328 ELECTROANALYTICAL CHEMISTRY AND INTERFACIAL ELECTROCHEMISTRY Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands

SHORT C O M M U N I C A T I O N S

The Lippmann equation. Comments on part X X I I of the paper "On the impedance of galvanic cells", by Timmer, Sluyters-Rehbach and Sluyters

In this note I wish to comment upon a statement in the paper indicated, which in my opinion is at variance with the history of electrocapillarity theory. According to TIMMER, SLUYTERS-~I~EHBACH AND SLUYTERSI:

"For an ideally polarizable electrode, the well-known Lippmann equation relates the charge, q, on the electrode to the interfacial tension, 7, by

d~, d E = q (3)

This equation cannot be used for a non-ideally polarized electrode. For an ideal re- versible metal-metal ion electrode, the modified Lippmann equation reads:

d E = q + n F F o (4)

The above authors cite MOHILNER'S paper ~, which contains the following statement regarding eqn. (4) : "This equation is the analog for a reversible electrode of the clas- sical Lippman equation for an ideal polarized electrode". Thus the paper under review and MOHIL•ER'S statement seem to infer that the "classical" Lippmann equation needs to be corrected to be applicable to the case of a non- ideally polarized electrode. Of course, the question as to which equation should be called the Lippmann equation is a mat ter of convention. I t seems to me, however, that it would be more correct to call so the equation which was actually derived by Lippmann. That equation is appli- cable to any electrode, since according to LIPPMANN 3 the quanti ty to which the deri- vative - dv/dE is equal is the "capacit6 61ectrique de l'unit6 de surface (I mm carr6)

difference 61ectrique constante", i.e., the amount of electricity to be applied to the electrode for its potential to remain unchanged with a unit surface increase. LIPPMANN did not consider the question of polarizability or non-polarizability of an electrode, but it is evident that LIPPMANN'S capacity at constant potential is q in the case of an ideally polarized and q + nFFo in the case of a reversible electrode.

Apparently, LIPPMANN'S name was first erroneously associated with the con- cept of a perfectly polarizable electrode (an equivalent of ideal polarizability) by KOEI~IG 4. According to I(OENIG : "Since its discovery, two thermodynamic theories of the electrocapillary curve have been advanced. The first, due chiefly to LIPPMANN,

HELMHOLTZ AND PLANCK, is that of the so-called "perfectly polarizable electrode" . . ." This statement contains a second error, since PLANCK'S definition of a "perfectly polarizable" electrode 5, as I have already pointed out 6, unlike KOENIG'S definition (which is widely used now) presumed not the impermeabili ty of the electrode- solution interface for charged particles, but an unambiguous dependence of the elec- trode state on the amount of electricity passed through it. In fact, according to PLANCK (loc. cit., p. 414): "Die einzige Variable des Zustandes: die durch die Electrode

j . Electroanal. Chem., 18 (1968) 328-329

SHORT COMMUNICATIONS 329

hindurchgegangene Electricit~tsmenge E wollen wir als die "Ladung" der Electrode bezeichnen, ohne damit etwas t~ber eine Aehnlichkeit der Electrode mit einem elec- trostatischen Condensator aussagen zu wollen. Insbesondere soll dadurch nichts tiber einen Zusammenhang yon E mit der Menge der an beiden Seiten der ElectrodenflSche lagernden, durch die Potentialdifferenz bedingten, freien Electricit~ten behauptet werden".

In conclusion, I would like to point out that the second term in the right-hand side of eqn. (4) was taken into consideration and its value for the case of the rever- sible metal -metal ion electrode was discussed from various points of view in the litera- ture on the electrocapillarity theory, long before MOHILNER'S publication, as, for example, in refs. 7 and 8.

Institute of Electrochemistry, Academy of Sciences of the USSR, Moscow (USSR)

A. N. FRUMKIN

I ]3. TIMMER, M. SLUYTERS-REHBACH AND J. SLUYTERS, J. Electroanal. Chem., 15 (1967) 343. 2 D. MOnlLNER, J. Phys. Chem., 66 (1962) 724. 3 G. LIPPMANN, Ann. Chim. Phys. (5) 5 (1875) 494. 4 F. KOENIG, dr. Phys. Chem., 38 (1934) I I I . 5 M. PLANCK, Ann. Physik, 44 (z89I) 385 . 6 A. FRUMKIN, O. PETRY AND 1~, MARVET, J. Eleetroanal. Chem., 12 (1966) 504. 7 KROGER, Nachr. Ges. Wiss. G6ttingen (19o4) 33; Z. Etektrochem., 19 (1913) 681. 8 A. FRtlMKIN, Phil. Mag., 4 ° (192o) 363; Z. Physik. Chem., lO3 (1923) 55-

Received February I4th, 1968

j. Electroanal. Chem., 18 (1968) 328-329

Two electrons v s . ECE in stationary electrode voltammetry

An interesting situation exists in the area of stationary electrode vol tammetry at present - - theory is far outstripping the experimental data. For several years, bits and pieces of the theory were to be found in the literature 1 but it was only recently that the qualitative and quantitat ive aspects of stationary electrode vol tammetry have been compiled and clearly elucidated in an exceptional series of papers by SHAIN and co-workers 1-6. Experimental verification of several portions of the derived theory have also been given in this series3,4, ~-~. With this elegant groundwork, others have recently built up the theoretical and experimental aspects of the field 9-2°. Stationary electrode voltammetry, and in particular cyclic vol tammetry (CV), is extremely useful in the elucidation of electrode mechanisms and the literature cited has been pointed in this direction. Many facets of the theory are best illustrated by practical examples and this note is intended for that purpose.

In the routine use of CV for qualitative studies of organic reactions, it would be very useful to be able to distinguish whether an oxidation or reduction process involves a fast ECE (electron transfer - chemical reaction - electron transfer) mecha- nism or is simply a two-electron transfer. This can usually be ascertained from the qualitative picture obtained from cyclic polarograms run at varying scan rates, but quanti tat ive data relating peak currents to the proposed mechanism are also desirable.

j. Electroanal. Chem., 18 (I968) 329-332