(199) Skobets, E. M.,Karnaukhov, A. I., i T k r . Khim. Zh. 30, 693 (1964). (200) Skobets Skobets, E. X,Karnaukhov, A. I., Karetskii, KaretsE N. S., Ibicl., D. 365. (201) Smoler, I., J. Eleciroanal. Chem. 6, 465 (1963). (202) Sooa, Z . G., Lingane, P. J., J . Phys. Chem. 68, 3821 (1964). (203) Specker, H., Schiewe, G., 2. Anal. Chem. 204, 1 (1964). (204) Spritzer, 11.S.,Costa, J. A I . , Elving, P. J., ANAL.CHEM.37,211( 1965). (205) Sriiiivasan, J-. S., T o w , G., Delahay, P., J . Electroanal. Chem. 10. 183 (1965). (206) Strzifelda, F., HanEil, Y., Kimla, A., Collecfzon Czech. Chem. Commvn. 30, 31S!?( 1965). (207) StrBfelda, F., Kimla, A., Ibzd., 30, 3607( 1965). ( 2 0 8 ) Strombere. A. G.. Zavodsk. Lab. 29. (209) Stromberg, A. G., Kaplin, A. A., I b d , 30, 525 (1964). (210) Stromberg, A. G., Zakharova, E. A., lbzcl , p. 261. (211) Sturrock. P. E.. J . Electroanal. Chem. 8. 425’11964). ‘ (212) Subbabky, W. J., J . Electrochem. Sor. 112, 923 (1965). (213) Suzuki, J., Ozaki, T., Bull. Chem. Soc. Japan 37, 230, 789 (1964). (214) Srvofford. H. S., Holifield, C. L., Ak.41,. CHEM.’ 37, 1509 (1965) (215) Ibid., p. 1513. (216) Swofford, II. S., 3lcCormick, P. G., l b i d . , p. 970.
(217) Swofford, H. S., Propp, J. H., Ibid., p. 974. (218) Tajima, N., Terada, H., Kurobe, M., Japan -4nalyst 11, 453 (1962). (219) Takahashi, R., Talanta 12, 1211 (1965). (220) Talanta 12 (NO. 12) 1061-379 (1965). (221) Taylor, J. H., J . Electroanal. Chem. 7, 206 (1964). (222) Taylor, J. K., J . Assoc. O j i c . Agr. Chemists 47, 21 (1964). (223) Thomason, P. F., Microchem. J . 8, 234 (1964). (224) Tsfasman, S. B., Salikhdzhanova, R. lT.-F., Zavodsk. Lab. 30, 133 (1964). 1225) Tiler. G. V.. Zaretskii. L. S.. ‘ Zavodsk L a b . 29, 1291 (1963).’ (226) Turner, W. R., Elving, P. J., ANAL. CHEM.37, 467 (1965). (227) Turnham, D. S., J . Electroanal. Chem. 9,440 (1965). 1228) Ibid.. 10. 19 11965). (229) Underkdfler, W.L., Shain, I., ~ ~ N A L . CHEM.37, 218 (1965). (230) Vanderborgh, N. E., Sellers, D. E., J . Am. Chern. Soc. 86, 2790 (1964). 12311 Van Rvsselberehe. P.. Electrochim. Acta 9, 1363 (1964r (232) T’ogel, J. J Collection Czech. Chem. Commun. 30,2252 (1965). (233) T-ogel, J. J., J . Electroanal. Chem. 8 , 82 (1964). (234) I’olke, J., Amer, 11. hl., Collection Czech. Chem. Comrnun. 29, 2134 (1964). (235) Yosburgh, IT. C., Bates, R. G., J . Electrochem. SOC.111, 997 (1964).
(236) Walter, J. L., Rosalie, Sr. >I., ANAL. CHEM.37, 45 (1966). (237) Wawzonek, S., Talanta 12, 1229 il966). (238) geller, K., J . ElectroanaL Chem. 10, 270 (1965). (239) Will, F. G., J . Electrochem. Soc. 112, 1157 (1965). (2401 Wilson. A. h1.. J . Electroanal. Chem. 10. 332 (lg65). (241j Rittick, J. J., Rechnitz, G. A., A x a CHEW ~ 37, 817 (1965). (242) Wolf, D., J . Electroanal. Chem. 5 , 186 (1963). (243) Yamada, S.,Sato, H., Suture 193, 261 (1962). (244) Yarnitsky, Ch., Ariel, AI., J . Electroanal. Chem. 10, 110 (1965). (245) Zakharov, h1. S.,Stromberg, A. G., Zh. Analit. Khim. 19, 913 (1964). (246) Zhdanov, S. I., Kislev, B. A., Dokl. Akad. S a u k S.S.S.R. 155, 651 (1964). (247) Zittel, H. E., hliller, F. J., AKAL. CHEM.36, 45 (1964). (248) Zittel, H. E., Miller, F. J., Ibid., 37, 200 (1965). (249) Zuman, P., in “Advances in Analytical Chemistry and Instrumentation,” C. N. Reilley, ed., p. 219, Wiley, Sew York. 1963 (2jO) Zuman, P., “Organic Polarographic ilnalysis,” Pergamon, New York, 1964. WORK supported in part through funds provided by the U. S. Atomic Energy Commission under Contract AT(30-1)905.
Electrochemical Relaxation Techniques W.
