Theory for the reorientational dynamics in glass-forming liquids

Abstract

The mode-coupling theory for ideal liquid-glass transitions is extended so that the structural relaxation for the reorientational degrees of freedom of a linear molecule, which is immersed in a system of spherical particles, can be described. Closed equations of motion for the correlation functions formed with tensor density fluctuations are derived, which deal with the molecule's translational and reorientational motion. From these equations the nonergodicity parameters of a hard dumbbell molecule are calculated, which quantify its arrest in a hard-sphere glass. For top-down symmetric molecules it is shown that the odd-angular-momentum variables can exhibit an ergodic-to-nonergodic transition, characterized by a continuous increase of the EdwardsAnderson parameters near the critical points. ͓S1063-651X͑97͒03011-0͔

Semischematic model for the center-of-mass dynamics in supercooled molecular liquids

“…The approach presented here is a first step towards a full MCT description, which will necessarily include orientational correlations, i.e. the geometry of the molecule [17][18][19][20]. Our semi-schematic approach provides evidence that the slow dynamics in complex molecular liquids can be quantitatively described by a very simple modification of the MCT equations for simple liquids, thus retaining the simplicity of the COM description.…”

“…Details on the calculation of the critical amplitudes h (1) q and h (2) q can be found in Ref. [24]. In the late α-region it is not possible to solve analytically Eq.1, but the numerical solution is well fitted by a stretched exponential law (Kohlrausch-William-Watts law)…”

“…The possibility of describing theoretically the slow dynamics in supercooled molecular liquids is of fundamental importance for assessing the limitations of the ideal MCT, in making contact with experiments, and in tackling the problem of the relation between translational and rotational motions in supercooled states. Theoretical work has recently been undertaken [17][18][19][20] in this direction and appears to offer in future the possibility of a detailed comparison between experiments and theory. In this Letter we propose a semi-schematic [21] mode-coupling model to describe the COM dynamics in molecular liquids and we compare the predictions of the model with the COM collective correlation functions, calculated from a long molecular dynamics (MD) simulation for a model of a network forming molecular liquid [14].…”

Idealized glass transitions for a system of dumbbell molecules

“…Extensions of MCT to molecular systems have been studied already, generalizing the concept of a densityfluctuation correlator to the one of infinite matrices of correlation functions formed with tensor-density fluctuations [14,15,16,17,18,19,20,21,22]. The results calculated for the glass-form factors for a model of water [16,18] and for a liquid of linear molecules [17] could be used to explain simulation data quantitatively.…”

“…Promising results for anomalous oscillation spectra for a dipolar-hard-sphere system have been calculated [20]. For the model of a dilute solute of linear molecules in a solvent of spherical particles, the MCT equations could be fully solved [21,22]. The solutions were used to demonstrate the applicability of the universal formulas also for reorientational motion and to explain the characteristic difference between the α-peaks for dielectric-loss and depolarized-light-scattering spectra, as they have been observed in some experiments for van-der-Waals liquids.…”