Extension of Compressibility-Route Cubic Equations of State and the Radial Distribution Functions at Contact to Multi-Component Hard-Sphere Mixtures

The equation of state (EOS) for hard-sphere fluid derived from compressibility routes of Percus-Yevick theory (PYC) is extended. The two parameters are determined by fitting well-known virial coefficients of pure fluid. The extended cubic EOS can be directly extended to multi-component mixtures, merely demanding the EOS of mixtures also is cubic and combining two physical conditions for the radial distribution functions at contact (RDFC) of mixtures. The calculated virial coefficients of pure fluid and predicted compressibility factors and RDFC for both pure fluid and mixtures are excellent as compared with the simulation data. The values of RDFC for mixtures with extremely large size ratio 10 are far better than the BGHLL expressions in literature.     

Extension of Compressibility-Route Cubic Equations of State and the Radial Distribution Functions at Contact to Multi-Component Hard-Sphere Mixtures

The equation of state(EOS) for hard-sphere fluid derived from compressibility routes of Percus-Yevick theory(PYC) is extended. The two parameters are determined by fitting well-known virial coefficients of pure fluid.The extended cubic EOS can be directly extended to multi-component mixtures, merely demanding the EOS of mixtures also is cubic and combining two physical conditions for the radial distribution functions at contact(RDFC) of mixtures.The calculated virial coefficients of pure fluid and predicted compressibility factors and RDFC for both pure fluid and mixtures are excellent as compared with the simulation data. The values of RDFC for mixtures with extremely large size ratio 10 are far better than the BGHLL expressions in literature.     

Modified equation of state for pure and hard sphere mixtures in mean ionic activity coefficient calculations by mean spherical approximation model

A hard sphere equation of state (EOS) based on tetrakaidecahedron cell geometry (instead of spherical shape) and highly optimized molecular dynamic simulation data is proposed. The EOS is extended to hard sphere mixture and its performance for compressibility factor calculation at different diameter size of hard sphere mixtures by using various mixing rule is compared with Monte Carlo simulation data. The results indicated that for all mixing rules, the proposed EOS has minimum error comparing with computer simulation data. Also the residual prosperities are derived by using the proposed EOS. The residual properties are used in mean spherical approximation model (MSA) to evaluate the mean ionic activity coefficient of aqueous electrolyte solutions. The results are compared with those obtained by similar hard sphere equations of state and it is shown that the proposed EOS has a better performance in predicting the mean ionic activity coefficient.     

A new correlation based on artificial neural networks for predicting the natural gas compressibility factor

In this study a new correlation of natural gas compressibility factor based on theory of Mohammadikhah-Mohebbi-Abolghasemi??s equation of state (MMA EOS) is developed using an artificial neural network. In MMA EOS, the compressibility factor as a function of M-factor (BP/RT) is expressed. An artificial neural network (ANN) is designed in which the M-factor, reduced temperature, and reduced pressure are selected as input variables, whereas the natural gas compressibility factor is selected as output. Then, a new correlation based on the weights of ANN is obtained. Results of this correlation are compared with some other equations and experimental data. Proposed correlation for 597 data points has an average absolute deviation (AAD%) of 0.6% and a correlation coefficient (R ² value) of 0.9999.     

Thermophysical properties of ionic liquids and their mixtures from a new equation of state

In our previous work, a perturbed hard-trimer-sphere equation of state (PHTS EOS) was developed for modeling the phase equilibria of pure ionic liquids (ILs) (M.M. Alavianmehr et al., Ionics 22 (2016) 2447–2459). In this work, we have successfully extended the model to the mixtures of IL + IL and IL + solvent. Two temperature-dependent parameters appearing in the EOS are correlated with two microscopic scaling constants σ, the effective hard-sphere diameter, and ε, the non-bonded interaction energy. The overall average absolute deviation (AAD) of the estimated densities from the literature data using the proposed model with and without non-additivity parameter (λ _ij) was found to be 0.44 and 0.79%, respectively. A modified Enskog equation and rough hard-sphere (RHS) theory are combined with our proposed equation of state to calculate the viscosity coefficient of ionic liquids and their mixtures. Finally, from the results obtained, a linear relation between logarithm of surface tension and viscosity property of ionic liquid was developed.     

