1999
DOI: 10.1063/1.478613
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The mechanism of thickness selection in the Sadler-Gilmer model of polymer crystallization

Abstract: Recent work on the mechanism of polymer crystallization has led to a proposal for the mechanism of thickness selection which differs from those proposed by the surface nucleation theory of Lauritzen and Hoffman and the entropic barrier model of Sadler and Gilmer. This has motivated us to reexamine the model used by Sadler and Gilmer. We again find a fixed-point attractor which describes the dynamical convergence of the crystal thickness to a value just larger than the minimum stable thickness, l min . This con… Show more

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Cited by 34 publications
(37 citation statements)
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“…Several models have been proposed to explain why the growth thickness converges to a value just above l min . 17 Indeed, according to the Gibbs-Thomson equation, the fact that the melting temperature is higher than the crystallization temperature means that the constant thickness of single crystallites should be larger than l min . This agrees with the crystal growth condition, i.e., ∂∆F(n)/∂n < 0.…”
Section: ∆F(n) ) -N|∆µ| + Aγmentioning
confidence: 99%
“…Several models have been proposed to explain why the growth thickness converges to a value just above l min . 17 Indeed, according to the Gibbs-Thomson equation, the fact that the melting temperature is higher than the crystallization temperature means that the constant thickness of single crystallites should be larger than l min . This agrees with the crystal growth condition, i.e., ∂∆F(n)/∂n < 0.…”
Section: ∆F(n) ) -N|∆µ| + Aγmentioning
confidence: 99%
“…In one approach the model is formulated in terms of a set of rate equations which can easily be solved numerically to yield the steady-state solution of the model [7,9]. This is the method that we used for the most part in our previous study of the Sadler-Gilmer model [13]. However, as we wish to examine the evolution of the system towards the steady state, we use kinetic Monte Carlo to grow a set of representative crystals.…”
Section: Methodsmentioning
confidence: 99%
“…The value of the thickness at the fixed point is l ‫ءء‬ . This mechanism has been found for two simple models of polymer crystallization [11][12][13]. In the first model the polymer crystal grows, as in the Lauritzen-Hoffman theory, by the successive deposition of stems (a stem is a straight portion of the polymer chain that traverses the thin dimension of the lamella) across the growth face [11,12].…”
Section: Introductionmentioning
confidence: 99%
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