Density-functional approach to two-dimensional classical fluids

Takamiya, Masaaki; Nakanishi, Koichiro

doi:10.1080/00268979000101341

Cited by 9 publications

(4 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As for the two-dimensional fluid system, Németh and Löwen [7] have studied the freezing problem of a hard-disk fluid S-C Kim in circular cavities. Takamiya and Nakanishi [8] have applied the two-dimensional weighteddensity approximation to calculate the structural properties of a two-dimensional Lennard-Jones fluid confined in the system with a special symmetry. However, for the structural properties of the two-dimensional polydisperse fluids they are much less well understood than systems compared with one-component hard-disk fluids.…”

Section: Introductionmentioning

confidence: 99%

Effect of repulsive and attractive interactions in the adsorption of confined polydisperse fluids

Kim

2000

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

A density functional perturbative approximation, which is based on the pair distribution function, has been developed to investigate the influence of attractive and repulsive interactions on the density behaviour of a confined polydisperse fluid. The calculated result shows that the attractive and repulsive interactions in the model potential are strongly affected on the adsorption of a confined polydisperse fluid as well as the cavity size and particle size ratio. The attractive interaction in a polydisperse square-well system increases the pore average mole fraction for small particles in a circular cavity. Whereas a repulsive interaction in a polydisperse square-shoulder system decreases the pore average mole fraction for small particles. The local relative concentration oscillates with a spatial period close to the diameter of a large particle as well as the equilibrium density distribution does.

show abstract

Section: Introductionmentioning

confidence: 99%

Effect of repulsive and attractive interactions in the adsorption of confined polydisperse fluids

Kim

2000

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

show abstract

“…The DF minimization of Ω[ρ] in (7.1) is then restricted to functions ρ(r) = ρ(z), so that the numerical problem of minimization is hugely reduced with respect to that of a 3D dependence of ρ(x, y, z). The weighted density inherits the same symmetry, and the elementary weighted densities may be calculated as 1D convolutionsρ 41) where the functions…”

Section: Hard Sphere Fluid Against a Planar Wallmentioning

confidence: 99%

“…However, its applications to HS systems have probably been the most successful. The WDA concept has also been used to get DF approximations for 2D HD fluids and to study their crystallization [41,42], although without reaching the specific features of 2D crystallization. The role of dislocations and disclinations of the perfect crystal phase and the possible presence of an intermediate hexatic phase would be very difficult targets for any DF treatment of the crystal, described as a self-structured fluid at the level of the one-particle density distribution, and they are certainly beyond the WDA.…”

Section: Other Applications and Variants Of The Wdamentioning

confidence: 99%

Density Functional Theories of Hard Particle Systems

Tarazona

Cuesta

Martı́nez-Ratón

Theory and Simulation of Hard-Sphere Fluids and Related Systems

117

147

View full text Add to dashboard Cite

To the memory of our friend Yasha Rosenfeld, who discovered the Fundamental Measure Theory, making this chapter grow into a thick one.This chapter deals with the applications of the density functional (DF) formalism to the study of inhomogeneous systems with hard core interactions. It includes a brief tutorial on the fundamentals of the method, and the exact free energy DF for one-dimensional hard rods obtained by Percus. The development of DF approximations for the free energy of hard spheres (HS) is presented through its milestones in the weighted density approximation (WDA) and the fundamental measure theory (FMT). The extensions of these approaches to HS mixtures include the FMT treatment of polydisperse systems and the approximations for mixtures with non-additive core radii. The DF treatment of non-spherical hard core systems is presented within the generic context of the study of liquid crystals phases. The chapter is directed to the potential users of these theoretical techniques, with clear explanations of the practical implementation details of the most successful approximations. IntroductionThe density functional (DF) formalism for classical particles [1] was developed to find out the equilibrium density distribution ρ(r) of inhomogeneous systems at interfaces or in the presence of an external potential V (r). In most cases, like the layering of fluids against walls or liquids confined in nano-capillaries, the sharpest level of structure in ρ(r) comes from the effects of molecular packing, and hence the development of DF theories for hard-core models has been a

show abstract

“…Not only the EOS, but also the structure of a hard-disc fluid has been explored in detail and is to date well understood [8,7,9,10]. Hard discs are popular also as model system to test advanced density functional theories [11,12], used, for instance, to study discs in cavities [13], or induced freezing and reentrant melting [14]. Many computer simulation studies of HD systems are available [1,15,16], of which the more recent ones have focused mainly on the melting properties of HD solids [16].…”

mentioning

confidence: 99%

Measuring the equation of state of a hard-disc fluid

et al. 2003

View full text Add to dashboard Cite

PACS. 05.20.Jj -Statistical mechanics of classical fluids.Abstract. -We use video microscopy to study a two-dimensional (2D) model fluid of charged colloidal particles suspended in water and compute the pressure from the measured particle configurations. Direct experimental control over the particle density by means of optical tweezers allows the precise measurement of pressure as a function of density. We compare our data with theoretical predictions for the equation of state, the pair-correlation function and the compressibility of a hard-disc fluid and find good agreement, both for the fluid and the solid phase. In particular the location of the transition point agrees well with results from Monte Carlo simulations.Hard-disc (HD) fluids play a prominent role in liquid state theories. This is due to the fact that, first, they often serve as reference systems in perturbation theories of two-dimensional (2D) liquids (just as hard-sphere fluids do for liquids in three dimensions), and that, secondly, at high densities the behavior of every 2D fluid is dominated by excluded volume effects, which in turn depends just on the short-ranged hard-core part of the interparticle potential. Mainly for theses two reasons, the HD equation of state (EOS) appears also in many theories on monolayer adsorption on solid surfaces [1,2], an aspect illustrated for example in Ref. [3] where the HD EOS is used in statistical mechanical theories modeling the binding of peripheral globular proteins on lipid membranes. The important role of the HD system explains the overwhelming number of theoretical studies on the EOS of a HD fluid, starting as early as 1959 with the presentation of results from scaled particle theory [4]. Most of all approaches to the EOS are based on particular resummations of the virial series and the construction of sophisticated Pade approximants [5,6,7], others use results from integral equation theories [8], or from theories based on overlap volume functions [9]. Not only the EOS, but also the structure of a hard-disc fluid has been explored in detail and is to date well understood [8,7,9,10]. Hard discs are popular also as model system to test advanced density functional theories [11,12], used, for instance, to study discs in cavities [13], or induced freezing and reentrant melting [14]. Many computer simulation studies of HD systems are available [1,15,16], of which the more recent ones have focused mainly on the melting properties of HD solids [16].All these theoretical efforts contrast with the situation on the experimental side. To our knowledge, the HD EOS has never been tested with experimental data. The present Letter aims at closing this gap. We report on experiments with a 2D model liquid of charged colloidal particles suspended in water. Correlation functions computed from real-space images, together with the virial equation, are used to calculate the pressure p of the 2D liquid as a function of the 2D particle density ρ, which in our experiment can be conveniently varied by means c EDP Sciences

show abstract

Density-functional approach to two-dimensional classical fluids

Cited by 9 publications

References 12 publications

Effect of repulsive and attractive interactions in the adsorption of confined polydisperse fluids

Effect of repulsive and attractive interactions in the adsorption of confined polydisperse fluids

Density Functional Theories of Hard Particle Systems

Measuring the equation of state of a hard-disc fluid

Contact Info

Product

Resources

About