The two-dimensional freezing transition is very different from its three-dimensional counterpart. In contrast, the glass transition is usually assumed to have similar characteristics in two and three dimensions. Using computer simulations we show tha
t glassy dynamics in supercooled two- and three-dimensional fluids are fundamentally different. Specifically, transient localization of particles upon approaching the glass transition is absent in two dimensions, whereas it is very pronounced in three dimensions. Moreover, the temperature dependence of the relaxation time of orientational correlations is decoupled from that of the translational relaxation time in two dimensions but not in three dimensions. Lastly, the relationships between the characteristic size of dynamically heterogeneous regions and the relaxation time are very different in two and three dimensions. These results strongly suggest that the glass transition in two dimensions is different than in three dimensions.
We use a long, all-atom molecular dynamics (MD) simulation combined with theoretical modeling to investigate the dynamics of selected lipid atoms and lipid molecules in a hydrated diyristoyl-phosphatidylcholine (DMPC) lipid bilayer. From the analysis
of a 0.1 $mu$s MD trajectory we find that the time evolution of the mean square displacement, [delta{r}(t)]^2, of lipid atoms and molecules exhibits three well separated dynamical regions: (i) ballistic, with [delta{r}(t)]^2 ~ t^2 for t < 10 fs; (ii) subdiffusive, with [delta{r}(t)]^2 ~ t^{beta} with beta<1, for 10 ps < t < 10 ns; and (iii) Fickian diffusion, with [delta{r}(t)]^2 ~ t for t > 30 ns. We propose a memory function approach for calculating [delta{r}(t)]^2 over the entire time range extending from the ballistic to the Fickian diffusion regimes. The results are in very good agreement with the ones from the MD simulations. We also examine the implications of the presence of the subdiffusive dynamics of lipids on the self-intermediate scattering function and the incoherent dynamics structure factor measured in neutron scattering experiments.
