(196) Schmidt, E., Gygax, H. R., Bohlen, P., Helv. Chim. Acta, 49, 733 (1966). (1‘37) Schneider, H., Strelow, H., J . Electroanal. Chem., 12, 530 (1966). (198) Schwabe, K., Geisler, H., Electrochim. Acta, 12, 147 (1967). (199) Shams el Din, A. M., Kamel, L. A., J . Electroanal, Chem., 1 1 , 111 (1966). (200) Shams el Din, A. R.I., Kamel, L. A., Abdel Wahab, F. >I., Zbid., 15, 21 (1967). (201) Shults, W. D., et al., 2. Anal. Chem., 224, 1 (1967). (202) Shults, W. D., Fisher, D. J., Schaap, W.B., ANAL.CHEM.,39, 1379 f 1967). (203j -Shults, W. D., Mueller, T. R., J . Electround. Chem., 12,354 (1966). (204) Shults, W. D., Schaap, W. B., ANAL.CHEM.39, 1384 (1967). D., Schaap, W. B., (205) Shults, 2. Anal. Chem., 224,22 (1967). (206) Silvestroni, P., Carelli, I., J . Electroanal. Chem., 15,317 (1967). (207) Smith, D. E., NcCord, T. G., Hung, H. L., ASAL.CHEM.,39, 1149 (1967). (208) Smoler, I., Collection Czech. Chenz. Commun., 31,703 (1966). (209) Smyrl, W. H., Tobias, C. W., J . Electrochem. SOC.,113, 754 (1966). (210) Sohr, H., Liebetrau, L., 2. Anal. Chem, 219,409 (1966). (211) StasnG, XI., StrAfelda, F., Collection Czech. Chem. Commun., 32, 2055 (1967). , (212) Stevens, W. G., Shain, I., ASAL. CHEM.,38,865 (1966). (213) Stevens, W. G., Shain, I., J . Phys. Chem., 70,2276 (1966). ’
bv.
\ - - -
(214) StrAfelda, F., HanEil, V., Kimla, A,, Collection Czech. Chem. Commun., 30.1416 (9965). (215j StrAfelda, ’F., Kimla, A., Zbid., 30, 3606 (1965). (216) StrAfelda, F., MatouBek, J., Zbid., 31,470 (1966). (217) StrAfelda, F., Siastnf., Siastnq, M., Ibid., 32,1836 (1967). (218) StTAfelda, F., TondrAk, D., Kimla, A., Zbzd., 31,4622 (1966). (219) Stromberg, A. G., Zavodskaya Lab., 31,1175(1965). (220) Stromberg, A. G., Kaplin, A. A., Zhr. Analzt. Khim., 20, ,1043 ( 1965). (221) Sturrock, P. E., Privett, G., Tarpley, A. R., J . Electroanal. Chem., 14,303 (1967). (2221 Subcaskv. W. S.. J . Electrochem. Sic., 112,92$\1965). ’ (223) Swain, C. G., et al., J . Am. Chem. SOC.,89,2648 (1967). (224) Swofford, H. S., Carman, R. L., AIVAL. CHEM.,38,966 (1966). (225) Tamamushi, R., J . ElectroanaL Chem., 11,65 (1966). (226) Tamamushi, R., hlatsuda, K., Zbid., 12,436 (1966). (227) Tanaka, N., Yamada, A., 2. Anal. Chem., 224,117 (1967). (228) Tenygl, J., Chemist-Snalyst, 55, 53 (1966). (229) Timmer, B., Sluyters-Rehbach, hl., Sluyters, J. H., J . Electroanal. Chem., 14, 169 (1967). (230) Trasatti, S., Electrochimica iTfetallorum, 2 , 1 2 (1967). (231) Urbach, H. B., Electrochim. Acta, 11,1651 ( 1966). ~
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WORK supported in part by the U. S. Atomic Energy Commission under Contract AT(30-1)-905.
Electrochemical Relaxation Techniques W . H . Reinmufh, Department o f Chemistry, Columbia University, N e w York, N. Y.
T
follows the line of the previous one in the series, confining attention to the literature published from January 1966 to January 1968 which was available to the author a t the time of writing. S o attempt is made to completely survey the literature, but rather attention is concentrated in those areas in which the reviewer felt competent to offer critical commentary. The reader seeking broader coverage is urged to scan the pages of Electroanalytical Abstracts. HE PRCSEXT REVIEW
SMALL AMPLITUDE RELAXATIONS
Possibly the most important and certainly the most widely discussed theoretical contribution in the area of small amplitude relaxation techniques in recent years has been the concept introduced by Delahay (50) of the a priori inseparability of faradaic and nonfaradaic currents. I n early treatments of the theory of small amplitude electrochemical relaxation processes it was assumed that faradaic and nonfaradaic processes proceed by parallel but independent paths, and further that the double layer charging process could be represented as a simple capacitance
which takes the same value in the presence and absence of the faradaic process. This was the model adopted by Randles (166) in his pioneering work and applied successfully by him and by later workers to a variety of systems. A second level of sophistication allows the possibility that the double layer charging process may be influenced by the presence of the faradaic reactants, but still assumes it to be representable as a pure capacitance in parallel with the faradaic impedence. A major contribution of Sluyters and coworkers (176) was to develop methods of data analysis which allowed treatment of experimental data when the second assumption was justified, and, equally importantly, which allowed recognition of its failure when that occurred. Prior to their work the methods of data analysis in common use not only relied on the validity of the first, less general, assumption but also often failed to give adequate indication of its failure. However, substantial evidence has aecumulated over the years that there exist experimental systems for which neither the first nor the second assumption is adequate-cf. (178). Attention has focussed on explana-
10027 tiors having to do with mechanistically complicated faradaic processes, and on the effects of experimental artifact on observed results. This work unquestionably constituted (and continues t o constitute) a valuable contribution to our knowledge, but still fails to eliminate the difficulty in the majority of cases where the source of complication lies in adsorption of the electroactive species. Most of the attempts to describe the effect of adsorption on small amplitude relaxation have focussed attent; on the faradaic branch of the equivalent circuit, and, by neglect, have implicitly assumed the applicability of assumption one or two above the nonfaradaic branch. Baticle and Perdu (19) have recently reviewed theoretical efforts in this area. Barker (12) was possibly the first to suggest the representation of the cell impedence in terms of a model in which the double layer charging process did not take the form of a simple frequency-independent capacitance. Incidentally, Barker’s classic paper seems worth reading once a year on general principle-it apparently contains enough ideas t o keep the rest of us busy for a long time to come. Barker’s suggestion was overlooked, probably in part beVOL. 40, NO. 5, APRIL 1968
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cause it was not developed in any detail, and also in part because in the same work he depreciated the practical i n portance of the effects it considered. Lorenz (116, 117 ) proposed similar ideas, but with embellishments, consideration of slow adsorption and partial charging, which made the implications of the basic idea even more difficult to envision. The Delahay approach (51, 48) starts with three basic equations: a mass bPlance equation relating the fluxes of the electroactive components to their swface excesses, a charge balance equation relating the total current to its sources, and an equation relating the surface excess of charge t o its components-the surface excesses of charged species. From these equations it develops a detailed model of the overall electrode impedence which effectively tdies account of the influence of adsorption of reactants not only on the faradaic process, as previous theory purports to do, but on the dynamic behavior of the nonfaradaic impedence as well. The vehemence of the audience reaction at the meeting at which these ideas were unveiled is hardly suggested by the published account (48). In part the reaction was doubtless engendered b:~ the fact that mathematical gremlins plagued initial work purporting to develop the consequences of the approach (56). Fortunately, these difficulties have now been cured (54, 82). Their elimination has changed the major implications of the theory very little, but has had the unfortunate effect of greatly increasing the complexity of the equations to be applied to experimental data, and the labor involved in their development. The most economic representation of the faradaic impedence in terms of independent experimental observables for the general case of a diffusion limited redox reaction requires eight parameters. I n principle, the approach is readily extendable to homogenous kinetic complications in solution or other modes of mass transport as well, but things are quite complicated enough without them. These parameters for the most part each contain several terms related to diffusional mass transport parameters, electrode kinetic and Yernst equilibrium parameters, End double layer parametws. Given the limited frequency range over which impedence measurements caq be conducted in practice and the limits of experimental accuracy, it will be a challenging task indeed to verify and apply the general expression. With eight adjustable parameters one could probably fit the Dow-Jones industrial average to an impedence equation if it had (or does it?) an imaginary component. Despite the discouraging complexity 186 R
