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2000b; Chitra and Smith, 2001a; Chitra and Smith, 2001b; Lin and Wood, 1996). In this formalism, the partial molar volume at infinite dilution can be calculated as V1(G G0 ) (4.7) v uv vv where Guv and Gvv are solute-solvent and solvent-solvent fluctuation integrals, respectively. The subscript u refers to the solute and v to the solvent. The superscript 0 and refer to the pure solvent or infinitely dilute co-solvent, respectively. These fluctuation integrals are a function of pair correlation functions (gij(r)): G 4 g (r)1r2dr (4.8) ij 0 ij Thus partial molar volumes depend on the relative strengths of the solute-solvent and solvent interactions. Pair correlation functions can be calculated directly from molecular simulations. The KB theory relates fluctuations in particle densities in the grand canonical ensemble to thermodynamic properties of mixtures. The pair correlation function or radial distribution function (RDF) can be calculated through simulations in canonical ensemble. The values of the integrals though RDFs can be obtained for a. solvent-solvent b. solvent-solute c. solute-solute The same integrals can be calculated for solvent and co-solvent, for mixture where we don’t have diluted solutions with introducing some modifications. 4.5.4 Isothermal Compressibility The way in which the volume of a material decreases with pressure at constant temperature is described by the isothermal compressibility, κT. Isothermal compressibility is one on the important properties of the fluid, which gives very 65PDF Image | MOLECULAR SIMULATION STUDIES IN THE SUPERCRITICAL REGION
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