Quasi-chemical Theory for the Statistical Thermodynamics of the Hard Sphere Fluid

Lawrence R. Pratt; Randall A. LaViolette; Maria A. Gomez; Mary E. Gentile

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Quasi-chemical Theory for the Statistical Thermodynamics of the Hard Sphere Fluid

Lawrence R. Pratt·Randall A. LaViolette·Maria A. Gomez·Mary E. Gentile

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Abstract

We develop a quasi-chemical theory for the study of packing thermodynamics in dense liquids. The situation of hard-core interactions is addressed by considering the binding of solvent molecules to a precisely defined `cavity' in order to assess the probability that the `cavity' is entirely evacuated. The primitive quasi-chemical approximation corresponds to a extension of the Poisson distribution used as a default model in an information theory approach. This primitive quasi-chemical theory is in good qualitative agreement with the observations for the hard sphere fluid of occupancy distributions that are central to quasi-chemical theories but begins to be quantitatively erroneous for the equation of state in the dense liquid regime of $ρd^3>$0.6. How the quasi-chemical approach can be iterated to treat correlation effects is addressed. Consideration of neglected correlation effects leads to a simple model for the form of those contributions neglected by the primitive quasi-chemical approximation. These considerations, supported by simulation observations, identify a `break away' phenomena that requires special thermodynamic consideration for the zero (0) occupancy case as distinct from the rest of the distribution. A empirical treatment leads to a one parameter model occupancy distribution that accurately fits the hard sphere equation of state and observed distributions.

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Lawrence R. Pratt, Randall A. LaViolette, Maria A. Gomez, Mary E. Gentile. 2001-04-05. Quasi-chemical Theory for the Statistical Thermodynamics of the Hard Sphere Fluid. https://arxiv.org/abs/physics/0104025

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