J. Matsui

A Unified Theory for the Glass Transition Dynamics and its Singularities

Vitrification is a gradual freezing process of supercooled liquids, during which a slow process is separated from the fast diffusive and microscopic motions. The slow process is identified as a non-trapped jump motion and can be characterized by the waiting time distribution (WTD) of the elementary relaxation process. The authors first show that the WTD can be expressed as a power law function in the long time limit in general with modest assumptions. Defining the glass transition temperature by vanishing diffusivity or the divergence of the mean waiting time, the authors relate the exponent to the Adam-Gibbs parameter Ts{sub C}(T) where T is the temperature and s{sub C}(T) is the excess entropy. They also show that the divergence of the fluctuation of WTD leads to a cross over in the non-Gaussianity and present a unified view of the dynamics in the vitrification process.

The observation of the longitudinal wave velocity in a model supercooled liquid

We have improved the non-equilibrium molecular dynamics measurement for the longitudinal wave (LW) velocity (the speed of sound) and have applied it to a model system in 2D and 3D. The LW velocity at temperature of the glass or supercooled liquid state reaches the range of in the 2D system and in the 3D system, with a gradual increase with increasing temperature under the isochoric and adiabatic conditions. In our previous paper [4] we analysed that the cooperative motion in intermediate time and length scales propagates with a speed depending on temperature and found that its dependency is opposed to that of the LWs. It suggests that the cooperative motion spreads over the system in a different way of sound.

Non-Gaussianity in the frequency domain

The non-Guassianity in the frequency domain is introduced in terms of the generalized susceptibility, which is shown to be a useful quantity to distinguish the nature of dynamics. The dynmaics of binary soft-spheres in the super-cooled state is analyzed by the non-Gaussianity.

The self-part of the generalized susceptibility of a supercooled binary soft-sphere system

Abstract Using molecular-dynamics simulation, the self-part of the generalized susceptibility χ s ″ ( q , ω ) is calculated for a binary soft-sphere system at various temperatures from the liquid state to the glassy state and at the wavelength equal to the mean inter-particle distance. The dynamical slowing is clearly seen in the imaginary part of χ s ( q , ω ); the α-peak splits out from the single main peak in the liquid state and moves toward the lower frequency side, as the temperature is reduced to the supercooled liquid state. In the glassy state, another slow dynamics identified as the fast process appears between the two separate peaks.

Molecular Dynamics Study of a Supercooled Binary Soft-Sphere System: Calculation of the Generalized Susceptibility in Supercooled and Glassy States

To study how the motion of atoms changes through a glass forming process, we have carried out the molecular dynamics simulation for a binary soft-sphere system and calculated the self-part of the generalized susceptibility x.(q,w) at various temperatures above/below T9 • At higher temperature, only one peak appears in the imaginary part of Xs, which corresponds to random motion of atoms in the liquid state. When the temperature is reduced, the a-peak tends to separate out from the main peak and to move to lower frequencies. At the lowest temperature, the peak disappears from our frequency window. We show that the temperature dependence of the peak frequency is well described by the Vogel-Fulcher low. We also test the mode coupling theory. The two exponents do not agree with the unixad versality of toe mode coupling theory, >. = F(1- a?/ F(1 + 2b) =const.

Separation of Diffusive Jump Motion and Trapped Motion of Atoms in a Glass Forming Process Via Molecular Dynamics Simulation

We have carried out the molecular dynamics (MD) simulation for a binary soft-sphere system and calculated the self part of the generalized susceptibility χ s ( q, ω ) at various temperatures. At higher temperatures in liquid state, only one peak appears in the imaginary part of Xa, which tends to split into two peaks, the so-called α- and β- peaks, as the temperature is reduced. The temperature dependence of the peak frequency is well described by the Vogel-Fulcher law for the α- peak, and the peak frequency does not change much for the α- peak. We have also measured the trajectory volume of a tagged atom V(t), which is related to the dynamical order parameter, the “generalized capacity”, in structural glass transitions recently proposed by J. F. Douglas. These results show the transition temperature which is in good agreement with that determined by the trapping diffusion model.