0
ANALYTICAL CHEMISTRY
of the general equation, one of its simplified forms has already scored an impressive success. An implication of the theory is that even for reversible systems, the dynamic low-frequency layer capacitance (measured by impedence techniques in the presence of the faradaic process) may differ from the static double layer capacitance (determined from the second derivative of the surface tension with potential). I n fact this implication was not apparent (indeed it was contradicted) in the initial formulation of Delahay and coworkers (46, 56). It was recognized independently by Sluyters and coworkers (192) who applied a corrected form of the Delahay theory to several experimental systems, verified the accuracy of its predictions, and were able to rationalize their results in terms of a simple model of the adsorption process. While the two groups are presently embroiled in conflict (47, 175) the a priori inseparability of their contributions to this research seems inescapable. Incidentally, one of the reasons that Delahay and coworkers failed t o recognize the implication of their equations is probably because they initially pursued the consequences of their model in detail for the case of deposition of bulk metal (to minimize mathematical complexity). I n this special case, the static and dynamic capacitances are the same. This is a consequence of the fact that it is, from a phenomenological viewpoint, meaningless to talk about the surface excess of metal ions in this case provided charge transfer is sufficiently rapid-(Le., reversible)-because a surface excess of metal ions countered by electrons in the electrode can always be thought of as metal itdelf-i.e., the electrode material. I n the more usual case of reduction to metal amalgam, although it is still impossible to separate operationally the surface excesses of metal and metal ions for reversible systems, the overall surface excess of the reactive couple remains thermodynamically accessible, and therein the difference lies. The Sluyters group has also verified this point experimentally for a mercury-mercurous system (179) although the “verification” in this case predated the Delahay model. The Sluyters work does not provide a test of the concept of a priori inseparability in an operational sense, because with their data assumption two above proved applicable in the frequency range they studied. The power of the Delahay theory in this case lay in its quantitative description of the difference between static and low-frequency dynamic double-layer capacitances in terms of variations of surface excesses of the reactants. There still exist some areas of controversy with regard to the Delahay work. One of these is reflected in dis-
cussion contributed by Barker and Gerischer (48). To discuss these it is necessary to introduce some equations. All sides seem agreed that it is possible conceptually to split the observed current into faradaic and nonfaradaic components-i.e.,
i = if
+ in/
where in, is defined as dqldt, the variation of the surface charge with time (whether the conceptual splitting has operational significance is another matter). While Equation 1 is not one of Delahay’s fundamental equations, it can be derived by combining them. -411also seemed to agree that (again conceptually and perhaps not operationally) the variation of q can be Taylor-expanded for small perturbations in the form w d t = (aqiaE),.,(dwdt)
+ +
(ap/aCo)ddco/dt)
This is identical to Barker’s representation in Figure 8 of (12) and is employed by Delahay and coworkers in (6‘4, 82). The point of the GerischerBarker arguments is that the possibility on conceptual separation of faradaic and nonfaradaic currents is all that is necessarily implied by previous theory, and that if this theory is correctly developed, it must lead to the same predictions as Delahay’s approach-Le., one can derive Delahay’s equations as readily from Barker’s equivalent circuit as vice versa. Incidentally, Elliott and Buchanan (63) have recently discussed such interconversion for chemical kinetic processes. As a pragmatic matter, one might argue because Delahay’s much more recent approach is the one which has been developed in detail, that it seems simpler and more direct. The heart of the Delahay contribution, however, lies in the explicit recognition that the formal conceptual separation represented by Equation 1 in general contains no operational significance. Although one may represent the cell impedence in a form which indicates terms two and three of Equation 2 as separate components, in the lumped impedence of the overall process they are incorporated in such a way that it is impossible to determine their individual values from experimental impedence measurements. I n particular, they are combined with parameters which arise in the faradaic branch of the circuit. Thus, it is unnecessary to approach the description of the electrode process through the a priori conceptual separation of faradaic and nonfaradaic branches, and this reflects itself in the a posteriori impossibility of calculating from experimental data the fraction of the current devoted to faradaic and nonfaradaic processes, at least
for reversible processes. For example, although in discussing the Sluyters work above (192) we have laxly spoken of their determination of the double layer capacitance, what the Delahay theory says is that although it is possible to describe this component quantitatively, it is impossible to decide the relative extents to which it is attributable to faradaic and nonfaradaic processes-this despite the fact that formally the Sluyters results agree with a very simple conceptual model of the splitting-ie., that inherent in agreement with assumption two. Still another area of controversy surrounding the Delahay approach is the practical importance of the effects it considers. Returning to Equation 2, if the partial differential coefficients of the second and third terms on the right were sufficiently small, these terms would be negligible compared to the first. Because the first term is operationally accessible, in this circumstance the faradaic and nonfaradaic branches of the equivalent circuit would be separable; the nonfaradaic branch would be representable as a simple capacitance; and the first or a t worst the second of the operational approaches cited earlier would be appropriate in the analysis of experimental data. Barker (48) has reiterated his earlier view ( l a ) that this is in fact the usual case. Delahay and coworkers, on the other hand, contend that the terms may be far from negligible, even for systems in which specific adsorption of the electroactive species is absent. This contention is based on the remarkably large theoretical values of the differential coefficient (Wo/C0)$ which they calculate by application of the Joshi-Parsons (90) equation to solutions of zinc ion in 0.1-If X a F solution (56 and in more refined form 82). I n applying this calculation to the prediction of faradaic impedence (82) interestingly enough these authors assume (ap/aC,)~ is zero-Le., they assume a priori separability, so that the significance of the calculation is the importance of diffuse double layer adsorption per se and not the necessity of applying the Delahay formalism t o it. A point of difficulty with the calculation is its direct identification of ( m o / 8 C o ) #with (Wo/dCo)B, where $ is the outer Helmholtz plane potential and E is the electrode potential. I n fact, pursuing the matter (IOS), ( a q / a C , ) ~is substantially smaller than (dp/aC,)$ but (no/ dC,), is only about 30y0 less than ( m o / 8 C 0 ) under ~ the conditions assumed in the calculation. A second more serious criticism of the calculation is that it assumes $ and ( a $ / a E ) c to be the same in the presence and absence of zinc. This allows small amounts of zinc to have very profound effects on the double layer structure. For example the assumptions of the Delahay
