Molecular simulation of crystal growth in alkane and polyethylene melts

Abstract

Molecular simulation has become a very powerful tool for understanding the process of polymer crystallization. By using carefully constructed simulations, one can independently observe the two phenomena responsible for melt crystallization: nucleation and growth. This research focuses on modeling the growth process using potentials that are well-parameterized for alkanes and polyethylene. In experiment and modeling of the kinetics of alkane crystallization, focus has been concentrated on growth rates very near the melting temperature, where the growth of these systems is optically observable. In this temperature range near .., diffusion is not a limiting factor, which has led to theory that models the thermodynamic driving force and its effect on kinetics. Phenomenologically, one observes a maximum growth rate at a temperature intermediate between the glass transition temperature ... and the melt temperature ... This arises as a competition between a thermodynamic driving force towards crystal growth, associated with locking chains into crystallographic registry and the ability of chains to diffuse to the new layer and rearrange themselves conformationally to satisfy the restrictions of crystal symmetry. The thermodynamic driving force is rate limiting at high temperatures, while melt mobility is rate limiting at low temperatures. Growth rates are of interest to the polymer processing community, who require accurate crystallization kinetic data over the entire temperature range, in order to predict solidification under process conditions and thus final fiber properties.

(cont.) A model which retains its connection to molecular structure would certainly be of benefit for purposes of product design; such connection is possible using molecular simulations. Nonequilibrium molecular dynamics enables us to observe growth for a range of temperatures around the temperature at which the maximum growth rate occurs. We present a molecular dynamics (MD) framework for measuring crystal growth rates for n-eicosane (C₂₀H₄₂, denoted C20), by simulating growth on a pre-existing crystal surface. We show that growth rates for short alkanes such as C20 are directly observable over a range of quench temperatures, for the case where the crystallization front is preceded by a supercooled amorphous region, and heat transfer occurs faster than the characteristic time for crystallization. We present data that we have acquired from these simulations through analysis of the propagation of orientational order, using the bond order parameter, and density changes, using Voronoi volumes. To determine molecular weight effects, we use the same technique to look at systems of C₅₀H₁₀₂ and C₁₀₀H₂₀₂ (denoted C50 and C100). With these higher molecular weight n-alkanes, we can also measure the occurrence of folds during crystal growth. From these MD simulations, we obtain data for the growth rate of n-alkane crystals over a range of temperatures and molecular weights. Qualitatively, we see frequent adsorption and desorption of chain segments on the surface in both C50 and C100 systems. We find evidence for a surface nucleus involving 4-5 chain segments, from multiple chains, that are approximately 20 beads long, shorter than the ultimate thickness of the chain stem in the crystal.

(cont.) We construct a general crystal growth model that can be parameterized entirely in terms of universal properties of polymer chains, described by polymer physics and chemically specific quantities that can be estimated polymer by polymer using molecular dynamics simulations. The model is an extension to polymer crystallization models to incorporate molecular weight effects, using a small number of chemically specific quantities that can be estimated from molecular dynamics simulations. It accounts for the thermodynamic driving force, using classical nucleation theory, and melt relaxation time, using WLF theory. Our model can predict rates as a function of temperature and molecular weight, up to the entanglement molecular weight. Past the entanglement molecular weight, the analysis reveals that the growth rate of alkanes and polyethylene can both be described by the same relationship. The appropriate relaxation time is used to describe the kinetic barrier to crystallization. For chains shorter than the entanglement length, this is the Rouse time. For chains longer than the entanglement molecular weight, kinetic limitations are modeled by the local relaxation of an entangled segment at the interface. Use of the model is illustrated for polyethylene crystallizing in a fiber spin line under conditions of slow cooling and fast cooling. Finally, we present a simplified framework for the study of polymer crystallization using Kinetic Monte Carlo (KMC). We have developed a general KMC algorithm for measuring growth of a polymer crystal phase during melt crystallization, based on the algorithm of Bortz et al.

(cont.) We have incorporated new moves into a general framework to allow multi-chain, three-dimensional growth and the escape of chains from the crystal to the melt, through the fold surface. We performed parametric studies on the melt-crystallization of C20 to study the effects of each energy barrier. In addition, the KMC algorithm allows us to consider the importance of individual moves in contributing to growth. We have shown, as a proof-of-concept, that this algorithm is capable of generating morphologies characteristic of several theories of secondary nucleation in polymer melts.