Inferring bulk self-assembly properties from simulations of small systems with multiple constituent species and small systems in the grand canonical ensemble

TL;DR

This paper extends methods to infer bulk self-assembly properties from small simulation systems, including multiple species and grand canonical ensembles, highlighting challenges in convergence and accuracy of extrapolations.

Contribution

It generalizes a previous methodology to handle multiple species, spatially localized particles, and grand canonical simulations for better bulk property inference.

Findings

Differences in cluster concentrations can be significant between small and bulk systems.

Convergence to bulk results can be slow and complex as system size increases.

The introduced methods enable evaluation of extrapolation accuracy.

Abstract

In this paper we generalize a methodology [T. E. Ouldridge, A. A. Louis, and J. P. K. Doye, J. Phys.: Condens. Matter {\bf 22}, 104102 (2010)] for dealing with the inference of bulk properties from small simulations of self-assembling systems of characteristic finite size. In particular, schemes for extrapolating the results of simulations of a single self-assembling object to the bulk limit are established in three cases: for assembly involving multiple particle species, for systems with one species localized in space and for simulations in the grand canonical ensemble. Furthermore, methodologies are introduced for evaluating the accuracy of these extrapolations. Example systems demonstrate that differences in cluster concentrations between simulations of a single self-assembling structure and bulk studies of the same model under identical conditions can be large, and that convergence on bulk results as system size is increased can be slow and non-trivial.