I
H. Reinmuth,
Department o f Chemistry, Columbia University, N e w York, N . Y.
review under the present title ( 1 4 4 , the reviewer presented a general survey of the field. The present paper will confine its attention largely to research appearing in the literature of 1964-65. X o pretense is made to completeness, coverage is confined almost entirely to papers to which the reviewer had direct access a t the time of writing. Because Electroanalytical Abstracts efficiently scavenges the literature for pertinent work, the reader is urged to rely on it for extensive review. and on the present work only for more intensive discussion of selected papers. N THE FIRST
SMALL AMPLITUDE TECHNIQUES
Small amplitude techniques have attracted interest largely as methods for evaluation of kinetic parameters of charge-transfer processes per se. The last two years have seen no dramatic breakthroughs in this area. Rather it seemed a period of consolidation. Basic theory and practice are well established, but early results gave many anomalies. N o w refinements in experimental techniques and methods of
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data analysis are elucidating some of the causes of the discrepancies. The transient techniques, galvanostatic, potentiostatic, voltostatic, coulostatic, uniformly suffer from complexity of theory when mass and chargetransfer and double layer capacitance contribute to the observed relaxation even when relatively simple linearized theoretical models are adopted. For galvanostatic results, it has been common practice to determine kinetic parameters by extrapolating data from relatively long tinies where diffusion becomes dominant and theory simpler. However, potential increases with time a t constant current, and, as it does, the basic premise of linearized theory (small potential excursions) becomes less tenable. The criterion by which the applicability of the theory is judged rests on its accuracy of prediction of potential a t any given time. Since deviations due to nonlinearity a t long times are systematic, however, kinetic parameters based on extrapolation may suffer much larger errors than this simple criterion would indicate. Birke and Roe (22) have attempted to deal with this difficulty by extending the
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linearized model to include higher order terms. It appears, however, that their approach is faulty (104) and that their result represents a first order approximation equivalent to the linearized approximation though differing from it in form. Sluyters-Rehbach and Sluyters (159) have indicated a related source of error of particular interest in connection with the Hg/Hg2+2 couple. I n the region of interest, the double layer capacitance changes quite dramatically with potential, and these workers suggest that failure to take account of this nonlinearity may have influenced previous results. I n principle nonlinearities of the types described above should be detectable by comparing results obtained by cathodic and anodic perturbation. Under true linear conditions such results would be identical. More detailed theoretical analysis of nonlinearities would be of interest. Birke and Roe (23) have examined a double pulse galvanostatic method which seems to be based on the same philosophy as Gerischer’s original (64), namely to get the double layer charging out of the way on the first pulse so that the faradaic reaction can be examined
more readily. The Birke-Roe modification differs in the form of the first pulse. When mass-transfer can be eliminated, theory becomes easier and layer amplitude potential excur:’-ions are more attractive. Linford and coworkers (92) have extended previous theory of this case for a single galvanostatic step transient, and Kravtsov and Siniakov (97) have discussed analysis of transients obtained on step changes in current. Schuldiner and Piesbrey (151) have studied the 12/1-/ l’t system with a constant current 1 1 ~ 1 s technique ~ in which results are analyzed both during and after the pulse. JYith care in cell design and lead placement they were able to obtain data in tniies as short as 25 nsec. They apply Lery simple theory to their resulti by neglecting both concentration polarization (because of the very short tinieh) and the reverce charge-transfer reaction (because of large potential excuriions). It does not appear to the reviewer that the simplifications are entirely ju5tified by their experimental conditions. Their work, honever, does indicate that by forhaking the theorel ical advantages of small potentials it is po-ible to gain more than an ordci of magnitude in time n ith commercially available electronics, and points the way for further work. Angerstein-I(ozlon.ska and Conway ( 5 ) ieconiniend deiivaiive readout of galvanostatic results as particularly suitcd foi studying “pseudo-capacitance” asiociated with adsorption reaction.. I n the simplest cases the capacitance is given directly. I n a related paper Conway and conorkers (46) discuss the relative merit- of galvanostatic and lineal potential scan methods for studying adsorption, and conclude that complications aqsociated with slow charge-traiiifer complicate interpietation less in the former case. They also dibcuss in this paper the equivalence beta een transient and a x . results in terms of a n “equixalent frequency” associated with the former. T o the reviewer’s mind, the clarity of the discusqion suffers froni their definition of pseudo-capacity as directly proportional to rate of change of adsorption, since electrically this constitutes not only a capacitance but charge-transfer resistance as well. The conclusions all seem to be in order, however, and the major point, that chargetransfer kinetics must be considered in studies of adsorption is well taken. With steady state results excluding mass-transfer polarization and double layer charging, results become simpler still. Only then does it become feasible to examine reaction mechanisms of extreme complexity. Wales (17‘0) has discussed analysis of low overvoltage Tafel plots to obtain kinetic parame-
