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 γ or the conjugated (mean) shear stress τ 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 μF(T) which at constant τ decay monotonously with T following the affine shear elasticity μA(T), i.e., a simple two-point correlation function. At variance, non-monotonous behavior with a maximum at the glass transition temperature Tg is demonstrated for μF(T) at constant γ. The increase of G below Tg is reasonably fitted for both models by a continuous cusp singularity, G(T)∝(1 − T/Tg)1/2, in qualitative agreement with recent theoretical predictions. It is argued, however, that longer sampling times may lead to a sharper transition.
Shear modulus of simulated glass-forming model systems: Effects of boundary condition, temperature, and sampling time
J. P. Wittmer, H. Xu, P. Polińska, F. Weysser, J. Baschnagel; Shear modulus of simulated glass-forming model systems: Effects of boundary condition, temperature, and sampling time. J. Chem. Phys. 28 March 2013; 138 (12): 12A533. https://doi.org/10.1063/1.4790137
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