calculation indicate that millimolar zinc ion would raise the double layer capacitance of 0.1M BaF solution at -1.05 V us. SCE from 16 to 25 pF (103). Experimentally (71) raising N a F concentration (in the absence of zinc) from 0.001 to 0.91631 raises the capacitance from 15 to 16 pF. Thus there seems reasonable room to doubt the assumptions on which the Delahay calculation is based. The last area of controversy involves Delahay (47, 52) as phenomenologist us. Sluyters (175) and Wier (195) as empiricists. The Sluyters method of data analysis allows identification of the best values of parameters of an equivalent circuit for a given set of data quite independently of any theoretical basis which may attach to that circuit. What the Delahay theory shows is that in some cases the previous theoretical bases for some of these equivalent circuit representations may not be generally valid; but published discussion has not always made clear the distinction between reservations about the theoretical significance of the circuit representations and the virtues of empirical analyses showing that data do fit them. I n view of the practical complications surrounding the application of the Delahay theory to data, and uncertainties as to its general practical importance, there still seems plenty of room for empiricists. Incidentally, the idea of operational inseparability has been implicit in descriptions of the faradaic impedence in more mundane ways for a long time. Thus the Warburg impedence can be formally separated into two diffusion impedences for the oxidized and reduced forms, but experimental measurements give only a lumped value. In the Delahay terminology then the diffusion of 0 and R are a priori inseparable. Of course, independent determination of one or both diffusion coefficients is readily accomplished and so no difficulty results. Borucka and Agar (29) have given a derivation of the linear rate expression for faradaic processes which does not rely on linearization of the absolute rate expression, but rather on much less restrictive assumptions (see 13s and 168 for discussion of the more conventional derivation). This is of interest in connection with the Delahay formalism because it allows some of the parameters which arise in that formalism t o be related to each other with some (but not much) simplification. I t might be asked whether the Delahay formalism is the last word in the description of relaxation processes. Apparently it is not, for one of the factors it neglects is migration and transference. I n the bulk of solution these effects can be taken into account simply by coupling Delahay’s equations t o an appro-
priate model of mass-transfer, but in the immediate vicinity of the electrode the problem is more complicated. Barker ( I S ) on the basis of a formalism developed by Grahame (72) has examined this matter for ideally polarized electrodes, and concludes that the effects become important only for very low concentrations of electrolytes or at very high frequencies. Double layer data from systems with very low electrolyte concentration are of theoretical interest, and continuation of recent studies by Delahay and coworkers (53) might uell lead to a test of Barker’s ideas. The Delahay model has other limitations as well, but they have been well stated by its author (51). Bauer (20) has speculated that apparent anomalies in charge-transfer kinetic data for the cadmium couple may be caused by double layer effects on charge-transfer parameters. There is no question that peculiarities occur in the way of rates decreasing with increasing potential in some systems. I n fact this phenomenon in indium provides the basis for an electrochemical oscillator (187, 188). However, data and calculations by Timnick and coworkers (70, 128) suggest that double layer effects of this type are not extreme enough to explain all the anomalies in the cadmium data. Much of the anomalouq data referred to by Bauer and the data of Timnick and coworkers as well is impedence data treated on the assumption that the double layer capacitance is the same in the presence and absence of cadmium ion. Unfortunately, a t least for cadmium chloride, the Sluyters (177) have given data indicating that the assumption is unjustified. While Barker (12) has suggested that this effect should not be important for data obtained from faradaic rectification or other nonlinear techniques, and Barker and Bolzan (14) have elaborated on Barker’s earlier ideas, the matter still seems very much up in the air. The major uncertainty is the significance of the effects suggested by the Delahay formalism. The possible sources of anomaly are thus many. 1lcLean and Timnick (128) by comparing rate constants for cadmium ion reduction in different supporting electrolytes corrected for Frumkin double layer effects infer that CdC1+ is the species actually reduced in chloride. The trouble is the Sluyters data again which suggests that cadmium ion is specifically adsorbed in chloride and therefore that the Frumkin correction may be inadequate. The ?rIcLeanTimnick idea seems a good one, but the particular case they chose leaves room for doubt. While considerable effort has focussed on artifactual sources of anomalies in small amplitude relaxation data, the Sluyters group (191) has elucidated an VOL 40, NO. 5, APRIL 1968
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interesting but hitherto unnoticed peculiarity inherent in even the simplest basic equations. First, there seems to be a prevalent misunderstanding that irreversible systems give no ac polarographic waves. Such waves do occur, however, they are merely substantially lower in amplitude than waves for reversible systems. The interesting point is that for sufficiently slow charge-transfer reactions the ac wave splits into two components (basically for the same reason that irreversible processes give split anodic and cathodic waves in dc polarography). I n previous work, such splitting in zinc systems has been identified with two-step reduction, and submitted in evidence of monovalent intermediates. The Sluyters group has shown that the same effect occurs in Eu(11)-Eu(II1) systems (where the intermediate hypothesis is doubtful) ; given a simple mathematical treatment of its origin; and concluded that earlier evidence for monovalent zinc (some of it their own) is of doubtful significance. It now seems established that a prime artifactual source of dispersion in double layer capacitance data a t low frequencies is associated with solution creepage between electrode and the capillary walls, and not, as earlier speculated, with shielding by the capillary. Susbielles’ (185) recent study of capillary shielding is in accord with this view. However, there is still uncertainty as to whether the dispersion is all artifactual. Bockris and coworkers (27) contend that slow dipole relaxation of water is an important effect, while deLevie (57) disputes the notion. If the Bockris effect proves real, it may be a serious source of added complexity in analysis of relaxation data. Sluyters and coworkers (100) have examined the range of applicability of the linearized rate expression for charge transfer. They conclude that estimates commonly employed may be overoptimistic, but point out that in experiments performed on systems consisting of identical electrodes back-toback nonlinearities tend to cancel, allowing the application of larger (and experimentally easier) amplitude perturbations than would be permissible with conventional arrangements. Budlewski and Stoinoff (37) have given simple experimental criteria for deciding whether systems are within the linear range. I n impedence measurements, the effect of nonlinearity is of lesser importance than in transient techniques because it affects readout only in third order rather than second. Delmastro and Smith (59) conclude theoretically that measurements with applied potentials as large as 30/n millivolts are feasible. McLean and Timnick (129) have given experimental data in support.
