Transitions between imperfectly ordered crystalline structures: A phase switch Monte Carlo study

TL;DR

This study uses phase switch Monte Carlo to accurately analyze phase transitions between imperfectly ordered crystalline structures in confined 2D colloids, overcoming hysteresis issues and distinguishing stable from metastable phases.

Contribution

It introduces the application of phase switch Monte Carlo to efficiently determine free energy differences in complex phase transitions of confined colloids.

Findings

Phase switch Monte Carlo accurately locates transition points.

The method distinguishes metastable from stable structures.

Standard ensemble equivalence is violated in this context.

Abstract

A model for two-dimensional colloids confined laterally by "structured boundaries" (i.e., ones that impose a periodicity along the slit) is studied by Monte Carlo simulations. When the distance D between the confining walls is reduced at constant particle number from an initial value D_0, for which a crystalline structure commensurate with the imposed periodicity fits, to smaller values, a succession of phase transitions to imperfectly ordered structures occur. These structures have a reduced number of rows parallel to the boundaries (from n to n-1 to n-2 etc.) and are accompanied by an almost periodic strain pattern, due to "soliton staircases" along the boundaries. Since standard simulation studies of such transitions are hampered by huge hysteresis effects, we apply the phase switch Monte Carlo method to estimate the free energy difference between the structures as a function of the misfit between D and D_0, thereby locating where the transitions occurs in equilibrium. For comparison, we also obtain this free energy difference from a thermodynamic integration method: the results agree, but the effort required to obtain the same accuracy as provided by phase switch Monte Carlo would be at least three orders of magnitude larger. We also show for a situation where several "candidate structures" exist for a phase, that phase switch Monte Carlo can clearly distinguish the metastable structures from the stable one. Finally, applying the method in the conjugate statistical ensemble (where the normal pressure conjugate to D is taken as an independent control variable) we show that the standard equivalence between the conjugate ensembles of statistical mechanics is violated.