Dynamic relaxation of a liquid cavity under amorphous boundary conditions

Abstract

The growth of cooperatively rearranging regions was invoked long ago by Adam and Gibbs to explain the slowing down of glass-forming liquids. The lack of knowledge about the nature of the growing order, though, complicates the definition of an appropriate correlation function. One option is the point-to-set correlation function, which measures the spatial span of the influence of amorphous boundary conditions on a confined system. By using a swap Monte Carlo algorithm we measure the equilibration time of a liquid droplet bounded by amorphous boundary conditions in a model glass-former at low temperature, and we show that the cavity relaxation time increases with the size of the droplet, saturating to the bulk value when the droplet outgrows the point-to-set correlation length. This fact supports the idea that the point-to-set correlation length is the natural size of the cooperatively rearranging regions. On the other hand, the cavity relaxation time computed by a standard, nonswap dynamics, has the opposite behavior, showing a very steep increase when the cavity size is decreased. We try to reconcile this difference by discussing the possible hybridization between MCT and activated processes, and by introducing a new kind of amorphous boundary conditions, inspired by the concept of frozen external state as an alternative to the commonly used frozen external configuration.

Completely rewritten version. After the first submission it was realized that swap and nonswap dynamics results are qualitatively different. This version reports the results of both dynamics and discusses the different behaviors. 17 pages, 18 figures

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