1204.5716 (Thomas E. Ouldridge)

Inferring bulk self-assembly properties from small simulations: multiple
constituent species and systems in the grand canonical ensemble    [PDF]

Thomas E. Ouldridge

For self-assembling systems of finite size, it is often simplest to simulate the formation of a single structure. If these simulations are performed in the canonical ensemble, such an approach leads to large differences in yields relative to bulk systems. We calculate these finite-size effects for objects which assemble from several distinct species of monomers. A scheme for extrapolating from the results of small simulations to bulk (and following the convergence as a function of system size), under the approximation that distinct clusters behave ideally, is introduced. Furthermore, we demonstrate that this procedure remains valid if one of the constituent particles of each assembly is localized in space. Finally, we demonstrate that small simulations performed in the grand canonical ensemble must sample the formation of multiple large clusters to accurately reproduce bulk yields, and introduce a methodology for inferring bulk cluster distributions if this is impractical.

View original: http://arxiv.org/abs/1204.5716