Continuum Theory of Polymer Crystallization

摘要

We present a kinetic model of crystal growth of polymers of finite molecularweight. Experiments help to classify polymer crystallization broadly into twokinetic regimes. One is observed in melts or in high molar mass polymersolutions and is dominated by nucleation control with $G \sim \exp(1/T \DeltaT)$, where $G$ is the growth rate and $\Delta T$ is the super-cooling. Theother is observed in low molar mass solutions (as well as for small molecules)and is diffusion controlled with $G \sim \Delta T$, for small $\Delta T$. Ourmodel unifies these two regimes in a single formalism. The model accounts forthe accumulation of polymer chains near the growth front and invokes anentropic barrier theory to recover both limits of nucleation and diffusioncontrol. The basic theory applies to both melts and solutions, and wenumerically calculate the growth details of a single crystal in a dilutesolution. The effects of molecular weight and concentration are also determinedconsidering conventional polymer dynamics. Our theory shows that entropicconsiderations, in addition to the traditional energetic arguments, can capturegeneral trends of a vast range of phenomenology. Unifying ideas oncrystallization from small molecules and from flexible polymer chains emergefrom our theory.