ters. llohliner (103) has considered effects of double layer on such data in multistep reactions. Gileadi and Srinivasen (65) have considered branched reaction mechanisms. Conway and Gileadi (44)have considered effects of adsorption. Despite the flurry of introductory coulostatic work reported in the last review, the technique is very sparsely represented in the last two years-one experimental study of ZniZn+2 kinetics (74) and a theoretical study (119) of relatively large amplitude relaxation with a reversible diffusion controlled system. The latter paper is primarily concerned with mathematical methods for dealing with such cases rather than the results themselves. Thus far, in cases as complicated as this in nhich numerical analysis must be resorted to for theory, results are of interest primarily as qualitative guides. Computer techniques are sufficiently well admnced that cornpariron of experimental data with numerical theory should be feasible, but little electrochemical work has been conducted along such lines. For potentiostatic relayations, theory does not become appreciably more complicated 1% hen potential excursions become too large for the linear approximat ion-priniarily because double layer capacitance appears only in an initial tranqient rather than throughout relalation. I t is particularly simple n hen the potential before charge-tranqfer is such that only one of the qpecie. of the redox couple is present before reaction. Groden, Aylnard, and Hayes (69) have given the theory of this case when reversible charge-tianqfer is followed by chemical kinetics. Holub and Koryta ( S I ) have conqidered diffusion limited adsorption (linear isotherm) followed by charge-transfer. Silverstroni and Ranipazo (167) have considered charge-tranifer preceded by chemical reaction betneen the depolarizer and an adsorbed Qpecies. Kastening (93) has considered competition beta een nonelectroactive suifactant and surface active depolarizer. For the inore mundane case of diffusion coupled with charge-transfer, Okinaka, Toshinia, and Okanirr-a (127) have made use of available theory to exaniine several experiniental systems. They simplify data analysis even further by restricting concideration to very qhoi t times where theory is simplified. Christie, Lauer, and Osteryoung (40) in similar evperiments simplify theory by adopting integral readout (charge-time rather than normal current-time) and restricting consideration to long times. Lingane and Christie (116) seem to have the best of both worlds. By combining both normal and integral readouts, they are able to eliminate most of the mathematical difficulties which plague either
alone, and can fit data from both long and short time ranges to theory without simplification. As they point out, the advantage gained is a very real one because, although restricting consideration to long or short times seems very simple in theory, in practice it is often difficult to decide which approximation, if either, is applicable to a given set of data. The Lingane-Christie approach should be applicable to other relaxation techniques as well. Combination of normal and integral readout of coulostatic results, normal and derivative readout of galvanostatic results, or normal readout of coulostatic and galvanostatic results bear relationships to each other (at least under linearized conditions) which more than superficially resemble the relationship betveen normal and integral potentiostatic readouts. While analysis of potentiostatic data for kinetic parameters seems to be making good progress, the prime liniitation of the technique remains the instrumental difficulty of providing true gotentiostatic conditions. Kithout such conditions the technique becomes voltostatic (169). I t insy be speculated whether anomalies in Lingane and Christie’s results (116) are not due to failure to maintain potentiostatic conditions. Okinaka et al. (127) noted that under their conditions potentiostat behavior limited the range of accessible data. 13ooiiian and Holbrook (24) have discussed analysis of fast potentiostat design. One of their conclusions is that’ a finite and not norinally negligible resistance must exist between indicator and reference electrodes for the potentiostat to control propeyly, Separation of this resistance from the charge-transfer resistance of the faradaic process presumably sets a limit to rate constants determinable potentiostatically. -Another paper (166) elaborates on the analysis of potentiostatic circuits and is critical of some earlier proposals. Seither paper offers any great hope that’ the limitations of potentiostats below the niicrosecond region will soon be overcome, but they do proride a rational basis for getting the most froni the existing state of the art. Keniec (118) has discussed the effect’ of reference electrode placement on effective ohmic resistance in three electrode potentiostatic arrangements. While his discussion is concerned primarily with polarography, it is equally pertinent to fast relaxation studies. It is not always apparent that the points Xeniec brings forth are adequately considered in published experimental work. Judging by the nuniber of papers published, alternating current techniques continue to be far more popular than transient t’echniques for studying electrode processes. DeLevie (51) has VOL. 38, NO. 5 , APRIL 1966
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extended Sluyters’ method of analyzing
ax. impedence results. Biegler and Laitinen (21) have described a convenient method of obtaining charge-transfer coefficients from ax. data. Hung, Delmastro, and Smith (86) have extensively considered theory of mechanisms involving multistep chemical reactions coupled with charge-transfer, and have suggested esperimental criteria for detecting such complications. Aylward and Hayes (13) have applied a simplified theoretical model to examination of coupled chemical reactions. Discrepancies appear in some cases between their results using this treatment and parameters deduced from d.c. polarography. While these are ascribed to double layer effects on kinetics, the explanation seems implausible to the reviewer for it would require the a.c. reaction layer thickness and double layer thickness to be comparable to each other but much smaller than the d.e. reaction layer thickness. In any case these authors conclude their approach to be no better than d.c. polarography, and more rigorous approaches to the theory of the a x . technique are available. Hale (73) has given theory of a x . impedence for reversible step-wise charge-transfer processes. Hung and Smith (83) and Aylward and Hayes (14) have discussed droptime dependence of a x . currents a t the DME, and a later exchange between these workers gives more results (Id,
161). Delmastro and Sniith (53) have elaborated further. Direct effects of drop curvature and growth rate on ax. results are not expected because the a x . frequency is large compared with growth rate and a.c. diffusion layer thickness is small compared with the radius of curvature. These factors do influence a x . results, however, through their effect on the mean (d.c.) concentrations a t the electrode surface. Consequently, mercury column-height variations affect a.c. results primarily in the same systems they affect d.c. re$ults. Theoretical studies of the aboxe workers have been conducted with the same expanding plane approximation which leads to the Ilkovic equation in d.c. polarography. Biegler and Laitinen’s experimental studies (91) have yielded a.c. results esplicable in terms of the same effects responsible for spherical correction in d.c. polarography. Damaskin (46, 4 7 ) has given a semiempirical theory which seems to account quantitatively for the forin of differential capacitance us. d.c. potential in the presence of surfactant. I n some cases of apparent nonconforniity peaks appearing in anomalous positions are ascribed to reorientation of adsorbates rather than to their desorption. Kastening, Gartmann, and Holleck (94) have studied interference of surfactants with
