A mapping from atomistic polymer models to coarse-grained models

Polymers (and we will focus on linear homopolymers here) are molecules with a complex internal structure. In fact, they display a self-similar scale invariant structure over a range of length scales, which depends on their degree of polymerization. For polymers in dense melts the scale invariant behavior is that of a random walk. The complex internal structure leads to an even larger spread in relevant time scales for the dynamics of polymers. For a chemically realistic polymer model, this range of time scales can easily cover 9 - 12 orders of magnitude. This renders computer simulations of polymer dynamics a formidable task and strongly limits the range of chain lengths and temperatures one can study with detailed models. The existence of a scale invariant structure over a certain range of length scales, however, also makes it conceivable to address the simulation of polymer melts using multi-scale modeling approaches like they are also applied to models at or near a critical point. The idea is therefore to use a mapping from atomistic to coarse-grained polymer models in "the same universality class" to equilibrate the large scale structure of the polymer melt under consideration.