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Delmastro and Smith (58) have also devoted considerable attention to the effect of spherical contribution of the D N E on ac impedence data. I n earlier work they had proposed diagnostic criteria for complicated reactions based on the effect of mercury column height on ac waves. The more recent work indicates such effects occur even for uncomplicated reactions because of the effect of spherical diffusion on the mean dc concentrations of the reactive couple generated in situ at the electrode. Phase angles, responsive primarily to the ratio of dc concentrations (and not their absolute values) , are relatively unaffected. Smith and coworkers (127) have also examined the effect of sphericity on nonlinear techniques and conclude that a number of peculiarities in published data can be explained on the basis of the effect. Hung and Smith (88) have examined still another source of complication, namely multistep charge-transfer. Advances in instrumentation for ac work include a simple modification of a commercially available dc instrument (23) and a phase sensitive instrument based on a lock-in amplifier (64). Buchanan and Elliott (36) describe a twin cell bridge arrangement which compensates for double layer capacitance of the base electrolyte (in the absence of electroactive species) and Smith and coworkers (35) have described a n electronic feedback instrument (also employing twin cells) which does the same. The dangers in relying on this type of compensation in kinetic studies should be apparent from some of the discussion above. The same difficulty arises in the differential potentiostatic method proposed by Costa (45). Of wider interest may be techniques for compensating for cell resistance through positive electrical feedback. Despite earlier difficulties, such methods now seem fully operational (33, 109). I n ac impedence studies, elimination of ohmic loss is largely a matter of convenience, because (however tedious it may be in practice) the data can be corrected after readout. I n transient (specifically controlled potential) techniques the ohmic influence on readout is more profound and the advantage gained by its elimination is a very real one. The feedback techniques have high frequency limitations because of inherent instability, and they also work, as presently formulated, only for constant resistance so that they do not compensate exactly for the varying resistance of a DME. However, despite the limitations they seem very promising-at least until the a priori inseparability of cell resistance becomes a problem. Levart and D’Orsay (113) propose Laplace transformation of impedence data to determine diffusion coefficients.
Brown, Smith, and DeFord (94) read out data to punched cards for computer assimilation. Small amplitude transient relaxation techniques seem to have fallen on hard times. Their problems can be traced primarily to the fact that data analysis becomes exceedingly complicated or unreliable when reaction mechanisms go beyond simple diffusion coupled to charge transfer. Not only that, but the foundations of some of the techniques seem to be eroding rapidly even for simple systems. Kooijman and Sluyters (99) have undertaken a critical examination of the errors involved in the double-pulse galvanostatic technique and conclude that the technique is no better than the single-pulse method. They also conclude that previously reported rate constants for fast reactions obtained by this method have no significance. Armed with these conclusions they have set out to improve the single-pulse method. A “semibridge” (97) to cancel ohmic drop, and identical back-to-back electrodes to cancel nonlinearities (98) are among their ploys. Things are still likely to get sticky though when systems complicated by adsorption are studied. The major advantage of transient techniques as compared with impedence has always been the hope that they would go faster. Weir and Enke (196) have pursued this quest with some sophisticated electronic and cell designs and a current-impulse technique (something of a cross between coulostatics and double-pulse galvanastatics). There are several peculiarities in their results which suggest that they may have fallen prey to difficulties of the type outlined by Kooijman and Sluyters (99) for the double-pulse technique. Several authors have used square waves (28, 30, 190), triangular waves (49, It??‘), or sine waves (190) in alternative methods to impedence techniques for the study of double layer capacitance and charge transfer kinetics. ,411 of the methods are more limited in scope and offer, a t best, some convenience provided it can be assumed the system is simple. Unfortunately, the only way of ensuring that the system is simple is to compare results with those obtained by ac impedence. Pulse polarographic study of chargetransfer kinetics (43) seems to work well enough for slow reactions ( k , = cm/sec). The effect of depletion for irreversible systems at stationary electrodes has been examined (150). Kinetic and catalytic currents and the effect of shielding on diffusion currents have also been studied (31, 69). Analytical applications of Kalousek polarography have been surveyed (94) with the conclusion that such advantages may possess over the competitive techniques lie in its ability to handle
irreversible systems. The motivation behind all these exotic variants of conventional polarography is the quest for high sensitivity in analytical applications. None of them is particularly attractive as compared with impedence measurements for kinetic studies. All seem to offer about two orders of magnitude increase in sensitivity over polarography with systems which are wellbehaved, but sad disillusionment awaits the naive prospective user who supposes that the results will be just like polarography only more sensitive. Second order relaxation techniques are represented by two papers concerned primarily with analytical applications of second harmonic polarography (21 , 139). The recent concern of kineticists with adsorption phenomena has dampened their enthusiasm for nonlinear relaxation. They seem to have quite enough first order problems. LARGE AMPLITUDE CONTROLLED CURRENT TECHNIQUES
Kew ideas in chronopotentiometry seem scarce. The basic cause, one suspects, is the rapidly expanding interest in potentiostatic techniques. Only a few years ago chronopotentiometry had in its favor the relative simplicity of its experimental apparatus and of the mathematical forms associated with its results for common reaction mechanisms. Now, with operational amplifiers in almost every laboratory and computers in many, the advantages of chronopotentiometry have become less compelling, and its liabilities more apparent. Basically the problem traces to the fact that a chronopotentiometric experiment must cover a range of potentials while a potentiostatic experiment (except for an initial transient) operates a t a fixed potential. The result is the possibility of avoiding potentiostatically many complications caused by charge-transfer, adsorption, and the like which plague the quantitative interpretation of chronopotentiometric results. When examination of a range of potentials is desirable, chronopotentiometry still seems to be losing out, in this case to linear or cyclic potential scan techniques. Broadhead and Hills (32) have demonstrated all is not lost with a novel application of chronopotentiometry to the determination of transport numbers. Marsh and Bruckenstein (123) have applied chemical stripping (which might be thought of as chronopotentiometry at zero current) to the determination of activity coefficients of metals dissolved in mercury. Peters and Burden (161) have espoused derivative chronopotentiometry as a method of circumventing some of the problems of determining (and indeed operationally defining) transition times. Their method involves measur-
