On the choice of diameters in a polydisperse model glassformer: deterministic or stochastic?

TL;DR

This study compares deterministic and stochastic methods for assigning particle diameters in polydisperse glassformers, revealing that the choice significantly affects low-temperature glassy dynamics and sample fluctuations.

Contribution

It demonstrates how deterministic and stochastic diameter assignment methods influence glassy dynamics and fluctuations in polydisperse systems through molecular dynamics simulations.

Findings

Stochastic scheme introduces sample-to-sample fluctuations explained by effective packing fraction.

Dynamic susceptibilities split into thermal and disorder-induced terms, with disorder dominating at low temperatures.

Choice of diameter assignment method impacts glassy dynamics in simulations.

Abstract

In particle-based computer simulations of polydisperse glassforming systems, the particle diameters $\sigma = \sigma_1, \dots, \sigma_N$ of a system with $N$ particles are chosen with the intention to approximate a desired distribution density $f$ with the corresponding histogram. One method to accomplish this is to draw each diameter randomly from the density $f$. We refer to this stochastic scheme as model $\mathcal{S}$. Alternatively, one can apply a deterministic method, assigning an appropriate set of $N$ values to the diameters. We refer to this method as model $\mathcal{D}$. We show that especially for the glassy dynamics at low temperatures it matters whether one chooses model $\mathcal{S}$ or model $\mathcal{D}$. Using molecular dynamics computer simulation, we investigate a three-dimensional polydisperse non-additive soft-sphere system with $f(s) \sim s^{-3}$. The Swap Monte Carlo method is employed to obtain equilibrated samples at very low temperatures. We show that for model $\mathcal{S}$ the sample-to-sample fluctuations due to the quenched disorder imposed by the diameters $\sigma$ can be explained by an effective packing fraction. Dynamic susceptibilities in model $\mathcal{S}$ can be split into two terms: One that is of thermal nature and can be identified with the susceptibility of model $\mathcal{D}$, and another one originating from the disorder in $\sigma$. At low temperatures the latter contribution is the dominating term in the dynamic susceptibility.