Anisotropic spatially heterogeneous dynamics on the $\alpha$ and $\beta$ relaxation time scales studied via a four-point correlation function

Abstract

We examine the anisotropy of a four-point correlation function $G_4(\vec{k},\vec{r};t)$ and it's associated structure factor $S_4(\vec{k},\vec{q};t)$ calculated using Brownian Dynamics computer simulations of a model glass forming system. These correlation functions measure the spatial correlations of the relaxation of different particles, and we examine the time and temperature dependence of the anisotropy. We find that the anisotropy is strongest at nearest neighbor distances at time scales corresponding to the peak of the non-Gaussian parameter ${\alpha }_2(t)=3<\delta r^4(t)>/[5<\delta r^2(t){>}^2]-1$, but is still pronounced around the $\alpha$ relaxation time. We find that the structure factor $S_4(\vec{k},\vec{q};t)$ is anisotropic even for the smallest wave vector accessible in our simulation suggesting that our system (and other systems commonly used in computer simulations) may be too small to extract the $\vec{q}\to 0$ limit of the structure factor. We find that the determination of a dynamic correlation length from $S_4(\vec{k},\vec{q};t)$ is influenced by the anisotropy. We extract an effective anisotropic dynamic correlation length from the small $q$ behavior of $S_4(\vec{k},\vec{q};t)$.

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• Lifetimes and Lengthscales of Structural Motifs in a Model Glassformer
• Strong geometric frustration in model glassformers
• Dynamic heterogeneities above and below the mode-coupling temperature. Evidence of a dynamic crossover
• Multi-time density correlation functions in glass-forming liquids: Probing dynamical heterogeneity and its lifetime
• Locally favoured structures and dynamic length scales in a simple glass-former
• Diverging length scale of the inhomogeneous mode-coupling theory: a numerical investigation
• Heterogeneous dynamics and its length scale in simple ionic liquid models: A computational study
• Reduced strength and extent of dynamic heterogeneity in a strong glass former as compared to fragile glass formers
• Dynamical Susceptibilities Near Ideal Glass Transitions
• Theory of the $\beta$-Relaxation Beyond Mode-Coupling Theory: A Microscopic Treatment