Generalized Flory-Huggins theory-based equation of state for ring and chain fluids

By modeling the ring-like molecule as a pearl necklace of freely jointed hard sphere, we develop a new equation of state (EOS) for the ring-like fluids on the basis of generalized Flory-Huggins (GFH) theory. Before proposing the new EOS of the ring-like fluids, we first modify the generalized Flory-Huggins theory for the chain fluids by incorporating a function related to the packing fraction into the insertion probability. The results indicate that the modified GFH EOS can predict the compressibility factors more accurately than the GFH EOS, especially for the intermediate and high packing fractions (η ≥ 0.157). Subsequently, the modified GFH theory-based EOS for the ring-like fluids is proposed. Compared to the Monte Carlo data of 3-mer, 4-mer, 5-mer, 6-mer, 16-mer, and 32-mer ring-like fluids, our EOS exhibits the best prediction among four EOSs for the compressibility factors at intermediate and high packing fractions (η ≥ 0.157), although our EOS also shows a slight underestimation for the compressibility factors at low packing fractions. In summary, this is the first report on the generalized Flory-Huggins theory-based EOS for the ring-like fluids. It is expected that the same strategy can be applied to these fluids with more complex architectures.     

Group contribution multifluid lattice theory for simultaneous predictions of thermodynamic properties of pure fluids and mixtures

A unified group contribution (GC) lattice equation of state (EOS) was formulated based on the multifluid approximation of the nonrandom lattice fluid theory. The GC-EOS requires segment size and interaction energy parameter from functional group characteristics. The unique feature of the approach is that a single set of group parameters are used for both pure fluids and mixtures. The approach was found to be quantitatively applicable for predicting thermodynamic properties of real pure fluids and mixtures. Its potential utility was demonstrated for vapor pressures, vapor–liquid coexistence densities of pure fluids and phase equilibrium properties of mixtures including polymeric solutions.     

A new coordination number model by using the local composition theory

A new coordination number model for square-well (SW) fluid is proposed in this work. It is based on the local composition theory and starts from the point that total site numbers around one molecule can vary with reduced density and reduced temperature. The total site numbers are correlated with reduced density and reduced temperature by using local composition theory and Monte Carlo (MC) simulation results. This new model agrees well with the MC simulation results for the pure SW fluids at the low-density limit and in the high-density region. In addition, it can predict the transition to the face-centered cubic (fcc) fluid property which is shown in Young and Alder’s [J. Chem. Phys. 73 (1980) 2430] phase diagram. An equation of state (EOS) is derived from this new coordination number model and gives satisfactory compressibility factors for SW fluids.     

A new cubic simplified perturbed hard-body equation of state

A new cubic equation of state (EOS) was developed in this study for vapor-liquid equilibrium (VLE) calculations of nonpolar fluids. The repulsive term of this EOS reexpressed the results of Walsh and Gubbins (1990) from their modified thermodynamic perturbation theory of polymerization into a simple form in which a non-spherical parameter was employed to account for the different shapes of molecules. The repulsive compressibility factors calculated from this EOS agree well with the molecular simulation data for various kinds of hard bodies ranging from a single hard sphere to tangent or fused long chain molecules. A simple attractive term was then coupled with the repulsive to complete the EOS in a cubic form. Equation parameters were determined for a diversity of nonpolar real fluids. These parameters were expressed in generalized forms for engineering computations. Satisfactory results from this EOS on the saturated properties of pure nonpolar fluids were obtained. This EOS was also extended to calculate the VLE of nonpolar fluid mixtures. The results are again satisfactory over wide ranges of temperature and pressure.     

