Shear modulus of simulated glass-forming model systems: Effects of boundary condition, temperature and sampling time

TL;DR

This study investigates how boundary conditions, temperature, and sampling time affect the shear modulus of simulated glass-forming systems in 2D and 3D, revealing ensemble-dependent behaviors and a cusp-like transition at the glass transition temperature.

Contribution

It provides a comparative analysis of shear modulus measurements under different ensembles and explores the nature of the glass transition in simulated systems.

Findings

Shear modulus G increases below T_g following a (1-T/T_g)^(1/2) law.

Ensemble choice significantly influences shear stress fluctuation behavior.

Longer sampling times may sharpen the observed glass transition.

Abstract

The shear modulus G of two glass-forming colloidal model systems in d=3 and d=2 dimensions is investigated by means of, respectively, molecular dynamics and Monte Carlo simulations. Comparing ensembles where either the shear strain gamma or the conjugated (mean) shear stress tau are imposed, we compute G from the respective stress and strain fluctuations as a function of temperature T while keeping a constant normal pressure P. The choice of the ensemble is seen to be highly relevant for the shear stress fluctuations mu_F(T) which at constant tau decay monotonously with T following the affine shear elasticity mu_A(T), i.e. a simple two-point correlation function. At variance, non-monotonous behavior with a maximum at the glass transition temperature T_g is demonstrated for mu_F(T) at constant gamma. The increase of G below T_g is reasonably fitted for both models by a continuous cusp singularity, G(T) is proportional to (1-T/T_g)^(1/2), in qualitative agreement with some recent replica calculations. It is argued, however, that longer sampling times may lead to a sharper transition. The additive jump discontinuity predicted by mode-coupling theory and other replica calculations thus cannot ultimately be ruled out.