ing the minimum value of dE/dt and multiplying its reciprocal by a factor determined by the reaction mechanism and whether charge-transfer is reversible. The problem, of course, is to figure out the appropriate factor for any given experimental curve. Sturrock and coworkers (184) have made use of the idea in analytical applications to micromolar solutions. Shults and I l u e ller (17.3) have given theoretical potential-time relationships for derivative programmed-current chronopotentiometry. Herman and Bard (80) have considered application of programmed currents to systems with ece kinetic complications. Murray and Gross (13.4) have given an account of some of the difficulties (spherical diffusion, capillary shielding, convection) which attend chronopotentiometry a t hanging mercury drops. The difficulties, of course, are not peculiar to chronopotentiometry, but rather to hanging drops. Lingane ( I f 4) has demonstrated the ambiguities which attend the analysis of chronopotentiometric data in the presence of adsorption by analysing computer synthesized data. Christie and Osteryoung (41,153) have pointed out a case of a hitherto unmentioned possibility in this regard namely desorption of an initially adsorbed species in a potential range preceding its reaction. Despite the inherent problems, X u r r a y and Gross (135) were reasonably successful in an experimental chronopotentiometric determination of adsorption in P b and Hg halide systems. How do they know they were successful? The chronopotentiometric results agreed with chronocoulometric results which it can be presumed are reliable. Kemula and Strojek (91, 92) employ very low current densities for anodic stripping of low concentrations of metals from hanging drops. I n some cases they tried a galvanic stripping process with no external current generator and current limited by a large resistance. Ultimate simplicity rather than accuracy seems the prime attribute of the variant. Vincent and Wise (193) have also tried analytical chronopotentiometric stripping. Blackburn (25) advocates a novel chronopotentiometric determination of hydroxide by anodic oxidation of hydrogen in palladium. Kuempel and Schaap (105) will appeal to the gadgeteers with a combined wire and hollow cylinder electrode that, through combination of positive and negative curvatures of its two parts, behaves, as regards diffusion, approximately like a plane. Plane geometry is simple mathematically, but not always experimentally, especially in micro or vivo systems, so the idea may have some practical merit. Deron and Laitinen (60) have performed some perturbation calculations
to derive approximate corrections for sphericity, smaller than usual potential excursions and double layer charging on data obtained by chronopotentiometry with current reversal. Although the approximations are not entirely successful in dealing with their data, the perturbation idea has long been fruitful for quantum mechanists and can be helpful electrochemically as well. Tanaka and Tamada (189) use the fact that the apparent diffusion coefficjent for a system of species depends on the equilibrium between them to determine equilibrium constants chronopotentiometrically. I t is a shame that the insensitivity of diffusion coefficients to structure prevents wider application of this idea. COULOSTATICS
Very little is happening coulostatically. Lauer (107’) has given the design of an electronic coulostat. Sorensen and Sympson (180) have followed the course of titrations coulostatically. To the reviewer this seems like shooting flies with cannons. Anson (9) proposes “charge-step chronocoulometry.” This seems something of a fraud however because the experiment is of the ordinary garden coulostatic variety with charge injection followed by chronopotentiometric readout. The translation to chroriocoulometry is done with pencil and paper knowing the double layer capacitance and the potential. One of the “in principle” advantages of coulostatics (and perhaps its major one) is the possibility of working relatively easily in high resistance media. Delahay and coworkers (53) have applied this idea practically in determination of double layer capacitances of low concentration solutions where conventional impedence methods fail. They claim that solvent purity rather than the method limit its application to distilled water, which is as good a recommendation as could be asked. POTENTIODYNAMICS
Large amplitude controlled potential techniques seem to have converged on two limits. Ten years ago a dozen voltage functions had proponents, now only two seem to attract much attention. Linear (or triangular wave) potential scan methods provide qualitative information while potentiostatic methods (in single or multistep variants) provide quantitative information. Qualitative though their mathematical complexity might seem to make them, linear scan methods are being provided with quantitative theory for more and more complicated reaction mechanisms. Wopschall and S h a h (198) treat the case of both 0 and R adsorbed by potential dependent Langmuirian isotherms with homogeneous kinetics thrown in as VOL 40, NO. 5, APRIL 1966
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well. Polcyn and Shain (163) treat reversible and irreversible (in combination) multistep reductions with coupled catalytic reactions. Olmstead and Xicholson (152) treat ec mechanisms at spherical electrodes. Hale and Greef (75) treat adsorption (without mass transport polarization) from a viewpoint that alloivs deduction of the adsorption isotherm from linear scan results. Srinivasan and Gileadi (181) treat Langmuirian adsorption on linear sweep. Saveant and Vianello (171) have given an extended discussion of the effect of coupled chemical reactions on linear scan results, including diagnostic criteria, simplified theory for special cases, etc. Xicholson (137) has improved on a previously proposed semiempirical method for deducing rate constants of following reactions. Savea n t (169) has treated ece mechanisms where the charge-transfer steps are separated in potential. H e also proposes (170) asymmetric triangular scans as advantageous in some kinetic studies. Evins and Perone (65) give theory and experimental studies on model systems for derivative readout linear scan in kinetic systems. The advantage is decreased double layer contribution a t fast scan rates. Schwartz and Shain (17dA) and DeVries (61) propose potential steps to generate species followed by linear scan to examine them. If nothing else, the foregoing list proves conclusively that the age of the computer is upon us. Almost without exception the boundary value problems were solved numerically with its aid. Experimentally, Perone (155) has successfully employed scan rates as high as 20,000 V/sec and more successfully 2000 V/sec. Because the characteristic time of a linear scan experime7t is of the order of ( R T / n F )(dE/dt), microsecond times seem to be a t hand. Perone and Stapelfeldt (160) employ derivative readout of linear scan results in stripping experiments to achieve 20% accuracy in 10-10 solutions. Olmstead and Sicholson (151) have given an experimental test of cyclic scan equations for spherical diffusion (Fick’s law still works). Clausen, Xoss, and Jordan (44) propose an electrode for linear scan studies (but presumably possessing the same advantages in other transient techniques) consisting of a glass frit in contact with mercury. The frit prevents convection and allows application of linear scans at polarographic sweep rates. The advantage to the analyst is the longer the time, the less the effect of doublelayer charging and kinetic complications. Insensitivity to solution stirring and vibration have other practical advantages too. Vaguely related is a trick proposed by Kuempel and Schaap (104) for making plane mercury electrodes-Le., without that meniscus.
