Local versus Global Stretched Mechanical Response in a Supercooled Liquid near the Glass Transition

Abstract

Amorphous materials have a rich relaxation spectrum, which is usually described in terms of a hierarchy of relaxation mechanisms. In this work, we investigate the local dynamic modulus spectra in a model glass just above the glass transition temperature by performing a mechanical spectroscopy analysis with molecular dynamics simulations. We find that the spectra, at the local as well as on the global scale, can be well described by the Cole-Davidson formula in the frequency range explored with simulations. Surprisingly, the Cole-Davidson stretching exponent does not change with the size of the local region that is probed. The local relaxation time displays a broad distribution, as expected based on dynamic heterogeneity concepts, but the stretching is obtained independently of this distribution. We find that the size dependence of the local relaxation time and moduli can be well explained by the elastic shoving model. arXiv:1812.04527v2 [cond-mat.dis-nn] 12 Feb 2019 Nonexponential or stretched exponential relaxation is ubiquitous in amorphous materials, and is recognized as one of the key features in supercooled liquid and glassy states [1,2].It appears in many relaxation processes at equilibrium or out of equilibrium, such as aging, stress relaxation and dielectric or mechanical relaxation spectra [3,4]. However, the origin of the stretching is still controversial [5]. Two hypotheses are typically put forward to explain the stretching: one identifies the stretched relaxation as resulting from dynamic heterogeneity in different regions of space, the other assumes that the relaxation in amorphous material is uniform, with stretched relaxation being a local feature [6,7].These different views can to some extent be reconciled within the now widely accepted concept of dynamical heterogeneity, which has been confirmed both in experiment and molecular simulation [8]. The supercooled liquid, for example, can be separated into fast regions of high mobility and slow regions with lower mobility, with a "slow" or "fast" character that persists over times comparable to the total α relaxation time. Mathematically, stretched exponential relaxation can be described as a superposition of simple exponential relaxation processes [9]. It is then a natural hypothesis to assume that the slow and fast regions associated with dynamical heterogeneity each have a simple exponential relaxation, and that the global stretching results from the different relaxation times associated with different regions, which may be broadly distributed. In fact, this natural assumption was recently formalized in a series of works by Masurel et al. [10][11][12], who developed a mesoscale model to describe the viscoelastic spectrum in a polymer model near the glass transition temperature. In their model, every local region is described as a single Maxwell Voigt element, with a single relaxation time assigned randomly from a broad (log normal) distribution. Based on the idea that dynamic and elastic heterogeneity are related, Schirmacher[13] also uses a local...

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