Mode coupling approach to the ideal glass transition of molecular liquids: Linear molecules

Abstract

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

Dielectric spectroscopy in benzophenone: Theβrelaxation and its relation to the mode-coupling Cole-Cole peak

“…It is a well established fact that usually the minimum caused by the fast β process of MCT has much smaller relative weight in dielectric spectra than in those obtained by scattering methods [2,29]. This can be understood, at least qualitatively, taking into account different coupling to density fluctuations and different tensorial properties of the experimental probes [26,29,30]. The recently established CC peak of MCT [13,14] is due to just the same fast β dynamics as the minimum and thus also here a smaller amplitude in dielectric spectra can be expected.…”

Relaxational dynamics in the glassy, supercooled liquid, and orientationally disordered crystal phases of a polymorphic molecular material

“…Instead, materials with a complexity ranging from ionics to high polymers have been scrutinized 4 and the results have sometimes been interpreted within the framework of theories couched for simple hard-sphere fluids. This problem is only recently being addressed with the introduction of mode coupling approximations which take explicit account of the nonsphericity of the particles 5 and orientation dependent forces.…”

Glass Transitions in Quasi-Two-Dimensional Suspensions of Colloidal Ellipsoids

“…Molecular mode-coupling theory (MMCT) predicts that particle anisotropy should lead to new phenomena in glass transitions [9,10], and some of these have been observed in recent 3D simulations of hard ellipsoids [11,12]. MMCT [10,13] suggests that hard ellipsoids with an aspect ratio p > 2.5 in 3D can form an orientational glass in which rotational degrees of freedom become glass while the center-of-mass motion remains ergodic [9]. Such a "liquid glass" [14], in analogy to a liquid crystal, has not yet been explored in 3D or even 2D experiments.…”