A new cubic equation of state for simple fluids: pure and mixture

A two-parameter cubic equation of state is developed. Both parameters are taken temperature dependent. Methods are also suggested to calculate the attraction parameter and the co-volume parameter of this new equation of state. For calculating the thermodynamic properties of a pure compound, this equation of state requires the critical temperature, the critical pressure and the Pitzer’s acentric factor of the component. Using this equation of state, the vapor pressure of pure compounds, especially near the critical point, and the bubble point pressure of binary mixtures are calculated accurately. The saturated liquid density of pure compounds and binary mixtures are also calculated quite accurately. The average of absolute deviations of the predicted vapor pressure, vapor volume and saturated liquid density of pure compounds are 1.18, 1.77 and 2.42%, respectively. Comparisons with other cubic equations of state for predicting some thermodynamic properties including second virial coefficients and thermal properties are given. Moreover, the capability of this equation of state for predicting the molar heat capacity of gases at constant pressure and the sound velocity in gases are also illustrated.     

Equations of state for tetra-dimensional hard-sphere fluids

An equation of state, a kind of generalised Padé approximants, first proposed for the hard-sphere fluid in cases of two, three, four and five dimensions is extended for the tetra-dimensional case with new simulation data available. The corresponding equations of state show good to excellent agreement with the above-mentioned data.     

Equation of state for square-well chain molecules with variable range. I: Application for pure substances

An equation of state (EOS) for square-well chain molecules with variable range developed on the basis of statistical mechanics for chemical association in our previous work is employed for the calculations of pVT properties and vapor–liquid equilibria (VLE) of pure non-associating fluids. The molecular parameters for 73 normal substances and 46 polymers are obtained from saturated vapor pressure and liquid molar volume data for normal fluids or pVT data for polymers. Linear relations are found for the molecular parameters of normal fluids with their molecular weight of homologous compounds. This indicates that the model parameters of homologous series, subsequently pVT and VLE, can be predicted when experimental data are not available. The predicted saturated vapor pressures and/or liquid volumes are satisfactory through the generalized model parameters. The calculated VLE and pVT for normal fluids and polymers by this EOS are compared with those from other engineering models, respectively.     

Transport coefficients of square-well fluids

We analyze the analytical form of the velocity time correlation function of a hard sphere system obtained by employing generalized Langevin equation for a square-well fluid. The self-diffusion coefficient and shear viscosity have been calculated using this analytical form of velocity tcf for a square-well fluid. The addition of an attractive square-well potential in place of hard sphere leads to a substantial influence on transport coefficients. Unlike harmonic model diffusion coefficient no longer vanishes. A breakdown of the Stokes–Einstein relation is observed at low densities for a square-well fluid.     

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.     

Equation of state for square-well chain molecules with variable range II. Extension to mixtures

An equation of state (EOS) developed in our previous work for square-well chain molecules with variable range is further extended to the mixtures of non-associating fluids. The volumetric properties of binary mixtures for small molecules as well as polymer blends can well be predicted without using adjustable parameter. With one temperature-independent binary interaction parameter, satisfactory correlations for experimental vapor–liquid equilibria (VLE) data of binary normal fluid mixtures at low and elevated pressures are obtained. In addition, VLE of n-alkane mixtures and nitrogen + n-alkane mixtures at high pressures are well predicted using this EOS. The phase behavior calculations on polymer mixture solutions are also investigated using one-fluid mixing rule. The equilibrium pressure and solubility of gas in polymer are evaluated with a single adjustable parameter and good results are obtained. The calculated results for gas + polymer systems are compared with those from other equations of state.     

A new equation of state for polar and nonpolar pure fluids

Chung, T.H., Khan, M.M., Lee, L.L. and Starling, K.E., 1984. A new equation of state for polar and nonpolar pure fluids. Fluid Phase Equilibria, 17: 351–372A new equation of state based on the concept of perturbation theory and the hard-convex-body equation of state has been developed successfully for nonpolar compounds. The equation can predict the thermodynamic properties (density, enthalpy departure and vapor pressure) of a wide range of pure fluids from small, spherical (argon-like) molecules to large, structurally complex molecules. For nonpolar compounds, the equation employs three parameters: the shape, size and energy parameters. For normal paraffins, the size parameter (hard-core volume) is related to the measurable van der Waals volume given by Bondi. For most other compounds, it is related to the critical volume. The shape-parameter values reflect the structure and degree of acentricity of the compound of interest. The equation has been extended to polar and associating compounds by using the mean-potential model. For polar compounds, a fourth parameter is required. The equation has been tested extensively for polar (dipolar and quadrupolar) and hydrogen-bonding compounds. The applicability of this equation for such a wide variety of substances provides an important first step in the development of a composition-dependent equation of state for mixtures.     

A crossover lattice fluid equation of state for pure fluids

A lattice fluid model is one of the most versatile, molecular-based engineering equations of state (EOS) but, in common with all analytic equations of state, the lattice fluid (LF) EOS exhibits classical behaviour in the critical region rather than the non-analytical, singular behaviour seen in real fluids. In this research, we use the LF EOS and develop a crossover lattice fluid (xLF) equation of state near to and far from the critical region which incorporates the scaling laws valid asymptotically close to the critical point while reducing to the original classical LF EOS far from the critical point. We show that, over a wide range of states, the xLF EOS yields the saturated vapour pressure data and the density data with much better accuracy than the classical LF EOS.     

