Viscoelastic shear stress relaxation in two-dimensional glass forming liquids

TL;DR

This study uses molecular dynamics simulations to compare viscoelastic relaxation in two- and three-dimensional glass-forming liquids, revealing dimensional differences in glassy behavior and the influence of Mermin-Wagner fluctuations.

Contribution

It demonstrates how viscoelastic relaxation differs between two and three dimensions, highlighting the impact of Mermin-Wagner fluctuations on glassy dynamics.

Findings

Two-dimensional dynamic modulus is more stretched and lacks a plateau at higher temperatures.

At lower temperatures, 2D dynamic modulus shows an intermediate plateau similar to 3D.

Differences in glassy behavior relate to distinct ordering scenarios in 2D and 3D.

Abstract

Translational dynamics of two-dimensional glass forming fluids is strongly influenced by soft, long-wavelength fluctuations first recognized by D. Mermin and H. Wagner. As a result of these fluctuations, characteristic features of glassy dynamics, such as plateaus in the mean squared displacement and the self-intermediate scattering function, are absent in two dimensions. In contrast, Mermin-Wagner fluctuations do not influence orientational relaxation and well developed plateaus are observed in orientational correlation functions. It has been suggested that by monitoring translational motion of particles relative to that of their neighbors, one can recover characteristic features of glassy dynamics and thus disentangle the Mermin-Wagner fluctuations from the two-dimensional glass transition. Here we use molecular dynamics simulations to study viscoelastic relaxation in two and three dimensions. We find different behavior of the dynamic modulus below the onset of slow dynamics (determined by the orientational or cage-relative correlation functions) in two and three dimensions. The dynamic modulus for two-dimensional supercooled fluids is more stretched than for three-dimensional supercooled fluids and it does not exhibit a plateau, which implies the absence of glassy viscoelastic relaxation. At lower temperatures, the two-dimensional dynamic modulus starts exhibiting an intermediate time plateau and decays similarly to the three-dimensional dynamic modulus. The differences in the glassy behavior of two- and three-dimensional glass forming fluids parallel differences in the ordering scenarios in two and three dimensions.