Continuum Theory of Polymer Crystallization

TL;DR

This paper introduces a unified kinetic model for polymer crystallization that explains different growth regimes by considering entropic barriers and molecular weight effects, bridging the understanding of small molecule and polymer crystallization.

Contribution

It presents a comprehensive model that unifies nucleation and diffusion-controlled crystallization regimes for polymers of finite molecular weight.

Findings

The model captures both nucleation and diffusion-controlled growth regimes.

Entropic barriers significantly influence crystallization kinetics.

The theory applies to melts and solutions, explaining experimental observations.

Abstract

We present a kinetic model of crystal growth of polymers of finite molecular weight. Experiments help to classify polymer crystallization broadly into two kinetic regimes. One is observed in melts or in high molar mass polymer solutions and is dominated by nucleation control with $G \sim \exp(1/T \Delta T)$, where $G$ is the growth rate and $\Delta T$ is the super-cooling. The other is observed in low molar mass solutions (as well as for small molecules) and is diffusion controlled with $G \sim \Delta T$, for small $\Delta T$. Our model unifies these two regimes in a single formalism. The model accounts for the accumulation of polymer chains near the growth front and invokes an entropic barrier theory to recover both limits of nucleation and diffusion control. The basic theory applies to both melts and solutions, and we numerically calculate the growth details of a single crystal in a dilute solution. The effects of molecular weight and concentration are also determined considering conventional polymer dynamics. Our theory shows that entropic considerations, in addition to the traditional energetic arguments, can capture general trends of a vast range of phenomenology. Unifying ideas on crystallization from small molecules and from flexible polymer chains emerge from our theory.