Relaxation moduli of glass-forming systems: temperature effects and fluctuations

Equilibrium and dynamical properties of a two-dimensional polydisperse colloidal model system are characterized by means of molecular dynamics (MD) and Monte Carlo (MC) simulations. We employed several methods to prepare quasi-equilibrated systems: in particular, by slow cooling and tempering with MD (method SC-MD), and by tempering with MC dynamics involving swaps of particle diameters (methods Sw-MD, Sw-MC). It is revealed that the Sw-methods are much more efficient for equilibration below the glass transition temperature T_g leading to denser and more rigid systems which show much slower self-diffusion and shear-stress relaxation than their counterparts prepared with the SC-MD method. The shear-stress relaxation modulus G(t) is obtained based on the classical stress-fluctuation relation. We demonstrate that the α-relaxation time τ_α obtained using a time-temperature superposition of G(t) shows a super-Arrhenius behavior with the VFT temperature T₀ well below T_g. We also derive novel rigorous fluctuation relations providing isothermic and adiabatic compression relaxation moduli in the whole time range (including the short-time inertial regime) based on correlation data for thermostatted systems. It is also shown that: (i) the assumption of Gaussian statistics for stress fluctuations leads to accurate predictions of the variances of the fluctuation moduli for both shear (μ_F) and compression (η_F) at T⪆T_g. (ii) The long-time (quasi-static) isothermic and adiabatic moduli increase on cooling faster than the affine compression modulus η_A, and this leads to a monotonic temperature dependence of η_F which is qualitatively different from μ_F(T) showing a maximum near T_g.