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charge-transfer and have given theory for the case. Leikis and coworkers (113) and DeLevie (52) have ascribed the anomalous frequency dispersion of double layer Capacitance data obtained at the DME to the effect of a solution film inside the capillary and presented calculations and data to support the postulate. Epelboin and coworkers (153) have discussed methods of detecting such artifacts. Bauer and Foo (18) have discussed the relative merits of current and voltage control in analytical a x . polarography and concluded that current control is superior. It is difficult to rationalize this conclusion on theoretical grounds for, as Smith has shown (160), under normal conditions the relationship between current and potential is independent of which of them is controlled. I n the simplest form of a x . polarography, double layer capacitive currcnt and faradaic current are not separated. While this technique has advantages over d.c. polarography in some cases (notahly in analysis of surfactants) one advantage lacking as compared with d.c. polarography is sensitivity. Double layer charging contributions are larger than in d.c. polarography and calibration curves are nonlinear because of the effect of cell resistance and the vectorial rather than the algebraic combination of faradaic and nonfaradaic components. Phase sensitive detection and three electrode arrangements can overcome these difficulties a t low frequencies a t the cost of instrumental complexity. Underkofler and Shain (16 7 ) , Hayes and Reilley (76), and Breiter (26) have recently described phase selective a x . instruments. When phase selection is used, a.c. polarography does have significantly greater sensitivity than d.c. polarography (when complications due to slow charge-transfer kinetics are absent) and its marriage to stripping techniques to produce even higher sensitivity has been assayed by Underkofler and Shain (167) n.ith promising results. On the other hand, Kaplan and Sorokovskaya (91) using a similar technique-square wave polarography-in similar circumstances encountered a number of practical difficulties-e.g., adsorption of surfactant impurities-which prevented realization of the full sensitivity of the combination and suggest that trace a x . polarography a t this point is far from routine. -it solid electrodes, a x . methods (and d.c. methods) have always been less satisfactory than a t the DJIE for a variety of reasons-e.g., changes of the electrode surface structure wjth time, adsorption of impurities, etc. There seem to br: two schools of thought on how to approach the problem. One school favors bridge measurements after the time-dependent phenomena have run their course. Bump and Remick’s
(37) recent work is an example. These workers chose a particularly simple cell arrangement consisting of two identical Pt electrodes. One of the problems of such an arrangement is that it depends for d.c. potential control on the poking of the redos couple itself, and the d.c. potential need not remain constant with respect to an external reference when a number of solutions are preparedparticularly when one of them contains background electrolyte alone. It is not clear that these workers have taken adequate account of this in their data interpretation. Breiter (26) and Ramaley and Enke (141)take the opposite tack in their solid electrode work, by superimposing the a.c. signal on a rapid linear scan. While forsaking the accuracy of bridge measurements, they also avoid the time-consuming bridqe balancing operations and (hopefully) time-dependent changes in the system under study. While most workers employ bridge niethods or rectification and d.c. readout for analysis of small amplitude a.c. results, several methods have been proposed based on oscilliscopic observation of a x . wave forms. Sluyters and Loeuwe (158) have used a sine wave technique for determination of double layer capacitance in the presence of diffusion controlled reversible faradaic reaction. Rek, Wijnen, and Sluyters (145)have used a square wive technique as a supplement to normal bridge methods in determining cell resistance. Ramaley and Enke (141) have used a triangular wave technique for determining double layer capacitance and detecting frequency dispersion in same. Ramaley and Enke (142) have suggested variation of double layer capacitance over the surface of solid electrodes as a source of the frequency dispersion which is observed in inipedence nieasurements. DeLevie (50)has given a detailed niathematical discussion and experimental results concerning the effects of surface roughness in producing the same anomaly. Gutmann (70) has cited data indicating the virtues of inclusion of pseudo-inductance as a component of inipedence in representation of ax. processes. The examples are rather estreme situations, however-e.g., ampere currents through commercial dry cells-and suggest to the reviewer that actual rather than pseudo-inductance may be important. Sluyters and coworkers (88,89) have continued their a x . impedence studies, but recently have turned their attention to streaming mercury electrodes. Their \Tork has been devoted thus far largely to examination of electrode designs, theory, and examination of model systems, but interesting anomalies have been uncovered with the Zn/Zn+2 system at amalgam electrodes. I n the area of techniques resting on faradaic nonlinearity, Kooijman and
Sluyters (96) have examined phase angles of second harmonic signals. Gnusin (196) has given theory and experimental verification of faradaic rectification signals a t controlled current. Bauer (16) has presented a theory of second harmonics, but it ignores the effect of the second harmonic component of concentration variation a t the electrode surface. This component is inversely related to frequency so that Bauer's results reduce t o the correct high frequency limit. However, its predictions are seriously in error a t low frequencies and his criticisms of earlier work in this region are unfounded. Bauer and Foo (17) h a r e performed experimental studies with relatively large (up to 170 niv.) a.c. signals and obtained satisfactory agreement with theory for amplitudes of first harmonic curients. Taylor (166) has described a square wave polarograph. While he emphasizes the virtues of its electronic simplicity, this comes a t the cost of omitting gating circuitry which pc'rmits elimination of double layer charging current and is not an unmixed blessing. Buchanan and NcCarten (SO) have described a three electrode gated square wave polarography based 011 operational amplifiers. Laforgue Kantzer and X u x a r t (109) have described some rather remarkable effects of a.c. potentials on drop-time of the DXE. They propose esplanations based primarily on mechanical resonance phenomena induced by variation of surface tension with potential. Narayan (11?) from similar phenomena postulates a slow relaxation phenomenon within the electrical double-layer. The mechanical resonance idea seems in far better accord with intuition. LARGE AMPLITUDE TECHNIQUES