Pair correlation function of short-ranged square-well fluids

We have performed extensive Monte Carlo simulations in the canonical (NVT) ensemble of the pair correlation function for square-well fluids with well widths lambda-1 ranging from 0.1 to 1.0, in units of the diameter sigma of the particles. For each one of these widths, several densities rho and temperatures T in the ranges 0.1< or =rhosigma(3)< or =0.8 and T(c)(lambda) less or approximately T less or approximately 3T(c)(lambda), where T(c)(lambda) is the critical temperature, have been considered. The simulation data are used to examine the performance of two analytical theories in predicting the structure of these fluids: the perturbation theory proposed by Tang and Lu [Y. Tang and B. C.-Y. Lu, J. Chem. Phys. 100, 3079 (1994); 100, 6665 (1994)] and the nonperturbative model proposed by two of us [S. B. Yuste and A. Santos, J. Chem. Phys. 101 2355 (1994)]. It is observed that both theories complement each other, as the latter theory works well for short ranges and/or moderate densities, while the former theory works for long ranges and high densities.     

Totally inclusive cubic equation of state with five parameters for pure fluids

A totally inclusive cubic equation of state (cubic EOS) is proposed. Although, its form is fairly simple as compared with the present cubic equations, it can include all of them as special cases. The EOS has five parameters. By fitting the experimental critical isothermal for six typical substances combining the critical conditions, the generalized expressions for the five parameters at critical temperature are established. The temperature coefficients of the five parameters for 43 substances are determined by fitting the experimental data of vapor pressure and saturated liquid density. These coefficients are correlated with the critical compressibility factor and acentric factor to obtain the generalized expressions. The predicted saturated vapor pressure, saturated liquid density, critical isothermal and coexistence curve near the critical point show that the equation gives the best results when compared with the Redlich–Kwong–Soave (RKS) and Peng–Robinson (PR) EOS.     

Direct determination of phase behavior of square-well fluids

We have combined Gibbs ensemble Monte Carlo simulations with the aggregation volume-biased method in conjunction with the Gibbs-Duhem method to provide the first direct estimates for the vapor-solid, vapor-liquid, and liquid-solid phase coexistences of square-well fluids with three different ranges of attraction. Our results are consistent with the previous simulations and verify the notion that the vapor-liquid coexistence behavior becomes metastable for cases where the attraction well becomes smaller than 1.25 times the particle diameter. In these cases no triple point is found.     

Liquid-vapor interface of square-well fluids of variable interaction range

Properties of the liquid-vapor interface of square-well fluids with ranges of interaction lambda=1.5, 2.0, and 3.0 are obtained by Monte Carlo simulations and from square-gradient theories that combine the Carnahan-Starling equation of state for hard spheres with the second and third virial coefficients. The predicted surface tensions show good agreement with the simulation results for lambda=2 and for lambda=3 in a temperature range reasonably close to the critical point, 0.8相似文献   

A crossover SAFT-VR equation of state for pure fluids: preliminary results for light hydrocarbons

SAFT is perhaps the most versatile, fundamentally, based engineering equation of state in use today. However, in common with all analytic equations of state, SAFT exhibits classical behavior in the critical region rather than the non-analytical, singular behavior seen in real fluids. Recently, so-called crossover equations of state have been developed which solve this shortcoming by incorporating the scaling laws valid asymptotically close to the critical point while reducing to the original classical equation of state far from the critical point. We have combined the SAFT-VR equation of state with an analytical crossover technique to obtain the SAFT-VRX equation of state. The SAFT-VRX approach combines the accurate low temperature behavior of SAFT-VR with a precise representation of the critical region. Preliminary results are presented for hydrocarbon systems which illustrate the accuracy of the SAFT-VRX approach over the entire fluid phase region.     

Equations of state for fluids: empirical temperature dependence of the second virial coefficients

In this paper, an empirical dependence of the second virial coefficients is derived from equations of state. The second virial coefficient B2 is found to be a linear function of 1/T1+beta, where T is the temperature and beta is a constant and has different value for different substances. Excellent experimental supports to this relationship are reported for nonpolar fluids, polar fluids, heavy globular molecule fluids, and quantum fluid He-4.     

Stokes-Einstein relation for pure simple fluids

The authors employed the equilibrium molecular dynamics technique to calculate the self-diffusion coefficient and the shear viscosity for simple fluids that obey the Lennard-Jones 6-12 potential in order to investigate the validity of the Stokes-Einstein (SE) relation for pure simple fluids. They performed calculations in a broad range of density and temperature in order to test the SE relation. The main goal of this work is to exactly calculate the constant, here denominated by alpha, present in the SE relation. Also, a modified SE relation where a fluid density is raised to a power in the usual expression is compared to the classical expression. According to the authors' simulations slip boundary conditions (alpha=4) can be satisfied in some state points. An intermediate value of alpha=5 was found in some regions of the phase diagram confirming the mode coupling theory. In addition depending on the phase diagram point and the definition of hydrodynamics radius, stick boundary condition (alpha=6) can be reproduced. The authors investigated the role of the hydrodynamic radius in the SE relation using three different definitions. The authors also present calculations for alpha in a hard-sphere system showing that the slip boundary conditions hold at very high density. They discuss possible explanations for their results and the role of the hydrodynamic radius for different definitions in the SE relation.     

