Segregation in noninteracting binary mixture

TL;DR

This paper investigates how stripe patterns form in a binary mixture of particles of two sizes without direct interactions, driven by entropy and external forces, revealing a logarithmic growth in stripe width over time.

Contribution

It introduces a novel analysis of entropy-driven stripe formation in noninteracting particles and explains the logarithmic growth mechanism.

Findings

Stripe width grows logarithmically with time.

Induced interactions are entropy-driven, not direct.

Mechanism explained by a random walk in a random potential.

Abstract

Process of stripe formation is analyzed numerically in a binary mixture. The system consists of particles of two sizes, without any direct mutual interactions. Overlapping of large particles, surrounded by a dense system of smaller particles induces indirect entropy driven interactions between large particles. Under an influence of an external driving force the system orders and stripes are formed. Mean width of stripes grows logarithmically with time, in contrast to a typical power law temporal increase observed for driven interacting lattice gas systems. We describe the mechanism responsible for this behavior and attribute the logarithmic growth to a random walk of large particles in a random potential due to the small ones.