Dilute Solution Theory of Polymer Crystal Growth: A Kinetic Theory of Chain Folding

Abstract

A kinetic theory of polymer crystallization from dilute solution is formulated for linear chain molecules of finite molecular weight (monodisperse). Two models of crystal growth are considered; both are essentially “regular” chain folding type models. Formulas for the crystal growth rates are derived as a function of the fundamental rate constants associated with the various states of molecular crystallization. These rate constants are evaluated as a function of polymer concentration, molecular weight, crystallization temperature, and crystal thickness. Consideration of finite molecular weight molecules requires an understanding of how these molecules are incorporated into the crystal and what happens to chain ends. Attention is focused on these problems and a description of how “cilia” are formed in polymer crystals is given. A remarkable aspect of cilia formation is that the uncrystallized portion of a chain molecule which dangles in the solution can participate in nucleating a new growth strip (fold plane) on the crystal face—a kind of “self-nucleating” mechanism.