A corresponding states principle for the equation of state of hard body fluid mixtures

A theoretically based corresponding-states principle is developed for athermal mixtures consisting of hard molecules. The principle states that when scaled appropriately, the excess compressibility factor for such mixtures reduces to a universal function of the effective packing fraction of the mixture. The latter represents the number density reduced by means of the effective molecular volume, which is defined as the volume a molecule excludes to any point of another molecule and depends on the geometry of both molecules. The scaling factor is related to a sort of effective nonsphericity parameter for the mixture that depends on composition as well as the nonsphericity parameters of the molecules which form the mixture and their effective molecular volumes. The universal function represents the excess compressibility factor of a pure hard-sphere fluid. Results are in good agreement with available simulation data.     

Generalized boublick equation: an accurate expression for the equation of state of hard fused spheres

Abstract

A simple expression to calculate the shape factor of hard bodies is proposed. Introducing this factor in the Boublik equation of state, very good results are obtained for hard dumbells and more complicated systems of linear homonuclear hard fused spheres. Agreement with available Monte Carlo results are also satisfactory enough for heteronuclear molecules. Furthermore, the new expression is reduced to the classical shape factor for hard convex bodies and provides a common basis to manage to concave and convex hard bodies.     

A consistent integral equation theory for hard spheres

The standard integral equation approach is used to extract the bridge function and other correlation functions of hard spheres fluid. To achieve this, we first use a recent consistent closure relation proposed by Bomont et al. [J. Chem. Phys. 119, 2188 (2003)] that has already proven to be accurate to describe the Lennard-Jones fluid properties. Second, we take advantage of the coherent scheme derived by Bomont [J. Chem. Phys. 119, 11484 (2003)] to calculate the excess chemical potential, the entropy and some relative transport properties. Very good agreement is obtained for structural quantities and thermodynamic properties as compared to exact data at densities ranging from 0.1 to 0.9.     

Application of a new equation of state to liquid refrigerant mixtures

A new general equation of state recently reported for pure liquids has been developed to predict the volumetric and thermodynamic properties of six binary and two ternary liquid refrigerant mixtures (including HCs and HFCs mixtures) at different temperatures, pressures, and compositions. The results show this equation of state can be used to reproduce and predict different thermodynamic properties of liquid refrigerant mixtures within experimental errors. The composition dependence of the parameters of this equation of state has been assumed as quadratic functions of mole fraction. Using these mixing rules, the agreement between calculated and experimental densities is better than 0.6% for binary mixtures and 2.3% for ternary mixtures. To compare the performance of this new equation of state against other well-known methods such as the COSTALD method, the density of some refrigerant mixtures, for which the parameters of COSTALD were available, has been computed and compared with those of this new equation of state.     

Modeling and simulation of equation of state for nonadditive hard disk mixtures

We present exact results for mixtures of nonadditive hard disks and use some of them to derive a consistent model for the equation of state. We also performed molecular dynamics simulation for hard disks over a wide range of size ratios. Comparison of the model to the data shows that the model is accurate for all densities in the case of additive and slightly nonadditive (nonadditivity parameter within ±0.1) mixtures. For large nonadditivity, the model is accurate for low to moderate densities only, and starts to deteriorate at high densities.     

Depletion potentials in colloidal mixtures of hard spheres and rods

The depletion potential between a hard sphere and a planar hard wall, or two hard spheres, imposed by suspended rigid spherocylindrical rods is computed by the acceptance ratio method through the application of Monte Carlo simulation. The accurate results and ideal-gas approximation results of the depletion potential are determined with the acceptance ratio method in our simulations. For comparison, the depletion potentials are also studied by using both the density functional theory and Derjaguin approximations. The density profile as a function of positions and orientations of rods, used in the density functional theory, is calculated by Monte Carlo simulation. The potential obtained by the acceptance ratio method is in good agreement with that of density functional theory under the ideal-gas approximation. The comparison between our results and those of other theories suggests that the acceptance ratio method is the only efficient method used to compute the depletion potential induced by nonspherical colloids with the volume fraction beyond the ideal-gas approximation.     

