Hard Convex Body Fluid Research Articles

Theoretical Study of Non-additive Hard Convex Body Fluid Mixtures

The structure of a dense fluid or liquid is largely determined by the repulsive intermolecular forces, so the hard core potential has been extensively employed to model real fluids and fluid mixtures. The properties of two dimensional hard body fluids and fluids mixtures have aroused a considerably interest in recent years. This is because they are treated as models of real fluids or fluid mixtures absorbed onto surfaces. The 2D hard-body fluids and fluid mixtures like their three-dimensional counter part are useful reference system in framing a perturbation theory for 2D real fluids and fluid mixtures of non-spherical molecules. The 2D hard-body systems are convex body (HCB) systems such as ellipse (HE) and hard discorectangles (HDR) and hard non-convex body systems i.e., fused hard discs (FHD) and planar hard dumbbell (HDB) systems. The equation of state of hard convex body fluid mixtures (HCB) is studied. Analytic expressions are given for the equation of state of the fluid mixture of the non-additive HCB. The numerical results are discussed for the non-additive hard dumbbell (HDB) fluid mixtures under different conditions for different values of non-additivity \(\Delta\). They depend on the conditions, shape parameters \(L^*_{11}\) and \(L^*_{22}\) , mole fractions \(x_1\) and \(x_2\) and \(\Delta\) in general and increase with the increase of packing fraction \(\Delta\).

Thermophysical properties of hydrogen along the liquid–vapor coexistence

We present Theoretical Calculations for the Liquid–Vapor Coexistence (LVC) curve of fluid Hydrogen within the first order perturbation theory with a suitable first order quantum correction to the free energy. In the present equation of state, we incorporate the dimerization of H2 molecule by treating the fluid as a hard convex body fluid. The thermophysical properties of fluid H2 along the LVC curve, including the pressure–temperature dependence, density–temperature asymmetry, volume expansivity, entropy and enthalpy, are calculated and compared with computer simulation and empirical results.

Phase diagram and thermodynamic properties of H2

A statistical mechanical-based theory is used to develop the equation of state for the molecular fluid of H(2). We incorporate in this equation the long-range correlations through the double Yukawa potential, dimerization of the H(2) molecule by treating the fluid as a hard convex body fluid, and first-order quantum correction which is important at low temperatures. We use this to calculate the liquid-vapor equilibrium of H(2), including the temperature and pressure dependence of compressibility factor, entropy, specific heat, compressibility, and sound velocity.

The equation of state of isotropic fluids of hard convex bodies from a high-level virial expansion

We have calculated virial coefficients up to seventh order for the isotropic phases of a variety of fluids composed of hard aspherical particles. The models studied were hard spheroids, hard spherocylinders, and truncated hard spheres, and results are obtained for a variety of length-to-width ratios. We compare the predicted virial equations of state with those determined by simulation. We also use our data to calculate the coefficients of the y expansion [B. Barboy and W. M. Gelbart, J. Chem. Phys. 71, 3053 (1979)] and to study its convergence properties. Finally, we use our data to estimate the radius of convergence of the virial series for these aspherical particles. For fairly spherical particles, we estimate the radius of convergence to be similar to that of the density of closest packing. For more anisotropic particles, however, the radius of convergence decreases with increased anisotropy and is considerably less than the close-packed density.

Semiclassical statistical mechanics of hard-body fluid mixtures

The thermodynamic properties of semiclassical hard-body fluid mixtures are studied. Explicit expressions are given for the free-energy, equation of state and virial coefficients of the classical hard convex-body fluid mixtures. The numerical results are discussed under different conditions. The agreement with the exact data is good in all cases. The first-order quantum corrections are also studied. The quantum effects depend on the condition, shape parameters L11* and L22*, and concentrations x1 and x2 in general and increase with an increase of packing fraction eta, in particular.

Thermodynamic properties of He-H2 fluid mixtures over a wide range of temperatures and pressures.

The effect of pressure P and temperature T on the properties of mixing of helium-hydrogen (He-H2 ) fluid mixture is studied based on statistical mechanical perturbation theory. The constituent species are considered to be interacting via a pair potential consisting of short range repulsion and a long range attraction which has been included through a double Yukawa (DY) potential. He and H2 are the lightest elements; therefore, the quantum effect is included via first-order quantum correction in the framework of Wigner-Kirkwood expansion. The dimerization of the H2 molecule is treated as a hard convex body fluid for which the equation of state (EOS) can be derived from hard sphere system based on scaled particle theory. An advanced and most recent EOS has been used for our investigation. The use of the DY potential, which can readily be simulated to empirical potentials, has enabled us to obtain analytical expressions for attractive and quantum energy contributions in terms of Laplace transforms. With a view to ensure internal consistency of the various thermodynamic functions to extract information on segregation and order in the mixture, different functions, such as compressibility factor, Gibbs free energy of mixing, entropy of mixing, and concentration fluctuations in the long wavelength limit, have been calculated as functions of composition of the mixture over an extended region of P and T. The results suggest that segregation, heterocoordination, or both may occur in the He-H2 mixture depending upon its composition, pressure, and temperature.