Stochastic hard-sphere dynamics for hydrodynamics of nonideal fluids

A novel stochastic fluid model is proposed with a nonideal structure factor consistent with compressibility, and adjustable transport coefficients. This stochastic hard-sphere dynamics (SHSD) algorithm is a modification of the direct simulation Monte Carlo algorithm and has several computational advantages over event-driven hard-sphere molecular dynamics. Surprisingly, SHSD results in an equation of state and a pair correlation function identical to that of a deterministic Hamiltonian system of penetrable spheres interacting with linear core pair potentials. The fluctuating hydrodynamic behavior of the SHSD fluid is verified for the Brownian motion of a nanoparticle suspended in a compressible solvent.     

Perturbation approach for equation of state for hard-sphere and Lennard–Jones pure fluids

In this paper we have established the equation of state (EOS) for liquids. The EOS was established for hard-sphere (HS) fluid along with Lennard–Jones (LJ) fluid incorporating perturbation techniques. The calculations are based on suitable axiomatic functional forms for surface tension S _m (r), r ≥ d/2 with intermolecular separation r, as a variable, and m is an arbitrary real number (pole). The results for βP/ρ from the present EOS thus obtained are compared with Percus-Yevick (PY), scaled particle theory (SPT), and Carnahan–Starling (CS). In addition, we have found a simple EOS for the HS fluid in the region which represents the simulation data accurately.     

On the compressibility equation of state for multi-component adhesive hard sphere fluids

The compressibility equation of state (EOS) for a multi-component sticky hard sphere model alternative to Baxter's one is investigated within the mean spherical approximation (MSA). For this model and this closure, as well as for a more general class of models and closures leading to Baxter functions q_ij(r) with density-independent stickiness coefficients, no compressibility EOS can exist for mixtures, unlike the one-component case (in view of this, an EOS recently reported in the literature turns out to be incorrect). The reason is the failure of the Euler reciprocity relation for the mixed second-order partial derivatives of the pressure with respect to the partial densities. This is in turn related to the inadequacy of the approximate closure (in particular, the MSA). A way out to overcome this drawback is presented in a particular example, leading to a consistent compressibility pressure, and a possible generalization of this result is discussed.     

Weighted-density approaches for polymer structure at solid–polymer interfaces

Weighted-density approximations (WDAs), which are based on the weighting function for the second-order direct correlation functions (DCFs) of the uniform polymeric fluids, have been developed to investigate the structural and thermodynamic properties of polymer melts at interfaces. The advantage is the simplicity of calculation of the weighting functions and their accuracies in the applications. They were applied to study the local density distributions and adsorption isotherms of the freely jointed tangent hard-sphere chain, Yukawa chain, and hard-sphere chain mixture in slit pores. The polymer reference interaction model (PRISM) integral equation with the Percus–Yevick (PY) closure has been used to calculate the second-order DCF of the polymeric fluids required as inputs. The mean-field approximation (MFA) has been used to calculate the weighting function for the attractive contribution of a freely jointed tangent Yukawa chain fluid, having attraction among the beads. The calculated results show that (i) for the freely jointed tangent hard-sphere chain, the present theory is in excellent agreement with the computer simulations over a wide range of chain lengths and bulk densities, (ii) the WDA approach for the attraction provides an accurate method for the local density distributions of a freely jointed tangent Yukawa chain fluid, and that (iii) the present theory also yields a reasonably good result for the structural properties of the freely jointed hard-sphere chain mixtures composed of the chain and monomer.     

A new integral equation for the radial distribution function of a hard sphere fluid

Based on a proposal by Shinomoto, a new integral equation is derived for the radial distribution function of a hard-sphere fluid using mainly geometric arguments. This integral equation is solved by a perturbation expansion in the density of the fluid, and the results obtained are compared with those from molecular dynamics simulations and from the Born-Green-Yvon (BGY) and Percus-Yevick (PY) theories. The present theory provides results for the radial distribution function which are intermediate in accuracy between those obtained from the BGY and from the PY theories.     

