Y. Hiwatari

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.

RESIDENCE TIME DISTRIBUTION OF A TRACER ATOM IN SUPERCOOLED FLUIDS

The residence time distribution of a tracer atom in soft-sphere supercooled fluids is discussed on the basis of the trapping diffusion model of the glass transition. An explicit relation between a parameter of the trapping diffusion model and the soft-sphere fluid is obtained.

A Molecular Dynamics Study for Lithium Metasilicate: Liquid and Quenched Supercooled States

Abstract A molecular dynamics (MD) simulation of the lithium metasilicate (Li2SiO3) system has been performed to study the dynamics and geometrical structure of a liquid state at 1673 K and a glassy state at 700 K. The long term dynamics of the glassy state is shown for the self-part of the van Hove correlation functions. In the glassy state, diffusion of lithium ion was found to occur mainly through jump motions among equilibrium sites surrounded by oxygen atoms. A geometric structural analysis with polyhedra made of oxygen atoms around lithium was applied to characterize the structure and dynamical behavior.

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...

Stochastic dynamics in a supercooled fluid

We discuss the stochastic motion of atoms in a supercooled fluid near the glass transition point on the basis of the trapping diffusion model. We obtain the dynamical singularities in the mean square displacement, diffusion constant, incoherent scattering function and non‐Gaussian parameter. It is shown that the stochastic jump motion produces α‐type relaxation.

A TWO-DIMENSIONAL POLYMER CHAIN WITH SHORT-RANGE INTERACTIONS

The effects of short-range interactions on a two-dimensional polymer chain are studied with Monte Carlo simulations. The quantities such as the average length of turns along the chain, the persistence length, and the winding angle are investigated, for different interaction ranges, as functions of temperature. The scaling properties of the winding angle are also studied.

A modified hypernetted-chain integral equation for the supercooled liquid of inverse power potentials

Abstract Using the integral equation of the theory of liquids, we discuss structural properties of highly supercooled soft-sphere liquids. Two different thermodynamic self-consistent (TC) integral equations, i.e., the Rogers-Young equation and the reference hypernetted-chain equation, have been tested for highly supercooled liquids. According to these results, we propose a new modified hypernetted-chain integral equation for highly supercooled liquids (MHNCS). The bridge function of the MHNCS equation is approximated by an appropriate interpolation of the bridge function of the Percus-Yevick hard-sphere model and that of the leading elementary diagram. We have obtained solutions of the MHNCS equation for sixth and twelveth inverse power potentials (soft-sphere model). Below the freezing point, the PDF calculated from the MHNCS approximation is found to show a splitting of the second peak, which is compatible with the results of computer simulations, while the TC equations show no such a splitting.

Stochastic model for a glass transition

Abstract A stochastic trapping model for the glass transition in simple liquids is presented. A sharp transition from diffusive to non-diffusive regimes is predicted when the jump rate obeys a power law distribution. In the glassy region, an anomalous diffusion is expected and the incoherent scattering function shows a stretched exponential decay. The non-Gaussian parameter is shown to be used as an order parameter of the transition.

Equilibrium Properties of a Charged Polymer Chain with Short Range Interactions

Abstract We study the equilibrium properties of a two-dimensional charged polymer with screened Coulomb interactions by Monte Carlo simulations on a two-lattice model. It is found that the local conformation of the polymer is substantially dependent on the range of the interaction between the ions of the monomers and their counterions. The scaling relation for the gyration radius of the neutral polymer works also for the charged polymer. It is suggested that the Flory exponent shows a temperature dependent behavior at low temperatures. The segment analysis was also made to obtain that the end segment dominates the average properties of the finite size polymer.