Kinetics of Crystallization in Multicomponent Systems: II. Chain-Folded Polymer Crystals

Using polyethylene as an example, the kinetics of growth of chain-folded polymer crystals is treated using a theory for the kinetics of growth of chains in multicomponent systems. The kinetic chain is considered to be a chain-folded strip growing on the lateral face of a chain-folded lamella, and the various components are the possible lengths l the polymer chain may form on folding at the end of the growing strip. Thus, the number of components is in principle infinite, but it is sufficient to take a number of the order of 20-50 for the calculations. By an iteration procedure, the calculations are carried out so that the average thickness of the strip is the same as that of the chain-folded lamella on which it grows. This necessitates modification of the rate constants that would be used without this requirement. The rate of growth, average thickness and its standard deviation, and the pair distribution are calculated as a function of undercooling and other relevant parameters of the system. The results for the rate of growth and thickness are similar to those of simpler theories, provided that the constant end-surface free-energy of those theories is replaced by a temperature dependent "effective" surface free-energy. The standard-deviation of the thickness is larger than commonly believed, values of 8 to 14 Å being typical. Consequently, the crystals as grown may have quite rough fold surfaces, although the equilibrium roughness will be less.