van der Waals theory for solids

J. Phys.: Condens. Matter

1997

Abstract. Using Monte Carlo simulations, we study the phase behaviour of systems with a short-ranged repulsive 'shoulder' potential. In analogy to systems with a short-ranged attractive interaction, the shoulder potential leads to an isostructural solid-solid phase transition. We show that the range of interactions for which a solid-solid transition is possible is much wider for repulsive than for attractive interactions.It is well known that weak, long-ranged attractive intermolecular forces lead to a liquidvapour transition (see e.g. [1]). Recently, we considered the opposite limit of attractions that act over distances that are small compared to the hard-core radius of the particles [2]. Such interaction can occur in certain colloidal systems. We found that a dense system of spherical particles with very short-ranged interaction may exhibit a solid-solid transition that is in many ways reminiscent of the liquid-vapour transition. In particular, the transition takes place between two phases that have the same structure. And secondly, the line of (first-order) solid-solid transitions ends in a critical point. We found that the critical density depends strongly on the range of the intermolecular interaction. In the square-well model considered in reference [2] the solid-solid critical point crosses the melting curve if the range of attraction is more than 6% of the hard-core diameter. The critical temperature is much less sensitive to the range of attraction.Subsequent theoretical studies support the existence of such behaviour for a variety of models [3][4][5][6], even though, thus far, direct experimental observation of this solid-solid transition is lacking. However, one of the predicted consequences of the vicinity of a solidsolid transition in two dimensions is the stabilization of the hexatic phase [7], and recent experiments by Marcus and Rice [8] seem to support this scenario.An isostructural solid-solid transition can also take place in systems involving only repulsive interactions. It is known that isostructural solid-solid transitions can occur in dense Cs and Ce [9]. These transitions are believed to be due to the softness of the intermolecular potential associated with a pressure-induced change in the electronic state of the metal ions. Theoretical work by Stell and Hemmer [10], and simulations by Alder and Young [11] indicate that such softness may indeed result in a solid-solid transition. Kincaid, Stell and Goldmark [12] modelled the interaction potential of such systems by a so-called square shoulder (a hard-sphere potential augmented with a repulsive plateau) and calculated the phase behaviour by applying perturbation theory. In this paper we compute the phase behaviour of a system of spherical particles interacting via a square-shoulder potential. The difference from earlier work is that we focus on a relatively short-ranged shoulder potential.

mentioning

confidence: 99%

Isostructural solid - solid transitions in systems with a repulsive `shoulder' potential

Bolhuis

J. Phys.: Condens. Matter

1997

“…6 Isostructural solid-solid transitions are expected to occur in crystalline alloys near a substitutional order-disorder transition or in systems of hard colloidal particles with a short-ranged attraction. [7][8][9][10] Here, we consider the latter case. Depending on the range of attraction, the solid-solid critical point may either be located in a stable or in a metastable part of the phase diagram.…”

Section: Consequences For Nucleationmentioning

confidence: 99%

Stresses Inside Critical Nuclei

Cacciuto

2004

J. Phys. Chem. B

The usual derivation of classical nucleation theory is inappropriate for crystal nucleation. In particular, it leads to a seriously flawed estimate of the pressure inside a critical nucleus. This has consequences for the prediction of possible metastable phases during the nucleation process. In this paper, we reanalyze the theory for crystal nucleation based on the thermodynamics of small crystals suspended in a liquid, due to Mullins (J. Chem. Phys. 1984Phys. , 81, 1436. As an illustration of the difference between the classical picture and the present approach, we consider a numerical study of crystal nucleation in binary mixtures of hard spherical colloids with a size ratio of 1:10. The stable crystal phase of this system can be either dense or expanded. We find that, in the vicinity of the solid-solid critical point where the crystallites are highly compressible, small crystal nuclei are less dense than large nuclei. This phenomenon cannot be accounted for by either classical nucleation theory or by the Gibbsian droplet model.The experimental determination of crystal nucleation rates is one of the prime sources of information on the free energy of solid-liquid interfaces (see, e.g., ref 2). The link between the observable quantity (number of crystal nuclei formed per unit time per unit volume) and the surface free energy is usually given by classical nucleation theory (CNT). CNT contains two ingredients: the first is a thermodynamic estimate of the reversible work needed to make a critical nucleus (i.e., a nucleus that is equally likely to dissolve as it is to grow to macroscopic size). This reversible work defines the free energy of a critical nucleus. A system that contains a critical nucleus is at a local free-energy maximum. This is important for what follows, because it means that the free energy is invariant under infinitesimal exchanges of mass or volume between the nucleus and the parent phase. In particular, it means that chemical potentials of all species are constant throughout the system. 3 The second ingredient of CNT is an estimate of the rate at which critical nuclei transform into macroscopic crystallites. In what follows, we focus on the equilibrium properties of critical crystal nuclei.According to CNT, the free energy of a spherical nucleus that forms in a supersaturated solution contains two terms. The first term accounts for the fact that the solid phase is more stable than the liquid. This term is negative and proportional to the volume of the nucleus. The second term is a surface term. It describes the free energy needed to create a solid/liquid interface. This term is positive and proportional to the surface area of the nucleus. The (Gibbs) free energy of a spherical nucleus of radius R has the following form:where F s is the number density of the bulk solid, ∆µ the difference in chemical potential between the solid and the liquid, and γ is the solid/liquid surface free energy density. The function ∆G has a maximum at R ) 2γ/(F s |∆µ|) and the corresponding height of the nucleation b...

“…For example, it has been shown that if the interaction range is made very short the vapor-liquid critical point moves to within the solid to become an expanded-solid-condensed-solid critical point. [19][20][21] So, the critical density depends on the range of the potential of mean force. What if the interaction is characterized by two ͑or more͒ ranges?…”

Section: Demixingmentioning

confidence: 99%

Phase separation in mixtures of a rodlike colloid and two or more rodlike polymers

Sear

The Journal of Chemical Physics

1996

A suspension of rodlike colloidal particles and rodlike liquid crystalline polymers is modelled as a mixture of thick ͑colloidal͒ and thin ͑polymeric͒ hard rods. Extensive immiscibility in the fluid phase is observed in the mixtures. For two species of polymers, one species much longer than the other, we observe two demixing critical points. For three polymer species we find three critical points. Polymer molecules of length l induce an attractive interaction of range l between colloidal rods. Two different polymers induce effective attractions of two different ranges. The range of the attraction determines the density at which the demixing occurs. The attractions of different ranges create demixing at different densities.