Effective potentials for representing polymers in melts as chains of interacting soft particles

This paper outlines the derivation of an analytical pair potential in a coarse grained description of polymer melts where each chain is represented as a collection of soft spheres. Each particle is located at the center of mass of a polymer subchain, while the polymer is divided into an arbitrary number of identical chain subsections, each comprised of a large number of monomers. It is demonstrated that the soft effective pair potentials acting between these center-of-mass sites is described by a soft repulsive region at separation distances less than the average size of each coarse grained unit and a long repulsive tail, with a small attractive component. The attractive component is located at a length scale beyond the size of the coarse grained unit and its form varies with the level of interpenetration between the coarse-grained units. Consistent with numerically derived potentials, it is found that the short range features of the potential dominate the liquid structure, while the long-tail features dominate the virial-route thermodynamics of the system. It follows that the accurate determination of the effective potential in both short and large separation distances is relevant for ensuring structural and thermodynamic consistency in the coarse-grained description of the macromolecular liquid. It is further shown that due to the sensitivity of thermodynamic properties to the large-scale features of the potential, which are irrelevant to the reproducibility of structural correlations, the determination of thermodynamically accurate potentials by numerical optimization of structure alone is not a reliable strategy in the high-density regime for high levels of coarse-graining.