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POTENTIOSTATICS
The key words in potentiostatics these days are double steps and chronocoulometry. Chronocoulometry is the variant of the controlled potential technique in which not the current, but its time integral, the charge, is the readout. The potentiostatic and double step potentiostatic variants have blossomed forth in the past two years. The time honored advantage of potentiostatic techniques as compared with other transient relaxation methods is the fact that the double layer charging disappears in a n initial transient leaving the relaxation after that point to be examined for charge or mass-transfer kinetics without additional complication. Integral readout brings the transient back again in the form of an additive constant to the charge passed. If the purpose of investigation is to study kinetics, integral readout possesses a t most the advantage of changing the mathematical form of the readout, but not (except for the added constant) the variables on which it depends. However, recalling the earlier discussion of the Delahay concept of “ u priori inseparability” and the furor surrounding it, one may deduce that in large measure the controversy is a reflection of our ignorance concerning the extent and nature of adsorption of electroactive species in the presence of supporting electrolytes. Classical electrocapillary techniques are not sufficiently sensitive to provide good information in this area. It now appears that chronocoulometry can give such data reliably and relatively simply. The initial charging transient which chronocoulometry makes accessible includes, as well as the double layer charging, a faradaic component due to reaction of the initially adsorbed material. By use of the double step variant, these two components can be separated. How does this fit in with the inseparability of faradaic and nonfaradaic currents? In principle, it doesn’t. I n practice, it circumvents the issue by choosing the initial potential so far removed from the reduction potential that chemical intuition permits the assumption that all the material is in either the oxidized or reduced form and the step potential far enough on the other side to assume the material all in the other form. If potentials between these extremes were chosen, all the complications of the Delahay theory might ensue. However, because adsorption is governed by the same kinds of factors in the region of the reduction potential as elsewhere, the information provided by the chronocoulometric technique seems likely t o prove extremely valuable. The initial description of the doublestep chronocoulometric technique was given by .inson (8),and he and his co-
workers have already given impressive demonstrations of its usefulness (10, 42). I n the single-step variant, which came first chronologically, independent measurement is needed to determine the nonfaradaic charge on the electrode at the initial and final potentials. Techniques for obtaining the quantities have been devised (8, 111) and again Anson and coworkers (11, 39) as well as others (118, 135) have put the technique to good use. I n the short time since our last review, the technique has matured sufficiently that multichannel digital readout (110), direct digital readout to computer (108), and nonlinear analog readout (144) are operational. Incidentally, James (89) has made a strong case for analog readout in general, the point being that analog manipulation a t time of readout where possible is usually superior to digital conversion later. I n study of homogeneous kinetics, the double step potentiostatic technique has come into its own. Like chronopotentiometry with current reversal, its galvanic analog, the technique is primarily useful for studying chemical reaction following charge transfer. Hovsepian and Shain (83) have presented a study of compound formation of zinc and cobalt in mercury using the method. Perone and Kretlow (159) have studied reaction of ascorbic acid. Koopman and Gerischer (101, 108) studied nitrophenol reduction in a particularly impressive investigation. .idsorption as well as chemical reaction was a source of complication in that case. Christie (40) advocates chronocoulometry-Le., integral readout, for such studies. I n plain old potentiostatics (which is still the workhorse basic from which the variants above have grown), the new ideas are more in the way of a mopping up operation. Pence and Booman (154) have given a careful discussion of the effect of instrumental factors on potentiostatic studies of kinetics. Harrar and Shain (78) have discussed problems of current and potential distribution at large electrodes. Microseconds and below are the order of the day in potentiostatic circuitry (24, 28, 186). Stevens and Shain (18R) have given theory and experimental verification of diffusion limited amalgam formation at spherical electrodes. Holub and Xemec (81) have given a description of diffusion limited Langmuirian adsorption at spheres, intended as a practical demonstration of the virtues of analog calculation. Fleischmann and Harrison (68) have examined electrocrystallization processes. Guidelli and Cozzi (73) have discussed catalytic mechanisms. Some years ago Shain and coworkers devised a trick method of getting diffusion coefficients easily on diffusion limited reduction at spherical electrodes. The trick lies in the fact that the govern.