Equations of state for polyamide‐6 and its nanocomposites. II. Effects of clay

The pressure‐volume‐temperature (PVT) dependencies of polyamide‐6 and its nanocomposites (polymeric nanocomposites) were measured at temperatures T = 300–600 K and pressures P = 0.1–190 MPa, thus spanning the range of molten and “solid” phases. The Simha‐Somcynsky (S‐S) cell‐hole equation of state (EOS) was used for describing the molten region. At T_g(P) ≤ T ≤ T_m(P), the “solid” phase is a mixture of the liquid polyamide‐6 with dispersion of crystals. Accordingly, the PVT behavior in this region was described as a combination of the S‐S EOS for the liquid phase and the Midha‐Nanda‐Simha‐Jain (MNSJ) EOS for the crystalline one. These two theories based on different models yielded two sets of the characteristic reducing parameters, P^*, T^*, V^* and the segmental molecular weight, M_s. Incorporation of 2 and 5 wt % clay increased P^* and reduced T^* and V^*, but the effects were small. Fitting the combination of S‐S and MNSJ EOS' to isobaric “solid” phase data yielded the total crystallinity, X_cryst, and the correcting excess specific volume, ΔV_m,c. Both parameters were sensitive to pressure, P, and the clay content, w—the former increased with P and w, whereas the latter decreased. The raw PVT data were numerically differentiated to obtain the thermal expansion and compressibility coefficients, α and κ, respectively. At T < T_m, addition of clay reduced their relative magnitude, whereas at T > T_m, the opposite effect was observed, most likely owing to the excess of intercalant in the polymeric nanocomposites samples. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 966–980, 2009     

Surface tension correlation for pure polar fluids by a new molecular model and SRK equation of state

In this work, a new model based on molecular thermodynamic was presented to correlate the surface tension of pure polar liquids. This model was developed based on the Davis theory. According to this theory, the surface tension is defined as a function of radial distribution function (RDF) and potential function (PF) as well. The proposed model includes three additive terms; hard sphere, dispersion and polar interactions. The RDF of Kolafa equation of state and Dirac delta function as a PF were used for hard sphere interaction. The RDF expression of Xu and Hu was considered for both dispersion and polar interactions. The presented model has two adjustable parameters, size and energy, which were obtained by optimization of an objective function for each pure fluid. This proposed approach was used for 19 pure polar fluids divided into 6 groups; organic acids, alcohols, ketones, ethers, aldehydes, and water. The average absolute deviation percent (AAD%) obtained for 19 fluids are 0.74. Also the surface tension of these 19 fluids was calculated by the use of SRK EOS and Sugden empirical formula in two cases. In case 1, Sugden's Parachor was calculated from Hugill and van Welsenes correlation and in case 2, it was obtained by optimization of an objective function for each component. The values of AAD% are 43.544 and 2.281 for cases 1 and 2, respectively. These results show the new model, which includes two adjustable parameters, can correlate the surface tension of the pure polar liquids with a high accuracy.     

Prediction of thermodynamic derivative properties of pure fluids through the Soft-SAFT equation of state

We present in this work the application of the soft-SAFT equation of state (EoS) to the calculation of some main derivative properties, including heat capacities, reduced bulk modulus, Joule-Thomson coefficient, and speed of sound. Calculations have been performed analytically through the derivation of a primary thermodynamic potential function. The application to the n-alkanes, n-alkenes, and 1-alkanols families has been done in a semipredictive manner, with the molecular parameters of the equation obtained from previous fitting to vapor-liquid equilibrium data of the same compounds. The equation is able to capture the typical extrema isothermal derivative properties exhibit with respect to density, providing quantitative agreement with experimental (or correlation) data in some cases. Results in the vicinity of the critical point are improved by adding a crossover treatment to take into account the long-range fluctuations present in this region. By taking advantage of the molecular nature of the equation, we have been able to separate and quantify the different contributions (reference fluid, chain, and association) to the total derivative properties. The association plays a predominant role in energetic properties, such as the heat capacities, while there is a competition between association and chain length as the chain length of the compound increases for volumetric properties, such as the isothermal compressibility. These results act in favor of the molecular-based equations, like soft-SAFT, as predictive tools for several applications.     

The performance of cubic equations of state on the critical isotherms of pure fluids

The potential of cubic equations of state for describing the critical isotherm of a pure fluid has been examined. Some mathematical results are derived which show that in this respect such equations have fundamental and far-reaching limitations, separate from their obvious failure in the critical region. The implications become clear in a numerical test of various equations on experimental critical-isotherm data. The present study provides insight into the relationship between the performance of a cubic equation of state and its parametric structure.