Alternative fundamental measure theory for additive hard sphere mixtures

The purpose of this short paper is to present an alternative fundamental measure theory (FMT) for hard sphere mixtures. Keeping the main features of the original Rosenfeld's FMT [Phys. Rev. Lett. 63, 980 (1989)] and using the dimensional and the low-density limit conditions a new functional is derived incorporating Boublik's multicomponent extension [Mol. Phys. 59, 371 (1986)] of highly accurate Kolafa's equation of state for pure hard spheres. We test the theory for pure hard spheres and hard sphere mixtures near a planar hard wall and compare the results with the original Rosenfeld's FMT and one of its modifications and with new very accurate simulation data. The test reveals an excellent agreement between the results based on the alternative FMT and simulation data for density profile near a contact and some improvement over the original Rosenfeld's FMT and its modification at the contact region.     

Extension of the new proposed association equation of state (AEOS) to associating fluid mixtures

Recently, a new statistical mechanic-based equation of state has been proposed by Mohsen-Nia and Modarress [M. Mohsen-Nia, H. Modarress, Chem. Phys. 336 (2007) 22–26] for associating pure fluids. The new association equation of state (AEOS) was successfully applied to calculate the saturated properties of water, methanol, and ammonia. In this work, the new proposed AEOS is used to evaluate the (vapour + liquid) equilibrium (VLE) of 25 associating pure compounds and the adjusted parameters are reported. The new AEOS is also extended to mixtures containing associating and non-associating compounds. The calculated saturated properties of the pure compounds are compared with those calculated by other AEOSs. The results of VLE calculation for various binary mixtures such as: alcohol/hydrocarbon, alcohol/CO₂, alcohol/aromatic-hydrocarbons, and the quaternary system (H₂O/CH₄/CO₂/H₂S) indicate the capability of the new proposed AEOS for associating pure and mixture calculations.     

A new non-cubic equation of state

A new non-cubic equation of state is presented in this work. This expression is obtained from the original Redlich—Kwong equation of state by assuming that the attraction parameter depends not only on temperature, but also on density. Vapour—liquid equilibria in the coexistence region and PVT properties for the liquid, gas and supercritical fluid phases are accurately calculated with four parameters per isotherm. The generalization of this equation by a corresponding states correlation enables it to be applied over wide ranges of temperature, pressure and hydrocarbon molecular weight.     

A quartic hard chain equation of state for normal fluids

A new empirical equation of state is proposed which is applicable to mixtures of chain-like molecules. The equation is based on a simple model which uses an approximate chain theory and an approximation of the Carnahan—Starling equation. The results for pure component properties of normal fluids are comparable to the common cubic equations of state. For mixtures of chain-like molecules, the new equation is as good or better than the Peng—Robinson equation.     

Equations of state of mixtures of hard dumbbells

Two ways to predict pVT behavior of hard-dumbbell mixtures in the fluid region are proposed. These are adaptations of the hard convex body equation devised by Boublik and an extension of the first Barker-Henderson perturbation theory. Calculated compressibility factors show good agreement with the ideal mixing assumption and yield a useful equation of state.     

On the equation of state of hard chain molecules

The chain-of-rotators (COR) equation of state developed by Chien, Greenkorn, and Chao makes an assumption on the hard chain partition function based on results for monomers and dimers, i.e., spheres and dumbbells. Here this assumption is checked for trimers by comparison with the results of Boubik's hard convex body equation. It turns out that the COR assumption is, in general, a good approximation. Its quality depends somewhat on the bond length and the bond angle which it does not consider. The agreement is especially good for angles somewhat less than 90°.     

Scaled particle theory of mixtures of hard spheres with negatively non-additive diameters

The scaled particle theory is solved for mixtures of hard spheres with arbitrary negative non-additive diameters in three dimensions. The results obtained with the Gibbs—Duhem relation show excellent agreement with the Monte-Carlo calculations. The results from the virial relation for high densities and high non-additivity are less satisfactory.     

