(334d) Correlation-Based Coarse Graining Approach To Multiscale Materials Modeling

For systems with interactions that are well described by pair-wise potentials, the pair correlation function (PCF) provides a vehicle for passing information from the molecular level to the macroscopic level of description. It serves as natural starting point for multi-scale models that couple directly atomic regions embedded in coarse grained regions. In order to model a specific process related to mechanical properties, an effective Hamiltonian is required to govern dynamics. We propose to use the free energy as the effective Hamiltonian which consists of kinetic energy, potential energy and entropy. The free energy functionals of the PCF especially the entropy and the relationship to multiscale modeling are discussed. We describe the Hamiltonian first in the limit of a totally atomic system, second in the limit of an entirely coarse grained system and finally we discuss the coupling between the two descriptions. For pair wise interactions, the number density and pair correlation function are used for coarse graining.