Fluid–solid equilibria of chain-like molecules

Abstract

van der Waals perturbation theory is used to calculate fluid–solid phase diagrams for a system of perturbed-hard-sphere chains. In both fluid and solid phases, the free energy is the sum of a hard-sphere-chain term as the reference system, and a van der Waals term as the perturbation. The reference system for both phases follows from the Percus–Yevick integral theory coupled with Chiew’s results for hard chains. An analytic model for the solid-phase reference term of a hard-chain system agrees well with computer-simulation data for the solid hard-chain compressibility. Simulation data for fluid–solid coexistence curves for hard spheres, and for 4-mer hard chains, are used to fit the reference Helmholtz free energy of the solid phase. The pressure and solid and fluid densities at the hard-chain melting point, predicted by our model, fairly reproduce the available simulation data at different chain lengths. The attractive perturbation term follows from an inverse-power potential with variable exponent n for both fluid and solid phases. The theory here presented reproduces the simulated phase diagrams of chain-like molecules and gives the correct trend for experimental melting points of normal alkanes.