| Coarse-graining and multi-scale approaches are rapidly becoming important tools for computer simulations of large complex molecular systems. Such theoretical models are powerful tools because they allow one to probe the essential features of a complex, many-bodied system on length and time scales over which emergent phenomena may occur. Because of the computational advantages and fundamental insight made available through coarse-grained methods, a vast array of various phenomenological potentials to describe coarse-grained interactions have been developed; nonetheless, the ability of these potentials to provide quantitative information about several different properties of the same system is not evident. On a theoretical level, it is not well-understood how small correlations in the long-range structure propagate through the coarse-graining procedure into the effective potential and lead to incorrect thermodynamics. Taking an alternative approach, this dissertation will discuss an analytical coarse-graining method for synthetic polymer chains of specific chemical structure, where a group of atoms on a polymer chain are represented by a variable number of soft interacting effective sites. The approach is based in liquid-state theory, providing a theoretical framework to address questions of thermodynamic consistency. It will be shown that the proposed method of coarse-graining maintains thermodynamic consistency for a variety of polymer models. In a multi-scale modeling scheme simulations of the same system represented by several different levels of detail may be joined to provide a complete description of the system at all length and time scales of interest.;This dissertation includes previously published and unpublished co-authored material. |
