Kinetic Model for Layer-by-Layer Crystal Growth in Chain Molecules

Abstract

A kinetic model is proposed to describe the structure and rate of advancement of the growth front during crystallization. Solidification occurs through the mechanisms of surface nucleation and lateral spreading of the solid phase within layers in the vicinity of the growth front. The transformation from liquid to solid within each layer is described by an equation similar to the two-dimensional variant of the Johnson–Mehl–Avrami (JMA) equation, but in which the finite size and shape of the critical nucleus and the dynamic evolution of the solid fraction of the underlying layers are taken into account. Connection to the regime theory of Hoffman and co-workers, for surface nucleation and spreading in one or two dimensions, is also made. Given only molecular level information regarding surface nucleation rates, lateral spreading rates, and critical surface nucleus geometry, the resulting set of coupled nonlinear equations for solidification in each layer is numerically integrated in time to obtain the structure and rate of advancement of the growth front, for arbitrarily large systems and long times. Using this kinetic model with input parameters obtained from molecular dynamics simulations, a multiscale modeling analysis of crystal growth in n-pentacontane (C50) is performed.