Fluctuating phases and fluctuating relaxation times in glass forming liquids

Gcina A Mavimbela,Azita Parsaeian,Horacio E Castillo

doi:10.1063/1.5065574

Abstract

The presence of fluctuating local relaxation times, τr→(t) has been used for some time as a conceptual tool to describe dynamical heterogeneities in glass-forming systems. However, until now no general method is known to extract the full space and time dependent τr→(t) from experimental or numerical data. Here we report on a new method for determining a local phase field, ϕr→(t)≡∫tdt′τr→(t′) from snapshots {r→(ti)}i=1…M of the positions of the particles in a system, and we apply it to extract ϕr→(t) and τr→(t) from numerical simulations. By studying how this phase field depends on the number of snapshots, we find that it is a well defined quantity. By studying fluctuations of the phase field, we find that they describe heterogeneities well at long distance scales.

Highlights

II A, some of the initial motivation for the picture of dynamical heterogeneity came from the idea that non-exponential relaxation in a macroscopic sample is due to the combined effect of local exponential relaxations with different relaxation times
In this work we have shown that a quantitative description of glassy relaxation in terms of local fluctuating phases and relaxation times is possible
On one hand, starting from the case of exponential relaxation we presented a line of phenomenological arguments that shows how a local phase function φr(t) can emerge in the description of the data, and how its time derivative can, under certain circumstances, be interpreted as a local fluctuating relaxation rate 1/τr(t)

Summary

Introduction

As glass-forming liquids enter the supercooled state, relaxation processes gradually but dramatically slow down, and at the same time they become non-exponential.[1,2,3,4] One possible way of understanding this behavior would be to think of the relaxation function F(t) as the sum of a large number of exponentially decaying contributions, each with different relaxation times; with each contribution corresponding to a particular region in the system.[2,3,4] This is one aspect of the picture of dynamical heterogeneity, in which mesoscopic regions relax differently from each other and from the bulk.[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] In this framework, it is assumed that the differences between regions are not frozen in but dynamical, i.e. as the system evolves, the local relaxation times τr(t) evolve, so that “fast” regions become “slow”, and viceversa. Direct evidence for dynamical heterogeneity has been found in particle tracking experiments in glassy colloidal systems[10,11,12] and granular systems,[14] and in numerical simulations.[15,16]

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