Microscopic theory of glassy dynamics and glass transition for molecular crystals

Abstract

We derive a microscopic equation of motion for the dynamical orientational correlators of molecular crystals. Our approach is based upon mode coupling theory. Compared to liquids we find four main differences: (i) the memory kernel contains Umklapp processes if the total momentum of two orientational modes is outside the first Brillouin zone, (ii) besides the static two-molecule orientational correlators one also needs the static one-molecule orientational density as an input, where the latter is nontrivial due to the crystal's anisotropy, (iii) the static orientational current density correlator does contribute an anisotropic, inertia-independent part to the memory kernel, and (iv) if the molecules are assumed to be fixed on a rigid lattice, the tensorial orientational correlators and the memory kernel have vanishing l,l(') = 0 components, due to the absence of translational motion. The resulting mode coupling equations are solved for hard ellipsoids of revolution on a rigid sc lattice. Using the static orientational correlators from Percus-Yevick theory we find an ideal glass transition generated due to precursors of orientational order which depend on X(0) and psi, the aspect ratio and packing fraction of the ellipsoids. The glass formation of oblate ellipsoids is enhanced compared to that for prolate ones. For oblate ellipsoids with X(0) < or = 0.7 and prolate ellipsoids with X(0) < or = 4, the critical diagonal nonergodicity parameters in reciprocal space exhibit more or less sharp maxima at the zone center with very small values elsewhere, while for prolate ellipsoids with 2 < or = X(0) < or = 2.5 we have maxima at the zone edge. The off-diagonal nonergodicity parameters are not restricted to positive values and show similar behavior. For 0.7 < or = X(0) < or = 2, no glass transition is found because of too small static orientational correlators. In the glass phase, the nonergodicity parameters show a much more pronounced q dependence.