Paolo V. Giaquinta

Phase diagram of the Gaussian-core model.

We trace with high numerical accuracy the phase diagram of the Gaussian-core model, a classical system of point particles interacting via a Gaussian-shaped, purely repulsive potential. This model, which provides a reliable qualitative description of the thermal behavior of interpenetrable globular polymers, is known to exhibit a polymorphic fcc-bcc transition at low densities and reentrant melting at high densities. Extensive Monte Carlo simulations, carried out in conjunction with accurate calculations of the solid free energies, lead to a thermodynamic scenario that is partially modified with respect to previous knowledge. In particular, we find that: (i) the fluid-bcc-fcc triple-point temperature is about one third of the maximum freezing temperature; (ii) upon isothermal compression, the model exhibits a fluid-bcc-fcc-bcc-fluid sequence of phases in a narrow range of temperatures just above the triple point. We discuss these results in relation to the behavior of star-polymer solutions and of other softly repulsive systems.

Phase diagram of softly repulsive systems: The Gaussian and inverse-power-law potentials

We redraw, using state-of-the-art methods for free-energy calculations, the phase diagrams of two reference models for the liquid state: the Gaussian and inverse-power-law repulsive potentials. Notwithstanding the different behaviors of the two potentials for vanishing interparticle distances, their thermodynamic properties are similar in a range of densities and temperatures, being ruled by the competition between the body-centered-cubic (bcc) and face-centered-cubic (fcc) crystalline structures and the fluid phase. We confirm the existence of a reentrant bcc phase in the phase diagram of the Gaussian-core model, just above the triple point. We also trace the bcc-fcc coexistence line of the inverse-power-law model as a function of the power exponent n and relate the common features in the phase diagrams of such systems to the softness degree of the interaction.

Hexatic phase in the two-dimensional Gaussian-core model

We present a Monte Carlo simulation study of the phase behavior of two-dimensional classical particles repelling each other through an isotropic Gaussian potential. As in the analogous three-dimensional case, a reentrant-melting transition occurs upon compression for not too high temperatures, along with a spectrum of waterlike anomalies in the fluid phase. However, in two dimensions melting is a continuous two-stage transition, with an intermediate hexatic phase which becomes increasingly more definite as pressure grows. All available evidence supports the Kosterlitz-Thouless-Halperin-Nelson-Young scenario for this melting transition. We expect that such a phenomenology can be checked in confined monolayers of charge-stabilized colloids with a softened core.

Evaluation of phenomenological one-phase criteria for the melting and freezing of softly repulsive particles

We test the validity of some widely used phenomenological criteria for the localization of the fluid-solid transition thresholds against the phase diagrams of particles interacting through the exp-6, inverse-power-law, and Gaussian potentials. We find that one-phase rules give, on the whole, reliable estimates of freezing/melting points. The agreement is ordinarily better for a face-centered-cubic solid than for a body-centered-cubic crystal, even more so in the presence of a pressure-driven reentrant transition of the solid into a denser fluid phase, as found in the Gaussian-core model.

Hexatic phase and water-like anomalies in a two-dimensional fluid of particles with a weakly softened core.

We study a two-dimensional fluid of particles interacting through a spherically symmetric and marginally soft two-body repulsion. This model can exist in three different crystal phases, one of them with square symmetry and the other two triangular. We show that, while the triangular solids first melt into a hexatic fluid, the square solid is directly transformed on heating into an isotropic fluid through a first-order transition, with no intermediate tetratic phase. In the low-pressure triangular and square crystals, melting is reentrant provided the temperature is not too low, but without the necessity of two competing nearest-neighbor distances over a range of pressures. A whole spectrum of water-like fluid anomalies completes the picture for this model potential.

Entropy, correlations, and ordering in two dimensions

The ordering of simple fluids in two dimensions was investigated using the residual multiparticle entropy (RMPE) as a measure of the relevance of correlations involving more than two particles in the configurational entropy of the system. To this end, we performed Monte Carlo simulations of two prototype systems, i.e., Lennard-Jones particles and hard discs. Consistent with previous studies, we found that, on approaching the freezing transition, the RMPE of the fluid undergoes a change from negative to positive values. However, in two dimensions the vanishing of the RMPE appears to be more directly related to the formation of six-fold orientationally ordered patches, a process which foreshadows the freezing transition. The specificity of the structural condition attained by the fluid in a state corresponding to a vanishing RMPE was further corroborated by an analysis of the shape of the radial distribution function (RDF): in fact, it turns out that the spatial profiles of the RDF of the Lennard-Jones flui...

Small-angle scattering from molten salts

Abstract The partial structure factors S++, S+- and 5−in molten salts are considered at small wavenumber k and the following results are established : (i) the term of order k2 in S++ - S– is determined by the difference in partial volumes of the two ionic species; (ii) a term of order k3 arises in the Sys from the presence of van der Waals dipole-dipole interactions; (iii) the charge-charge structure factor, S++ + S– - 2S+- , is determined at order k4 by the true screening length of the system and affected by van der Waals interactions only at order K 5. Similar expansions are reported for the corresponding direct correlation functions, which are of interest for fluctuation theories of the surface properties of these liquids. All the relevant coefficients in the various expansions (both those that reflect the thermodynamic fluctuation behaviour of the liquid and those that reflect its microscopic behaviour) are evaluated for a charged-hard-spheres model of the family of molten alkali halides in the mean s...

Entropy-based measure of structural order in water

We analyze the nature of the structural order established in liquid TIP4P water in the framework provided by the multiparticle correlation expansion of the statistical entropy. Different regimes are mapped onto the phase diagram of the model upon resolving the pair entropy into its translational and orientational components. These parameters are used to quantify the relative amounts of positional and angular order in a given thermodynamic state, thus allowing a structurally unbiased definition of low-density and high-density water. As a result, the structurally anomalous region--within which both types of order are simultaneously disrupted by an increase of pressure at constant temperature--is clearly identified through extensive molecular-dynamics simulations.

Statistical entropy and density maximum anomaly in liquid water

We studied the configurational entropy of liquid water at ambient pressure and extracted the cumulative contribution associated with spatial correlations involving more than two particles. This quantity, the so-called residual multiparticle entropy (RMPE), is a sensitive indicator of structural modifications and incoming thermodynamic transitions, being positive in the more disordered phase and negative in the more ordered one. The vanishing of the RMPE has been successfully exploited as a rather general ordering criterion in a variety of model fluid systems. We carried out molecular-dynamics calculations on the TIP4P model at ambient pressure for temperatures between 230 K and 350 K and found that the ordering threshold estimated through the zero-RMPE criterion falls close to the temperature of maximum density.

Scaling of local density correlations in a fluid close to freezing

We simulated the equilibrium properties of some reference model fluids, with hard-core, Yukawa and Lennard-Jones interactions, and compared their local density profiles in thermodynamic states where the residual multiparticle entropy (RMPE), an established and rather sensitive indicator of the incipient ordering of the fluid into a more structured phase, happens to vanish. We found that, once interparticle distances have been referred to the average separation between nearest-neighbor particles, the radial distribution functions (RDF) coalesce—from the second coordination shell onwards—onto nearly the same spatial profile. This property was ascertained for different model systems in different thermodynamic conditions but for the shared zero-RMPE constraint. The emergence of a scaling relation for the RDF’s in the fluid phase further enlightens the nature of the structural condition that is singled out by the vanishing of the RMPE.