Effective one-component model of binary mixture: molecular arrest induced by the spatially correlated stochastic dynamics

TL;DR

This paper introduces an effective one-component model driven by spatially correlated noise to describe molecular arrest and glass transition phenomena in dense binary mixtures, capturing various arrested states.

Contribution

It develops a thermodynamically consistent SCN-driven Langevin model that analytically predicts glass-like arrest and identifies a diverging dissipation length at critical packing.

Findings

Predicts molecular arrest similar to glass transition

Identifies a diverging characteristic length at critical density

Reproduces multiple arrested disorder modes

Abstract

Spatially correlated noise (SCN), i.e. the thermal noise that affects neighbouring particles in a similar manner, is ubiquitous in soft matter systems. In this work, we apply the over-damped SCN-driven Langevin equations as an effective, one-component model of the dynamics in dense binary mixtures. We derive the thermodynamically consistent fluctuation-dissipation relation for SCN to show that it predicts the molecular arrest resembling the glass transition, i.e. the critical slow-down of dynamics in the disordered phases. We show that the mechanism of singular dissipation is embedded in the dissipation matrix, accompanying SCN. We are also able to identify the characteristic length of collective dissipation, which diverges at critical packing. This novel physical quantity conveniently describes the difference between the ergodic and non-ergodic dynamics. The model is fully analytically solvable, one-dimensional and admits arbitrary interactions between the particles. It qualitatively reproduces several different modes of arrested disorder encountered in binary mixtures, including e.g. the re-entrant arrest. The model can be effectively compared to the mode coupling theory.