Hiroh Miyagawa

Dynamical singularities near the liquid-glass transition: Theory and molecular dynamics study

Abstract This review article discusses recent developments in the study of the dynamical property of supercooled liquids close to the liquid-glass transition, in particular the dynamical singularity accompanied by the transition. The glass transition is a dynamical transition in the sense that when a liquid is rapidly cooled or compressed beyond the freezing point, the system can go into a quasi-equilibrium, metastable or nonequilibrium state, characterized by long structural relaxation times. Therefore, investigations on the dynamical properties of the supercooled liquids are essential to understanding the nature of the liquid-to-glass transition, which are the main issues of this article. The article reviews recent molecular dynamics studies on the dynamical properties of highly supercooled liquids and glasses and the theoretical developments about the liquid-glass transition based on mode-coupling approximations, generalized nonlinear hydrodynamic equations and a trapping diffusion model which have extensively been studied over the past decade. The molecular dynamics simulations prove to be an extremely useful and increasingly valuable aid to the elucidation of glass transition phenomena and the study of amorphous structures, but care is needed in the interpretation of the simulation results on the dynamical properties of such highly supercooled liquids and glasses, in which dynamical slowing down is essential, and consequently the relaxation time exceeds far over the order of the time investigated in computer experiments. We examine a variety of results on the dynamical behaviors obtained by molecular dynamics simulations and theoretical works from different points of view, and elucidate the dynamical singularity near the transition, which we call “quasi critical phenomena”, as in the second-order phase transition.

Calculation of the generalized susceptibility for a highly supercooled fluid through molecular-dynamics simulation

Abstract A new method of computation of generalized susceptibility and dynamical structure factor through molecular dynamics (MD) simulation is proposed. This gives rise to a reliable and accurate result more than that calculated from a conventional method with a direct Fourier transformation. Computational results are presented for the imaginary part of the generalized susceptibility, X″ (ω), for a binary soft-sphere fluid with a super-long-time molecular dynamics (MD) simulation. Both α- and β-peaks in X″ (ω) in a supercooled fluid is shown for the first time through the present MD computation. The MD result obtained is in a good agreement with that obtained by the trapping diffusion model, which we have previously proposed for the glass transition.

Molecular dynamics study of binary alloys near the glass transition

Abstract The nature of the glass transition of simple binary fluids is argued with molecular dynamics simulations for a two-component soft-sphere model. We will focus our attention on the dynamical properties of supercooled fluids and the dynamics of the liquid-glass transition. For these purposes, we have carried out long-time molecular dynamics simulations for rapidly quenched samples by various different routes (cooling rates and initial conditions). Not only the dynamic properties associated to single atom motions, but also the behaviors of collective motions of atoms, longitudinal and transverse sound waves, and stress autocorrelations for the supercooled fluids of binary soft-sphere mixtures are examined in detail.

Molecular‐dynamics study of highly supercooled liquids: Dynamical singularities near the liquid‐glass transition

We report on the molecular‐dynamics (MD) study of the binary soft‐sphere fluids, focusing our attention on their dynamical properties of the supercooled fluid phase and the dynamical anomalies associated with the liquid‐glass transition. The time dependent behavior of the mean‐square displacement, intermediate scattering functions, both of the self (incoherent) and total correlations, also the dynamical structure factor and non‐Gaussian parameter (NGP) are examined. Because of a rather short time window searched by the MD simulation, it is only an apparent dynamical behavior (e.g. on the diffusion coefficient, the long‐time decay of the density autocorrelation function and so on) that we can observe through the MD simulation in the vicinity of the transition, in which the longest relaxation time far exceeds the time scale of the MD simulation. Therefore, it accompanies severe difficulties in practice with an accurate determination of the glass transition temperature of the system from the properties of th...

Study of the α and β relaxations in a supercooled fluid via molecular-dynamics simulations

Incoherent scattering function (self-part of the density autocorrelation function) Fs(k, t) is computed by molecular-dynamics (MD) simulation in supercooled fluids of binary soft-sphere mixtures. The full density autocorrelation function F(k, t) was also computed. It is found that Fs(k, t)s at various temperatures and wavenumbers can be fitted over a wide range of time steps (at least over three orders of the decay) by a Williams-Watts stretched exponential function Fs(k, t) = A exp[ -(t/t0)β], where A, β and t0 are adjustable parameters. Significant dynamical behaviours are also presented for mean square displacements and non-Gaussian parameters. With results obtained from different system size, N = 500 and N = 4000 a significant size dependence is suggested. Generalized susceptibility χ(k, ω) and dynamical structure factor S(k, ω) are also computed over a wide range of ω (over five orders) using a new algorithm for the numerical integrations. Computational results are presented for the imaginary part of the generalized susceptivility, χ′(k, ω), which indicates both α and β peaks in such spectra for the first time by the present MD computation. The present MD results are in good agreement with the predictions of the trapping diffusion model, which we have previously proposed for the glass transition.

Molecular-Dynamics Simulations for the Density Autocorrelation Function in a Supercooled Fluid Phase

Abstract We have re-calculated the self part of the density autocorrelation function Fs(k, t) (incoherent scattering function) for the binary soft-sphere fluid with a much longer molecular-dynamics (MD) simulation than our previous MD calculations, and with a larger system size (N = 4000) to a longer time window as well as to study a system-size dependence, if it exists. The full density autocorrelation function F(k, t) was also computed. It is found that all F(k, t)s that we have computed in this work can be fitted over a wide range of time steps (at least over three figures of the decay) by a Williams-Watts stretched exponential function Fs(k, t) = A exp [— (t/t 0)β], where A, β and t 0 are adjustable parameters. Other significant dynamical behaviours were also presented in mean square displacements and non-Gaussian parameters for highly supercooled fluids with N = 4000. The present results are compatible to our previous computations with N = 500, but a significant size dependence is suggested.

Dynamical singularity of the glass transition in molten lithium iodide

Abstract The liquid-glass transition in molten lithium iodide has been investigated by means of constant-pressure and constant-temperature molecular dynamics. Both static and dynamic properties were calculated, with a microscopic analysis of the ionic motions. In the vicinity of the glass transition, the mean-square displacement shows a non-linear time dependence and the incoherent scattering function is well fitted by a ‘stretched exponential’ function. The maximum value of the non-Gaussian parameter increases drastically on approaching the glass transition. The glass transition temperature is estimated by trapping diffusion theory.

MOLECULAR-DYNAMICS STUDY OF BINARY ALLOYS: DYNAMICAL CORRELATIONS OF THE SUPERCOOLED LIQUIDS NEAR THE GLASS TRANSITION OF BINARY SOFT-SPHERE MIXTURES

With the aid of molecular-dynamics simulations of soft-sphere mixtures we have computed the longitudinal and transverse collective modes (sound waves). The shear stress autocorrelation function is also computed. It is shown that the stress autocorrelation function exhibits characteristic slow relaxation phenomena (long-time tails) near and beyond the glass transition, compatible with the previous result obtained from the density autocorrelation functions. However, the decaying form of both functions at long times appears to be significantly different.

Dynamical correlations in binary soft-sphere glasses

Abstract Dynamical correlations in binary fluids are investigated by use of molecular dynamics simulations for soft-sphere mixtures. Longitudinal and transverse collective modes (sound waves) are studied by computing the dynamical structure factors and the Fourier transforms of the transverse current correlation function, respectively. The stress autocorrelation function is also computed. It is shown that the stress autocorrelation function exhibits characteristic slow relaxation phenomena (long-time tails) near and beyond the glass transition, compatible with the previous result obtained from the analysis of the density autocorrelation functions.