Effect of a finite substrate length upon polymer crystal lamellar growth rate

The polymer crystal lamellar growth rate G is an often-measured property of semicrystalline polymers. In this paper, we investigate the dependence of G upon the length of the substrate, L, the surface nucleation rate of new growth layers per unit length per unit time, i, the velocity with which the growth layer covers the substrate, g, and the thickness of the growth layer, b. For the purposes of this paper, L is the average length where the polymer segments in the substrate are in crystallographic register. We show that G = b i L / n, where n is the average number of nuclei that contribute to each growth layer. We show that Ii depends only on the dimensionless parameter z = i L 2/4g. We have not obtained n explicitly, but we can place upper and lower limits on Ii that closely define G in regime I, where G " b i L and into a transition region between regime I and regime II where G 0:. b(ig)1 12 . The experimental results for several polymers are analyzed and some are found to be in or near regime I, and others in or near regime II.