On Statistical Thermodynamics of the Electric Double Layer at A Polarizable Liquid/Liquid Interface

The fundamental of Statistical Thermodynamics for electrical double layer at the interface between two immiscible electrolyte solution（ITIES） are discussed.
According to MVN model,the ITIES was represented by that the two space charge regions are separated by an inner layer of the oriented solvent molecules. Assuming that the ions were allowed to penetrated into the compact solvent layer over some distance, then the grand canonical partition function of the inner layer at ITIES can be given,in which the mean field approximation is employed to estimte the interactive patential energy of the system,including the dipole-dipole, dipold-ion and ion-ion interaction.
The thermodynamics properties of system,such as inner layer configuration entropy （△S_m）, differential capacity（C₁） and others for the L/L interface are derived,and the fitting curves of the △S_m/or C₁ as a function of the surface charge densily （σ^m） to an image W/O interface are given. In the grand canonical ensemble theory,the inner layer differential capacity （C₁） or which reciprocal capacity （I/C₁）can be expressed by the surface charg fluctuation/or by the fluctuation of potential drop （Δψ₁） across the inner layer at ITIES.