the pulse were examined by Krizan (22Fj and a complete instrument was designed (23F)to allow measurement of fast dissociation reactions. Both pulse injection and positive feedback were included to provide an option depending upon solution resistance. A variety of improvements in pulse polarographs have resulted from popularity of the technique. Kalvoda and Trojanek (I9F) used a double pulse and successive, subtractive integration to decrease the noise level in their instrument. Modifications to the PAR Model 174 have been made by a variety of users; representative citations are noted ( I F , 6F, 11F). Distortion of the curve due to the output filter prompted these changes. Some problems and partial solutions relating to the use of normal pulse voltammetry with redox couples were described ( 2 7 0 ;another possible solution would be to short the indicator to the counter electrode with an electronic double-throw switch between pulses. Barker (4F) has described a multimode polarograph including four types of operation: linear scan, radiofrequency, square wave, and square wave intermodulation. Real-time displays of coulombs vs. square root of time were accurately achieved (20F) with a programmed read-only-memory and digital-to-analog converter to obtain the time base. A potentiostat was designed for electrosynthesis by Hand and Nelson (17F). Its power capabilities, 25 A a t 70 V, are sufficient to boil water. A potentiostat claimed to provide full resistance compensation was described (14F). An alternate approach, using a voltage adjustable current source, was said to have complete stability (16F). Use of two reference electrodes ( 3 3 0 and an interrupter technique (28F) achieved the same goal in potentiostat designs. A very useful suggestion by Anderson (2F) makes it easy to gauge the minimum frequency response of operational amplifier circuits in linear scan voltammetry. From the wave shape, he deduced that the circuit should have a bandwidth of a t least 5 nv (Hz), where n is the number of electrons and v is the scan rate in VIS. Three circuits were devised to compensate for charging current in dc polarography (3IFj. A small ac signal was superimposed and the resulting ac current was processed to approximate the charging current due to drop growth, assuming ac faradaic currents were negligible. Results were not impressive in view of the complexity of the circuit. Intermodulation ac polarography (7F, 32F) was implemented with an analog multiplier and compared with second harmonic methods. The latter was better in terms of background levels. A new analog multiplier, RC 4200, with a linearity of 0.1% was recently announced by Raytheon Semiconductors; this device should promote further interest in this technique and in phase selective detection. Pulsed dc potentials in place of the usual linear potential scan in ac polarography were reported (BF) to allow a decrease in charging current by difference measurements. Resistance effects in ac polarography were analyzed (I8F) in terms of the error signal produced by phase shifts. Electrode impedance measurements were facilitated (35F) by an alternating current bridge which provided compensation for ohmic drops. Sources of errors in impedance measurements by phase-sensitive detection were noted and analyzed ( 1 5 0 ,and an improved circuit for broad band cross-correlation measurements over a wide frequency range was made possible by new MOS switches (26F). Noise spectra of electrochemical processes were measured by a differential cross-correlation (5F) and Barker (3F) discussed the meaning of the results; some doubt exists as to their value. In galvanostatic measurements, the use of derivative techniques to measure transition times was extended to the submillisecond region (37F) and double pulse circuitry was again improved ( Z I F ) to decrease transients to about 60 ns. With the aid of data acquisition and computer processing, galvanostatic transients were corrected for charging currents and ohmic drops (I3F). A low-cost signal generator for potential scan was designed ( 2 5 0 for a wide range of ramp rates. A drop time triggered by the current transient ( 2 9 n and another based upon a high frequency oscillator (43F) were reported. The former provides digital readout of the average of u p to 1024 drops.
ANALYTICAL CHEMISTRY, VOL. 50, NO. 5, APRIL 1978 LITERATURE CITED
