The fifth virial coefficients of fused hard sphere fluids (original) (raw)
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Analytical expressions for the fourth virial coefficient of a hard-sphere mixture
Physical Review E, 2009
A method of numerical calculation of the fourth virial coefficients of the mixture of additive hard spheres is proposed. The results are compared with an exact analytical formula for the fourth partial virial coefficient B 4 ͓1͔ ͑i.e., three spheres of diameters 1 and one sphere of diameter 2 ͒ and a semiempirical expression for B 4 ͓2͔ ͑i.e., two spheres of each kind͒. It is shown that the first formula is nonanalytic and the implication to the equations of state for hard-sphere mixtures is discussed.
Linear hard sphere models Virial coefficients and equation of state
Molecular Physics, 1994
Virial coefficients of tangent hard spheres in a linear configuration have been determined numerically. Trends of the virial coefficients with the molecular anisotropy are similar to those of other linear models, such as hard spherocylinders or hard ellipsoids. Theoretical predictions of virial coefficients from different equations of state of hard body fluids are compared with the numerical results. None of them provides a completely satisfactory description of the lower virial coefficients when the anisotropy of the molecule is large. We propose a new method to build up an equation of state of hard linear models (prolate or oblate) from the knowledge of the first five virial coeff•
Equations of state for hard-sphere fluids
International Journal of Thermophysics, 1988
Equations of state and contact values of hard-sphere radial distribution functions (rdf's) which are given by a linear combination of the Percus-Yevick and scaled-particle virial expressions are considered. In the one-component case the mixing coefficient 0(r/) is, in general, a function of the volume fraction q. In mixtures the coefficient 0(r/i, di), in general, depends upon the volume fraction rh and diameter d i of each species, i and j. For the contact values Y,j of the rdf's, the mixing coefficients O~(qk) also depend on species i and j. Density expansions for the exact 0 for the one-component hard-sphere fluid are obtained and compared with several approximations made in earlier works and in our own work, as well as with simulations. For a mixture, it turns out that one cannot obtain the exact fourth virial coefficient by using a linear combination of the Percus-Yevick and scaled-particle virial expressions for Yo unless one allows O U to depend on mole fractions x~ even at the zeroth order of its density expansion. We also find that O~j must depend on particle species i and j in order to satisfy the exact limits obtained earlier by Sung and Stell. A new equation of state for the binary hard-sphere mixture which satisfies all the exact limits we have considered is suggested.
Binary mixtures of hard spheres: how far can one go with the virial equation of state?
Fluid Phase Equilibria, 2003
We describe a technique to calculate partial virial coefficients up to seventh order in a binary mixture of hard spheres, using hit-and-miss Monte-Carlo (MC) numerical integration. The algorithm makes use of look-up tables of all the blocks contributing to each partial virial coefficient. All topologically equivalent graphs are listed in this table so as to improve the statistical efficiency of the calculation. For the case of additive hard spheres, we report the partial contributions to the sixth and seventh virial coefficients, for size ratios ranging from 0.1 to 0.9. For the non-additive mixture we truncated the expansion at sixth order and only considered one set of potential parameters: size ratio 0.1 and non-additivity factor +0.1. In line with previous work, our results indicate that for additive spheres with a size ratio in the region of 0.1, there would appear to be a liquid-liquid de-mixing transition but at an overall packing fraction that would imply that this is meta-stable with respect to a fluid-solid transition. A positive non-additivity serves to increase the tendency for liquid-liquid de-mixing, but appears to have an adverse effect on the rate of convergence of the virial series.
The Journal of Chemical Physics, 2010
Different theoretical approaches for the thermodynamic properties and the equation of state for multicomponent mixtures of nonadditive hard spheres in d dimensions are presented in a unified way. These include the theory by Hamad, our previous formulation, the original MIX1 theory, a recently proposed modified MIX1 theory, as well as a nonlinear extension of the MIX1 theory proposed in this paper. Explicit expressions for the compressibility factor, Helmholtz free energy, and second, third, and fourth virial coefficients are provided. A comparison is carried out with recent Monte Carlo data for the virial coefficients of asymmetric mixtures and with available simulation data for the compressibility factor, the critical consolute point, and the liquid-liquid coexistence curves. The merits and limitations of each theory are pointed out.
The Journal of Chemical Physics, 2003
The bonded hard-sphere ͑BHS͒ theory is extended to fluids consisting of rigid, linear, homonuclear molecules, each of them formed by n fused hard spheres. The theory shows excellent agreement with the Monte Carlo NpT simulation data which are also reported for reduced bond lengths l*ϭ0 . The accuracy of the BHS prediction in comparison to simulation is similar to that of generalized Flory-dimer theory and superior to that of thermodynamic perturbation theory.
Accurate equation of state of the hard sphere fluid in stable and metastable regions
Physical Chemistry Chemical Physics, 2004
New accurate data on the compressibility factor of the hard sphere fluid are obtained by highly optimized molecular dynamics calculations in the range of reduced densities 0.20-1.03. The relative inaccuracy at the 95% confidence level is better than 0.00004 for all densities but the last deeply metastable point. This accuracy requires careful examination of finite size effects and other possible sources of errors and applying corrections. The data are fitted to a power series in y/(1 À y), where y is the packing fraction; the coefficients are determined so that virial coefficients B 2 to B 6 are reproduced. To do this, values of B 5 and B 6 are accurately recalculated. Virial coefficients up to B 11 are then estimated from the equation of state.
Virial coefficients of the additive hard-sphere binary mixtures up to the eighth
Molecular Physics, 2016
The fifth to eighth virial coefficients of the additive hard-sphere binary mixtures are accurately calculated in the whole range of sphere diameter ratios. Calculations are based on an extension of the technique for topological analysis of the Ree-Hoover diagrams and the standard Metropolis Monte Carlo algorithm. The results for the fifth to the seventh partial virial coefficients are compared with literature data. The eighth virial coefficients are new. The results are also compared with a semi-empirical analytical equation due to Wheatley and discussed.
A simple method of generating equations of state for hard sphere fluid
Chemical Physics, 2007
We present in this paper a simple method of obtaining various equations of state for hard sphere fluid in a simple unifying way. Using the first several virial coefficients of hard sphere fluid, we will guess equations of state by using the asymptotic expansion method. Among the equations of state obtained in this way are Percus-Yevick, Scaled Particle Theory, and Carnahan-Starling equations of state. Also by combining the Monte Carlo results on hard sphere fluid with the asymptotic expansion method many other equations of state for hard sphere fluid can be found where all of them give essentially similar results in the region of isotropic hard sphere liquid, i.e., up to g < 0.5, in which g is the packing fraction. In addition we have found a simple equation of state for the hard sphere fluid in the metastable region which represents the simulation data accurately.
Hard-sphere fluid-to-solid transition and the virial expansion
Journal of Statistical Physics, 1983
An exhaustive Pad~ approximant study of the Mayer virial series expansion is carried out for the classical hard-sphere system. As one increases the order of the different approximants a clear tendency is seen to reproduce both the random close packing divergence of the fluid branch as well as its instability (towards the crystalline phase) at the spinodal point.