Phase diagram of Hertzian spheres

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 find multiple re-entrant melting and first-order transitions between crystals with cubic, trigonal, tetragonal and hexagonal symmetries.

The zero-temperature phase diagram of soft-repulsive particle fluids

“…(2.4), as sum-marized in Table 5. A rather complex behaviour shows up for this bounded potential, much more complex than reported in [25], especially if compared with the simple phase portrait of the GCM. In fact, the phases listed in Table 5 are only those stable for P < 400 since apparently the sequence of T = 0 phase transitions never comes to an end (as observed in…”

“…[25], there is no room for clustering in the Hertz model). This unique behaviour, never documented before, is the effect of a complex interplay between energy and volume considerations in the minimization of enthalpy as a function of pressure.…”

Anomalous phase behavior of a soft-repulsive potential with a strictly monotonic force

“…Phase diagrams with solid polymorphism and multiple re-entrant melting have been observed at high pressures in some elements, such as Sr [29] and predicted by ab-initio simulation for others [30]. Concerning model systems, a phase behavior with features similar to those noted above was found for the hard-core plus repulsive step potential [16] and for Hertzian spheres [19].…”

“…These unconventional features are usually referred to as water-like anomalies. Although these substances are all characterized by local tetrahedral order, in the last years water-like anomalies have been found also in systems with spherically symmetric potentials, provided that the repulsion is of the softened-core type [8,9,10,11,12,13,14,15,16,17,18,19,20] In order to investigate the existence of anomalies in our system, we first analysed the behavior of the number density in the fluid phase above the melting line. We find that in the region lying approximately above the re-entrant portion of the bcc-fluid coexistence line, decreasing temperature at constant pressure leads first to a density increase and then, contrary to standard behavior, to a density decrease for further cooling (Fig.…”

“…More recently, intense investigation of the phase behavior of potentials with a softened core has shown that these models can yield, even for isotropic one-component systems, unusual properties such as a melting line with a maximum followed by a region of re-entrant melting, polymorphism both in the fluid and solid phases, and a rich hierarchy of water-like anomalies [8,9,10,11,12,13,14,15,16,17,18,19,20].…”