Kinetics of Polymer Crystallization II. Growth Regimes

From the models of paper I, exact expressions are found for the steady-state growth rate of a portion of the edge of a lamellar crystal in terms of the number of polymer segments M in the portion, the nucleation rate α on the edge and the folding rate ν of polymer chains. Both hexagonal and square crystal structures are analysed. Simpler expressions are given in various limiting cases or regimes. One such regime is the continuum model of Bennett et al. (J. statist. Phys. 24, 419 (1981)). We find that the growth rates in our models differ substantially from this continuum limit when edge roughness is significant. The continuum growth rate provides an exact upper bound on the growth rate in Frank's model (Frank, F. C. J. Cryst. Growth 22, 233 (1974)), which is sometimes exceeded by Frank's approximation.