ing equation for diffusion to spheres has an extra term over that for planes, and combining the two terms gives the diffusion coefficient more simply than competitive methods. Stevens and Shain (183) now apply the same trick to diffusion out of spherical electrodes, while Phillips (162) applies it t o diffusion limited adsorption. Barnartt and Johnson (17) have applied Barnartt’s (16) absolute rate description of higher order charge-transfer processes to prediction of potentiostatic curves. AIcIntyre (132) has considered heterogeneous chemical kinetics. Oldham (147, 148) has evolved an approximate diffusion layer treatment for such complications as ohmic drop in potentiostatic experiments. Oldham and Osteryoung (149) have critically examined techniques for analyzing data from systems subject to charge-transfer kinetic complications, and found that analyses in some previously published work were inadequate. Hawley and Feldberg (79) have pointed out that those of us who consider ece mechanisms have been overlooking what may be a serious complication, namely the possibility of homogeneous second order equilibrium between intermediates and the initial reactant and final product. An experimental study (1) verifies that the effect can be important. THIN LAYER CELLS
Thin layer cells are continuing to enjoy the recent wave of interest which we noted in the last review. Most thin layers fall in one of two categories: bounded layers are those from which no electroactive material can enter or leave except a t the electrode-e.g., thin mercury films into which amalgam forming metals are plated-nonbounded layers are ones a t which the concentration of electroactive material at the boundary other than the electrode is maintained constant-e.g., membrane coated electrodes with convection assuring constant concentration a t the edge of the membrane in contact with bulk solution. Cells with the electrolyte between two identical electrodes with current flow between often fall into the second category, because they possess a point of symmetry midway between the electrodes which is a point of constant concentration. The important advantage of bounded layers is that, provided the time scale of (D, diffusion the experiment allows coefficient; t, time) to greatly exceed the layer thickness, one can dispense with concern for concentration polarization and calculate concentrations within the layer directly from Faraday’s law. Elimination of mass transport eliminates the major source of error in many electroanalytical techniques and produces
advantages in sensitivity as well. The advantages of nonbounded geometry lie primarily in the possibility of achieving steady state and are the same as those inherent in hydrodynamic techniques. Presently the difficulties with thin layer cells are those of fabrication. If the advantages of such cells are to be enjoyed to the fullest, the layers must be as thin as possible, to allow the smallest possible effective time constant. For reasons mentioned below in connection with hydrodynamic electrodes, nonbounded layers are theoretically advantageous for studying charge-transfer kinetic processes, and conversely bounded cells are advantageous for studying homogeneous kinetics. With cells of dimensions thus far reported in the literature the rates of processes of both types which can be studied advantageously in thin layer cells are of the same order of magnitude as those which can be studied by conventional polarography. Studying more rapid processes requires experiments with shorter time constants. The mathematics of finite diffusion enters with cells of the smallest dimensions practical a t present, and is relatively complicated. In such circumstances, semi-infinite diffusion-Le., more conventional cell design, is to be preferred. Even a t present thin layer techniques can be competitive with conventional polarography and with large scale coulometry. This covers a fair fraction of analytical electrochemistry, and it is to be anticipated that when reasonably priced and relatively fool-proof thin-layer cells become commercially available, their virtues will be recognized rapidly. Reilley and coworkers have been the major recent proponents of nonbounded thin layer systems, employing identical facing electrodes. A general paper ( 7 ) deals with results to be expected on application of a variety of techniques to systems subject to various complications. Other papers present experimental studies of the benzidine rearrangement (230, 146) and uranium(V) disproportionation (131). SchmidtWeinmar ( 1 72) has discussed determination of individual ionic mobilities. Dahms (46) has discussed diffusion limited currents. Perone and coworkers (157, 158) and DeVries and Van Dalen (62) have examined various techniques for stripping metals from thin film amalgam electrodes. Long term stability proved a problem with graphite backed mercury electrodes (158) and some deviations from identity were observed (167), but on the whole, in accord with other previous work these electrodes seem to work reasonably well in practice. The more generally useful case is bounded thin layers of solution. McClure and Maricle (116) used a simple dip cell for determination of coulometric n values. Hubbard and =Inson (85, 86) have given
the theory of linear potential scan and some practical applications. Hubbard, Osteryoung and Anson (87) have returned to the study of adsorption of iodide on platinum. With bounded cells, under ideal conditions only the total volume of the thin layer and not its thickness (provided it is not too thick) determines the electrochemical behavior. This, in principle, simplifies cell design. However there remains the problem of coupling the thin bounded layer to some reference electrode and here two problems arise. At the point of juncture material can enter or leave the bounded layer, and, if it does so in significant amount, will produce serious complications. However, designs which minimize the problem seem necessarily to produce problems of high resistance and nonuniformity of current density over the electrode. For simple coulometry, the most useful quantitative analytical technique in these systems, the effects are unimportant. For linear potential scan unhappily they need not be. At present the engineering difficulties are still with us, but the day in which the experimenter chooses cells as well as techniques t o fit the problem a t hand may not be too far distant.
HYDRODYNAMIC ELECTRODES
Hydrodynamic electrodes are very milch in evidence. Their advantages lie in the ability t o utilize steady state conditions with resulting greater precision in measurement and absence of the double layer complications of transient techniques. Their difficulties are both mathematical and practical. Fabrication of ring-disc electrodes is a real engineering feat. Achieving constant current density over the surface of the electrode is another. Such electrodes, however, also have some theoretical peculiarities. The advantage of hydrodynamics over diffusion is in study of charge-transfer kinetics where larger departures from Nernstian equilibrium can be maintained the larger the mass transport rate. Oddly the effect is in the opposite direction when homogeneous kinetics are under investigation. High mass transport rates tend to maintain surface concentrations near their bulk solution-Le., equilibrium valuesand minimize the kinetic effect. This problem is in part responsible for the interest in ring-disc electrodes. With such electrodes, the products and hopefully intermediates of reaction a t the center disc can be analyzed a t a concentric surrounding ring. The rotating disc seems Re11 established as the favorite of the hydrodynamic possibilities. Recent work includes a refinement of the limiting current expression ( 1 4 9 , a theory of following chemical reactions and cataVOL 40, NO. 5, APRIL 1968
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lytic reactions (74), a study of ece mechanisms (119), a study of the effect of inactive areas of the electrode on currents (106), a study of potentiostatic transients (36),a study of the effect of ohmic effects on uniformity of current distribution (84, 141, I d s ) , an electrode design for use a t high temperatures (197) and another which minimizes deviations from hydrodynamic ideality (165). One which fascinated us was the rotating anthracene electrode (Ilb)--definitely not recommended for most purposes. Albery, Bruckenstein, S a p p , and Johnson in various combinations (2-6) have come up with an exact method of treating the theory of the ring-disc electrode, and have exhaustively examined its implications for various kinetic processes including heterogeneous and higher order homogeneous processes, transients, and steady state. Xekrasov (140) has examined multistep reactions. On the experimental side, Bruckenstein and coworkers (138) have described instrumentation for independent potential control and current measurement at disc and ring. Zhutaeva and Shumilova (199) have discussed fabrication of ring-disc electrodes. While hydrodynamic electrodes come in all shapes, a prime advantage of the rotating disc is that, at least under ideal conditions, the current density is uniform over the electrode surface. This is by no means a general characteristic and its absence might be a serious source of complication in the study of charge-transfer reactions. Blaedel and Klatt (26, 95) have examined tubular electrodes and find that although the effect of nonuniform current density is pronounced, it can be taken into account. Slotter, Weaver and Parry (174) report a similar study for the streaming mercury electrode. Arvia and coworkers have examined theoretically (120) and experimentally (88, 38) laminar flow past discs and (93) similarly cones. Kholpanov studied spheres and cylinders. X a t suda has given theoretical studies of blunt cone electrodes (124) which do have the uniform current characteristic as well as tubular electrodes (125) which do not. Obviously tubular electrodes may have some engineering advantages in certain circumstances. Of the remaining alternatives to the rotating disc or ring-disc thus far proposed, none seems very attractive. The criterion is experimental convenience. Most other electrodes require subsidiary systems to produce solution flow past the stationary electrode. Not only is ensuring laminar flow a difficult trick, but it also usually requires inordinate amounts of solution to fill the fancy plumbing. The rotating disc with its built-in flow generation seems here to stay.
