Enumeration of Self-Avoiding Random Walks on Lattices as Model Chains in Polymer Crystals

Abstract

Recent simulation studies have revealed a wealth of distinct crystal polymorphs encountered in the self-organization of polymer systems driven by entropy or free energy. The present analysis, based on the concept of self-avoiding random walks (SAWs) on crystal lattices, is useful to calculate upper bounds for the entropy difference of the crystals that are formed during polymer crystallization and thus to predict the thermodynamic stability of distinct polymorphs. Here, we compare two pairs of crystals sharing the same coordination number, ncoord: hexagonal close-packed (HCP) and face centered cubic (FCC), both having ncoord = 12 and the same packing density, and the less dense simple hexagonal (HEX) and body centered cubic (BCC) lattices, with ncoord = 8. In both cases, once a critical number of steps is reached, one of the crystals shows a higher number of SAWs compatible with its geometry. We explain the observed trends in terms of the bending and torsion angles as imposed by the geometric constraints of the crystal lattice.

Keywords

• self-avoiding random walk
• lattice model
• crystallization
• hexagonal close-packed
• face centered cubic
• body centered cubic