NOV.20,1962
_ b S O R P T I O S OF
NEUTRAL SUBST-INCE AT METAL-ELECTROLYTE ISTERFACE
hampered by the absence of quantitative knowledge of the other terms which affect A F for the unfolding process. The general theory, in the context of which our Aiu terms have been placed, is useful as a framework for assessing the importance of hydrophobic interactions, but i t is too crude to permit analysis of those aspects of protein denaturation which do not directly arise from hydrophobic interactions.
[CONTRIBUTIOS FROM
THE
42447
Acknowledgments.-The author is greatly indebted to Drs. J. T. Edsall, K. Kauzmann and I. M. Klotz for reading and criticizing an earlier draft of this paper. He also acknowledges the support of this work by research grant (2-17477, from the Xational Science Foundation, and by research grant A-4576, from the National Institute of Arthritis and .Metabolic I )iw:tws9 I ‘iiitetl States Public Health Service.
COATES CHEMICAL LABORATORY, LOUISIANA STATE GSIVERSITY, BATONROUGE3, LOUISIANA]
Rate Equation for Adsorption of a Neutral Substance at a Metal-Electrolyte Interface BY PAULDELAHAY AND DAVIDM. MOHILNER’ RECEIVED APRIL9, 1962 An equation is derived for the rate of adsorption of a neutral substance a t a metal-electrolyte interface for processes obeying the logarithmic Temkin isotherm. A recent investigation in this Laboratory has indicated that this isotherm is obeyed over a rather wide range of concentrations by a number of organic substances of varied structure .Idsorption kinetics is characterized by an exchange rate zia which is expressed in terms of a standard rate constant k o , the activity of adsorbed species in solution a , the charge-dependent part AG‘ of the standard free energy of adsorption AGO, a c o v r r n ~ e parameter (not the coverage) X (0 < X < 1)and a charge parameter p (0 < p < 1). Variations 6(AGq) with the charge density q on the electrode can be determined experimentally from the dependence of AGO on q. More conveniently 6( A @ ) is obtained from the variations of the potential E with In a a t constant q f b E / b In a a t constant q is the Esin and Markov coefficient.) The parameters X and p are determined from ( b In oo/bIn a ) a t constant q and ( b In a 0 / 3 A G ‘ ~ a) t constant u The adsorption rate is expressed in terms of zio, the parameter b characterizing the isotherm, X, p, the variation 6(AG‘i) of AGq and the variation 6I’ of the surface concentration I’ which result from a change of q. Correction for mass transfer and for the double layer structure is indicated. The principle of a new coulostatic method for the measurement of yo is discussed, and correlation of the present theory with other methods for ao determination is outlined. The basic equation for adsorption rate reminds one of the Butler, Erdey-Gruz, Volmer equation for electrode kinetics; no is the counterpart of the exchange current, and the charge parameter p is analogous to the transfer coefficient in electrode kinetics.
The thermodynamics of adsorption of a neu- the logarithmic Ternkin isotherm is approximately tral substance a t a metal-electrolyte interface, obeyed for a number of organic neutral substances which is based on the Gibbs adsorption isotherm, of varied structure over a fairly wide concentrais well understood but hardly anything is known tion range. (iii) The equations given by Temkin4 about adsorption kinetics, except for purely dif- for the rates of adsorption and desorption of a gas fusion controlled processes. ?. The kinetic prob- on a solid apply (see below). (iv) The influence lem is attacked here for adsorption of a neutral of the charge density on rates of adsorption and substance obeying the logarithmic Temkin iso- desorption can be expressed in terms of a charge therm,4 and a basic equation is derived which parameter defined below and the charge-dependexpresses the rate of adsorption as a function of ent part of the standard free energy of adsorption. experimental quantities. This equation appears to This idea is novel, to our knowledge, and is the key be quite general as will be shown below and may to the following treatment. Any surface process serve as a basis for the development of adsorption subsequent to adsorption will be neglected or kinetics a t metal-electrolyte interfaces. The key assumed to be sufficiently fast and consequently ideas are: (i) I n the thermodynamic analysis of not rate-determining. A more general treatment adsorption a t a metal-electrolyte interface, i t is of adsorption processes followed by a slow surface often convenient to choose the charge density q process is now being considered. as the independent electrical variable rather than the electrode potential E.5 The charge density Rate Equation for the Adsorption-Desorption Process q, rather than E , is the “natural” electrical paramActivities and Isotherm.--U~e represent the adeter in the treatment of adsorption, whereas the opposite holds for electrode processes. (ii) It is sorption of a neutral substance 0 a t a metalinferred from recent work in this Laboratory that electrolyte interface by (1) Postdoctoral fellow, 1960-1962. (2) For a review, cf. R. Parsons, Chap. 1 in “Advances in Electrochemistry and Electrochemical Engineering,” Vol. I, edited by P. Delahay, Interscience-Wiley, Kew York, K. IT., 1961, pp. 1-64. (3) Adsorption kinetics with diffusion control has been worked o u t for linear a n d Langmuir isotherms. T h e main significance of this work resided in showing t h a t diffusion-Controlled adsorption can be slow. This point had been overlooked in a number of investigations, especially with the dropping mercury electrode. (4) Af. I. Ternkin, Z h w . fiz. Khim., 16, 296 (1941); translation available. The logarithmic Temkin isotherm, often referred t o as a “Temkin isotherm,” is only a particular f o r m of the more general equation derived by Temkin. ( 6 ) R . Parsons, T v n n r . Raradar S o c . , 51. 1.518 (195.5)
RT/p, the first exponential is negligible in comparison with the second. Consequently, a plot of In v t - o against 6(AGq) for either of these conditions is linear (Fig. 31, i.e., one has in adsorption kinetics the analog of Tafel lines is electrode kinetics. The extrapolated lines intersect a t a point whose abscissa corresponds to 6(AGq) = 0 and whose ordinate is In DO. Experimental determination of these lines may be quite impossible when uo is high and adsorption is essentially diffusion controlled, even for very short times, for the rather large values of S(3Gq) which are required. Extrapolation of rates t o time t = 0 is then very uncertain or impossible. Further, variations of potential corresponding to 6(AGq) may be so large as t o cause the electrode to operate under conditions in which it is no longer an ideal polarized electrode. (ii) For small departure froin equilibriutn, eq. 29 can be linearized in t h e form
-
=
llL." 0
- (7,".1
