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, (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 X0 and ϕ, 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 X0 0.7 and prolate ellipsoids with X0 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 X0 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 X0 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.

High-frequency excitations in glassy crystals

“…This notion was promoted in [55], based on measurements on canonical glass formers and strongly doped semiconductors. For glass-forming liquids, the MCT predicts contributions from a fast process in this region, in reasonable accord with the experimental results; and there are indications that this may also be the case for PCs [29,51].…”

“…Thus, in light of the results of Fig. 2, one may ask if there is an analogue to the cage effect in PCs and in fact some strong indications for the applicability of the MCT to PCs were obtained recently [29,51]. For a quantitative comparison of the dielectric results with MCT predictions, similar to that performed in glycerol [31], a more complete set of data is necessary.…”

Effects of site-occupation disorder on the low-temperature thermal conductivity of molecular crystals

“…[19]. The sample container was filled with liquid samples under 4 He gas flow. The thermal history followed in the present measurements started from the OD phase attaining crystallization into the low-temperature phase by cooling at ≈1 K min −1 .…”

“…In fact, detailed theoretical consideration of molecular liquids [3] and some classes of molecular crystals [4] have enabled the establishment of some connections with theoretical results derived from several statistical mechanics approaches where glassiness appears in the dynamics of simple, idealized objects [2]. Such model * Electronic address: josep.lluis.tamarit@upc.edu systems show trivial, non-interacting, equilibrium behaviors but nonetheless, interesting slow dynamics features appear due to restrictions on the allowed transitions between configurations.…”

Multiple time scales in the microscopic dynamics of simple and complex liquids as studied by radiation scattering

“…Kinetic theories portray such a transition in terms of the onset of stochastic mass transport and reorientational motions signalling liquid-flow taking place beyond a characteristic temperature usually referred to as T c located a few tens of Kelvin above the calorimetric glass-transition temperature T g . This theory constitutes the only predictive tool presently at our disposal which is capable of describing glassy phenomena in simple liquids [19], molecular liquids [22], and molecular crystals [23].…”