Phase diagram of Hertzian spheres

TL;DR

This study maps the phase diagram of Hertzian spheres, revealing complex melting and crystal transition behaviors in a model relevant for soft macromolecules, using advanced simulation techniques.

Contribution

It provides the first detailed phase diagram of Hertzian spheres, including re-entrant melting and multiple crystal structures, using thermodynamic integration and Monte Carlo simulations.

Findings

Multiple re-entrant melting transitions.

First-order transitions between various crystal symmetries.

Accurate free energy calculations for fluid and crystal phases.

Abstract

We report the phase diagram of interpenetrating Hertzian spheres. The Hertz potential is purely repulsive, bounded at zero separation, and decreases monotonically as a power law with exponent 5/2, vanishing at the overlapping threshold. This simple functional describes the elastic interaction of weakly deformable bodies and, therefore, it is a reliable physical model of soft macromolecules, like star polymers and globular micelles. Using thermodynamic integration and extensive Monte Carlo simulations, we computed accurate free energies of the fluid phase and a large number of crystal structures. For this, we defined a general primitive unit cell that allows for the simulation of any lattice. We found multiple re-entrant melting and first-order transitions between crystals with cubic, trigonal, tetragonal, and hexagonal symmetries.