Vapor-liquid equilibria simulation and an equation of state contribution for dipole-quadrupole interactions

A systematic investigation on vapor-liquid equilibria (VLEs) of dipolar and quadrupolar fluids is carried out by molecular simulation to develop a new Helmholtz energy contribution for equations of state (EOSs). Twelve two-center Lennard-Jones plus point dipole and point quadrupole model fluids (2CLJDQ) are studied for different reduced dipolar moments micro*2=6 or 12, reduced quadrupolar moments Q*2=2 or 4 and reduced elongations L*=0, 0.505, or 1. Temperatures cover a wide range from about 55% to 95% of the critical temperature of each fluid. The NpT+test particle method is used for the calculation of vapor pressure, saturated densities, and saturated enthalpies. Critical data and the acentric factor are obtained from fits to the simulation data. On the basis of this data, an EOS contribution for the dipole-quadrupole cross-interactions of nonspherical molecules is developed. The expression is based on a third-order perturbation theory, and the model constants are adjusted to the present 2CLJDQ simulation results. When applied to mixtures, the model is found to be in excellent agreement with results from simulation and experiment. The new EOS contribution is also compatible with segment-based EOS, such as the various forms of the statistical associating fluid theory EOS.     

Mixing rules for van-der-Waals type equation of state based on thermodynamic perturbation theory

A concept based on the thermodynamic perturbation theory for a `simple fluid' has been applied to the attractive term of a van-der-Waals type equation of state (EOS) to derive a simple mixing rule for the a parameter. The new mixing rule is a small correction to the original one-fluid approximation to account for the influence of particles of j-type on the correlation function of ii-type in a mixture consisting of particles of i and j types. The importance of the correction has been shown by comparison of the calculated results for binary mixtures of Lennard–Jones fluids with the data obtained by numerical method (Monte-Carlo simulation). The new mixing rules can be considered as a flexible generalization of the conventional mixing rules and can be reduced to the original v-d-W mixing rules by defaulting the extra binary parameters to zero. In this way the binary parameters already available in the literature for many systems can be used without any additional regression work. Extension of the new mixing rules to a multicomponent system do not suffer from `Michelsen–Kistenmacher syndrome' and provide the correct limit for the composition dependence of second virial coefficients. Their applicability has been illustrated by various examples of vapor–liquid and liquid–liquid equilibria using a modified Patel–Teja EOS. The new mixing rules can be applied to any EOS of van-der-Waals type, i.e., EOS containing two terms which reflect the contributions of repulsive and attractive intermolecular forces.     

Crossover Peng-Robinson equation of state with introduction of a new expression for the crossover function

In this research, we use the original Peng-Robinson (PR) equation of state (EOS) for pure fluids and develop a crossover cubic equation of state which incorporates the scaling laws asymptotically close to the critical point and it is transformed into the original cubic equation of state far away from the critical point. The modified EOS is transformed to ideal gas EOS in the limit of zero density. A new formulation for the crossover function is introduced in this work. The new crossover function ensures more accurate change from the singular behavior of fluids inside the regular classical behavior outside the critical region. The crossover PR (CPR) EOS is applied to describe thermodynamic properties of pure fluids (normal alkanes from methane to n-hexane, carbon dioxide, hydrogen sulfide and R125). It is shown that over wide ranges of state, the CPR EOS yields the thermodynamic properties of fluids with much more accuracy than the original PR EOS. The CPR EOS is then used for mixtures by introducing mixing rules for the pure component parameters. Higher accuracy is observed in comparison with the classical PR EOS in the mixture critical region.     

Density-functional theory for polymer-carbon dioxide mixtures: A perturbed-chain SAFT approach

We propose a density-functional theory (DFT) describing inhomogeneous polymer-carbon dioxide mixtures based on a perturbed-chain statistical associating fluid theory equation of state (PC-SAFT EOS). The weight density functions from fundamental measure theory are used to extend the bulk excess Helmholtz free energy to the inhomogeneous case. The additional long-range dispersion contributions are included using a mean-field approach. We apply our DFT to the interfacial properties of polystyrene-CO(2) and poly(methyl methacrylate) CO(2) systems. Calculated values for both solubility and interfacial tension are in good agreement with experimental data. In comparison with our earlier DFT based on the Peng-Robinson-SAFT EOS, the current DFT produces quantitatively superior agreement with experimental data and is free of the unphysical behavior at high pressures (>35 MPa) in the earlier theory.     

