This article reviews the various theories of polymer crystallization which have been proposed over the last thirty years. Their background in thermodynamics and crystal growth theories of simple substances is laid out in some detail. This provides the basis for a discussion of the application of surface nucleation and surface roughening concepts to polymer crystallization. The widely used nucleation model of Lauritzen and Hoffman is examined in depth with emphasis on its consistency with experimental evidence and including its recent modifications and extensions. Alternative approaches are also analyzed, in particular Point's ‘multipath’ model and the ‘roughness/pinning’ model by Sadler and Gilmer, but also ‘molecular nucleation’ and ‘chain sliding’. The aim of this article is to lead to a better understanding of the basic hypotheses of the various models and to give guidance to the theorist in improving the models as well as to the experimentalist in interpreting his/her data. It will hopefully make the subject more accessible and stimulate discussion and further research directed at resolving the controversial issues.

Polymer crystallization theories

United-atom Langevin dynamics simulations have been performed in an effort to understand early-stage polymer crystallization at the microscopic level. We have modeled the crystallization process by following the competition between the attraction among nonbonded beads and torsional energies along chain backbones. We have monitored three processes: spontaneous formation of initial nuclei and their subsequent growth in time by an isolated chain as a function of degree of undercooling, crystallization at a growth front as a function of commesurability between the thickness of the growth front and the length of crystallizing chains, and cooperative crystallization by several chains into lamellae. The details of growth kinetics here have been captured by explicit visual displays of chain conformations, radius of gyration of labeled chains and aggregates, local and global orientation order parameters, and interaction energies all as functions of time. We observe that the kinetic pathway of lamellar thickening is stepwise and quantized for small degrees of undercooling and that the lamellar thickness is inversely related to the degree of undercooling. The crystallization is found to be more efficient if chain length is an integer multiple of the thickness of the growth front. We have compared several of our key simulation results with experimentally observed results reported in the literature and found that the simulations exhibit many salient features of polymer crystallization in dilute solutions.

Langevin dynamics simulations of early-stage polymer nucleation and crystallization

Polymer crystallization of ultrathin films on solid substrates

We report the first computer experiments with supercooled polymer melts of chains long enough to form chain-folded structures. These structures resemble the lamellae of polymer crystals, and the inverse of the lamellar thickness is related linearly to the crystallization temperature as found in experiments. The small- and wide-angle scattering intensities start growing at about the same time. However, the wide-angle scattering signal is very weak at the beginning. We use molecular dynamics (MD) simulations with a coarse-grained polymer model for chain lengths of N = 100 monomers. The model consists of spherical beads connected by harmonic springs with an additional angle bending potential reflecting the torsional states of the underlying atomistic backbone. It demonstrates that chain stiffness alone without an attractive interparticle potential is a sufficient driving force for the formation of chain-folded structures. We discuss the evolution of structure in the homogeneous nucleation regime as well as t...

Formation of Chain-Folded Structures in Supercooled Polymer Melts Examined by MD Simulations

We have used atomic force microscopy to investigate the patterns obtained by isothermal crystallization of quasi-2-D monolayers of poly(ethylene oxide) adsorbed onto bare silicon wafers. These monolayers were prepared by a pseudo-dewetting process. Fingerlike branched structures were observed with a characteristic width which increased rapidly with crystallization temperature. The patterns are explained by a simple model considering the interplay of transport on the surface and the probability of attachment to the crystal. The influence of molecular weight was also studied. The average stem length increases with increasing temperature for the longer polymer. The shorter one crystallized in the (almost) fully extended form for all temperatures investigated. Temperature jumps during crystallization resulted in patterns with two different length scales.

Polymer crystallization in quasi-two dimensions. I. Experimental results

A new lattice model of polymer crystallization is described. Results of numerical solutions of rate equations for crystallization of a two-dimensional "crystal" are presented. It is shown that the crystal thickness varies inversely with supercooling and that kinetics similar to secondary nucleation occurs. This is true even though the growth face is intrinsically rough and hence there cannot be any nucleation. The presence of a low-entropy saddle point during growth is explained, and its influence on the crystal thickness and lamellar morphology is discussed.

D. M. Sadler

Papers

Rate-theory model of polymer crystallization.