Benito, J.; Urrutia, U.; Karayiannis, N.C.; Laso, M. Enumeration of Self-Avoiding Random Walks on Lattices as Model Chains in Polymer Crystals. Crystals2023, 13, 1316.
Benito, J.; Urrutia, U.; Karayiannis, N.C.; Laso, M. Enumeration of Self-Avoiding Random Walks on Lattices as Model Chains in Polymer Crystals. Crystals 2023, 13, 1316.
Benito, J.; Urrutia, U.; Karayiannis, N.C.; Laso, M. Enumeration of Self-Avoiding Random Walks on Lattices as Model Chains in Polymer Crystals. Crystals2023, 13, 1316.
Benito, J.; Urrutia, U.; Karayiannis, N.C.; Laso, M. Enumeration of Self-Avoiding Random Walks on Lattices as Model Chains in Polymer Crystals. Crystals 2023, 13, 1316.
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 on crystal lattices, is useful to calculate upper bounds for the entropy difference of the crystals that are formed during polymer crystallization and thus provide predictions on polymorph thermodynamic stability. 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 hexagonal (HEX) and body centered cubic (BCC) lattices, with ncoord = 8. In both cases, once a critical step length is reached, one of the crystals shows a higher number of SAWs compatible with the crystal. We explain the observed trends in terms of the bending and torsion angles corresponding to the different chain geometry 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; polymer; self-organization; perfection; crystal polymorph
Subject
Chemistry and Materials Science, Polymers and Plastics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
