Relaxation Scenarios in a Mixture of Large and Small Spheres: Dependence on the Size Disparity

TL;DR

This study explores how varying size disparity in a mixture of large and small soft spheres affects their relaxation dynamics, revealing complex behaviors including time scale separation and logarithmic relaxation linked to Mode Coupling Theory predictions.

Contribution

It provides a detailed computational analysis of relaxation scenarios in size-disparate sphere mixtures, connecting observed dynamics to Mode Coupling Theory and identifying potential higher-order transition points.

Findings

Large disparity causes significant time scale separation.

Small particles exhibit extremely stretched and logarithmic relaxation.

Self- and collective dynamics become fully separated at high disparity.

Abstract

We present a computational investigation on the slow dynamics of a mixture of large and small soft spheres. By varying the size disparity at a moderate fixed composition different relaxation scenarios are observed for the small particles. For small disparity density-density correlators exhibit moderate stretching. Only small quantitative differences are observed between dynamic features for large and small particles. On the contrary, large disparity induces a clear time scale separation between the large and the small particles. Density-density correlators for the small particles become extremely stretched, and display logarithmic relaxation by properly tuning the temperature or the wavevector. Self-correlators decay much faster than density-density correlators. For very large size disparity, a complete separation between self- and collective dynamics is observed for the small particles. Self-correlators decay to zero at temperatures where density-density correlations are frozen. The dynamic picture obtained by varying the size disparity resembles features associated to Mode Coupling transition lines of the types B and A at, respectively, small and very large size disparity. Both lines might merge, at some intermediate disparity, at a higher-order point, to which logarithmic relaxation would be associated. This picture resembles predictions of a recent Mode Coupling Theory for fluids confined in matrixes with interconnected voids [V. Krakoviack, Phys. Rev. Lett. {\bf 94}, 065703 (2005)].