An extension of a kinetic theory of polymer crystallization through the exclusion of negative barriers

Abstract

Abstract : The simplest version of the Lauritzen-Hoffman (LH) model of polymer crystallization, which applies to infinitely long model polymer molecules crystallizing on an existing substrate of infinite width, is reexamined. The mathematical expressions for the model free energy barriers are observed to take on negative values at high supercooling. Since such negative barriers appear to be physically unrealizable for the crystallization process, the LH model is extended by imposing a mathematical constraint on the expressions for the barriers, to forbid them from ever being negative. The extended model contains one parameter gamma which varies from 0 to 1 and is analogous to the parameter psi of the LH model. For all values of gamma less than 1, the extended model predicts a finite lamellar thickness at every supercooling; moreover, this thickness at large undercooling, decreases monotonically with increasing undercooling, in agreement with experiment but in marked contrast to the LH model which exhibits the well-known delta l catastrophe. The relative insensitivity of the calculated lamellar thicknesses to the parameter delta supports the use of gamma = 0 as a first approximation for mathematical convenience in practice.