Properties of Effective Pair Potentials that Map Polymer Melts onto Liquids of Soft Colloid Chains
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The ability to accurately represent polymer melts at various levels of coarse graining is of great interest because of the wide range of time and length scales over which relevant process take place. Schemes for developing effective interaction potentials for coarse-grained representations that incorporate microscopic level system information are generally numerical and thus suffer from issues of transferability because they are state dependent and must be recalculated for different system and thermodynamic parameters. Numerically derived potentials are also known to suffer from representability problems, in that they may preserve structural correlations in the coarse-grained representation but many often fail to preserve thermodynamic averages of the coarse-grained representation. In this dissertation, analytical forms of the structural correlations and effective pair potentials for a family of highly coarse-grained representations of polymer melts are derived. It is shown that these effective potentials, when used in mesoscale simulations of the coarse-grained representation, generate consistent equilibrium structure and thermodynamic averages with low level representations and therefore with physical systems. Furthermore, analysis of the effective pair potential forms shows that a small long range tail feature that scales beyond the physical range of the polymer as the fourth root of the number of monomers making up the coarse-grained unit dominates thermodynamic averages at high levels of coarse graining. Because structural correlations are extremely insensitive to this feature, it can be shown that effective interaction potentials derived from optimization of structural correlations would require unrealistically high precision measurements of structural correlations to obtain thermodynamically consistent potentials, explaining the problems of numerical coarse-graining schemes. This dissertation includes previously published and unpublished co-authored material.