A new two-parameter cubic equation of state for predicting phase behavior of pure compounds and mixtures

In this work, a new two-parameter cubic equation of state is presented based on perturbation theory for predicting phase behavior of pure compounds and of hydrocarbons and non-hydrocarbons. The parameters of the new cubic equation of state are obtained as functions of reduced temperature and acentric factor. The average deviations of the predicted vapor pressure, liquid density and vapor volume for 40 pure compounds are 1.116, 5.696 and 3.083%, respectively. Also the enthalpy and entropy of vaporization are calculated by using the new equation of state. The average deviations of the predicted enthalpy and entropy of vaporization are 2.393 and 2.358%, respectively. The capability of the proposed equation of state for predicting some other thermodynamic properties such as compressibility, second virial coefficient, sound velocity in gases and heat capacity of gases are given, too. The comparisons between the experimental data and the results of the new equation of state show the accuracy of the proposed equation with respect to commonly used equations of state, i.e. PR and SRK. The zeno line has been calculated using the new equation of state and the obtained result compared with quantities in the literatures. Bubble pressure and mole fraction of vapor for 16 binary mixtures are calculated. Averages deviations for bubble pressure and mole fraction of vapor are 9.380 and 2.735%, respectively.     

Application of the Quartic Hard Chain equation of state to polymer mixtures

The Quartic Hard Chain equation of state proposed by Kubic is a simple model for chain-like molecules. This study considers the application of this equation to polymer solutions. The equation was not found to be a useful predictive model because polymer parameters could not be reliably predicted from pure component properties. However, the equation was found to be a useful empirical form for representing polymer solution data. Because the Quartic Hard Chain equation is applicable to the vapour—liquid equilibria of normal fluids, this method is potentially useful for representing high pressure vapour—liquid equilibria in systems with dissolved polymer.     

Application of hard convex body and hard sphere equations of state to the critical properties of binary mixtures

The critical properties of hydrocarbon mixtures, perfluorocarbon + hydrocarbon, perfluoromethylcyclohexane + siloxane, acetone + hydrocarbon and polydimethyl siloxane mixtures have been calculated from an equation of state for hard convex bodies and from Guggenheim's equation of state for hard spheres. In general, the results of both equations agree well with experimental data.It appears, however, that taking shape factors into account (by using the hard convex body equation) does not lead to a significant improvement in the agreement between theory and experiment for the critical properties.     

Integral equation theory for symmetric nonadditive hard sphere mixtures

An integral equation theory is presented for the pair correlation functions and phase behavior of symmetric nonadditive hard sphere mixtures with hard sphere diameters given by sigma(A)(A)() = sigma(BB) = lambdad and sigma(AB) = d. This mixture exhibits a fluid-fluid phase separation into an A-rich phase and a B-rich phase at high densities. The theory incorporates, into the closure approximation, all terms that can be calculated exactly in the density expansion of the direct correlation functions. We find that the closure approximation developed in this work is accurate for the structure and phase behavior over the entire range of lambda, when compared to computer simulations, and is significantly more accurate than the previous theories.     

A simple non-classical equation of state for fluids and fluid mixtures

A method for improving the behavior of classical equations of state (EOS) in the critical region, originally proposed by Fox [J.R. Fox, Fluid Phase Equilibria 14 (1983) 45–53], has been modified in this work for the Patel–Teja (PT) EOS [N.C. Patel, A.S. Teja, Chem. Eng. Sci. 37, 463–473]. The application of the new equation (NPT) for predicting PVT and vapor pressure behavior of pure substances, as well as vapor–liquid equilibrium behavior of binary mixtures, is demonstrated. The NPT equation is simple to use and requires the same input information as the original PT equation. However, it reproduces the correct PVT behavior in the critical region. Limitations of both the PT and NPT equations in calculating the isochoric heat capacity are discussed.     

Pure component vapour pressure from a Carnahan-Starling equation of state: theoretically based temperature law for the attractive parameter

The proposed equation of state associates the Carnahan-Starling hard-sphere repulsion term with an attraction term of the Redlich-Kwong type containing a temperature function α(T_r). It is applied for calculating the vapour pressures of 14 pure hydrocarbon and non-hydrocarbon components. For α(T_r), three empirical laws and one law deduced from the Clausius-Clapeyron equation are investigated. This last one gives the best results, and its two adjustable parameters may be generalized as a function of the acentric factor.