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Analytical Electrochemistry: Theory and Instrumentation of Dynamic Techniques David K. Roe D e p a r t m e n t of Chemistry, P o r t l a n d State University, Portland, Ore. 97207
Two years ago, this review appeared under the title “Electrochemical Relaxation Techniques” ( 8 A ) ; the title originated by William Reinmuth in 1964. Since then, much of analytical electrochemistry has been concerned with the development and application of relaxation techniques. As a result, there has been an increasing amount of overlap with the “Polarographic Theory, Instrumentation, and Methodology review. To meet the understandable demands of the editor to keep these reviews succinct, Peter Kissinger and I decided to divide and review the territory according to the new titles. Thus, applications, noninstrumental details, and results will be found primarily in the accompanying review by Kissinger. A number of publications may be cited in both reviews, since many authors have adopted the following format for their articles: 8R
A N A L Y T I C A L C H E M I S T R Y , V O L . 46, N O . 5 , A P R I L 1974
i) derive a few equations; ii) describe the new or modified instrumentation that permits the necessary measurements; iii) make a series of measurements on a model system (usually cadmium). Consequently, we must wait until we can read each other’s review to assess the degree to which we have saved space and the reader’s time. A change has also been made in the organization of this review. Instead of emphasizing the technique-potentiostatic, rotating ring-disk electrode, etc.-the general headings are phenomenological. Although this is contrary t o the way that many of us think about electrochemical methods, it does allow a rapid assessment of progress in an area having a common chemical or physical basis. And that is why reviews are written.
David K. Roe is associate professor at Portland State University, Portland, Ore. He received his AB degree from Pacific Lutheran University in 1954, the SM degree from Washington State University in 1956, and the PhD degree from the University of Illinois in 1959. After a postdoctoral year in Stuttgart, Germany, he was with the Corrosion Department of Shell Development, Emeryville. Calif., for two years and then was an assistant professor in the Chemistry Department at MIT and associate professor at the Orecon Graduate Center. His research interests are in electrochemistry and its analytical applications and In electronic instrument design.
The articles cited in this review were selected from approximately lo00 references related to the title topic. The sources were Chemical Abstracts and the Interface Newsletter, December 1971 to December 1973. Up until 1968, the growth of analytical electrochemistry literature was reported (SA) to be exponential. A change in the growth constant seems to have occurred last year, judging from the number of citations dated 1973. Perhaps some past contributors have moved into related areas. Even so, analytical electrochemistry is becoming mature in theory, b u t it is still a plaything in instrumentation. The paucity of good, commercial instruments definitely hinders its adoption outside of the specialist’s laboratory and impedes its development within. No, polarography is not dead, to answer the question posed by Florence (3A), and neither are its many offsprings. Together, under the general term of voltammetry, they are the most active part of analytical electrochemistry included in this review, with demonstrated utility in many scientific disciplines and potential for much more. Of general interest is Kortuem’s ( 4 A ) “Textbook of Electrochemistry,” now in its fifth edition. In the new series, “Techniques of Electrochemistry,” will be found extensive reviews on overpotential measurements ( 5 A ) and nonelectrochemical methods for the study of electrode processes @ A ) . A text on the interfacial aspects of electrochemistry was recently completed (7A) and one on transfer coefficients ( I A ) . Other reviews are included in the following sections.
MASS TRANSPORT Theoretical descriptions of mass transport, either by diffusion or influenced by hydrodynamic flow, provide the basis for quantitative determinations of solution concentrations by analytical electrochemical measurements. Additionally, diffusion coefficients and/or the number of electrons involved in the overall electrode reaction may be determined, and these models are the starting point for kinetic modifications. The many different models which have been treated since the days of Ilkovii: differ in the electrode-solution geometric and stimuli (potential or current), and it might be presumed that all useful situations have been explored. During the review period, however, there have been several interesting and remarkable contributions to this subject, including semiintegral electroanalysis, finite diffusion, and charge step voltammetry. After several years of development of a new mathematical method for the solution of diffusion problems, Oldham (39B) announced the possibility of a new technique, termed semiintegral electroanalysis. In the further development of the theory and its verification (21B), it was shown that the semiintegral of the current-time response under controlled potential changes, produces a quantity which is proportional to the concentration of the species undergoing electron transfer. Two things are unique: the semiintegral is independent of the path between the initial and final potentials, provided these points meet some ordinary requirements and, further, the semiintegral rapidly approaches a constant value as the surface concentration approaches zero. Thus, the method is independent of the form of the excitation signal (which may be a nonlin-
ear potential ramp) and also of solution resistance, provided the required final potential is attained in reasonable time. In a practical device, a simple meter would suffice to read a quantity proportional to concentration. Initially, the semiintegral was obtained by summing a series; however a n analog method was developed (40B) which has an output in units of amplomb/volt. (Amplomb is the name given to the quantity having the dimensions of ampere secl/2; the designation “oldham” would be less confusing.) A number of properties of plots of amplomb us. potential (termed neopolarograms) have been derived (20B) and demonstrated for various degrees of reversibility of electrode reactions. Oldham’s involvement in the mathematics which led to this method is extensive; a text entitled “Fractional Calculus” will be published soon. Imbeaux and Saveant (26B) have developed in an extensive manner, a technique called convolution potential sweep voltammetry. the convolution integral is applied to the current by a digital computer and amounts to the same process as described by Oldham. Their interest, however, is in elucidation of mechanisms of electrode reactions, and many reaction schemes are described, including multiple waves ( 3 B ) . Finite diffusion has usually been avoided in analytical electrochemistry because of mathematical complexities and because the two extremes-infinite diffusion and thin layer linear diffusion-were usually obtainable by proper cell design. Keller and Reinmuth (27B) have found a way to express current for linear potential scans with finite diffusion in terms of an exponential series. The range of cases considered embraces many previously derived or calculated results and is applicable to diffusion complicated by other rate processes. An immediately useful result is that experimental conditions of scan rate and s o h tion layer thickness can be related such that agreement with a limiting model can be ensured. If for example, the solution layer thickness is less than 0.2 d D R T / n F u ( u is volts/sec.), then agreement with the as,sumption of linear diffusion holds to