Large amplitude techniques have enjoyed a very active two-year period. The virtual monopoly of chronopotentionietry in application to chemical kinetic studies due to its relative theoretical and instrumental simplicity seems to be yielding. On the one hand, numerical computer methods are conqurring the mathematical complexity of linear potential scan techniques, and on the other hand, operational amplifiers are mastering the instrumental difficulties of potentiostatic techniques. I n general papers, .Ishley and Reilley (11) have discussed pseudo-first order chemical kinetics coupled with diffusion a t planar electrodes, Rangarajan (149) has discussed surface diffusion, and DeLevie (50) has discussed surface roughness effects. -Ill these papers give specific theoretical results for niore than one technique. Theory and practice of linear potential scan techniques continues to be extended
t o more complicated systems. While useful for analytical work and for qualitative kinetic studies, this technique has attracted fewer followers for quantitative kinetic work. Conway and coworkers (49, 45) have discussed some of the complications involved in getting information on adsorption from linear scan studies. While their discussion is concerned priinarily with complex mechanisms of the type found in fuel cell studies, the complexity of linear scan theory extends to simpler systems. This complesity rests on a more fundamental difficulty-namely, that the current-potential characteristic normally depends both on charge-transfer and mass transfer kinetics. I n contrast to the situation in chronopotentionietry or potentiostatic studies, these phenomena cannot readily be separated and data analysis is thereby complicated. For example, Xicholson and Shain (122) have presented theory and esperiiiiental results for cyclic linear scan in a system with a chemical step interposed between two charge transfers. Kinetic paranieters deduced from the data agreed well with those obtained earlier potentiostatically and chionopotentionietrically, However, the analysis of the linear scan results required reversibility of the first charge-transfer process which was not required in the other two determinations. Recently, Buck (3.5) has given theory for slow-charge transfer processes in series form. Nicholson and Sham (121) have given extenqive numerical theory for cyclic linear scan in cases of fast slow charge transfer coupled with various chemical or catalytic steps. Kicholson (119) has given numerical theory for second order chemical kinetics coupled with charge-transfer. Mamantor and comorkeis (99) have extended previous work on metal depoqition on solids. Saveant and Vianello (150) have extended the theory of catalytic reactions. Nicholson (220) has analyzed slow charge-transfer on cyclic linear scan. The analysis indicated that the separation of anodic and cathodic peaks is insenqitive to chargetransfer coefficient. This enabled X c h Olson to propose a very simple method of determining charge-transfer rate constants based on peak separation as a function of frequency. While it will doubtless not replace more accurate methods, its convenience makes it attractive for obtaining rapid estimates. Osteryoung and Parry (131) have examined linear scan methods in analysis of mistures. Their method of starting scan from the plateau region of an easily reduced component to remove its interference in determination of subsequently reduced species was esaniined some years ago by Ross, Dellars, and Shain (148). -1sticky practical detail in linear scan is the effect of ohmic drop. While a
load line method of correction has been proposed (1S9), it seems grossly inadequate on a number of grounds. Fortunat'ely, two rigorous treatments of the effect have appeared (56, 119). The two works obtain solutions of the prob-lem by different numerical methods, and the second contains a critical comparison of the methods employed. The staircase method (100) is a variant of the linear scan method in which the linear scan is replaced by a series of small incremental potential steps. I t s virtues rest on the fact' that double-layer charging current decays quite rapidly as compared with faradaic current a t each step discontinuity. 11s appropriate gating techniques, the readout can be made to reject most or all of the double layer current while providing a readout otherwise similar in form to linear scan. l l a n n (101)has described an operational amplifier based instrument suitable for staircase studies (and also linear scan). The sensitivity claimed (-10-7-II) is comparable to that' claimed for pulse polarography, derivative readout d.c. polarography, and phase selective a.c. polarography at, the IIlIE. Aillappear to be limited by capillary noise. .A second paper (125) gives some theory and analytical applications. X third paper (42) gives more detailed theory. At its present stage the technique is primarily of interest for tracbe analytical ITork. As compared with its conipetitors cited above, this technique may be more readily applicable to solid electrodes and therefore somewhat more versatile. A wide range of sweep rates, desirable for kinetic studies, presents problems in gating and control circuitry. l l a n n ' s inst'runient' cited above, for esample, gives steps of inininiuin one nisec. duration which restricts useful scan rates to -20 volty/sec. 13y reversing the gating, it is possible to reject faradaic current and observe double layer capacitance. Krischer and Osteryoung (98)have studied double layer capacitance at solid electrodes in this way. With relatively complicated situations a t solid electrodes, Gilrnan (66,67) finds that' reproducibility and interpretability of linear scan results can be improved by applying sequences of constant potential steps to pretreat the system prior to scan. Perone and coworkers (134-186) have published a number of papers on derivative readout and multiple derivative readout techniques to linear scan results. Theoretical and experimental results have been given for a variety of types of systems. Christie, Lauer, and Osteryoung ( 4 1 ) on the other hand, suggest integral readout for the same kinds of results. Integral readout is not particularly convenient for diffusion limited systems because the integral in principle keeps increasing monotonically without VOL. 38, NO. 5, APRIL 1966
