Kinetic Monte Carlo simulations of the growth of polymer crystals

Doye, Jonathan P. K.; Frenkel, Daan

doi:10.1063/1.477992

Cited by 65 publications

(61 citation statements)

References 40 publications

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“…This feature also causes a build-up in probability at stem lengths at or just shorter than the thickness of the previous layer. Therefore, as we saw in our previous model, 18,19 there is a range of stem lengths between l min and the thickness of the previous layer which are thermodynamically viable, and it is the combined effect of the FIG. 5.…”

Section: ͑17͒mentioning

confidence: 51%

“…[17][18][19] Our results suggest that some of the assumptions of the Lauritzen-Hoffman ͑LH͒ theory do not hold and led us to propose a new picture of the mechanism by which the thickness of polymer crystals is determined. First, we examined the free energy profile for the crystallization of a polymer on a surface.…”

Section: Introductionmentioning

confidence: 90%

“…One of the main aims of this paper is to discover whether the mechanism of thickness determination that we found for the ULH model 18,19 also holds for the SG model. Central to this mechanism was a fixed-point attractor that related the thickness of a layer to the thickness of the previous layer.…”

Section: Fig 3 ͑A͒mentioning

confidence: 96%

“…We also found that the average stem length in a layer is not determined by the properties of the initial nucleus, and that the thickness of a layer is, in general, not the same as that of the previous layer. 18,19 Furthermore, during growth lamellar crystals select the value of the thickness, l**, for which growth with constant thickness can occur, and not the thickness for which crystals grow most rapidly if constrained to grow at constant thickness. This thickness selection mechanism can be understood by considering the free energetic costs of the polymer extending beyond the edges of the previous crystalline layer and of a stem being shorter than l min , which provide upper and lower constraints on the length of stems in a new layer.…”

Section: Introductionmentioning

confidence: 99%

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

Doye¹,

Frenkel

1999

The Journal of Chemical Physics

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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 convergence arises from the combined effect of two constraints on the length of stems in a layer: it is unfavorable for a stem to be shorter than l min and for a stem to overhang the edge of the previous layer. The relationship between this new mechanism and the explanation given by Sadler and Gilmer in terms of an entropic barrier is discussed. We also examine the behavior of the Sadler-Gilmer model when an energetic contribution from chain folds is included.

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Section: ͑17͒mentioning

confidence: 51%

Section: Introductionmentioning

confidence: 90%

Section: Fig 3 ͑A͒mentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Doye¹,

Frenkel

1999

The Journal of Chemical Physics

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“…1 As to the pathway to the lamellar crystal phase, a number of competing mechanisms have been proposed in the literature. [1][2][3][4][5] Experiments 6,7 and simulations of simplified models 8,9 are not yet in complete agreement on a single mechanism. To understand the freezing mechanism in detail, simulations of realistic polymer models are needed, which can quantitatively reproduce experimentally measured quantities and provide information at the atomic length scale, which is difficult to gather from real experiments.…”

Section: Introductionmentioning

confidence: 99%

Numerical calculation of the melting phase diagram of low molecular-weight polyethylene

Das

Frenkel

2003

The Journal of Chemical Physics

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Using thermodynamic integration, we calculate free energies of the melt and the crystalline phases of a model system of C 198 H 398 with a realistic all-atom potential. We use the Gibbs-Duhem integration scheme to calculate the melting curve over the experimentally relevant pressure range. The crystal structure and the melting curve obtained from our simulation are in good quantitative agreement with the available experimental results.

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Crystallization Kinetics

Hobbs¹

2004

Encyclopedia of Polymer Science and Technology

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Crystallization kinetics is the area of polymer science that deals with the rate at which randomly ordered chains transform into highly ordered crystals, and includes every aspect of the resultant structure that is dependent on the route that was taken between those different states. It is a broad and mature area of scientific research, given and uncommon diversity when compared to the crystallization of small molecules because of the wide range of different chemistries and chain topologies that are available to macromolecules. These add layers of comlexity that can make it difficult to find generalizing principles. The article concentrates on principles and observations that have the widest applicability. Crystallizable polymers form semicrystalline materials containing chains or fractions of chains that are trapped in nonequilibrium, amorphous states. Because of this semicrystalline nature, the crystal morphology, rather than the underlying crystal structure, often controls the final properties of a polymer article. Because polymers crystallize so far from equilibrium conditions, a simple examination of the phase diagram gives us little insight into the crystal morphology that is formed or the route that is taken to its formation. To understand, and ultimately control, such behavior, it is necessary to gain an understanding of the kinetics of crystallization, as it is the kinetics of the process that define the structure and properties of the material.

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Kinetic Monte Carlo simulations of the growth of polymer crystals

Cited by 65 publications

References 40 publications

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

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

Numerical calculation of the melting phase diagram of low molecular-weight polyethylene

Crystallization Kinetics

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