The crystallization of hard disks induced by a temperature gradient

TL;DR

This study investigates how a temperature gradient influences the behavior of hard-disk systems, revealing that large gradients induce crystallization at the cold boundary, with implications for understanding nonequilibrium phase transitions.

Contribution

It demonstrates that temperature gradients can induce boundary crystallization in hard-disk systems, a novel insight into nonequilibrium phase behavior under thermal gradients.

Findings

Crystallization occurs at the cold boundary for large temperature differences.

Diffusivity decreases significantly at the liquid-crystal interface.

Velocity distribution remains Boltzmann, indicating equipartition in nonequilibrium conditions.

Abstract

While uniform temperature has no effect on equilibrium properties of hard-core systems, its gradient might substantially change their behaviour. In particular, in hard-disk system subject to temperature difference $\Delta T$ disks are repelled from the hot boundary of the system and accumulate at the cold one. Using event-driven molecular dynamics simulations we show that for sufficiently large $\Delta T$ or coverage ratio $\rho^*$, crystal forms at the cold boundary. In this spatially inhomogeneous system a significant decrease of diffusivity of disks clearly marks the stationary interface between liquid and crystal. Such a behaviour is also supported through calculation of the radial distribution function and the bond order parameter. Simulations show that for this nonequilibrium system the equipartition of energy holds and velocity obeys the Boltzmann distribution.