The mean-squared displacement of a molecule moving in a glassy system

The mean-squared displacement (MSD) of a hard sphere and of a dumbbell molecule consisting of two fused hard spheres immersed in a dense hard-sphere system is calculated within the mode-coupling theory for ideal liquid-glass transitions. It is proven that the velocity correlator, which is the second time derivative of the MSD, is the negative of a completely monotone function for times within the structural-relaxation regime. The MSD is found to exhibit a large time interval for structural relaxation prior to the onset of the $\alpha$-process which cannot be described by the asymptotic formulas for the mode-coupling-theory-bifurcation dynamics. The $\alpha$-process for molecules with a large elongation is shown to exhibit an anomalously wide cross-over interval between the end of the von-Schweidler decay and the beginning of normal diffusion. The diffusivity of the molecule is predicted to vary non-monotonically as function of its elongation.Comment: 18 pages, 12 figures, Phys. Rev. E, in prin

Static and Dynamic Properties of a Viscous Silica Melt Molecular Dynamics Computer Simulations

We present the results of a large scale molecular dynamics computer simulation in which we investigated the static and dynamic properties of a silica melt in the temperature range in which the viscosity of the system changes from O(10^-2) Poise to O(10^2) Poise. We show that even at temperatures as high as 4000 K the structure of this system is very similar to the random tetrahedral network found in silica at lower temperatures. The temperature dependence of the concentration of the defects in this network shows an Arrhenius law. From the partial structure factors we calculate the neutron scattering function and find that it agrees very well with experimental neutron scattering data. At low temperatures the temperature dependence of the diffusion constants $D$ shows an Arrhenius law with activation energies which are in very good agreement with the experimental values. With increasing temperature we find that this dependence shows a cross-over to one which can be described well by a power-law, D\propto (T-T_c)^gamma. The critical temperature T_c is 3330 K and the exponent gamma is close to 2.1. Since we find a similar cross-over in the viscosity we have evidence that the relaxation dynamics of the system changes from a flow-like motion of the particles, as described by the ideal version of mode-coupling theory, to a hopping like motion. We show that such a change of the transport mechanism is also observed in the product of the diffusion constant and the life time of a Si-O bond, or the space and time dependence of the van Hove correlation functions.Comment: 30 pages of Latex, 14 figure

Mechanical Relaxation in Glasses and at the Glass Transition

The Gilroy-Phillips model of relaxational jumps in asymmetric double-well potentials, developed for the Arrhenius-type secondary relaxations of the glass phase, is extended to a formal description of the breakdown of the shear modulus at the glass transition, the flow process.Comment: 13 pages, 11 figures, 49 ref

Neutron scattering and molecular correlations in a supercooled liquid

We show that the intermediate scattering function $S_n(q,t)$ for neutron scattering (ns) can be expanded naturely with respect to a set of molecular correlation functions that give a complete description of the translational and orientational two-point correlations in the liquid. The general properties of this expansion are discussed with special focus on the $q$-dependence and hints for a (partial) determination of the molecular correlation functions from neutron scattering results are given. The resulting representation of the static structure factor $S_n(q)$ is studied in detail for a model system using data from a molecular dynamics simulation of a supercooled liquid of rigid diatomic molecules. The comparison between the exact result for $S_n(q)$ and different approximations that result from a truncation of the series representation demonstrates its good convergence for the given model system. On the other hand it shows explicitly that the coupling between translational (TDOF) and orientational degrees of freedom (ODOF) of each molecule and rotational motion of different molecules can not be neglected in the supercooled regime.Further we report the existence of a prepeak in the ns-static structure factor of the examined fragile glassformer, demonstrating that prepeaks can occur even in the most simple molecular liquids. Besides examining the dependence of the prepeak on the scattering length and the temperature we use the expansion of $S_n(q)$ into molecular correlation functions to point out intermediate range orientational order as its principle origin.Comment: 13 pages, 7 figure