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bound. Thus the expedient' of integrating between set limits of potent,ial must be adopted. For adsorption studies, however, integration does yield results in convenient form. It appears to t'he reviewer that in almost every case in which integral readout of linear scan results is of interest, integral readout of potentiostatic result's should be just as useful and easier to interpret. This seems a good point to digress on the merits of integral and derivative readout in general for they form the basis for a wide variety of innovations cited a t various points in the present review. I n principle, such readouts can not change the amount of chemical information available in the original signal for they operate only electrically on that signal. However, there is no question that in many situations integrals or derivatives are more readily interpretable than the original signal. When this is the case, differentiation or integration a t the time of readout is usually far more efficient than a t some later time for such operations are much better performed in analogue than by digital or manual calculation. The gain of electronic differentiators increases directly with frequency. This makes operational differentiators inherently unstable as well as causing thein to emphasize short' term noise. Integrators have the opposite characteristics. Practical differentiators involve greater compromises in design, particularly if they must work at high frequencies. Either a differentiator or an integrator can improve signal to noise ratio if the noise is contained in an appropriate part of the frequency spectrum. 13y the same token, either can deleteriously affect signal to noise rates if improperly used. The point is that because integration or differentiation does not increase the information available from the signal, neither is a panacea for transforming bad techniques to good. Seither should be applied indi.scriniinately, but only with realization of these limitations and a specific objective in view. 1paper by I3reiter (87) has discussed digital manipulabion of linear scan results. With the age of the computer upon us, the surface of the subject has been barely scratched, but this paper gives some good indicat'ions of things to come. Linear scan techniques have long been popular for stripping analysis of electroactive species previously concentrated on or in an electrode by controlled potential electrolysis. Recently considerable attention has focused on t'he virtues of these mercury film electrodes as compared with more commonly used mercury drop electrodes. While the innovation is not new in practice, detailed consideration of its theory has made its potential virtues more apparent. DeVries and Van Dalen (55) gave 274 R
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a rather cumbersome approximate treatment and later DeVries (64) returned to give an exact numerical treatment. Roe and Toni's approximate treatment (147) will probably prove of greatest interest to the analyst, for it is under conditions such that this treatment holds that the advantages of thin film electrodes become most apparent. Basically the thin film technique offers two advantages : high efficiency in recovery of plated material during stripping, hence high sensitivity; and less tailing of stripping peaks than from electrodes of large volume, hence higher resolution. Their problems appear to lie in the difficulty of preparing thin films reproducibly. H ~ ever, M Roe and coworkers (102) have had wccess n ith Hp plated on graphite despite the fact that viwal inspection of the electiode demonstrates that a uniform thin film is a rather poor approximation to the esisting surface. Igolinikii and Stromberg (87) are able to get away with spreading mercury on a platinum suiface with filter paper. I t would seem that such electrodes may be easier in practice than their theory would indicate. Reilley and colvorkers (225,1!?6) have examined linear scan methods with thin solution films. With slow scan, coinplete electrolysis occurs, and integral readout gives total material present. Thus far, cell difficulties leave much to be desired in the way of accuracy. If these difficulties can be overcome, the method is potentially the analytical electrochemical technique for situations now thought of as polarographic. Ariel and coworkers (9) improve on normal stripping analj-siq by switching solutions between the plating and stripping steps. Khile sti ipping techniques usually thought of in connection with metal depoqition, they apparently work for surfactants (137) and other insoluble species too (20). Chronopotentiometry continues as the most popular technique for quantitative chemical kinetic studies. An important recent contribution by Feldberg and -1uerbach (61) is a numerical theoretical treatment of second order (uranium disporportionation) chemical kinetic mechanism. Second order kinetics have been largely circumvented in the past because the theory is not susceptible to simpler mathematical methods, but they seem to be yielding to the computer. The favored nonoperational definition of chronopotentiometric transition-time is the time a t which the concentration of the relative species becomes zero a t the electrode. Evans (69) in a discussion of stepwise and alternate path reductions, however, cites a mechanism in which the wave for reaction of a species starts after its concentration has already become zero. I n another paper, Evans (58) calls attention to the need for careful double layer
corrections in kinetic studies by correcting earlier published data to yield more satisfactory results. Chronopotentiometric studies of adsorption have given mixed results. Detection of adsorption is relatively easy, although even this is sometimes questioned ( 7 , 12). The real problem is to convert the raw data into a quantitative measure of the amount adsorbed. Discussions in several recent studies (6, 110, 165) indicate some of the ambiguities involved. Osteryoung and Anson's study of adsorption (130) in the 12/I-/Pt system and discussions thereof (8,151) are also illuminating with regard to the pitfalls of studying adsorption electrochemically in complicated systems by any single technique. Murray (108) has suggested the virtues of programmed current chronopotentiometry in adsorption studies. Anderson and llacero (2) have approached the problem of obtaining charge-transfer kinetic parameters from quasireversible chronopotentiometric potential-time curves. They propose a computer computation for fitting data to theory. Hale (71)has discussed reversible multistep reactions and proposed methods for analyzing data. Xorris (105) and Laity and McIntyre (112) have analyzed the influence of electrical migration on chronopotentiometric results. Neither result casts doubt3 on its neglect in usual conditions. Bro (29) has given experimental results on systems in which migration is present. Lingane and coworkers have published a number of papers on analytical applications of chronopotentiometry. While the end results have been good, almost each system they have studied has shown some little peculiarity of its own: Pt+4/Pt+*reaction occurs cleanly a t P t only if the electrode has a P t black surface (114); effective changes in surface area of the electrode during ;iuClrreduction may be significant (60) ; correction for oxide film formation on Pt electrodes presents a practical problem (106) and the problem is a bit more complicated in multicomponent reactions (107). =ill this suggests that those 1% ho approach analytical chronopotentiometry with the Sand equation and a prayer, may wish they had chosen spectrophotometry instead. If real systems become too complicated for the faint-hearted, electronic analogue models are now available (56'). I n the long run such models may prove more satisfactory than digital computations in giving a "feel" for results to be expected in complicated mechanisms. The example given-diffusion in a bounded layer-is one for which exact results are available but in series forin and their ramifications are not easily grasped by inspection as they are from analogue readout. More investigations in this area may well prove fruitful.
