Shaw Kambayashi

Dynamic Slowing-Down and Nonexponential Decay of the Density Correlation Function in Soft-Sphere Supercooled Liquids

Molecular dynamics simulations were carried out for supercooled soft-sphere liquids. The computed density correlation function shows a clear nonexponential decay in intermediate times, as the liquid-glass transition is approached. The overall time dependence of the correlation function can be fitted by a stretched function of the type: exp [-( t / t 0 ) α ], where the exponent α varies from 1, in stable liquids, down to about 0.5, in the vicinity of the liquid-glass transition. The average correlation time =(1/α) G (1/α) t 0 ( G ( x ) being the gamma function) can be reasonably fitted by a scaling law of the type: \({\langle}T{\rangle}{\propto}(\varGamma_{\text{g}}-\varGamma)^{-\theta}\), where \(\varGamma\) is a coupling constant, the suffix g denotes the glass transition, and the exponent θ varies from about 2 to 5, depending on wave number k . The wave number dependence of the correlation function is discussed.

Numerical Calculation of the Bridge Function for Soft-Sphere Supercooled Fluids via Molecular Dynamics Simulations

Abstract Isokinetic molecular dynamics simulations have been performed for 13,500 soft-spheres interacting through the inverse-power potential, e([sgrave]/r)n , near and below the freezing temperature. The bridge function for the integral equation of the theory of liquids is extracted from the pair distribution function (PDF) obtained by the computer simulations for n = 6 and 12. The result is compared with that of approximate theories, i.e., the Rogers-Young (RY) approximation and a modified hypernetted-chain approximation for supercooled soft-sphere fluids (MHNCS approximation). Below the freezing temperature, the bridge function obtained by the computer simulation begins to oscillate around zero at intermediate distances where the second peak of the PDF appears. Such oscillatory behavior of the bridge function is well reproduced by the MHNCS approximation which includes correlations given by the leading elementary diagram, in remarkable contrast to that of the RY approximation. The present result sugge...

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.

Ab Initio Molecular Dynamics for Simple Liquid Metals Based on the Hypernetted-Chain Approximation

Abstract We present an ab initio molecular dynamics (MD) method for simple liquid metals based on the quantal hypernetted-chain (QHNC) theory derived from exact expressions for radial distribution functions (RDFs) of the electron-ion model for liquid metals. In our method based on the QHNC equations, the classical MD is performed repeatedly to determine a self-consistent effective interionic potential, which depends on the ion-ion RDF of the system. This resultant effective ionic potential is obtained to be consistent with the density distribution of a pseudoatom and the electron-ion RDF, as well as the ion-ion RDF and the ion-ion bridge function, which are determined exactly as a result of the repeated MD simulation. We have applied this QHNC-MD method for Li, Na, K, Rb, and Cs near the melting temperature using upto 16,000 particles for the MD simulation. It is found that the convergence of the effective interionic potential is fast enough for practical applications; typically two MD runs are enough fo...

NEW EMPIRICAL BRIDGE FUNCTIONS OF INTEGRAL EQUATION: APPLICATION TO THE BINARY SUPERCOOLED LIQUIDS OF THE TWELFTH INVERSE POWER POTENTIAL

The MHNCS equation, proposed very recently by us, based on the improved hypernetted-chain approximation for the classical one-component plasma has been found to work well for one-component soft-sphere fluids above and below the freezing point. For a more crucial test, the MHNCS equation is extensively studied for the binary soft-sphere liquids. Thermodynamic properties depending on the core size ratio and the concentration will be discussed.