Theory and simulation of hard-chain mixtures: Equations of state, mixing properties, and density profiles near hard walls

Abstract

A combination of theoretical modeling and computer simulation is used to study the equation of state of binary mixtures of hard chains, where each chain is modeled by a series of freely jointed, tangent, hard spheres. Three approximate equations of state are derived, based on our previous work on one-component fluids. These equations contain no adjustable parameters and relate properties of the chain mixture to properties of pure monomer and dimer fluids at the same total volume fraction. Their predictions are tested against Monte Carlo results for the pressure of mixtures of 8-mers and monomers and mixtures of 8-mers and 4-mers, obtained using a hard-wall technique. Very good agreement is obtained using an equation of state developed here, in which the compressibilty factor of the mixture is set equal to the molar average of the compressibility factors of the pure components at the same overall volume fraction, as well as from Wertheim’s second-order thermodynamic theory of polymerization (TPT2). Using the equations developed here, we also examine the mixing properties of hard-chain fluids. For mixing at constant pressure, the free energy and entropy of mixing range from ideal-solution behavior at low pressures to Flory–Huggins behavior at high pressures. For mixing at constant volume fraction, the free energy and entropy of mixing reduce directly to the Flory–Huggins result without recourse to the usual lattice approximations. Site-density profiles obtained from the simulations indicate that chains are depleted near the walls at low densities and are enhanced near the wall at high densities; monomers, by contrast, are enhanced near the walls at all densities.