Kinetics of crystallization in multicomponent systems. II. Chain-folded polymer crystals

Abstract

Using polyethylene as an example, the kinetics of growth of chain-fold ed polymer crystals is treated using a theory for the kinetics of growth of chains in multicomponent systems. The kinetic chain is co nsidered to be a chain-folded strip growing on the lateral face of a chain-folded lamella, and the various components are the possible lengths I) 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 co nstant end-surface free-energy of those theories is replaced by a temperature dependent "effective" surface free-energy. The standard-deviati on of the thickness is larger than commonly believed, values of 8 to 14 A being typical. Consequently, the crystals as grown may have quite rough fold surfaces, although the equilibriu m roughness will be less.

Homogeneous nucleation in polyethylene: Molecular weight dependence

“…74 ,and 23.0 K re present a region whe rein Tm is rapidl y changing with molec ular weight and (J 2a e is expected to s how stron g molec ular weight e ffects. The re mainin g samples are in a region where Till chan ges slowly and a 2 (Je should show little molecula r weight dependence [20].…”

“…For samples 9.70, 11.74, and 23.0 K one expects a 2 a e to increase rapidly due to a decrease in the number of cilia per chain fold as the molecular weight increases [20]. This effect should be of much less importance in the higher molecular weight fractions.…”

“…For the time being, if we regard (J'2(J' [20]. Hoffman et al [1] have shown that from all the information available it is reasonably certain that (J' for polyethylene li es between 12 and 15 ergs/ cm 2.…”

A Review on Polymer Crystallization Theories

“…(1) I << g. This corresponds to Regime I [78], usually at high temperatures, where the nucleation rate is much smaller than the lateral spreading rate. Once a nucleation event occurs, subsequent lateral growth will rapidly overspread a layer, and wait for the next nucleation event.…”

“…In addition, it will lead to an unphysical result: if stems are adsorbed on the crystal surface, all surface energy must be overcome first before any gain of bulk free energy. Subsequently, Frank and Tosi [66], as well as Lauritzen and Passaglia [78], developed corresponding theories that considered fluctuations. However, any theory based on the framework of HL-type with non-zero ψ will eventually lead to δl catastrophe.…”