Problem remains with chronopoten tiometry in analysis of results a t short times or low concentrations because of double layer interference. Neither theoretical corrections based on very simple models-e.g., constant fraction of the total current goes to double layer charging-nor empirical graphical methods work uniformly well. This is not surprising because in principle, even if the double layer capacitance remained constant (which it does not) the forni of the current-potential relation for the particular couple under study would determine the form the correction should take in each case. Laity and 3lcIntyre (112) have suggeded a more tedious but less empirical method than those commonly in use, based on nieasurement of the slope of the chronopotentiogram manually a t several points along the curve. calculating froni this and the double layer capacitance the actual fiaction of current devoted t o double layer charging. Without independent estimate of the double layer capacitance, this niethod relies on an approximation which can be conveniently obtained from the slope of the chronopotentiogram before the onset of faradaic reaction. I n our laboratory (124) this procedure has not proved very satisfactory, apparently because of failure of its assumption regarding the double layer. Enke (57’)has automated the same technique with electronic diffeientiation and feedback to vary total current so t h a t faradiac current remains constant during the chronopotentiogram. h fancier method of correction (156) uses two cells, one with and one without reactant. It follows the same basic approach as the others, but the use of two cells permits operation on the basis of less restrictive assumptions regarding the double layer capacitance. Double layer capacitance as determined from the second cell provides, through electronic feed-back, for compensation of current in the first cell to constant faradiac current. Electronic compensations of this type appear to be limited to fairly slow times by inherent instability. Even the more sophisticated technique assumes the double layer capacitance to be unchanged by the presence of reactant. However, for low concentration analytical work neither of these problems may be important. As yet the feasibility of trace chronopotentiometry remains unproved. The effects of electrode geometry have received attention. Hurwitz (86) has given a theoretical treatment of cylindrical and spherical electrodes. Peters and Cruser (138) have also discussed cylindrical electrode effects on multistep reactions. Some of the remarks in the latter paper indicate interpretation of results would have been easier had the electrode been planar, and serve to rein-
force the reviewer’s prejudice against nonplanar electrodes despite their advantage of experimental simplicity. Bruckenstein and Rouse (34) have discussed the effect of curvature a t moving pool electrodes. Using projected plane areas appears to lead to errors as large as 207,. Lingane (115) has examined edge effects a t unshielded planar electrodes. hnson and coworkers have vigorously pursued the special advantages of chronopotentiometry in solution layers. Chemical kinetics of relatively slow reactions (39) and adsorption (85) seem to be particularly amenable to such study. The experimental problems of working with thin films have not been eliminated, but workable cell designs are available (84, 126). I n the area of cyclic controlled current techniques, Kalvoda (90) has discussed the large amplitude square wave currents as compared with the sinuqoidal currents employed in the HeyrovskyForejt technique. d complication with both techniques i s the fact that the potential is driven to solvent or other break down potential on each half-cycle and products of these reactions can complicate interpretation of results. Sturrock (164) has improved by switching constant current froiii anodic to cathodic and vice versa a t preselected potentials rather than a t constant time increments. He also employs dE/dt us. E readout in the manner of the Heyrovsky-Forej t technique. His method differs from Herman and Bard’s cyclic chronopotentionietric one (76-78) only in the forin of the readout. Kheress Herman and Bard have emphasized measurement of sivitching tinies for quantitative kinetic studies, Sturrock’s mode of operation seems better suited to qualitative mechanistic studies. The reviewer still prefers the cyclic (triangular wave) potential method for qualitative work because it seems easier to instrument and more convenient to apply a t the DME. Herman and Bard’s apparatus (78) with electronic switching of current offers substantial advantage over mechanical switching (129, 140) which has relatively low switching rates. Large amplitude potentiostatic relaxation is directly competitive with chronopotentiometry for studies of chemical kinetic phenomena and adsorption. With complicated systems constancy of potential should be a distinct advintage in simplifying interpretation; yet the vast preponderance of studies is performed chronopotentiometrically. Instrumentation is more of a problem in potentiostatic work, but can be readily devised for the time range to which chronopotentiometry is applicable. While the theory of the potentiostatic relaxations for complicated mechanisms has not received much attention,
the theory of polarographic limiting currents for such cajes is voluniinous and can be readily trans1 with considerable siniplifi man and Pence (25) have given thpory for second order chemical reactions. Rek, Rijnen, and Sluyters (146) have considered diffusion limited linear adsorption. hnson ( 7 ) has applied integral readout to potentiostatic step relaxations for examination of adsorption. Laitinen and Chambers (111) h a r e dizcuswd sources of difficulty in interpreting adsorption data n-ith ~iarticularreference to Anson’s work and their own earlier chronopotentionietric studies. Schwartz and Shain (154) h a w allplied the potentiostatic analoguc of current reversal chronopotmtionietryusing a double stell-to the situation in which it is particularly uqcful, a cheiiiical reaction folloniiig charge-transfer, Soos and Linganc (162) h a r e given a theory of edge effects at d k k electrodes on potentiostatic results. Pulse polarography is a variant of the potentiostatic niethod invented by Barker and coworkm (15) and useful in anal iants are possible. I method a potential pulse is applied near the end of drop-life a t a DJIE to a system initially a t a potential at’ which no reaction occurs. Successive pulses (for successive drops) apply successively larger potentials. Readouts are similar in form to ordinary polarograms, but currents are higher, and electronic gating eliminates double 1 Ter charging current so that sensitivity enhanced. I n the derivative form, pulses of constant, amplitude are superimposed on normal d.c. potential scans again near the end of drop-life. Here again charging is eliminated and current is enhanced, but readout is roughly derivative in forni to normal polarography \vhich improved resolution. Recently, I3rinknian and Los (28) have considered the theory of the integral technique. Parry and Osteryoung (132)have discussed various pract’ical factors involved in application of both the integral and derivative techniques. The virtues of the technique are most apparent in trace analysis; at routine polarographic concentrations, the instrumental simplicit,y of conventional polarography is strongly in its favor. OTHER METHODS
