A New Approach to Interfacial Energy. 3. Formulation of the Absolute Value of the Solid−Liquid Interfacial Energy and Experimental Collation to Silver Halide Systems

Abstract

A new theoretical formula for the absolute value of the interfacial energy of the solid−liquid interface has been derived on the basis of the fundamental theory of interfacial energy described in J. Colloid Interface Sci. 1996, 181, 259; 1996, 183, 299. Namely, the intrinsic specific interfacial energy of a solid−liquid interface without adsorption is given by γ = − N σ λ kT ln x ( ∞ ), where N σ is the surface density of the surface monomers of the solid, λ is the ratio of the number of open bonding sites of a surface monomer to that of a free monomer, k is the Boltzmann constant, T is the absolute temperature, and x ( ∞ ) is the solubility of the bulk solid in terms of mole fraction of the monomers in the liquid phase against the total mole numbers of the solution components including the solvent molecules. Here, “monomer” refers to the minimum subunit of the solid such as AgCl, AgBr, etc. The formula has been collated to the experimental results of γ for AgCl, AgBr, and AgI, determined by potentiometric measurement of the size-dependent solubilities of these silver halide particles with the Gibbs−Thomson equation. The experimental results were in excellent agreement with the theoretical values for the silver halides. Also, some fundamental problems were found to be involved in Tolman's theory for size dependence of γ, and it has been deduced that γ must be independent of particle size, as has been confirmed by experiment.