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(208) Oldham, K. B., J . Electroanal. Chem. Interfacial Electrochem. 1976, 72(31. 371-8. (218)' herini, P., Newman, J., J . flectrocbem. Soc. 1977, 124(5), 701-6. (228) Ramamun, A. C., Rangarajan, S. K., J . Electroanai. Chem. Interfacial Nectrochem. 1977, 77(3), 267-86. (238) Razumney, G., Wroblowa, H. S., Schrenk, G. L., J . Eiectroanal. Chem. Interfacial Electrochem. 1976, 69(3), 299-315. (248) Rifkin, S. C., Evans, D. H., Anal. Chem. 1976, 48(11), 1616-18. (258) Selman, J. R., Tobns, C. W., J. Elec&oanal. Chem. InterfacialEkctrcchem. 1975. 65(1), 87-85. (268) Tokuda, K., Matsuda, H , J flectroanal Chem. Interfacial flectrocbem 1977, 79(2), 237-50. (278) Tokuda, K., Matsuda, H., J . Electroanai. Chem. Interfacialflectrochem. 1977. 82(1). 157-71. (28B) Trainham, J. A., Newman, J., J . Electrochem. SOC. 1977, 124(10), 1528-40. (29B) Van Bennekom, W. P., Schute, J. B., Anal. Chim. Acta 1977, R9(1), 71-82
(308) White, R., Newman, J., J . Eiectroanal Chem. Interfacial Electrochem. 1977, 82(1), 173-86. Charge Transfer (1C) Barker. G ,C.. Gardner, A. W.. J. Ekc&oanal. Chem. InterfacialEkctrcchem. 1975, 65(1). 95-100 (2C) Bond, A M , O'Halloran. R , Ruzic, I , Smith, D E , Anal. Chem 1976, 48(6), 872-883. (3C) Caban, R., Chapman, T. W., J . Electrochem. SOC.1977, 124(9), 1371-9. (4c) Casadio, S., J . Nectroanal. Chem. Interfacial Electrochem. 1976, 72(2), 243-50. (5C) Dillard, J. W., Hanck, K. W., Anal. Chem. 1976, 48(1), 218-22. (6C) Dogonadze, R. R., Kuznetsov, A. M., J . flectroanal. Chem. Interfacial Electrochem. 1975, 65(2), 545-54. (7C) Glarum, S. H., J . Electrochem. SOC. 1977, 124(4), 518-24. (8C) Goto, M., Oldham, K. B., Anal. Chem. 1976, 48(12), 1671-6. (9C) Goto. M.. Kato, M., Ishii. D.. Nlmon Kagaku Kaishi1977, ( l ) , 42-7: Chem. Abstr , 1977, 87, 15423k (10C) Harima Y , Aoyagui S J Eiectroanal Chem Interfacal Eletrochem 1976 .. - . -69(31 - \ - , . 419-22 (11C) Koizumi, N., Saji, T., Aoyagui, S., J . Electroanal. Chem. Interfacial Electrochem. 1977, 81(2), 403-5. (12C) Kruse, R., Electrochim. Acta 1976, 21(2), 85-92. (13C) Lorenz, W., Ender, V., Z. Phys. Chem. (Leipzig) 1976, 257(6), 1123-36. (14C) Nagy, Z., Electrochim. Acta 1977, 22(2), 191-5. (15C) Rosanske, T. W., Evans, D. H., J . Eiectroanal. Chem. Interfacial Electrochem. 1976, 72(3), 277-85. (16C) Ruzic, I., J . Electroanal. Chem. InterfaclalElectrochem., 1977, 75(1). 25-44. (17C) Schrnickler. W., Electrocblm. Acta 1976, 21(10), 777-81. (18C) Schwall, R. J., Bond, A. M., Smith, D. E., Anal. Chem. 1977, 49(12), 1805-12. (19C) Schweickert, H., El Miligy, A. A., Meiendez, A., Lorenz, W. J., J. E k c t r a a ~ l . Chem. Interfacial Electrochem. 1976, 68(1), 19-30. (2OC) Smith, D. E., Anal. Chem. 1976, 48(2), 221A. (21C) Smith, D. E., Anal. Chem. 1976, 48(6), 517A. (22C) Stonehart, P.,Ross. P. N., Jr., Electrochim. Acta 1976, 21(6), 441-5. (23C) Tamamushi. R., MatsuQ. K.. J. E/ec&oaml.Chem. Interfaciaifktmhem. 1977, 80(l), 201-8. (24C) Weaver. J. J.. J . Phys. Chem 1976, 80(24), 2645-51 ~~~
Surface Effects (ID) Angerstein-Kozlowska,H., Klinger J., Conway, B. P., J. Electroanal. Chem. Interfacial Electrochem. 1977, 75(1). 45-80. (2D) Angerstein-Koziowska.H., Klinger, J., Conway, B. E., J . fkctroanal. Chem. Interfacial Electrochem. 1977, 75(1), 61-75. (3D) Anson, F. C., Flanagan, J. B., Takahashi, K., Yamada, A,, J . Electroanal. Chem. Interfacial Electrochem. 1976, 67(2), 253-9. (4D) Blurn, L., J , Phys. Chem. 1977, 81(2), 136-47. (5D) Brown, A. P., Anson, F. C . , Anal. Chem. 1977, 49(11), 1589-95. (6D) Clark, M. M., Harrison. J. A,. Thirsk, H. R., Z . Phys. Chem. (Frankfurt am Main) 1975, 98(1-6), 153-60. (7D) Conway, B. E., Angerstein-Kozlowska. H.. Sharp, B. A,, Z. Phys. Cbem. (Frankfurt am Main) 1975, 98(1-6), 61-74. (8D) Cooper, I. L., Harrison, J. A,, J . Electroanal. Chem., 1975, 66(2), 85-98. (9D) De Tacconi, N. R., Zerbino, J. O., Arvia, A. J., J . Electroanal. Chem. Interfacial flectrochem. 1977, 79(2), 287-305. (10D) Durand, R., Nguyen, E., Barbier, M. J., J . Chim. Phys. Phys.-Chim. Bioi. 1975, 72(9), 1085-73. (11D) Farina, C J. E., Oldham. K. B., J . Electroanal. Chem. Interfacial Electrochem. 1977, 81(1). 21-36. (12D) Fawcett, W. R., Levine. 'S., J, flecfroanal. Cbem. Inferfacialflecfrochem. 1975, 65(2), 505-21. 113Dl Fawcett. W. R . . Gardner. C. L.. J . Nectroanal. Chem. Interfaciai Ejectrochem. 1977, 82(1), 303-15. (14D) Fisher. O., Dracka. O., Kalab, P., Collect. Czech. Chem. Commun. 1976. 41(3), 703-13. (l5D) Flanagan, J. B.,Takahashi. K.. Anson, F. C., J . flectroanal. Chem. Interfacial Electrochem. 1977, 81(2), 261-73. (16D) Frumkin, A. N., Damaskin, B. B., Petrii. 0. A., EleMrokhim&a 1976, 12(l), 3-9. (17D) Guidelli, R . , J . Nectroanal. Cbem. InterfacialElectrocbem. 1976, 74(3), 347-87. (18D) Harrison, J. A., Lorenz, W. J., J . Electroanai. Chem. Interfacial Electrochem. 1977, 76(3), 375-82. (19D) Kashchiev, D.. Thin Solid Films 1975, 29(2), 193-209. (20D) Koppitz, F. D., Schultze, J. W., Electrochim. Acta 1976, 21(5), 337-43.
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