Viscoelastic shear stress relaxation in two-dimensional glass-forming liquids

Translational dynamics of 2D 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 2D 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 2D supercooled fluids is more stretched than for 3D supercooled fluids and does not exhibit a plateau, which implies the absence of glassy viscoelastic relaxation. At lower temperatures, the 2D dynamic modulus starts exhibiting an intermediate time plateau and decays similarly to the 2D dynamic modulus. The differences in the glassy behavior of 2D and 3D glass-forming fluids parallel differences in the ordering scenarios in two and three dimensions.