A fast algorithm for simulating flow-induced nucleation in polymers

Abstract

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.

Understanding flow-induced crystallization in polymers: A perspective on the role of molecular simulations

“…Due to its relative simplicity the GO model strongly suggests that the total number monomers in a nucleus is an appropriate projection choice. Indeed, this projection has been shown to accurately predict the model's nucleation kinetics [85,86,88], at least for moderate flow rates and blend compositions.…”

“…This approach was used to capture quiescent crystal growth [82,83] A fast nucleation algorithm [85] has allowed the simulation of high nucleation barriers, which has enabled successful comparison with FIC experiments [86]. All kMC algorithms require a priori choices for which moves are simulated and their rates.…”

“…This is a very widely occurring problem across molecular simulation and a number of powerful techniques exist to bias the simulation towards sampling transition events [62,[89][90][91][92]. Indeed, such an approach has allowed arbitrarily low undercooling to be simulated in the GO model [85] and Yi et al [57] used rare event techniques to extrapolate their quiescent MD simulations to low undercooling. Extending rare event techniques to MD simulations of polymer nucleation under flow, although technically challenging, will provide a plausible route to simulating experimentally relevant temperatures.…”

“…This section will focus on predicting the nucleation rate under flow as a prerequisite to explaining and predicting more drastic FIC effects such as shish-kebab formation. I will use the GO model as an illustrative example because some integration tools are already in place [85,88] and some analytic solutions are known for this model [86,87]. Similar approaches may also enable other coarse-grained simulation methods, such as [80,81], to bridge from MD to continuum models.…”

Prediction of Flow Effect on Crystal Growth of Semi-Crystalline Polymers Using a Multi-Scale Phase-Field Approach

“…In morphological research, there have been many simulation approaches available, which include molecular dynamics methods [10,11,12,13], coarse-grained Monte Carlo methods [14,15,16,17,18,19], mesoscopic methods [20,21,22,23,24,25] and phenomenological methods [26,27,28,29]. Among these methods, the molecular dynamics methods are at the highest level of detail.…”