Microscopic Theory of Density Scaling: Coarse-Graining in Space and Time

TL;DR

This paper develops a first-principles microscopic framework using space and time coarse-graining to explain and predict density scaling in liquids, especially glass-forming materials, bridging the gap between experiments and atomistic simulations.

Contribution

It introduces a novel coarse-graining approach that enables ab initio estimation of density scaling coefficients and provides a microscopic theory underpinning density scaling.

Findings

Coarse-graining reduces molecular complexity while preserving key fluctuations.

The framework accurately predicts density scaling coefficients for ortho-terphenyl.

Microscopic theory links density scaling to excess entropy and slow molecular fluctuations.

Abstract

Understanding the structure and dynamics of liquids is pivotal for the study of larger spatiotemporal processes, especially in glass-forming materials at low temperatures. Density scaling, observed in many molecular systems through experiments, offers an efficient means for exploring a vast range of time scales along a one-dimensional phase diagram. However, the theoretical foundation provided by isomorph theory is of limited use for molecular systems, since currently no first-principles theory exists that can explain the origins of density scaling or make predictions based on it. In this work, we propose a first-principles framework employing coarse-graining in space and time. Spatial coarse-graining reduces a molecule to a center-of-mass-level description by eliminating fast degrees of freedom, while temporal coarse-graining involves averaging fluctuations or correlation functions over characteristic time scales. We show that both approaches enable ab initio estimation of the density scaling coefficient for ortho-terphenyl, consistent with experimental values. Building on these findings, we employ excess entropy scaling to derive a microscopic theory that underpins density scaling from fully atomistic simulations. Our results illuminate the role of coarse-graining in assessing slow fluctuations in molecules and unravel the microscopic nature of density scaling. Ultimately, our proposed framework enables systematic bottom-up approaches for predicting transport coefficients that are otherwise experimentally inaccessible and computationally prohibitive.