The mechanism of thickness selection in the Sadler-Gilmer model of polymer crystallization

TL;DR

This paper reexamines the Sadler-Gilmer model of polymer crystallization, revealing a fixed-point mechanism for thickness selection driven by stem length constraints, and discusses its relation to entropic barrier theories.

Contribution

It provides a detailed analysis of the Sadler-Gilmer model, identifying a fixed-point attractor for crystal thickness and exploring the effects of chain fold energetics.

Findings

Identification of a fixed-point attractor near minimum stable thickness

Demonstration of the combined effect of stem length constraints on thickness selection

Analysis of the model with energetic contributions from chain folds

Abstract

Recent work on the mechanism of polymer crystallization has led to a proposal for the mechanism of thickness selection which differs from those proposed by the surface nucleation theory of Lauritzen and Hoffman and the entropic barrier model of Sadler and Gilmer. This has motivated us to reexamine the model used by Sadler and Gilmer. We again find a fixed-point attractor which describes the dynamical convergence of the crystal thickness to a value just larger than the minimum stable thickness, l_min. This convergence arises from the combined effect of two constraints on the length of stems in a layer: it is unfavourable for a stem to be shorter than l_min and for a stem to overhang the edge of the previous layer. The relationship between this new mechanism and the explanation given by Sadler and Gilmer in terms of an entropic barrier is discussed. We also examine the behaviour of the Sadler-Gilmer model when an energetic contribution from chain folds is included.