In order to be able to simulate long time and large space scale properties of polymer melts one has to resort to coarse grained models, for example by subdividing all polymers into parts and restricting attention to the center of mass positions and velocities of these parts. The dynamics of these variables is governed by Langevin equations in which the free energy obtained by integrating the remaining variables provides the potential of the conservative forces. In general this leads to many particle interactions on the coarse-grained level. Methods suggested in the literature to represent these many particle interactions by effective two body interactions are reviewed and a new method, based on the Gibbs-Bogoliubov inequality, is proposed. The reason why none of these methods is able to reproduce the pressure of the underlying atomistic model is discussed.
- Coarse Graining
- Thermodynamic Variation Principle
- Virial Distribution