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Over the past decade, the Mie λ-6 (generalized Lennard-Jones) potential has grown in popularity due to its improved accuracy for predicting vapor-liquid coexistence densities and pressure compared to the traditional Lennard-Jones 12-6 potential. This manuscript explores the hypothesis that greater accuracy in characterizing the coexistence properties may lead to greater accuracy for viscosity predictions. Four united-atom force fields are considered in detail: the Transferable Potentials for Phase Equilibria (TraPPE-UA and the recently developed TraPPE-2) model of Siepmann and coworkers, the Transferable Anisotropic Mie (TAMie) model of Gross and coworkers, the fourth generation anisotropic-united-atom (AUA4) model of Ungerer and coworkers, and the model of Potoff and coworkers. Equilibrium molecular dynamics simulations are analyzed using the Green-Kubo method for viscosity characterization. Simulations are performed for linear alkanes with two to twenty-two carbons and branched alkanes with four to eight carbons. Simulation conditions follow the saturated liquid from reduced temperatures of 0.5–0.85 and along the 293 K isotherm in the dense liquid region. In general, the more accurate force fields for coexistence properties do indeed predict viscosity more accurately. For saturated liquids, both Mie-based potential models (Potoff and TAMie) provide roughly 10% accuracy for linear alkanes, while deviations are between 20 and 50% for TraPPE-UA. For branched alkanes, the performance is slightly diminished, but Potoff still provides roughly 15–20% accuracy, while the TAMie force field results in deviations of 20–40%, and TraPPE-UA has deviations of approximately 25–60%. The AUA4 deviations are 10–20% for ethane and 30–60% for 2,2-dimethylpropane, the only compounds tested with the AUA4 force field. The TraPPE-2 deviations for ethane are similar to those using the original TraPPE force field, namely, between 10 and 20%. The percent deviations for each compound and force field tend to increase with decreasing temperature, with the exception of the Potoff deviations for propane, which are nearly constant to the triple point temperature. For compressed liquids, the Mie-based potential models perform better once again than the Lennard-Jones-based force fields, but tend to over estimate the viscosity at very high densities. As the Potoff and TAMie models also tend to over estimate the pressure at high densities, a fortuitous cancellation of errors leads to predictions of viscosity with respect to pressure that are accurate to within about 10%. The comparison with experimental viscosity data is limited to pressures below 200 MPa for most normal and branched alkanes. However, accurate predictions are obtained for propane near 1000 MPa with the Potoff force field.

The process of formation of an equilibrium liquid-gas interface, beginning with a sharp stepwise interfacial surface between phases with equal pressures, temperatures and chemical potentials, has been reproduced in molecular dynamics (MD) simulation of one- and two-component Lennard-Jones systems. In binary mixtures, the second component was a volatile impurity that is adsorbed in the interfacial layer. The tasks of this study are quantitative estimations of the establishment time of mechanical equilibrium between phases, the magnitude of the non-equilibrium surface tension and the time of its relaxation, the characteristic times of achieving equilibrium values of the composition, the shape and the thickness of the interface, as well as the effect of the volatile component on the relaxation processes in liquid-gas interfaces and nucleation in a superheated solution. Time dependences of the surface tension, the thickness of the interfacial layer and the relative adsorption of the volatile component have been obtained, and the times of their relaxation have been determined for a temperature close to the temperature of the solvent triple point, at the concentration range of the volatile component in the liquid phase cl from 0 to 0.25 mol fraction. It is shown that the maximum value of the non-equilibrium surface tension exceeds the equilibrium value 1.2 to 1.6 times. The relaxation time of the surface tension to equilibrium increases from 10 to 100 ps with an increase in cl. In a two-component system with a limited volume of the gas phase an equilibrium interfacial layer forms in two stages. At the first stage the volatile component is transferred into the interfacial layer from the near-surface regions of the gas phase and liquid phase. While achieving the equilibrium partial density of the volatile component in the gas phase, a transition to the second stage takes place, when particles are mainly transferred from the liquid phase, which leads to a considerable increase in the relaxation time of the relative adsorption and surface tension. Comparison of the data obtained with the results of an MD study of nucleation in solution shows that the time for establishment of adsorption equilibrium in a liquid-gas interfacial layer exceeds by an order of magnitude the time in which the equilibrium composition and the size of a vapor-gas bubble are established. This can lead to the fact that when the top of the activation barrier of nucleation is passed, the surface tension at the bubble-solution interface can exceed its equilibrium value.

