A Molecular Theory of Solutions at Liquid Interfaces

Consideration of a liquid interface that fluctuates requires proper account of mechanical and chemical balance between the phases. The description of spatially inhomogeneous fluids can be performed on the basis of Bom-Green-Yvon (BGY) integro-differential equation [14,15] 

Chandler and Andersen introduced the site-site Omstein-Zemike (SSOZ) integral equation for the radial correlation functions between pairs of interaction sites of polyatomic species [14,27], 

The parameter r can be optimized for thermodynamic consistency between the virial and compressibility routes to the free energy of the system. As discussed in Section 5.3.2, the KHM closure (7) brings about an additional long-range term in the direct correlation functions in the critical regime. 

The RISM integral equations in the KH approximation lead to closed analytical expressions for the free energy and its derivatives [29-31]. Likewise, the KHM approximation (7) possesses an exact differential of the free energy. Note that the solvation chemical potential for the MSA or PY closures is not available in a closed form and depends on a path of the thermodynamic integration. With the analytical expressions for the chemical potential and the pressure, the phase coexistence envelope of molecular fluid can be localized directly by solving the mechanical and chemical equilibrium conditions. 

FIGURE 5.1. Liquid/vapour coexistence curves of SPC water (solid line) and OPLS methanol (dashed line) following hrom the RISM-KH theory. Molecular simulation results for water [45] and methanol [46] (open circles and squares, respectively) and critical point extrapolations (filled symbols). 

KH approximation (6) includes a non-linear, quadratic term in addition to the linearized MSA form, 

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A. Kovalenko and F.FFTa.ta, in Interfacial Nanochemistry Molecular Science and Engineering at Liquid-Liquid Interfaces, H. Watarai, N. Teramae, and T. Sawada (Eds.), Kluwer Academic/Plenum, New York, 2005, p. 97, A Molecular Theory of Solutions at Liquid Interfaces. 

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