Monte-Carlo integration for virial coefficients re-visited: hard convex bodies, spheres with a square-well potential and mixtures of hard spheres

Techniques to adapt the hit-and-miss Monte-Carlo numerical integration are proposed with the aim to determine virial coefficients up to eighth order in fluids of hard convex bodies, hard spheres with an attractive square-well potential and a two-component mixture of hard spheres. These algorithms make use of look-up tables of all the blocks contributing to the coefficients. Each type of block is represented in the tables by several entries. These correspond to all possible topologically equivalent graphs that can be generated by the Monte-Carlo process. This rendered the Monte-Carlo method statistically more efficient. In the case of a two-component system the look-up tables had to have representations of blocks having two sorts of vertices. The reported data are: improved values of the seventh and eighth virial coefficients for hard spheres, the sixth, seventh and eighth coefficients of spheroids, spherocylinders and cutspheres, fifth virial coefficient of spheres with a square-well potential of relative range 1.25; 1.5; 1.75 and 2.0 and the partial contributions of the sixth virial coefficient for a mixture of hard spheres with the size ratio 0.1.

Equation of state extended from SAFT with improved results for non-polar fluids across the critical point

Based on the thermodynamic perturbation theory of Wertheim, statistical associating fluid theory (SAFT) has became a successful equation of state for the description of thermodynamic properties of fluids, especially for systems including polymers. In recent years, different versions of SAFT have been developed based on square-well and Lennard–Jones reference fluids and improvements are achieved. In this paper SAFT is modified with two improvements in order to calculate the properties near the critical points of non-polar fluids. One improvement is the consideration of the segment shape in chain molecules using the hard convex body equation of state as the reference term and the relative expression for chain formation with the radial distribution function of hard convex body fluid is also included. The another improvement is the exclusion of the dispersion energy between intramolecular segments with a newly derived term based on the perturbation theory. The first improvement gives a better prediction of the critical points for one-segment non-spherical molecules and the second for chain molecules. The new equation of state includes four parameters for every non-polar fluid: the segment number m, the segment non-spherical parameter α, the segment volume v 00 and the segment interaction parameter u 0. The saturated pressures and saturated liquid densities up to the critical point can be calculated with average absolute deviations of 0.6 and 0.8% for 44 non-polar fluids including n-alkanes, branched alkanes, cycloalkanes, alkenes, alkynes and aromatics. Critical temperatures, pressures and densities are calculated with the average absolute deviations of 0.2, 1.2 and 2.9%. The new equation of state was used to predict such thermodynamic properties as PVT lines, and vaporization enthalpies. The prediction results are also in good agreement with experimental data from literature.

Equation of state for hard convex body fluid mixtures

A model previously developed for the equation of state of pure fluids consisting of hard convex body molecules is extended to mixtures. The parameters of the model can be determined from the geometrical characteristics of the molecules which form the mixture. The equation of state is in excellent agreement with simulation data for mixtures of hard spheres with hard spherocylinders.

Equation of state for hard convex body fluid mixtures

A model previously developed for the equation of state of pure fluids consisting of hard convex body molecules is extended to mixtures. The parameters of the model can be determined from the geometrical characteristics of the molecules which form the mixture. The equation of state is in excellent agreement with simulation data for mixtures of hard spheres with hard spherocylinders.

Prediction of transport properties of dense molecular fluids using the effective diameter hard sphere theory

The present paper explores the ability of the effective diameter hard sphere theory to estimate the transport properties of a fluid made up of particles interacting through the Gaussian overlap model. This method relies on the assumption that at high densities the behaviour of a fluid is dominated by harsh repulsive forces. Hence, the properties of the fluid can be given in terms of a hard convex body fluid, and the properties of this fluid can also be expressed in terms of an effective hard sphere fluid. The state-dependent diameter of the reference hard sphere fluid is obtained through the blip function theory, well known in the equilibrium liquid theory of molecular fluids, in terms of the Gaussian overlap model parameters. Comparisons with measured thermal conductivities and shear viscosities for nitrogen and benzene were made, because of the lack of molecular dynamics data. Our results are in good agreement with experimental data over wide density ranges, and the sources of discrepancy could be expla...

Invariant expansions of the radial distribution function for fluids of hard convex bodies

The radial distribution functions (RDF) for systems consisting of a single nonspherical convex body in a fluid of spheres and for a pure fluid of nonspherical convex bodies are expressed in terms of the minimum surface-to-surface separation and a set of angles derived from the surface normal. The orthogonal function expansion of the anisotropic RDF, g, has the property that the first anisotropic contribution vanishes at zero density and is directly proportional to the nonsphericity of the particle; however, the resulting convex body orthogonal polynomials depend on the surface-to-surface separation. An invariant expansion of the product of the Jacobian and the RDF, S12g, has anisotropic expansion coefficients even at zero density, but the expansion functions are the spherical harmonics (independent of the surface-to-surface coordinate). Monte Carlo simulations are conducted on the two dimensional system consisting of a single convex ellipse in a bath of circular disks. A comparison is made between the center-to-center expansion of the RDF, an expansion based on the orthogonal function expansion, and the S12g (or Kabadi–Steele) expansion.

Orientational correlations in fluids of hard convex bodies. I. General theory

A version of scaled particle theory (SPT) is developed for a thermodynamic system comprised of a single hard convex body (HCB) in a fluid of spheres. In two limits, corresponding to an infinitesimally and a macroscopically scaled HCB, the present version of SPT yields the same angle-dependent constraints on the contact radial distribution function (rdf) as those derived by Boublik for the angle-averaged rdf. For noninfinitesimally scaled HCB’s, a new orientation-dependent condition on the contact rdf is determined by means of a differential bulging technique.

An accurate equation of state of a hard convex body fluid mixture

A method enabling to calculate the contact-point values of the pair correlation function of convex body fluids from a semi-empirical equation of state is presented and the accurate Nezbeda equation of the pure hard convex body fluid is extended to mixtures. Comparison of results for one- and two-component systems with Monte Carlo simulation data shows excellent agreement.