Entire-curve Wagner analytics are treated as “true” or “best” values, and Antoine analytic values are used as surrogate experimental data. Limited-data Wagner constants are estimated from Antoine analytics for the fully-determined case for fifty-five species, from which reduced vapor pressures below and above the interval are predicted and compared with the entire-curve Wagner analytics to estimate the ability of limited VLE data to be used to accurately represent the entire two-phase curve. The Antoine intervals have a pressure range of 0.02–2 bars for most species, an average reduced temperature interval width of 0.20, and an average lower bound reduced temperature of 0.53. The Wagner constants estimated from Antoine analytics have an average entire-curve error of 4.8%, with the majority of the error occurring when extending down towards the triple point (9.55%), compared to 1.36% average error when extending up to the critical point. Such limited-data Wagner constants produce less predictive error for alcohols, while the semi-theoretical Riedel equation has the advantage for organic acids, and the empirical Ambrose-Walton equation produces less error for the remaining species. A comparison of Wagner and Antoine analytic values strictly over the Antoine interval indicates that disagreement of VLE data in the literature averages around 2% but varies considerably between species. Data disagreement is not found to be a strong indicator of predictive power of the limited-data Wagner constants; however, it is found to be a discriminator of performance relative to that of Riedel and Ambrose-Walton for some polar species.

The Riedel vapor pressure correlation is a useful model that has been employed for decades. The shape of the temperature dependent correlation is a strong function of the value of the final coefficient (denoted as E), particularly at the low temperature end. Vapor pressure data can be accurately correlated with different values of E, but properties derived from vapor pressure are more sensitive to the value of E. Such properties include enthalpy of vaporization and liquid heat capacity. Because these three properties are linked through rigorous thermodynamic relationships (including the Clapeyron equation and the derivative of enthalpy of vaporization), a multi-property optimization is possible to obtain the value of E that will give the best thermodynamic picture for the compound. To determine the effects of the final coefficient on subsequent properties, E was varied from 1 to 6 in integer steps and for E = 0.5, and vapor pressure data were fit for several well-known compounds. These correlations were then tested to see how well they predict enthalpy of vaporization and liquid heat capacity data. The results indicate that the traditional practice of setting E = 6 rarely produces the best thermodynamic consistency, and that E = 2 is superior for many compounds. The improved vapor pressure correlations were then used to predict triple point pressures with favorable results that compare well with the literature.

Vapor pressure, heat of vaporization, liquid isobaric heat capacity, and ideal gas isobaric heat capacity can be measured for pure organic compounds between the triple point and critical point. Additionally, heat of vaporization is proportional to the derivative of vapor pressure with respect to temperature through the Clapeyron equation, and the difference of liquid and ideal gas heat capacities are proportional to the derivative of heat of vaporization with respect to temperature. These relationships and experimental data were compared for several compounds to interpolate and extrapolate available data and increase consistency amongst these properties. A methodology for assessing the thermodynamic consistency amongst data sets and optimizing the accepted property values has been developed so that this procedure can be applied to other compounds in the DIPPR 801 database for which there are fewer experimental data available. The process involves critically evaluating available experimental data and the correlations used to fit these temperature-dependent properties. Multi-property optimization includes weighting the various data values based on the accuracy of the data and on the perceived relative importance of the properties in process design. User-defined weighting systems will be established to provide optimization flexibility across these properties for future use of the DIPPR 801 database.

Based on the extended three-parameter corresponding states principle and the most reliable experimental data of cyclic hydrocarbons, a generalized fundamental equation of state for technical calculations has been developed. This equation is in the form of the reduced Helmholtz free energy and takes the reduced density, reduced temperature, and acentric factor as variables. The proposed equation satisfies the critical conditions and Maxwell rule, shows correct behavior for the ideal curves and for the derivatives of the thermodynamic potentials, and allows the calculation of all thermodynamic properties excluding critical region of cyclic hydrocarbons over a temperature range from the triple point to 700 K with pressures up to 100 MPa in the range of variation of the acentric factor ω = 0.2–1.1.

