A multilayer model of a solid-regular solution interface

Abstract

A multilayer model of the interface between a solid and a regular solution has been developed by treating the solution phase in the grand canonical ensemble. The partition functions necessary for the evaluation of the grand partition function are obtained using either the quasi-chemical or Bragg-Williams approximations. The equilibrium concentration profile normal to the interface is then found from the maximum term in the multiple sum for the grand partition function. The adsorption, surface tension, and heat of wetting for the multilayer model are derived, and methods of obtaining the model parameters from experimental data are suggested. A comparison has been made between the quasi-chemical and Bragg-TVilliams approximations for the multilayer model. The monolayer model is also discussed, and compared with the multilayer for both the solid-regular solution and the low-density vapour-regular solution interfaces. It is shown that the monolayer model can often be fitted to the multilayer model by a suitable choice of parameters. It is concluded that in the absence of absolute methods of obtaining the area of the solid-solution interface, the experimental data may not provide outright support for the multi- layer model, but internal inconsistencies discourage the use of the monolayer model. There is an increasing interest in the properties of the interface between a solid and a non-electrolyte solution.1 The majority of experimental studies of this type of interface have been restricted to the measurement of adsorption, but in some instances the heat of wetting as a function of bulk phase composition has also been determined. In most cases, the complexity of the liquid phase and the surface region has allowed only a qualitative interpretation of the experimental results. Neverthe- less, there have been a few investigations in which solutions of comparatively simple molecules have been used and the experimental results have been treated in a quantitative manner.2-5 Some simple monolayer models of the solid-solution inter- face have been proposed for which the structure of the solid phase has been ignored, Division of Applied Chemistry, CSIRO Chemical Research Laboratories, Melbourne, Vic. 3001. Kipling, J. J., "Adsorption from Solutions of Non-Electrolytes." (Academic Press: London 1965.) Billet, D. F., Everett, D. H., and Wright, E. H. &I., Proc. chem. Soc. 1964, 216. 3 Blackburn, A., and Kipling, J. J., J. chem. Soc., 1954, 3819. 4 Blackburn, A., Kipling, J. J., and Tester, D. A., J. chem. Soc. 1957, 2373. 5 Wright, E. H. &I., Trans. Paraday Soc., 1966, 62, 1275. Aust. J. Chem., 1968, 21, 827-51