Percus-Yevick integral-equation theory for athermal hard-sphere chains

Abstract

A theoretical method for the modelling of athermal freely jointed tangent hard-sphere chain fluids, of fixed length r, is developed based on a ‘particle-particle’ description of the chain system. This approach is based on the Percus-Yevick (PY) theory in the context of the particle-particle Ornstein-Zernike integral equation subject to some imposed connectivity constraints. Analytical expressions for the compressibility equations of state are derived for homonuclear chains, heteronuclear chains, blends or mixtures of homonuclear and heteronuclear chains, and homonuclear chains in a hard-sphere solvent. The PY compressibility equation of state for the athermal hard-sphere chain system is found to consist of (i) a non-bonded hard-sphere PY compressibility pressure contribution, and (ii) a PY bonding contribution due to chain formation. In the case of homonuclear chains the Percus-Yevick solution is found to yield excellent agreement with computer-simulation data reported in the literature. By replacing the PY hard-sphere compressibility pressure contribution with the Carnahan-Starling hard-sphere pressure, the accuracy of the PY bonding term for homonuclear chains is identified. We are, however, unable to determine the accuracy of the PY compressibility pressure of heteronuclear chains, chain mixtures and homonuclear chains in a hard-sphere solvent since computer-simulation data for these systems are not available.