Using molecular dynamics computer simulations, we investigate the dynamics of the rotational degrees of freedom in a supercooled system composed of rigid, diatomic molecules. The interaction between the molecules is given by the sum of interaction-site potentials of the Lennard-Jones type. In agreement with mode-coupling theory (MCT), we find that the relaxation times of the orientational time correlation functions C (s)2 (t) and C 1 (t) show at low temperatures a power-law with the same critical temperature T c , and which is also identical to the critical temperature for the translational degrees of freedom. In contrast to MCT we find, however, that for these correlators the time-temperature superposition principle does not hold well and that also the critical exponent γ depends on the correlator. We also study the temperature dependence of the rotational diffusion constant D r and demonstrate that at high temperatures D r is proportional to the translational diffusion constant D and that when the system starts to become supercooled the former shows an Arrhenius behavior whereas the latter exhibits a power-law dependence. We discuss the origin for the difference in the temperature dependence of D (or the relaxation times of C
The mode coupling theory for the ideal liquid glass transition which was worked out for simple liquids mainly by Götze, Sjögren and their coworkers, is extended to a molecular liquid of linear and rigid molecules. By use of the projection formalism of Zwanzig and Mori an equation of motion is derived for the correlators S m m l l , ' ' (q,t) of the tensorial one-particle density ρ lm (q,t), which contains the orientational degrees of freedom for l > 0. Application of the mode coupling approximation to the memory kernel results into a closed set of equations for S m m l l , ' ' (q,t), which requires the static correlators S m m l l , ' ' (q) as the only input quantities. The corresponding MCT-equations for the non-ergodicity parameters () f q f m m m l l l ≡ , (qe 3) are solved for a system of dipolar hard spheres by restricting the values for l to 0 and 1. Depending on the packing fraction ϕ and on the temperature T, three different phases exist: a liquid phase, where translational (TDOF) (l = 0) and orientational (ODOF) (l = 1) degrees of freedom are ergodic, a phase where the TDOF are frozen into a (non-ergodic) glassy state whereas the ODOF remain ergodic, and finally a glassy phase where both, TDOF and ODOF, are non-ergodic. From the non-ergodicity parameters
Extending mode-coupling theory, we elaborate a microscopic theory for the glass transition of liquids confined between two parallel flat hard walls. The theory contains the standard mode-coupling theory equations in bulk and in two dimensions as limiting cases and requires as input solely the equilibrium density profile and the structure factors of the fluid in confinement. We evaluate the phase diagram as a function of the distance of the plates for the case of a hard sphere fluid and obtain an oscillatory behavior of the glass transition line as a result of the structural changes related to layering.
We present a detailed derivation of a microscopic theory for the glass transition of a liquid enclosed between two parallel walls relying on a mode-coupling approximation. This geometry lacks translational invariance perpendicular to the walls, which implies that the density profile and the density-density correlation function depends explicitly on the distances to the walls. We discuss the residual symmetry properties in slab geometry and introduce a symmetry adapted complete set of two-point correlation functions. Since the currents naturally split into components parallel and perpendicular to the walls the mathematical structure of the theory differs from the established mode-coupling equations in bulk. We prove that the equations for the nonergodicity parameters still display a covariance property similar to bulk liquids.
For hard ellipsoids of revolution we calculate the phase diagram for the idealized glass transition. Our equations cover the glass physics in the full phase space, for all packing fractions and all aspect ratios X0. With increasing aspect ratio we find the idealized glass transition to become primarily driven by orientational degrees of freedom. For needlelike or platelike systems the transition is strongly influenced by a precursor of a nematic instability. We obtain three types of glass transition line. The first one (straight phi((B))(c)) corresponds to the conventional glass transition for spherical particles which is driven by the cage effect. At the second one (straight phi((B'))(c)), which occurs for rather nonspherical particles, a glass phase is formed that consists of domains. Within each domain there is a nematic order where the center of mass motion is quasiergodic, whereas the interdomain orientations build an orientational glass. The third glass transition line (straight phi((A))(c)) occurs for nearly spherical ellipsoids where the orientational degrees of freedom with odd parity, e.g., 180 degrees flips, freeze independently from the positions.
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