Monte Carlo simulations and integral equation theory for microscopic correlations in polymeric fluids

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Abstract
Monte Carlo simulations are performed for polymer chains modeled as pearl necklaces of freely jointed tangent hard spheres; chains composed of 20, 50, and 100 beads are studied at volume fractions ranging from 0.1 to 0.35. The mean‐square end‐to‐end distance, the radius of gyration, and the intramolecular and intermolecular site–site distribution functions are monitored in the simulations. Various approximations for the intramolecular structure factor, ŵ(k), are tested. It is found that the ŵ(k) from the semi‐flexible chain model is the most accurate. The polymer ‘‘reference interaction site model’’ (PRISM) theory of Curro and Schweizer is tested using both approximate and exact expressions for ŵ(k). It is found that, at the densities examined here, the theory is accurate for the local structure except near contact where it tends to overestimate the value of the intermolecular site–site distribution function, g(r). The polymer‐RISM theory is also solved with the generalized mean spherical approximation (GMSA), which uses a Yukawa closure for the direct correlation function. The contact value of g(r), required in the GMSA, is obtained approximately, but accurately, via a perturbation expansion for a hypothetical fluid and the generalized Flory dimer equation of state. The GMSA theory results in improved predictions for g(r) when compared with the original polymer‐RISM theory, but there are still some differences between theoretical predictions and simulation results near contact.