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PHOTONS AND RELAXATIONS
The development of photometric techniques to solve problems concerning electrochemical systems which electrochemical techniques cannot answer is proceeding rapidly. Murray and coworkers (136) report an optically transparent thin layer electrolysis cell. This type of approach is useful for analysis of bulk solution. Walker (194) has described a remarkable (!) experiment involving specular reflectance of a laser beam from polished silver electrodes, aimed at detecting intermediates in the hydrogen evolution reaction. Such an approach can work only when the bulk solution does not absorb appreciably. More attention has focussed on internal reflectance spectometry in the electrode where matters are under better experimental control and where the results are more directly dependent on species in the vicinity of the interface. Hansen, Osteryoung, and Kuwana (76, 77) have made extensive study of tin oxide coated glass electrodes in the visible region and hlark and Pons (122) have used germanium electrodes in the infrared. Mark and coworkers (164) have recently tried thin film platinum electrodes. The last are by far the most attractive electrochemically, and happily appear to be workable optically as well. The applications for such electrodes seem boundless. O’Brien and coworkers continue their laser interferometric studies, a recent one (112) is of the D M E . The new idea seems to be holographic interferometry (96). Perhaps in return for the advantage photometry seems about to afford the electrochemist, electrochemical techniques are taking a photochemical turn. Perone and Birk (166) have applied potentiostatic techniques to study of flash photolysis reactions. More directly of interest are the papers by Barker and coworkers (15) and Delahay and Srinivasan (55), both concerned with irradiation of mercury electrodes with ultraviolet light. The former is the more extensive study and the main theme seems to be photoejection of electrons and their ultimate disposition. A. related topic of current interest is electrochemiluminescence. Early studies were concerned with systems in which ac electrolysis generated cation and anion radicals from an aromatic molecule which then produced light emission on annihilation. Zweig and coworkers (201) found the same process with heterocycles. Feldberg (66,67)has solved (numerically) the nonlinear Fick’s law problem associated with this process for double step potentiostatic generation. The more recent problem is the origin of the fluorescence when potential excursions are insufficient to produce both cation and anion. hlari-
cle and Maurer (121) found with rubrene that impurity reactions were the cause, but Zweig and coworkers (200) seem to have shown with phenanthrene that the triplet state can be formed as a result of electrochemical reduction and reoxidation. This seems a fruitful line of experiments for charge-transfer theorists to follow. The last review in this series wound up with a suggestion for a quick and dirty experiment of the type that excites the interest of Nobel prize committees. I n the absence of published response we suggest an alternative. The recent Palladium medal address (49) gives some excellent hints on how to gain recognition as an electrochemist the hard way-Le., by shaping the course of the field for twenty years. LITERATURE CITED
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~~
Organic Polarography Donald J. Piefrzyk, Department of Chemistry, University o f Iowa, Iowa City, Iowa 52240
T
HIS RI,VII;W covers articles which have been described in Chemical
Abstracts, Analytical Abstracts, Electroanalytical Abstracts, and readily available journals ending S o v . 1, 1967. As
in the past, duplications and reinvestigations of previous work appear widely. Two general trends in the application of polarography appear to be taking place. In one case, references to polarography as an analytical tool for following all sorts of synthetic, kinetic, and biochemical reactions are frequently found. The second trend is the use of polarographic o-dation or reduction to characterize not only organic compounds but also organo-metallic and metal ion-organic ligand complexes, thus, complementing the ubually measured physical constant5 and spectral data. There are, unfortunately, many instances where only the half-wave potential data are reported in these cases and very little information i q given about the conditions under which they are obtained. It is hoped that such a practice will not become widespread. This period has seen the publication of a special issue of Talanta [12, 1059-1380 (1965)l honoring the 75th year for Prof. Jaroslav Heyrovqky. d wide variety of polarographic review articles by his former students and associates are included and the ones which are organic in 194 R
ANALYTICAL CHEMISTRY
nature are individually cited in this review. .ilthough Prof. Heyrovsky died March 27, 1967, his important work in polarography and his vital role in the development of the technique, which has become an important toot in electrochemistry, analytical chemistry, and in many other areas of science and technology, will remain with us (1466). Several new books on polarography and related topics became available during this period. Specific topics covered are substituent effects (1465), electrochemical kinetic> (1377), oscillographic polarography (61l), and reaction kinetics in polarography (1461). The papers given at the Proceedings of the Third International Congress on Polarography (504, 505) and the papers presented as a tribute to Prof. Isaniu Tachi (614) are now available in book form. Organic polarographi papers in the former are individually cited in this review while those in the latter, which were also published in Reviews of Polarography (Kyoto), [11 (1963) ] were cited in the previous review. General polarographic books were also published (67,501,744,873,1059). Recent trends in organic polarography (1464) and general polarographic reviews (201, 499, 1092, 1109, 1150, 1290, 1462, 1463) have appeared. Other reviews are concerned with the use of 8
polarography to determine the stability constants of compleyes (458),kinetics of electrode processes (398), paths of organic oxidation-reduction processes a t the DlIE (332, 1258), methods of determining electrode proceqseq (1037, 1076), electrode processes in ac polarography (293), and methods for the determination of the number of electrons involved in electrode reactions (793). The use of electron spin resonance spectrometry in evaluating electrode reactions in R hich radicals are formed has continued to grow (3, 166, 1396). Reviews on the application of polarography to the study of ions, radicals, and in electrochemical syntheqis (1396) and free radicals in electrolysis of organic compounds (1317 ) have appeared. Numerous reviews have appeared on the applications of polarography to insecticide analysis (97, 181, 394, 1107); protein analysis (140); peroxide analysis (591); biochemical problems (334, 463, 866, 1062) ; protein complexes (552); problems in the clinical laboratory (517); analysis of pharmaceutical compounds (321, 1271); analysis of monomers, impurities in monomers, catalysts, metals, and end groups in plastics and polymers (175, 1349); analysis of penicillins, streptomycins, and other drugs (1405); petroleum product analysis (1296); and dithiocarbamic
