Liquid-state theory of semidilute and concentrated polymer solutions

We present a theory for thermodynamic and equation-of-state properties of polymer solutions over the entire concentration range, and for homopolymer melts, based on analytic polymer reference interaction site model (PRISM) methods. A single polymer is modeled as either an effectively Gaussian thread, or as a Gaussian string which approximately accounts for the effects of a nonzero chain thickness. Both good (athermal) and Θ solvent conditions are considered within a molecular closure approximation scheme. Good agreement is found with experimentally measured second and third virial coefficients, and with the osmotic pressure and screening length, in dilute and semidilute athermal solutions. Experimentally observed deviations from the power law dependence on chain length (N) of the athermal second and third virial coefficients is interpreted in terms of finite segmental hard core interchain packing effects at low molecular weights; these finite size effects are predicted to vanish in the limit N → ∞. For long chains in the semidilute regime the theory predicts the irrelevance of the finite size of the segments, in accord with scaling and field theoretic approaches. The breakdown of power law scaling behavior for the screening length and osmotic pressure is identified with the emergence of the concentrated solution regime at roughly 25-30% volume fraction of polymer. For concentrated solutions and melts, calculations of the equation of state based on the string model show good agreement with simulations of athermal chains for appropriately chosen model parameters. Comparison with experimental PVT data for polyethylene melts at elevated temperatures and pressures shows that the analytic theory provides an accurate description of the temperature and pressure dependences of the isothermal compressibility and the coefficient of thermal expansion.