Low-temperature specific heat and thermal conductivity of glycerol

We have measured the thermal conductivity of glassy glycerol between 1.5 K and 100 K, as well as the specific heat of both glassy and crystalline phases of glycerol between 0.5 K and 25 K. We discuss both low-temperature properties of this typical molecular glass in terms of the soft-potential model. Our finding of an excellent agreement between its predictions and experimental data for these two independent measurements constitutes a robust proof of the capabilities of the soft-potential model to account for the low-temperature properties of glasses in a wide temperature range.Comment: 4 pages, 3 figures. To be published in Phys. Rev. B (2002

Energy landscape - a key concept for the dynamics of glasses and liquids

There is a growing belief that the mode coupling theory is the proper microscopic theory for the dynamics of the undercooled liquid above a critical temperature T_c. In addition, there is some evidence that the system leaves the saddlepoints of the energy landscape to settle in the valleys at this critical temperature. Finally, there is a microscopic theory for the entropy at the calorimetric glass transition T_g by Mezard and Parisi, which allows to calculate the Kauzmann temperature from the atomic pair potentials. The dynamics of the frozen glass phase is at present limited to phenomenological models. In the spirit of the energy landscape concept, one considers an ensemble of independent asymmetric double-well potentials with a wide distribution of barrier heights and asymmetries (ADWP or Gilroy-Phillips model). The model gives an excellent description of the relaxation of glasses up to about T_g/4. Above this temperature, the interaction between different relaxation centers begins to play a role. One can show that the interaction reduces the number of relaxation centers needed to bring the shear modulus down to zero by a factor of three.Comment: Contribution to the III Workshop on Nonequilibrium Phenomena in Supercooled Fluids, Glasses and Amorphous Materials, 22-27 September 2002, Pisa; 14 pages, 3 figures; Version 3 takes criticque at Pisa into account; final version 4 will be published in J.Phys.: Condens.Matte

Dynamics in a supercooled molecular liquid: Theory and Simulations

We report extensive simulations of liquid supercooled states for a simple three-sites molecular model, introduced by Lewis and Wahnstr"om [L. J. Lewis and G. Wahnstr"om, Phys. Rev. E 50, 3865 (1994)] to mimic the behavior of ortho-terphenyl. The large system size and the long simulation length allow to calculate very precisely --- in a large q-vector range --- self and collective correlation functions, providing a clean and simple reference model for theoretical descriptions of molecular liquids in supercooled states. The time and wavevector dependence of the site-site correlation functions are compared with detailed predictions based on ideal mode-coupling theory, neglecting the molecular constraints. Except for the wavevector region where the dynamics is controlled by the center of mass (around 9 nm-1), the theoretical predictions compare very well with the simulation data.

Broadband Dielectric Spectroscopy on Glass-Forming Propylene Carbonate

Dielectric spectroscopy covering more than 18 decades of frequency has been performed on propylene carbonate in its liquid and supercooled-liquid state. Using quasi-optic submillimeter and far-infrared spectroscopy the dielectric response was investigated up to frequencies well into the microscopic regime. We discuss the alpha-process whose characteristic timescale is observed over 14 decades of frequency and the excess wing showing up at frequencies some three decades above the peak frequency. Special attention is given to the high-frequency response of the dielectric loss in the crossover regime between alpha-peak and boson-peak. Similar to our previous results in other glass forming materials we find evidence for additional processes in the crossover regime. However, significant differences concerning the spectral form at high frequencies are found. We compare our results to the susceptibilities obtained from light scattering and to the predictions of various models of the glass transition.Comment: 13 pages, 9 figures, submitted to Phys. Rev.

Harmonic Vibrational Excitations in Disordered Solids and the "Boson Peak"

We consider a system of coupled classical harmonic oscillators with spatially fluctuating nearest-neighbor force constants on a simple cubic lattice. The model is solved both by numerically diagonalizing the Hamiltonian and by applying the single-bond coherent potential approximation. The results for the density of states $g(\omega)$ are in excellent agreement with each other. As the degree of disorder is increased the system becomes unstable due to the presence of negative force constants. If the system is near the borderline of stability a low-frequency peak appears in the reduced density of states $g(\omega)/\omega^2$ as a precursor of the instability. We argue that this peak is the analogon of the "boson peak", observed in structural glasses. By means of the level distance statistics we show that the peak is not associated with localized states