Abstract
Metropolis Monte Carlo has been employed with remarkable success over the years to simulate the dense phases of polymer systems. Owing, in particular, to the freedom it provides to accelerate sampling in phase space through the clever design and proper implementation of even unphysical moves that take the system completely away from its natural trajectory, and despite that it cannot provide any direct information about dynamics, it has turned to a powerful simulation tool today, often viewed as an excellent alternative to the other, most popular method of Molecular Dynamics. In the last years, Monte Carlo has advanced considerably thanks to the design of new moves or to the efficient implementation of existing ones to considerably more complex systems than those for which these were originally proposed. In this short review, we highlight recent progress in the field (with a clear emphasis in the last 10 years or so) by presenting examples from applications of the method to several systems in Soft Matter, such as polymer nanocomposites, soft nanostructured materials, confined polymers, polymer rings and knots, hydrogels and networks, crystalline polymers, and many others. We highlight, in particular, extensions of the method to non-equilibrium systems (e.g., polymers under steady shear flow) guided by non-equilibrium thermodynamics and emphasize the importance of hybrid modeling schemes (e.g., coupled Monte Carlo simulations with field theoretic calculations). We also include a short section discussing some key remaining challenges plus interesting future opportunities.
Highlights
Metropolis Monte Carlo is a powerful simulation technique for equilibrating the dense phases of complex systems and predicting their key physicochemical properties because of the freedom it provides to sample new points in phase space thanks to the design of artificial trial moves that can take the system completely away from its natural trajectory
We start by presenting the basic concepts underlying the method, we review progress in the development of new Monte Carlo moves or interesting implementations of existing moves to new systems, we discuss the development of new software for the more friendly execution of Monte Carlo simulations, and we discuss findings from several applications to polymer systems
All components of the tensor a had to be recomputed in order for the GENERIC Monte Carlo predictions to match the direct nonequilibrium molecular dynamics (NEMD) ones for the overall conformational properties of the polymer (Figure 10), gratifying agreement was observed between the two methodologies in the regime of weak flows, but some systematic deviations were noted in the regime of weak-tostrong flows
Summary
Metropolis Monte Carlo is a powerful simulation technique for equilibrating the dense phases of complex systems and predicting their key physicochemical properties because of the freedom it provides to sample new points in phase space thanks to the design of artificial (even fictitious) trial moves that can take the system completely away from its natural trajectory. In particular, with methods such as replica exchange, these moves can accelerate system equilibration by several orders of magnitude compared to dynamic methods such as Molecular Dynamics (MD). This is especially important at low temperatures or for systems characterized by highly dense structures, since dynamics becomes too slow to be followed reliably and ergodically by a detailed dynamic method
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