The mechanism of thickness selection in the Sadler-Gilmer model of polymer crystallization

Recent work on the mechanism of polymer crystallization has led to a proposalfor the mechanism of thickness selection which differs from those proposed bythe surface nucleation theory of Lauritzen and Hoffman and the entropic barriermodel of Sadler and Gilmer. This has motivated us to reexamine the model usedby Sadler and Gilmer. We again find a fixed-point attractor which describes thedynamical convergence of the crystal thickness to a value just larger than theminimum stable thickness, l_min. This convergence arises from the combinedeffect of two constraints on the length of stems in a layer: it is unfavourablefor a stem to be shorter than l_min and for a stem to overhang the edge of theprevious layer. The relationship between this new mechanism and the explanationgiven by Sadler and Gilmer in terms of an entropic barrier is discussed. Wealso examine the behaviour of the Sadler-Gilmer model when an energeticcontribution from chain folds is included.Comment: 15 pages, 13 figures, revte