Development of a perturbed hard-sphere equation of state for pure and mixture of ionic liquids

A perturbed hard-sphere equation of state (PHS EOS) was previously proposed to present the volumetric properties of ionic liquids by employing a variable parameter β being a function of acentric factor to justify the range of vdW dispersion forces (M. M. Papari, J. Moghadasi, S. M. Hosseini, F. Akbari, J. Mol. Liq. 158 (2011) 57–60). The main aim of the present study is to revise an attractive part of the preceding EOS by re-evaluating the above-mentioned variable parameter as well as the repulsive term. Two temperature-dependent parameters appearing in the revisited EOS have been determined from the corresponding states correlations using the interfacial properties of ILs, i.e., surface tension and liquid density, both at room temperature. The revisited EOS has been employed to model the volumetric properties of ionic liquids (ILs). The predictive power of the proposed model has been assessed by comparing the results obtained with 2189 experimental data points related to 24 ILs over a broad range of pressures and temperatures. The overall average absolute deviation (AAD) of the calculated densities from literature data was found to be 0.62 %. Furthermore, the revisited PHS EOS has been employed to model the volumetric properties of 23 mixtures including IL + IL and IL+ solvent over the vast range of temperatures. From 1580 data points of the binary mixtures of interest, the AAD of the correlated densities from the measurements was found to be 0.47 %.     

TPT2 and SAFTD equations of state for mixtures of hard chain copolymers

We present the second-order thermodynamic perturbation theory (TPT2) and the dimer statistical associating fluid theory (SAFTD) equations of state for mixtures consisting of hetero-nuclear hard chain molecules based on extensions of Wertheim's theory for associating fluids. The second-order perturbation theory, TPT2, is based on the hard sphere mixture reference fluid. SAFTD is an extension of TPT1 (= SAFT) and is based on the non-spherical (hard disphere mixture) reference fluid. The TPT2 equation of state requires only the contact values of the hard sphere mixture site-site correlation functions, while the SAFTD equation of state requires the contact values of site-site correlation functions of both hard sphere and hard disphere mixtures. We test several approximations for site-site correlation functions of hard disphere mixtures and use these in the SAFTD equation of state to predict the compressibility factor of copolymers. Since simulation data are available only for a few pure copolymer systems, theoretical predictions are compared with molecular simulation results for the compressibility factor of pure hard chain copolymer systems. Our comparisons show a very good performance of TPT2, which is found to be more accurate than TPT1 (= SAFT). Using a modified Percus-Yevick site-site correlation function SAFTD is found to represent a significant improvement over SAFT and is slightly more accurate than TPT2. Comparison of SAFTD with generalized Flory dimer (GFD) theory shows that both are equivalent at intermediate to high densities for the compressibility factor of copolymer systems investigated here.     

Thermodynamic properties of liquid metals,temperature dependent hard-sphere model

An analytic solution of the Percus-Yevick equation for the hard-sphere model of a liquid is used to investigate the thermodynamic properties of liquid metals near the triple point. The temperature dependence of the packing fraction (or hard-sphere diameter) is introduced by the phenomenological method using the compressibility equation. Agreement between theory and experiment is improved for both the thermal pressure coefficient and specific heat.     

Density functional theory for Baxter's sticky hard spheres in confinement

It has recently been shown that a free energy for Baxter's sticky hard-sphere fluid is uniquely defined within the framework of fundamental measure theory (FMT) for the inhomogeneous hard-sphere fluid, provided that it obeys scaled-particle theory and the Percus-Yevick (PY) result for the direct correlation function [H. Hansen-Goos and J. S. Wettlaufer, J. Chem. Phys. 134, 014506 (2011)]. Here, combining FMT weighted densities with a new vectorial weighted density, we regularize the divergences of the associated strongly confined limit. The free energy that emerges is exact in the zero-dimensional limit, leaves the underlying equation of state unaffected, and yields a direct correlation function distinct from that of PY. Comparison with simulation data for both the bulk pair-correlation function and the density profiles in confinement shows that the new theory is significantly more accurate than the PY-based results.     