Application of the crossover lattice equation of state for fluid mixtures

In previous work, we developed the crossover lattice equation of state (xLF EOS) for pure fluids and the xLF EOS yielded the saturated vapour pressure and the density values with a much better accuracy than the classical LF EOS over a wide range. In this work, we extended xLF EOS to fluid mixtures. Classical composition-dependent mixing rules with only adjustable two binary interaction parameters same as the LF EOS are used. A comparison is made upon experimental data for fluids mixtures in the one- and two-phase regions. The xLF EOS shows more improved representations than the LF EOS, especially in the critical region.     

Yukawa流体的相平衡和界面张力研究

应用二阶微扰理论, Duh-Mier-Y-Teran状态方程和在平均球近似(mean spherical approximation, MSA)的基础上获得的直接相关函数, 建立了适用于均匀流体和非均匀流体的状态方程. 结合此状态方程, 重整化群理论(renormalization group theory, RG)和密度泛函理论(density functional theory, DFT), 分别研究了Yukawa流体的相平衡和界面张力. 结果与分子模拟数据吻合良好.     

A novel equation of state for the prediction of thermodynamic properties of fluids

This work proposes a new equation of state (EOS) based on molecular theory for the prediction of thermodynamic properties of real fluids. The new EOS uses a novel repulsive term, which gives the correct hard sphere close packed limit and yields accurate values for hard sphere and hard chain virial coefficients. The pressure obtained from this repulsive term is corrected by a combination of van der Waals and Dieterici potentials. No empirical temperature functionality of the parameters has been introduced at this stage. The novel EOS predicts the experimental volumetric data of different compounds and their mixtures better than the successful EOS of Peng and Robinson. The prediction of vapor pressures is only slightly less accurate than the results obtained with the Peng-Robinson equation that is designed for these purposes. The theoretically based parameters of the new EOS make its predictions more reliable than those obtained from purely empirical forms.     

Crossover SAFT equation of state for pure supercritical fluids

A crossover statistical associating fluid theory (SAFT) equation of state (EOS) is used to fit the parameters of eight common pure supercritical fluids (water, ammonia, carbon dioxide, R134a, ethane, propane, ethene and propene) and calculate their thermodynamic properties. Over a wide range including the critical region, the EOS reproduces the saturated pressure data with an average absolute deviation (AAD) of about 1% and the saturated densities with an AAD of about 2%. In the one-phase region, the EOS represents the experimental values of pressure with an AAD of about 1–3%. The results are satisfactory.     

由L-J流体的FMSA状态方程计算流体的PVT性质

运用Tang等提出的Lennard-Jones (L-J)流体两参数的一阶平均球形近似(FMSA)状态方程, 计算了流体的汽液共存相图和饱和蒸汽压曲线, 以及非饱和区的PVT性质, 并与文献数据进行比较. L-J参数由Tr＜0.95的汽液相共存数据回归得到. 计算结果表明, 对于分子较接近球形的流体, 除临界点附近外, 该方程可以在较大的温度和压力范围内计算真实流体的PVT性质, 结果满意. 对于球形分子, 该方程的精确度随分子尺寸的变大基本保持稳定. 该方程不适用于强极性物质. 在高密度区, 该方程的计算结果明显优于P-R方程. 对于分子偏离球形较远的流体, 该方程的适用性变差, 此时要考虑分子形状的影响, 可采用三参数的FMSA状态方程进行计算.     

Empirical correction to the Peng–Robinson equation of state for the saturated region

This work presents an empirical correction to improve the Peng–Robinson equation of state (PR EOS) for representing the densities of pure liquids and liquid mixtures in the saturated region using the volume translation method. A temperature-dependent volume correction is employed to improve the original PR EOS so that it can match the true critical point of pure fluids. The volume correction is generalized as a function of the critical parameters and the reduced temperature. The volume translation PR (VTPR) EOS with the generalized volume correction accurately represents the saturated liquid densities for different polar and non-polar fluids, including alkanes, cycloparaffins, halogenated hydrocarbons, olefins, cyclic olefins, aromatics and inorganic molecules. The average relative deviations for 91 pure compounds was 1.37%. The generalized VTPR EOS was also used to predict the saturated liquid density of 53 binary mixtures with a relative deviation of 0.98%. The generalized VTPR EOS can also be extended to other materials. The accuracy of the generalized VTPR EOS compares well with other methods and equations of state.     

