Statistical-Mechanical Study of Stability of Folded-Chain Polymer Crystals with Irregular Fold Surfaces

Publisher Website
Google Scholar
Abstract
A model of folded‐chain crystals of polymers is considered, in which the length of crystalline sequences between folds is assumed to be uniform, while the number of segments comprising the folds is allowed to vary. The partition function is formulated by the generating function technique, with the fixed crystalline layer thickness introduced as an additional parameter of the system. The random‐walk problem in the presence of a barrier, as the representation of folds, is solved for simple and body‐centered cubic lattices. As variants of the basic model, the two ends of the fold are either assumed constrained in adjacent positions in the adjacent re‐entry model, or are allowed at an arbitrary separation in the random re‐entry model. The free energy of the system as a function of crystalline layer thickness exhibits no minimum, confirming the extend‐chain crystals as the thermodynamically most stable. As the temperature is raised toward the melting point, the number of segments in folds increases beyond bound in the random re‐entry model; while they remain about 10 in the adjacent re‐entry model. In both models the size of the amorphous chain ends grows much faster than that of folds with increasing temperature. The frequency distribution of fold sizes is very broad. Even when the majority of folds consists of tight loops of a small number of segments, the fraction of very large folds is small but still significant. The entropy term of the surface free energy, calculated for the random and adjacent re‐entry models, differs by as much as 50 erg/cm2.

This publication has 16 references indexed in Scilit: