Approximating the dynamical evolution of systems of strongly interacting overdamped particles

Abstract

We describe collective-move Monte Carlo (MC) algorithms designed to approximate the overdamped dynamics of self-assembling nanoscale components equipped with strong, short-ranged and anisotropic interactions. Conventional MC simulations comprise sequential moves of single particles, proposed and accepted so as to satisfy detailed balance. Under certain circumstances such simulations provide an approximation of overdamped dynamics, but the accuracy of this approximation can be poor if, for example, particle–particle interactions vary strongly with distance or angle. The twin requirements of simulation efficiency (trial moves of appreciable scale are needed to ensure reasonable sampling) and dynamical fidelity (true in the limit of vanishingly small trial moves) then become irreconcilable. As a result, single-particle moves can under-represent important collective modes of relaxation, such as self-diffusion of particle clusters. However, one way of using MC simulation to mimic real collective modes of motion, retaining the ability to make trial moves of reasonable scale, is to make explicit moves of collections of particles. We outline ways of doing so by iteratively linking particles to their environment. Linking criteria can be static, conditioned upon properties of the current state of a system, or dynamic, conditioned upon energy changes resulting from trial virtual moves of particles. We argue that the latter protocol is better suited to approximating real dynamics.

Keywords:

• Monte Carlo simulation
• self-assembly
• patchy particles
• crystalisation

Acknowledgements

I thank Rob Jack and Jocelyn Rodgers for comments on the paper. I am grateful to Phill Geissler for the collaboration that led to the development of the virtual-move algorithm (Ref. [24]), and I thank Alex Wilber, Tom Ouldridge and Jon Doye for identifying omissions in preprint- and published versions of that paper. This study was performed at the Molecular Foundry, Lawrence Berkeley National Laboratory, and was supported by the Director, Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under Contract No. DE-AC02–05CH11231.