Structural and Thermodynamic Properties of Hard-Sphere Fluids

Abstract

This Perspective article provides an overview of some of our analytical approaches to the computation of the structural and thermodynamic properties of single-component and multicomponent hard-sphere fluids. For the structural properties, they yield a thermodynamically consistent formulation, thus improving and extending the known analytical results of the Percus--Yevick theory. Approximate expressions linking the equation of state of the single-component fluid to the one of the multicomponent mixture are also discussed.

arXiv comment34 pages, 10 figures; v2: Minor changes. Featured in https://aip.scitation.org/action/doSearch? SeriesKey=jcp&AllField=10.1063%2F5.0023903&ConceptID=19590&quickLinkYear=&quickLinkVolume=. arXiv admin note: text overlap with arXiv:0704.0157

References in corpus (67)

• Mean field theory of hard sphere glasses and jamming
• Influence of Particle Size Distribution on Random Close Packing
• Ninth and Tenth Order Virial Coefficients for Hard Spheres in D Dimensions
• Predicting phase equilibria in polydisperse systems
• Basic Understanding of Condensed Phases of Matter via Packing Models
• A theory of amorphous packings of binary mixtures of hard spheres
• Equilibrium fluid-solid coexistence of hard spheres
• Pair correlation function of short-ranged square-well fluids
• Contact values of the radial distribution functions of additive hard-sphere mixtures in d dimensions: A new proposal
• Depletion potentials in highly size-asymmetric binary hard-sphere mixtures: Comparison of accurate simulation results with theory
• New results for virial coefficients of hard spheres in D dimensions
• A simple effective rule to estimate the jamming packing fraction of polydisperse hard spheres
• Structure of hard-hypersphere fluids in odd dimensions
• Equation of state of non-additive $d$-dimensional hard-sphere mixtures
• Solution of the Percus-Yevick equation for hard hyperspheres in even dimensions
• A square-well model for the structural and thermodynamic properties of simple colloidal systems
• Direct Observation in 3d of Structural Crossover in Binary Hard Sphere Mixtures
• Equilibrium equation of state of a hard sphere binary mixture at very large densities using replica exchange Monte-Carlo simulations
• Virial series for fluids of hard hyperspheres in odd dimensions
• Class of consistent fundamental-measure free energies for hard-sphere mixtures
• Virial coefficients and equations of state for mixtures of hard discs, hard spheres and hard hyperspheres
• The analyticity region of the hard sphere gas. Improved bounds
• Structure of penetrable-rod fluids: Exact properties and comparison between Monte Carlo simulations and two analytic theories
• Structure of the square-shoulder fluid
• On the liquid-glass transition line in monatomic Lennard-Jones fluids
• Equation of state of polydisperse hard-disk mixtures in the high-density regime
• Low-temperature and high-temperature approximations for penetrable-sphere fluids. Comparison with Monte Carlo simulations and integral equation theories
• Virial coefficients, thermodynamic properties, and fluid-fluid transition of nonadditive hard-sphere mixtures
• A branch-point approximant for the equation of state of hard spheres
• Chemical-Potential Route: A Hidden Percus-Yevick Equation of State for Hard Spheres
• Contact values of the particle-particle and wall-particle correlation functions in a hard-sphere polydisperse fluid
• Metastable Dynamics of the Hard-Sphere System
• On the relation between virial coefficients and the close-packing of hard disks and hard spheres
• Penetrable-Square-Well fluids: Analytical study and Monte Carlo simulations
• Janus fluid with fixed patch orientations: theory and simulations
• On the radial distribution function of a hard-sphere fluid
• Multicomponent fluids of hard hyperspheres in odd dimensions
• Are the energy and virial routes to thermodynamics equivalent for hard spheres?
• On the equivalence between the energy and virial routes to the equation of state of hard-sphere fluids
• Chemical-potential route for multicomponent fluids
• Structural properties of fluids interacting via piece-wise constant potentials with a hard core
• Chemical potential of a test hard sphere of variable size in a hard-sphere fluid
• Structural properties of the Jagla fluid
• Rational-function approximation for fluids interacting via piece-wise constant potentials
• Depletion potential in the infinite dilution limit
• Multicomponent fluid of hard spheres near a wall
• Thermodynamic consistency of energy and virial routes: An exact proof within the linearized Debye-Hückel theory
• Nonadditive hard-sphere fluid mixtures: A simple analytical theory
• Depletion force in the infinite-dilution limit in a solvent of nonadditive hard spheres
• Structure of ternary additive hard-sphere fluid mixtures
• Note: An exact scaling relation for truncatable free energies of polydisperse hard-sphere mixtures
• Exact solution of the Percus-Yevick integral equation for fluid mixtures of hard hyperspheres
• Rescaled density expansions and demixing in hard-sphere binary mixtures
• Communication: Inferring the equation of state of a metastable hard-sphere fluid from the equation of state of a hard-sphere mixture at high densities
• Test of a universality ansatz for the contact values of the radial distribution functions of hard-sphere mixtures near a hard wall
• Multicomponent fluid of nonadditive hard spheres near a wall
• Structural properties of additive binary hard-sphere mixtures
• Chemical potential of a test hard sphere of variable size in hard-sphere fluid mixtures
• Comment on "Theory and computer simulation for the equation of state of additive hard-disk fluid mixtures"
• Equation of state of additive hard-disk fluid mixtures: A critical analysis of two recent proposals
• Contact values for disparate-size hard-sphere mixtures
• Thermodynamic consistency between the energy and virial routes in the mean spherical approximation for soft potentials
• Equation of State of Four- and Five-Dimensional Hard-Hypersphere Mixtures
• Theoretical approaches to the structural properties of the square-shoulder fluid
• Direct correlation function from the consistent fundamental-measure free energies for hard-sphere mixtures
• Virial coefficients, equation of state, and demixing of binary asymmetric nonadditive hard-disk mixtures
• Simple relationship between the virial-route hypernetted-chain and the compressibility-route Percus--Yevick values of the fourth virial coefficient

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• Colloidal Hard Spheres: Triumphs, Challenges and Mysteries
• Why neural functionals suit statistical mechanics
• Connecting packing efficiency of binary hard sphere systems to their intermediate range structure
• Comparative study of force-based classical density functional theory
• Carnahan Starling type equations of state for stable hard disk and hard sphere fluids
• Structural properties of hard-disk fluids under single-file confinement
• Comparing four hard-sphere approximations for the low-temperature WCA melting line
• Hard-Sphere Jamming through the Lens of Linear Optimization
• Structural properties of additive binary hard-sphere mixtures. II. Asymptotic behavior and structural crossovers
• Structural and thermodynamic properties of fluids whose molecules interact via one-, two-, and three-step potentials
• Evolutionary optimization of the Verlet closure relation for the hard-sphere and square-well fluids
• A heuristic approach for the densest packing fraction of hard-sphere mixtures
• Determining the chemical potential via universal density functional learning
• Theory of Generalized Hertzian Hyperspheres
• Structural properties of additive binary hard-sphere mixtures. III. Direct correlation functions
• Cavity volume and free energy in many-body systems
• Predicting random close packing of binary hard-disk mixtures via third-virial-based parameters
• Leaky Cell Model of Hard Spheres
• Gaseous Diffusion as a Correlated Random Walk
• Critical point for de-mixing of binary hard spheres