Multiple linear regression equations using Abraham descriptors have been constructed for enthalpies of sublimation at 298.15 K. For a data set of 898 varied organic, organometallic and inorganic compounds the regression standard deviation is 9.9 kJ mol −1, somewhat better than previous analyses of general data sets, 11.4 and 14.7 kJ mol −1. We have also constructed equations on the same lines, using the data set of Gharagheizi on enthalpies of sublimation at the triple point temperature. The set of 963 compounds yielded an equation with a regression standard deviation of 6.6 kJ mol −1, about the same as previous analyses, 4.2–7.9 kJ mol −1. Predictions of further enthalpies of sublimation through our equations can be made using simple arithmetic – no computer programs are needed.

We here report a three-parameter correlation for the temperature T dependent thermal conductivity λ of different kinds of saturated liquids including n-alkanes, refrigerants and others such as argon and nitrogen. The correlation is proven to be more accurate than other known correlations. Compared with the REFPROP data in NIST, the proposed correlation reproduces the corresponding data with the average absolute deviation (AAD) less than 1.20% for all the liquids considered. At the same time, it well holds in a wider temperature range which begins from the triple point temperature and ends at about 0.98 times the critical temperature, at which the thermal conductivity experimentally takes a minimal value for the liquids we study. Engineers and researchers can use the proposed correlation to directly estimate/calculate the thermal conductivity of the liquids considered here with high accuracy. Thermal conductivity related industrial and engineering equipment designs and chemical process designs will benefit from it greatly.

We here report that the corresponding state principle well stands for the temperature dependent thermal conductivity of the saturated refrigerants liquids by using the reduced quantities proposed here. A corresponding state principle based correlation is proposed and proven to be accurate in the temperature range from the triple point temperature to 0.90 times the critical temperature. Additionally, this correlation also stands for the saturated n-alkanes liquids. For the 23 refrigerants and 11 n-alkanes considered here, the proposed correlation can reproduce the REFPROP data with AAD

Direct molecular-simulation results of the thermodynamic Gruneisen parameter, γG, and the density scaling exponent, γ, are reported for the Lennard-Jones and the Gaussian core model potential in extended fluid-phase regions, and are compared with results calculated from equations of state. The direct molecular simulation method is based on the calculation of so-called phase-space functions and allows, in principle, the investigation of any thermodynamic property without any restrictive approximation. The Gruneisen parameter and the density scaling exponent are key quantities in the theory of strongly correlating liquids. Therefore, we paid special attention on the relationship between γG and γ for the Lennard-Jones system as a strongly correlating fluid. Because the Gruneisen parameter can be related to experimentally accessible thermodynamic properties, we analysed in detail the decomposition of γG into the thermal expansion coefficient, the isothermal compressibility, the isochoric heat capacity, and the thermal pressure coefficient. Moreover, we show that a predicted effective density scaling exponent of γ ≈ 6 for the Lennard-Jones fluid can be found close to the triple point of the system. The investigation of γG for the Gaussian core model, which is not a strongly correlating fluid, revealed anomalous behaviour at higher densities with negative values of γG.

An equation of state to describe the complete phase diagram of a pure substance is developed. The equation of state is constructed by using a generic cubic equation plus the term − fT / ( v − e ) 10 . This term (where f > 0 and e are adjustable parameters) is the attractive contribution of the solid phase. It has a volume short-range contribution, and extends the traditional use of a cubic equation, incorporating the thermodynamics description of the solid phase, which allows to represent the experimental triple point, the solid–liquid, and the solid–vapor phase transitions, together with the traditional description of the liquid–vapor transition. For the solid–liquid phase coexistence at any temperature, molar volume predictions of the solid phase define a curve which never connects to its corresponding liquid phase curve. This feature is in agreement with experimental evidences that seem to not accept the existence of a solid–liquid critical point. Finally, calculations for the complete phase diagram for carbon dioxide and argon were carried out in order to show the capabilities and features of the equation of state, and these results were also compared with other predictions from the literature.

The Somayajulu correlation for the surface tension was proposed in 1988. It is a three-parameter generalised equation with certain theoretical basis, which is valid for temperatures from the triple point to the critical point. According to its author, this equation not only fits the data well but also is good for interpolation between the normal boiling point and the critical point. As the data used in the original paper where published earlier than 1975, it seems to be adequate to revise the validity and accuracy of the correlation by adding more recent experimental values. For that, we use here mainly the data included in the DIPPR and DETHERM databases for the 64 fluids considered in the original Somayajulu paper. Some data in the mentioned databases were not considered when a clear disagreement between them was found. Moreover, for some particular fluids other available sources of data were added. We found a good general agreement between the Somayajulu correlation predictions and the data for 45 fluids. Moreover, for another 15 fluids the model can be improved, so that new values for the parameters are given here. Finally, we found that for another four fluids: hydrogen telluride, krypton, neon, and nitrosyl fluoride, the published parameters lead to values in clear disagreement with the available data. New parameters are also given for them. In conclusion, the Somayajulu correlation is an accurate model when the appropriate parameters are considered.

