Why χ Is Seldom Zero for Polymer−Solvent Mixtures

Typical good nonpolar solvents for nonpolar polymers have values of the Flory interaction parameter χ of 0.3 or higher. This is striking since miscible nonpolar polymer blends exist with well-matched solubility parameters and resulting very small χ values of 10−2 or less. Using a cell model, it has been previously argued that there is a generic contribution to χ in polymer−solvent systems of about 0.3, which ultimately arises from the difference in affinity for free volume of bonded chain mers and otherwise identical solvent mers. We explore this result with off-lattice MC simulations of hard-sphere freely jointed chains in identical hard-sphere solvent. We observe reductions in chain radii of gyration and of virial coefficients for dimers among hard-sphere solvents versus in vacuum, consistent with the cell model results. Finally, we extract free volume distributions and observe reduced free volume of chain mers compared to solvent. With a model of a single mer in a fluctuating cell surrounded by hard-sphere fluid, we construct free volume distributions in good agreement with our MC results and previous work of Sastry et al. on hard-sphere liquids.