00134686/90 13.00+0.00 Pergamon Press plc. zyxwvutsrq SURFACE TENSION AT THE ELECTROLYTE SOLUTION-METAL ELECTRODE INTERFACE-III. POLYVALENT AND NON-SYMMETRICAL ELECTROLYTES A. M. GABOVICH and A. I. VOITENKO Institute of Physics, Academy of Sciences of the UkSSR, 252650, Kiev-28, Prospekt Nauki 46, U.S.S.R. (Received 17 January 1989) zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPON Abstract-The dependences of excess non-specific adsorption I- and extra Coulombic contribution Acr to the surface tension on molecule concentration N are calculated for the metal electrode-non-symmetrical (symmetrical polyvalent) electrolyte solution interface. The dependences T(N) and Au(N) are non-mono- tonous and change their signs from positive to negative and vice versa respectively. 1. INTRODUCTION In previous papers[l-31 the Coulombic contribution Aa to the surface tension at the 1: 1 electrolyte solution-metal electrode interface was calculated for the point of zero charge. The existence of Au is due to the polarization forces (image forces)[4] which lead to an excess non-specific surface adsorption I-* for ions of both kinds. Consideration of the spatial dispersion of static dielectric function c(q) for both media[4,5] was a substantial factor for the calculations[ l-31. The theory[l-31 is generalized in this work to treat poly- valent and non-symmetrical electrolytes. A consideration of ions with charge zie (lzil > 1, e is the elementary charge) comes across some difficult- ies-violation of conditions necessary for the validity of assumptions embodied in the basis of calculations[l-31. Namely, during various stages of the consideration the smallness of ion concentration Ni in a solution was suggested and the linearization of the Poisson-Boltzmann equation for an electrostatic potential was carried out. We shall analyse this subject below and indicate using these approximations the corresponding limitations for Ni. On the other hand, if the electrolyte is non-sym- metrical the charged double layer appears near the interface, so that the electrostatic potential q(x) is not zero near the interface even at the point of zero charge[6,7]. In this work the dependences of adsorptions I-* and image force contribution Aa on solute molecule con- centration N were calculated. It was shown that these dependences are non-monotonous, that agrees quali- tatively with experiments[S, 93. Both analytical and numerical methods were used in the calculations. 2. BOUNDARY PROBLEM SOLUTION FOR THE ELECTROSTATIC POTENTIAL The spatially non-homogeneous system under con- sideration (Fig. 1) consists of a metal electrode (x < 0) and two-component (generally speaking, non-sym- metrical) electrolyte solution (x > 0). The interface coincides with the plane YOZ. The metal screening properties are described in the quasiclassical Thomas-Fermi approximation and are characterized by the dielectric constant Ed and effective wave num- ber Kh( =(6nn,eZ/@,,)‘/*, where nM is a concentra- tion and E,, is a Fermi energy of metal electrons. The screening properties of the solution are treated using the restricted primitive model[ lo] with point electro- lyte ions, so that there are two relevant parameters: the solvent dielectric constant E, and the inverse Debye-Hiickel screening radius: > 112 . (1) Here vi= N,/N are the stoichiometrical coefficients, LB =e2/c,k,T is the Bjerrum length, T is the absolute temperature, k, is the Boltzmann constant. The additional energy E,,(x) of the ith ion at the point x of the non-symmetrical electrolyte solution will be described (in the spirit of [6]) by the sum of two terms: the image force potential energy W,(x) and the electrostatic potential energy ez,cp(x) mentioned above. Such a separation is an approximation. It is correct if one can neglect the interconnection between q(x) and W,(x). The interdependence of these quant- ities is due to the x-dependence of K, near the interface Fig. 1. The system under consideration: metal electrode (x ~0, Hg)/two-component electrolyte solution (x >O). 545