Spectral theory of anisotropic fluids

The spectral theory of symmetric viscoelastic fluids with arbitrary anisotropy, which is based on the generalized Maxwell relaxation law, is developed. A feature of the proposed approach is the use of a spectral (canonical) representation of tensors that describe the anisotropic properties of fluids. Simple special cases of the spectra of viscosity and relaxation-time tensors are considered. The orientation dynamics of anisotropic fluids is discussed. A theory of generation of eigenmodes that are related to stress relaxation is developed. On the basis of the spectral theory, the possibility of the existence of soft (zero energy) modes in anisotropic fluids with deep anisotropy is considered. The proposed theory opens up new alternatives for classifying anisotropic fluids.     

On the Calculation of Surface Tensions of <Emphasis Type="Italic">n</Emphasis>-Alkanes Using the Modified SAFT-BACK-DFT Approach

Density functional theory is combined with the modified SAFT-BACK EOS to investigate liquid–vapor interfaces of n-alkanes. We evaluate the temperature dependence of the interfacial width and the surface tension. Differences in chain length of the alkanes lead to differences in the thermodynamic properties of the fluids. A single curve for the reduced width of the interface as a function of reduced temperature serves to correlate interfacial properties of a wide variety of linear chain fluids (excluding methane and ethane) with sufficient accuracy for our purposes.     

The extension of coordination number model by using the local composition theory: mixtures

The extension of a new coordination number model to mixture is presented in this work. Extended model agrees well with the Monte Carlo (MC) simulation results for square-well (SW) mixture fluids and shows better results compared with other models. To test our model, we compare the compressibility factors from various models for SW fluids at different λ values and for SW fluid mixtures at λ=1.5. Although our model is obtained by fitting simulation data at λ=1.5, it shows better results for the different λ values than other coordination number model. Compared with the compressibility factors of various binary mixtures of SW fluids calculated from other models, this model presents better results. Because our model considers the temperature dependency importantly by using the total site number, it predicts coordination number and compressibility factor well in the wide temperature range and enables one to derive an equation of state (EOS) through integration of the coordination number equation.     

Critical points of hydrocarbon mixtures with the Peng–Robinson,SAFT, and PC-SAFT equations of state

The phase behavior of fluids at high pressures can be rather complex, even for mixtures of relatively simple molecules, such as hydrocarbons. In this work, we use the Hicks and Young algorithm to calculate mixture critical points, comparing five modeling options: Peng–Robinson EOS: (1) original and (2) with parameters fitted from molar volume and vapor pressure data; (3) SAFT EOS; and PC-SAFT EOS: (4) original and (5) with refitted parameters to match pure component critical data. Calculations were carried out for binary hydrocarbon mixtures and 29 multicomponent mixtures. The SAFT EOS provided the worst representation of the systems tested and, interestingly, the conventional cubic EOS provided, in general, the best representation.     

An equation of state for electrolyte solutions by a combination of low-density expansion of non-primitive mean spherical approximation and statistical associating fluid theory

A two-parameter equation of state (EOS) for electrolyte solutions is developed. The equation is in terms of Helmholtz free energy and incorporated with our previous results of the low-density expansion of non-primitive mean spherical approximation (MSA). The concentration dependent dielectric constant is thus inherently included in the model. The statistical associating fluid theory (SAFT) is introduced to represent the association interactions, including the solvent–solvent and ion–solvent. The EOS is tested for 15 aqueous alkali halide solutions at ambient condition. The equation can represent simultaneously the mean ionic activity coefficients, the osmotic coefficients and densities in a good accuracy up to saturated concentration. The comparisons with EOSs published earlier in the literature are carried out. The limitations of the model are also discussed.