Molecular simulation data on the vapor–liquid equilibrium and the Henry's law constant of carbon dioxide in mixtures of cyclohexane + cyclohexanone are presented. The agreement between simulation results and the available experimental data is good. For the present predictions, new molecular models for cyclohexane and cyclohexanone are developed. The resulting molecular models for cyclohexane and cyclohexanone show mean unsigned deviations with respect to experimental data considering the whole temperature range from triple point to critical point of 0.4% and 0.9% for the saturated liquid density, 3% and 2.7% for the vapor pressure, and 6% and 5.3% for the enthalpy of vaporization, respectively. The carbon dioxide model is taken from preceding work.

In the present work, a new equation for estimating vaporization heat was developed by applying wagner vapor pressure equation and using the Clausius–Clapeyron equation. The new proposed equation was valid over the entire range from the triple point to the critical point for most of the substances. The vaporization heat of 76 pure liquids was calculated to verify the new equation, with the average absolute deviation 0.80%, compared with the literature values.

The SOF cohesion function for cubic equations of state is based on the behavior of the residual energy of pure fluids. It contains two adjustable parameters for each component, which have been obtained for over 800 substances by regression of pure-fluid saturation pressures, and correlated in terms of a four-parameter corresponding states principle. In the present work, we compare the performance of this function and of the original Soave cohesion function with the Redlich–Kwong and Peng–Robinson equations of state in the prediction of vapor–liquid equilibria and enthalpy–composition diagrams for the polar system {ammonia + water}. We use simple van der Waals one-fluid mixing rules, linear for the covolume and quadratic for the cohesion parameter with one (symmetric) and two (asymmetric) binary interaction parameters. The non-linear least squares minimization algorithm lsqnonlin, in Matlab ® , is used to adjust the interaction parameters to phase equilibrium and enthalpy data taken from the IAPWS fundamental formulation. Upper and lower bounds of the optimized interaction parameters are obtained using Matlab ® bootstrap with 95% confidence of a normal distribution sampling. The validity of the parameters as functions of temperature is between the triple point of water and the critical point of ammonia. At lower temperatures, a rapid increase of statistical uncertainties is observed that can be attributed to the scarcity of phase equilibrium data. The two-parameter SOF cohesion function and the cubic equations of state are shown to give accurate predictions of the VLE and enthalpies of {ammonia + water}. Both equations of state give very similar results. Statistical analysis of the interaction parameters shows that their values (within the range of validity mentioned above) are effectively the same for both cohesion functions. At higher temperatures, however, extrapolation of the two cohesion functions gives different results, and correspondingly requires different interaction parameters.

Solid vapor pressures ( P S ) of pure compounds have been estimated at several temperatures using a hybrid model that includes an artificial neural network with particle swarm optimization and a group contribution method. A total of 700 data points of solid vapor pressure versus temperature, corresponding to 70 substances, have been used to train the neural network developed using Matlab. The following properties were considered as input parameters: 36 structural groups, molecular mass, dipole moment, temperature and pressure in the triple point (upper limit of the sublimation curve), and the limiting value P S → 0 as T → 0 (lower limit of the sublimation curve). Then, the solid vapor pressures of 28 other solids (280 data points) have been predicted and results compared to experimental data from the literature. The study shows that the proposed method represents an excellent alternative for the prediction of solid vapor pressures from the knowledge of some other available properties and from the structure of the molecule.

An equation of state based on the statistical associating fluid theory for potentials of variable range (SAFT-VR) has been applied to model 35 pure associating and non-associating fluids and 15 binary mixtures. The pure components consist of alkanes, alcohols, water, aromatics and polar or multi-polar compounds like ammonia and H2S. In contrast to other attempts which have used the SAFT-VR model for various thermodynamic calculations using the square-well or Yukawa potentials, the short-range dispersion interactions have been accounted for here using the Sutherland potential, while hydrogen bonding interactions are explicitly taken into account as in other versions of the SAFT approach. The Sutherland potential is particularly useful for modeling the interactions among multi-polar species. Model parameters for the pure components have been optimized by fitting available experimental data on vapor pressure, saturated vapor density and saturated liquid density for temperatures ranging from near the triple point up to reduced temperatures of 0.9. The effect of several simplifying assumptions aimed at reducing the number of model parameters has been investigated, and the resulting trends in parameters has been discussed. Binary interaction coefficients have been obtained for the binary systems by fitting experimental data on vapor–liquid equilibrium pressure and phase concentrations. Results have been compared to those obtained using other versions of the SAFT-VR model.

