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Translational dynamics of two-dimensional glass forming fluids is stronglyinfluenced by soft, long-wavelength fluctuations first recognized by D. Merminand H. Wagner. As a result of these fluctuations, characteristic features ofglassy dynamics, such as plateaus in the mean squared displacement and theself-intermediate scattering function, are absent in two dimensions. Incontrast, Mermin-Wagner fluctuations do not influence orientational relaxationand well developed plateaus are observed in orientational correlationfunctions. It has been suggested that by monitoring translational motion ofparticles relative to that of their neighbors, one can recover characteristicfeatures of glassy dynamics and thus disentangle the Mermin-Wagner fluctuationsfrom the two-dimensional glass transition. Here we use molecular dynamicssimulations to study viscoelastic relaxation in two and three dimensions. Wefind different behavior of the dynamic modulus below the onset of slow dynamics(determined by the orientational or cage-relative correlation functions) in twoand three dimensions. The dynamic modulus for two-dimensional supercooledfluids is more stretched than for three-dimensional supercooled fluids and itdoes not exhibit a plateau, which implies the absence of glassy viscoelasticrelaxation. At lower temperatures, the two-dimensional dynamic modulus startsexhibiting an intermediate time plateau and decays similarly to thethree-dimensional dynamic modulus. The differences in the glassy behavior oftwo- and three-dimensional glass forming fluids parallel differences in theordering scenarios in two and three dimensions.

Viscoelastic shear stress relaxation in two-dimensional glass forming liquids