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Title
| - Quasi-Chemical Theory for the Statistical Thermodynamics of the Hard-Sphere Fluid
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Abstract
| - We develop a quasi-chemical theory for the study of packing thermodynamics in dense liquids. The situationof hard-core interactions is addressed by considering the binding of solvent molecules to a precisely definedcavity in order to assess the probability that the cavity is entirely evacuated. The primitive quasi-chemicalapproximation corresponds to an extension of the Poisson distribution used as a default model in an informationtheory approach. This primitive quasi-chemical theory is in good qualitative agreement with the observationsfor the hard-sphere fluid of occupancy distributions that are central to quasi-chemical theories but begins tobe quantitatively erroneous for the equation of state in the dense liquid regime of ρd3> 0.6. How the quasi-chemical approach can be iterated to treat correlation effects is addressed. Consideration of neglected correlationeffects leads to a simple model for the form of those contributions neglected by the primitive quasi-chemicalapproximation. These considerations, supported by simulation observations, identify a “break away” phenomenathat requires special thermodynamic consideration for the zero (0) occupancy case as distinct from the restof the distribution. An empirical treatment leads to a one-parameter model occupancy distribution that accuratelyfits the hard-sphere equation of state and observed distributions.
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