Using Monte Carlo to Simulate Complex Polymer Systems: Recent Progress and Outlook

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.

Ab initio predictions for 3D structure and stability of single- and double-stranded DNAs in ion solutions

“…Afterward, the simulation of a DNA system with a given monovalent/divalent ion condition is performed from a high temperature (e.g., 120°C) to the target temperature (e.g., room/body temperature). At each temperature, conformational changes are accomplished via the translation and pivot moves, which have been demonstrated to be rather efficient in sampling conformations of polymers [ 80 , 81 ], and the changes are accepted or rejected according to the standard Metropolis algorithm [ 66 , 70 ]. The equilibrium conformations at different temperatures during the cooling process are used to analyze the stability of the DNA.…”

Ab initio predictions for 3D structure and stability of single- and double-stranded DNAs in ion solutions

“…Afterward, the simulation of a DNA system with a given monovalent/divalent ion condition is performed from a high temperature (e.g., 120℃) to the target temperature (e.g., room/body temperature). At each temperature, conformational changes are accomplished via the translation and pivot moves, which have been demonstrated to be rather efficient in sampling conformations of polymers (77,78), and the changes are accepted or rejected according to the standard Metropolis algorithm (65,69). The equilibrium conformations at different temperatures during the cooling process are used to analyze the stability of the DNA.…”

Direct calculation of the functional inverse of realistic interatomic potentials in field-theoretic simulations

“…Complex polymer systems are not easy to simulate using detailed (atomistic) particle-based models because the longest relaxation time associated with phase transitions and morphology development remains orders of magnitude longer than the times that can be accessed today even with some of the most powerful computing systems available, which has motivated the development of new simulation methodologies based on coarse-graining 21 or on powerful Monte Carlo techniques using efficient (and, quite often, fictitious) moves to offer a robust sampling of configurational phase space. 22 From a technical point of view, and given a suitable particlebased model, a technique for transforming the many-particle model…”