The enthalpies of vaporization of freons CF3CH2CHCl2 (R-243), Δ vap H ° m ( 298.15 ) ( calor ) = 34.05 ± 0.04 kJ mo l − 1 , and CF3CH2CCl3 (R-233), Δ vap H ° m ( 298.15 ) ( calor ) = 36.76 ± 0.08 kJ mo l − 1 , have been calorimetrically determined at T = 298.15 K. The ideal gas thermodynamic functions S°(T), C ° p ( T ) , H°(T) − H°(0), and −[G°(T) − G°(0)]/T of freons CF3CH2CH2Cl (R-253fa) and R-243 were calculated over the temperature range from 100 to 1000 K by statistical thermodynamics and Density Functional Theory methods using the Gaussian 03 software package. Experimental vapour pressures determined lately at the “atmospheric” pressure range 7(44)–99.5(87) kPa were extended to the entire range of the liquid phase for 10 freons and 2 dichloroethanes. Reviewed data on the normal boiling temperatures, the enthalpies of vaporization, critical parameters, triple point temperatures, enthalpies of fusion, and entire temperature ranges of the liquid phases were tabulated for 13 freons and 8 halogenated ethanes and propanes.

Knowledge of thermo-physical properties of organic chemicals is essential to chemical and process design applications. Vapor pressure is one such property used directly in process calculations and as input to property-prediction models. Although experimental determination of vapor pressures remains an option, often it is not possible to measure vapor pressure data experimentally for toxic or yet to be synthesized molecules. Current vapor pressure models, which utilize traditional physical properties as inputs, are limited by their range of applicability and/or by poor suitability for generalization. Further, recent quantitative structure–property relations (QSPR) models for vapor pressure have been limited to single-temperature generalizations (e.g., 298 K); thus, the distinct advantages offered by advances in computational chemistry as they relate to structure–property model generalizations have not been fully realized. In this study, we present an integrated approach for developing a generalized model which is capable of predicting accurately the vapor pressure of organic chemicals over the entire saturation range (the triple point to the critical point). The approach uses a theoretical framework to develop the fluid behavior model and QSPR to generalize the parameters of the model. Specifically, we first apply our scaled variable reduced coordinates (SVRC) model to a diverse dataset containing over 1221 molecules involving 73 classes of chemicals, and then we generalize the SVRC parameters using structure–property (SP) models. For this modeling effort, reliable experimental vapor pressure data were obtained from the DIPPR database. The results for 52,445 data points indicate that: (a) the SVRC model represents these saturated vapor pressure data with 0.35% average absolute deviation (AAD), and (b) the generalized SVRC–QSPR model predicts the saturated vapor pressures with 0.5% AAD.

Several literature relations to calculate the vapour pressures of pure compounds are re-examined to evaluate their reliability in predicting the experimental data in a very low pressure range, chosen between the triple point and 1 mmHg. Following a previous work of the author, the performances of the Riedel equation are greatly improved by allowing a temperature dependence of the Riedel parameter 0.0838, which is assumed constant in the unmodified Riedel equation. The resulting relations, which vary for each class of compounds, embody only pure component parameters which can be evaluated by knowing only the normal boiling temperature and the critical constants. With these modifications, the Riedel equation is significantly better than the Miller, Lee–Kesler and Ambrose–Walton equations. This superiority is particularly evident in the case of strongly associated compounds, like alcohols. The strong dependence of the calculated pressures at very low temperatures on the critical temperature value is also stressed. The proposed method is verified on the basis of nearly 90 compounds, by using as “true” experimental data those reported in three sources: the DIPPR Data Compilation of Pure Compounds Properties, Project 801, the NIST program and a literature paper.

A method for determining quadruple points of a two-component system containing a simple hydrate phase is proposed. This method utilizes the quasi-static change of the system along three-phase equilibrium lines and was proved to be able to determine the quadruple points as accurately as the conventional method. By using this method, even though some preparation is necessary, a quadruple point can be determined in just a single experimental run. The behavior of the system near the quadruple points was also examined experimentally, for both the quasi-static and the irreversible change cases. At the quadruple points, the temperature and pressure of the system were kept constant for a while, as at the triple point of water. In both cases, the representative point of the state of the system passed through the quadruple point on a p – T diagram.

