Scaling behavior in the $\beta$-relaxation regime of a supercooled Lennard-Jones mixture

TL;DR

This study uses molecular dynamics simulations to analyze the $eta$-relaxation regime in a supercooled Lennard-Jones mixture, confirming some mode-coupling theory predictions but also revealing discrepancies in diffusion behavior.

Contribution

It demonstrates the existence of a master curve in the $eta$-relaxation regime and tests the power-law dependencies predicted by mode-coupling theory in a Lennard-Jones system.

Findings

Master curve in $eta$-relaxation regime fits power-law

Relaxation time follows a power-law with temperature

Diffusion constants also follow a power-law but with different exponents

Abstract

We report the results of a molecular dynamics simulation of a supercooled binary Lennard-Jones mixture. By plotting the self intermediate scattering functions vs. rescaled time, we find a master curve in the $\beta$-relaxation regime. This master curve can be fitted well by a power-law for almost three decades in rescaled time and the scaling time, or relaxation time, has a power-law dependence on temperature. Thus the predictions of mode-coupling-theory on the existence of a von Schweidler law are found to hold for this system; moreover, the exponents in these two power-laws are very close to satisfying the exponent relationship predicted by the mode-coupling-theory. At low temperatures, the diffusion constants also show a power-law behavior with the same critical temperature. However, the exponent for diffusion differs from that of the relaxation time, a result that is in disagreement with the theory.