Of systems for providing forced convective flow of reactant to the electrode, the rotating disk remains the most popular, but Arvia and coworkers (10) have examined mass transfer under turbulent flow conditions a t rotating cylindrical electrodes. These workers have also examined tubular electrodes under VOL. 30, NO. 5, APRIL 1966
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laminar flow conditions (19). Ross and Wragg (149) have studied annular electrodes under both laminar and turbulent flow conditions. Jordan and coworkers (38) have continued their kinetic studies. Fried and Elving (68)have discussed transient response5 to linear potential scan a t a rotating disk These workers have also given an experimental study of the same subject (63). Hale (72) has given a more rigorous treatment of transient and steady state responses t o galvanostatic transients. Kholpanov (96) and Xlbery ( I ) have considered migration currentq. Hintermann and Suter (80) have described instrumentation for rotating diqk studies. Bruckenstein aiid Johnson (33) have performed coulometric titrations within the hydrodynamic layer at a ring disk electrode. I n effect the technique e+ tends the sensitib ity of voltameters at the disk electrode t o species nhich do not react rapidly electrochemically, but react rapidly chemically with species which can be generated electrochemically. Transit times for species to be transported from disk to ring are discussed by Bruckenstein and Feldman (32). Tens of milliseconds seem to be the order of half-lives of species examinable a t present. Other secondary electrode systeiiis for examining products formed by electrolysis a t a primaiy iiorking electrode, include a double ring system proposed by Heusler and Schurig (79) aiid an unstirred system by Valenta and Koryta (168) for show work. I n a related area, Anderson and Reilley (4) have discussed steady state electrolysis between electrodes separated by a very thin solution layer. Delahay and coworkers (48, 49, 163) have studied techniques based upon measurement of electrode potential at open circuit with varying electrode area. Variation of area tends to change the charge-density of the electrode and hence its potential. I n the presence of an electro-active couple this tendency is opposed by faradaic reaction. Since no net current flows, techniques based on this principle should be applicable to solutions of Iery high resistance \vhich are inaccessible by more conventional means. h number of techniques were proposed and apparently examined, but experimental results have been presented thus far only for a system employing a streaming mercur) electrode. A related technique is the “electrode scrape” method studied by Eyring and coworkers (3, 138). Scraping an electrode to make a completely fresh surface produces a potential transient, the peak of which it is proposed corresponds to the potential of zero change. Another ingenious “non-electrical” electrical technique appai ently useful for trace analysis works as follows (31).
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A known amount of silver is deposited on an inert electrode which is then exposed to an unknown solution of oxidizing agent. Chemical stripping is mass transfer controlled and can be followed potentiometrically . For those who read reviews such as these and wonder whether anything worth doing is left, Oppenheim (128) has proposed a method for determining that old thermodynamics bug-bear the single electrode potential. It awaits merely a practical method of implementation. LITERATURE CITED
(1) Albery, W. O., Trans. Faraday SOC. 61. 2063 (19651. (2) Anderson, L.’B., hlacero. D. J., AXAL. CHEM.37, 322 (1965). (3) Anderson, T. S . , Perkins, R. S., Eyring, H., J . Am. Chem. SOC.,86, 4496 11964). (4) Anderson, L. B., Reilley, C. N., J . Electroanal. Chem. 10, 295 (1965). (5) .4ngerstein-Koslowska, H., Conway, B. E., J . Electroanal. Chem. 7,109 (1964). (6) Anson, F. C., AN.AL. CHEM.36, 521 (1964). (7) Ibid.. I). 932. (8j Anson, F. C., Osteryoung, R. A,, Ibid., p. 2511. (9) Ariel, M., Eisner, U.,Gottesfeld, S., J . Electroanal. Chem. 7, 307 (1964). (10) Arvia, A. J., Carroaza, J. S. W., hlarchiano. S. L.. Electrochim. Acta 9. 1483 (1964‘). (11) Ashley, J. W., Reilley, C. S . , J . Electroanal. Chem. 7, 253 (1964). (12) Aylward, G. H., Hayes, J. W., ANAL. CHEY.36, 2218 (1964). (13) Ibzd., 37, 195, 197 (1965). (14) Aylward, G. H., Hayes, J. W., J . Electroanal. Chem. 8 , 442 (1964). (15) Barker, G. C., Gardner, A. W., Z. Anal. Chem. 173, 79 (1960). (16) Bailer, H. H., Australian J . Chem. 17, 591 (1964). (17) Bauer, H. H., Foo, D. C. S., Ibid., p. ,510. (18, Bauer, H. H., Foo, D. C. S.,J . Electroanal. Chem. 1, 392 (1964). (19) ,Bazan, J. C., Arvia, A. J., Electrochzm. Acta 9, 17, 667 (1964). (20) Berge, H., Jeroschewski, P., 2. Anal. Chem. 212, 278 (1965). (21) Biegler, T., Laitinen, H. A., ANAL. CHEM.37, 572 (1965). (22) Birke, Ii. L., Roe, D. K., Ibid., p. 450. (23) Ibid., p. 465. (24) Booman, G. L., Holbrook, W. B., Ibid., p. 395. (25) Booman, G. L., Pence, D. T., Ibid., p. 1330. (26) Breiter, hl. W., J . Electroanal. Chem. 7, 38 (1964). (27) Breiter. 11.W.. J . Electrochem. SOC.. 112. 845 (1965’1. ’ (28) Brinkman, A. A. A. M., Los, J. hi., J . Electroanal. Chem. 7, 171 (1964). (29) Bro, P., J . Electrochem. SOC.111, 1104 (1964). (30) Buchanan, E. B., Alecarten, J. B., ANAL.CHEW.37, 29 (1965). (31) Bruckenstein, S.,Bixler, J. W., Ibid., p. 786. (32) Bruckenstein, S., Feldman, G. A., J . Electroanal. Chem. 9,395 (1965). (33) Bruckenstein, S., Johnson, D. C., ANAL.CHEM.36,2186 (1964). (34) Bruckenstein, S., Rouse, T. O., Ibid., p. 2039. (35) Buck, R. P., Ibid., p. 947. (36) Bucur, R. ST., Covaci, O., Miron, C., J . Electroanal. Chem. 8 , 277 (1964). ,
I
(37) Bump, D. D., Remick, A. E., J. Electrochem. SOC.11 1 , 981 (1964). (38) Cat