Non-ergodicity transition and multiple glasses in binary mixtures: on the accuracy of the input static structure in the mode coupling theory

We examine the question of the accuracy of the static correlation functions used as input in the mode coupling theory (MCT) of non-ergodic states in binary mixtures. We first consider hard-sphere mixtures and compute the static pair structure from the Ornstein-Zernike equations with the Percus-Yevick closure and more accurate ones that use bridge functions deduced from Rosenfeld's fundamental measures functional. The corresponding MCT predictions for the non-ergodicity lines and the transitions between multiple glassy states are determined from the long-time limit of the density autocorrelation functions. We find that while the non-ergodicity transition line is not very sensitive to the input static structure, up to diameter ratios D(2)/D(1)?=?10, quantitative differences exist for the transitions between different glasses. The discrepancies with the more accurate closures become even qualitative for sufficiently asymmetric mixtures. They are correlated with the incorrect behavior of the PY structure at high size asymmetry. From the example of ultra-soft potential it is argued that this issue is of general relevance beyond the hard-sphere model.     

Reflected shock experiments on the equation-of-state properties of liquid deuterium at 100-600 GPa (1-6 mbar)

New laser-driven shock experiments have been used to study the equation-of-state (EOS) properties of liquid deuterium. Reflected shocks are utilized to increase the shock pressure and to enhance the sensitivity to differences in compressibility. The results of these experiments differ substantially from the predictions of the Sesame EOS. EOS models showing large dissociation effects with much greater compressibility (up to a factor of 2) agree with the data. By use of independent techniques, this experiment offers the first confirmation of an earlier observation of enhanced compressibility in liquid deuterium.     

HFC混合物二元交互作用系数研究

目前国际上已商业化使用或提出的潜在的环保工质,大多数为氢氟烃(HFC)混合物,利用状态方程描述混合工质热力性质时,交互作用系数是重要参数之一。本文应用Peng-Robinson状态方程对多种HFC二元混合物的气液相平衡(vapor—liquid equilibrium,VLE)实验数据进行了回归,得到了相应混合物的交互作用系数。提出了交互作用系数新关联式,结果表明所得到的交互作用系数能很好的应用于描述HFC混合物气液相平衡性质,计算精度可以满足工程应用的需要。     

A perturbed hard-sphere equation of state extended to imidazolium-based ionic liquids

A perturbed hard-sphere equation of state (EOS) has been previously employed to predict pressure–volume–temperature properties of some ionic liquids (ILs) with phosphonium-, pyridinium-, and pyrrolidinium cations. In this work, we have extended the considered EOS to another class of ILs in compressed states. This class consists of 14 imidazolium-based ILs. The predicted densities were compared with those obtained from the experiment, over a broad pressure range from 0.1 to 200 MPa. From 1,122 data points examined for the aforementioned ILs, the total average absolute deviation was found to be 1.05%.     

An equation of state for the isotropic phase of linear,partially flexible and fully flexible tangent hard-sphere chain fluids

A new equation of state is developed that accurately describes the isotropic phase behaviour of linear, partially flexible and fully flexible tangent hard-sphere chain fluids and their mixtures. The equation of state is based on the equation of state of Liu and Hu [H. Liu and Y. Hu, Fluid Phase Equilibr. 122, 75 (1996)] for fully flexible chain fluids. The effect of molecular flexibility is described by a pure-component parameter that is introduced in the theory at the level of the cavity correlation function of next-to-nearest neighbour segments in a chain molecule. The equation of state contains a total of three adjustable model constants. The extension to partially flexible- and linear chain fluids is based on a refitting of the first model constant to numerical data of the second virial coefficient of partially flexible and linear tangent hard-sphere chain fluids. The numerical data were obtained from an analytical approximation for the pair-excluded volume. The other two parameters were adjusted to molecular simulation data for the pressure of linear tangent hard-sphere chain fluids. For both, pure component systems and mixtures of chains of variable flexibility, the pressure and second virial coefficient obtained from the equation of state, are in excellent agreement with the results from Monte Carlo simulations. A significant improvement to TPT1, TPT2, generalised Flory-dimer theory and scaled particle theory is observed.