Analytic calculation of nucleation rates from a kinetic Monte Carlo simulation of flow induced crystallization in polymers

Hamer, Matthew J.; Wattis, Jonathan A. D.; Graham, Richard S.

doi:10.1016/j.jnnfm.2010.06.012

Cited by 13 publications

(21 citation statements)

References 20 publications

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“…When combined with the high degree of coarse-graining and the relative simplicity of the simulation algorithm, this suggests that some analytic calculations of the model's results should be possible. Indeed, recent combinatoric calculations [53] have computed analytically the quasistatic nucleation barrier and, from this barrier, accurately predicted the simulated nucleation rates. This demonstrates the possibilities for developing a complementary analytic framework for this simulation model.…”

Section: Highly Coarse-grained Kinetic Monte Carlo Simulationsmentioning

confidence: 92%

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Molecular modelling of flow-induced crystallisation in polymers

Graham

2010

J Eng Math

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Flow-induced crystallisation (FIC) in polymers is simultaneously of great fundamental and practical importance. Current work on the molecular origins of FIC is providing insight into this fascinating, kinetically driven, non-equilibrium phase transition. This understanding also has the potential to be hugely beneficial to the plastics industry. In this article the main processes active during flow of crystallising polymers in complex geometries and the ways they are coupled are reviewed. Each of these processes individually presents a substantial modelling challenge, drawing on a diverse range of areas in polymer physics. Recent progress is reviewed and likely future directions indicated.

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Section: Highly Coarse-grained Kinetic Monte Carlo Simulationsmentioning

confidence: 92%

“…The latter form has been used to empirically fit measured nucleation rates from flowing polydisperse melts [48], despite its poorer agreement at large stretch. Recent simulation results [53] suggest that a hybrid of these two forms is required to describe model bimodal blends,…”

Section: Highly Coarse-grained Kinetic Monte Carlo Simulationsmentioning

confidence: 99%

Molecular modelling of flow-induced crystallisation in polymers

Graham

2010

J Eng Math

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“…Here, calculating the energy landscape becomes vastly more complicated 16 and practical direct calculation is limited to small nucleus sizes (N t < 30) due to the computational cost of the nested sums. Here, calculating the energy landscape becomes vastly more complicated 16 and practical direct calculation is limited to small nucleus sizes (N t < 30) due to the computational cost of the nested sums.…”

Section: Analytic Calculation Of the Quiescent Nucleation Barriermentioning

confidence: 99%

“…16 Thus we can no longer calculate analytically the free energy landscape and the normalisation constant Z eff , the distribution initial states in the reduced simulation and the input flux J f in into the reduced region. This means that the sum required for the partition function cannot be extensively factorised, as in Eq.…”

Section: B General Casementioning

confidence: 99%

A fast algorithm for simulating flow-induced nucleation in polymers

Jolley

Graham

2011

The Journal of Chemical Physics

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We present a fast computer simulation algorithm for high dimensional barrier crossing simulations. The algorithm is described with reference to the Graham and Olmsted (GO) model of flow-induced nucleation in polymers [R. S. Graham and P. D. Olmsted, Phys. Rev Lett. 103, 115702 (2009)]. Inspired by Chandler's barrier crossing algorithm [D. Chandler, J. Chem. Phys 68, 2959 (1978)], our algorithm simulates only the region around the top of the nucleation barrier, where the system deviates most strongly from equilibrium. When applied to the kinetic Monte Carlo (kMC) routine used in the GO model, our algorithm has two advantages: it requires very little additional coding; and it is simple enough to be applied to any barrier crossing problem that can be written in terms of a kMC simulation. Our fast nucleation algorithm is shown to vastly decrease the computer time required to perform the kMC simulations of high barrier crossing.

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“…Monte Carlo simulation is more popular among computer simulation methods. Many researchers paid attention to the study of macromolecular configurations by various Monte-Carlo (MC) devices [13][14][15][16][17] . Currently, few papers have been published on Monte Carlo study of isothermal crystallization kinetics.…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo Simulation Study of Isothermal Crystallization Kinetics of Polyethylene Glycol

Sun

Feng

Wang

et al. 2011

Polymer-Plastics Technology and Engineering

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Isothermal crystallization kinetics of polyethylene glycol (PEG) was investigated by use of Monte Carlo computer simulation. Nucleation mechanism, some crystallization parameters used in simulation and the crystalline morphology of PEG were first measured with a hot stage polarizing microscope (HSPOM). The results showed that under an instantaneous nucleation condition, PEG exhibited well-defined and large spherulites as being crystallized from the melt at various crystallization temperatures. The linear growth rate of PEG decreased as the crystallization temperature increased. The Avrami equation was suitable to describe the primary simulated isothermal crystallization process of PEG. With the increase of crystallization temperature, the overall crystallization rate decreased, while the Avrami exponent, approaching 3, almost remained unchanged. Differential scanning calorimetry (DSC) was employed to confirm the validity of the established simulation model. INTRODUCTIONUnderstanding the crystallization kinetics of polymer is important for assessing their processing-property interrelationship. The physical and mechanical properties of polymer are dependent on the developed crystallinity governed by the combined influence. The morphology of polymer can vary depending upon the relative crystallization times and the extent of crystallization as a function of temperature of the component polymers. Information regarding these parameters is necessary in order to understand the microstructure development in melt processing. Therefore, study of the crystallization kinetics is necessary for optimizing industrial processes and establishing the

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Analytic calculation of nucleation rates from a kinetic Monte Carlo simulation of flow induced crystallization in polymers

Cited by 13 publications

References 20 publications

Molecular modelling of flow-induced crystallisation in polymers

Molecular modelling of flow-induced crystallisation in polymers

A fast algorithm for simulating flow-induced nucleation in polymers

Monte Carlo Simulation Study of Isothermal Crystallization Kinetics of Polyethylene Glycol

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