Equation of State for Nonattracting Rigid Spheres

Carnahan, Norman F.; Starling, K.E.

doi:10.1063/1.1672048

Cited by 5,019 publications

(2,333 citation statements)

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“…Other equations of state, and coarse-graining approaches, have been suggested. For instance, Tarazona and Evans (Tarazona & Evans , 1984) based their free energy functional on the Carnahan-Starling (Carnahan & Starling , 1969) equation of state for hard spheres which yields a configurational free energy per particle…”

Section: The Fine-grained Gvdw Theorymentioning

confidence: 99%

A Classical Density Functional Theory of Ionic Liquids

2011

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Classical Density Functional Theory of Ionic Liquids 3 Other approachesILs are fascinating from a theoretical standpoint. In order to treat ILs, a theory must account for both electrostatic and steric correlations. Attempts to develop such a theory have appeared in the literature. These include the lattice based model by Kornyshev and co-workers (Fedorov et al. , 2008;Kornyshev , 2007). In another lattice approach by Lauw and coworkers (Lauw et al. , 2009), both cations and anions were modelled by a star-like architecture, with each monomer subject to an independently specified dielectric response. Under certain circumstances, these models were able to qualitatively reproduce the so-called "camel-shaped" differential capacitance, C D , profile observed in imidazolium ILs at carbon electrodes (Islam et al. , 2009;Lockett et al. , 2008a). This behaviour is an indication of subtle structuring effects at charged surfaces and is a stern test for theory. Although camel-shaped C D profiles are predicted, qualitative discrepancy against experimental results remains. This is not surprising since these crude theories lack a proper description of electrostatic correlations despite accounting for steric contributions. Charge-charge correlations have been shown to be important in interfacial phenomena of highly coupled electrostatic fluids. As with dispersion forces, ionic correlations are always attractive and lower the total energy. Thus, we expect that they will also play a role in establishing the camel shape of the C D . That this is the case, is seen from both simulations (Lamperski & Zydor , 2007;Vatamanu et al. , 2010) (Fedorov et al. , 2010;Trulsson et al. , 2010), play an important role in determining their properties. In this work, we will use a model for ILs wherein the molecular ions interact via dispersion, as well as electrostatic, forces and the cation has an oligomeric structure consistent with imidazolium ions. This model has also been adopted by us in previous recent publications (Forsman et al. , 2011;Trulsson et al. , 2010), and employs the methods of polymer free energy density functional theory (DFT) (Woodward , 1991). The result will be a simple, albeit approximate DFT for ILs. We have already introduced the salient features of the theory in a previous publication (Forsman et al. , 2011). Here, we will present a much more thorough treatment, emphasizing the relation to theories of simpler fluids. We will also extend the scope of the study with some emphasis on temperature dependence and the effects of ion-specific adsorption. The IL-DFT that we will discuss here is an off-lattice theory, whose accuracy can be straightforwardly tested against computer simulations of the same molecular model. We will begin with a discussion of relevant earlier work, in order to introduce the essential mechanistic components that will be combined in our density functional theory for ionic liquids. Classical density functional theory (DFT) of simple fluidsThe ideal gas law is known and used by most physicists and chemist...

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Section: The Fine-grained Gvdw Theorymentioning

confidence: 99%

A Classical Density Functional Theory of Ionic Liquids

2011

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“…An empirical correction of the high-density behavior of the PY compressibility result has been given by Carnahan and Starling [24]. The CS equation of state has subsequently been generalized to hard-sphere mixtures resulting in the Boublík-Mansoori-CarnahanStarling-Leland (BMCSL) pressure p BMCSL [25,26].…”

Section: The New Functionalmentioning

confidence: 99%

Density functional theory for hard-sphere mixtures: the White Bear version mark II

Hansen-Goos¹,

Roth²

2006

J. Phys.: Condens. Matter

197

286

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Abstract. In the spirit of the White-Bear version of fundamental measure theory we derive a new density functional for hard-sphere mixtures which is based on a recent mixture extension of the Carnahan-Starling equation of state. In addition to the capability to predict inhomogeneous density distributions very accurately, like the original White-Bear version, the new functional improves upon consistency with an exact scaled-particle theory relation in the case of the pure fluid. We examine consistency in detail within the context of morphological thermodynamics. Interestingly, for the pure fluid the degree of consistency of the new version is not only higher than for the original White-Bear version but also higher than for Rosenfeld's original fundamental measure theory.

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“…We computed the solid-fluid coexistence curve by means of thermodynamic integration. The Helmholtz free energies of the square-shoulder solid and fluid were calculated according to equation (2) using data from our simulations in combination with the known free energies of the hardsphere reference fluid [17] and solid [16]. For the simulation of both the fluid and the solid, we used a system of 108 square-shoulder spheres in a periodic cubic box.…”

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confidence: 99%

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

Bolhuis

Frenkel

1997

J. Phys.: Condens. Matter

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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.

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Equation of State for Nonattracting Rigid Spheres

Abstract: A new equation of state for rigid spheres has been developed from an analysis of the reduced virial series. Comparisons with existing equations show that the new formula possesses superior ability to describe rigid-sphere behavior.

Cited by 5,019 publications

References 10 publications

A Classical Density Functional Theory of Ionic Liquids

A Classical Density Functional Theory of Ionic Liquids

Density functional theory for hard-sphere mixtures: the White Bear version mark II

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

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