(Solid+liquid) and (vapour+liquid) equilibria for the binary systems (propane+adamantane) and (ethane+adamantane) were determined according to the synthetic method in the temperature range 300–510 K and in the pressure range 0.3–10 and 0.3–180 MPa, respectively. For both systems also the three-phase curve (solid adamantane+liquid+vapour) was determined and some vapour–liquid critical points at low mole fractions of adamantane. In the case of (propane+adamantane) the three-phase curve (solid adamantane+liquid+vapour) is continuous and shows a pressure maximum at a temperature higher than the critical temperature of propane. In the case of (ethane+adamantane) the three-phase curve (solid adamantane+liquid+vapour) is split into a low-temperature branch which runs from low temperature with a positive slope dP/dT to higher temperature and ends at a first critical endpoint at T=309.55 K and P=5.17 MPa. The high temperature branch of this curve starts at the second critical endpoint T=432.65 K and P=15.85 MPa, runs to higher temperature with a negative slope dP/dT and ends at the triple point of adamantane.

This paper deals with the evaluation of 10 recent van der Waals type equations of state (EOS) for their ability to predict the three important regularities. The studied regularities included: (i) the linearity of Zeno contour of reduced temperature against reduced density from the Boyle temperature to the triple point, (ii) the common bulk modulus point on the isotherms of the reduced bulk modulus versus reduced density, and (iii) the near linearity of reduced isothermal bulk modulus as a function of reduced pressure (Tait–Murnaghan equation) over the vapor pressure curve to the freezing line. The investigated equations of state are Kubic–Martin (KM), Adachi–Lu–Sugie (ALS), Yu–Lu (YL), Trebble–Bishnoi (TB), Iwai–Margerum–Lu (IML), Twu–Coon–Cunningham (TCC), modified Patel–Teja (MPT), Nasrifar–Moshfeghian (NM), Peng–Robinson (PR) and Soave–Redlich–Kwong. The best overall performance for Zeno contour is obtained based on the SRK, TB, KM and PR EOS, whilst the NM and ALS EOS produce the worst performances. The Zeno line prediction using the SRK, TB, KM and PR EOS approach the experimental reduced Boyle temperature at low-density, confirming their accuracy in supercritical region. The low-density region of the isothermal bulk modulus of CH4, as a spherical molecule, is well matched by SRK and KM EOS, but is closely matched by TB, IML and NM EOS. In compressed liquid, we observe that the slope and curvature of the calculated bulk modulus of CH4 obtained by SRK and KM EOS consistently performs better than the other EOS. For C2H6, C3H8 and n-C4H10 the predictive ability of the isothermal bulk modulus obtained from the cubic EOS are usually poor, especially at higher densities. We have also shown that the most accurate prediction of Tait–Murnaghan regularity of CH4 is KM, SRK, PR and MPT EOS for both subcritical and supercritical fluids in a wide pressure range, while the TB and NM EOS predict the Tait–Murnaghan regularity for supercritical fluids.

A corresponding-states correlation for the prediction of the orthobaric liquid density of molten metals has been developed. The correlation is the extension of the recently developed correlation by Iglesias-Silva and Hall, which needs the values of the critical and triple point constants as well as an adjustable parameter. The critical constants are scarce for almost all metals. Our corresponding-states correlation uses the normal boiling and melting point constants plus an adjustable parameter. While the present correlation is simpler in form than the correlation by Iglesias-Silva and Hall, all of its input data are more readily available for almost all metals. In this work, we have applied the present correlation to molten alkali metals, mercury, bismuth, tin, and lead. From about 150 data points for pure liquid metals the average absolute deviation and the maximum deviation are 0.29 and 1.06%, respectively. Also, we have extended the correlation to mixtures of any number of components. The predicted results for the liquid densities of K–Cs and K–Na mixtures over the whole range of concentrations and that of a ternary molten eutectic of K–Na–Cs at temperatures ranging from melting point up to several hundred degrees above the normal boiling point are in excellent agreement with experimental data. From 247 data points examined for molten alloys, the average absolute deviation and the maximum deviation are 0.59 and 1.91%, respectively.

The heat capacity of Freon R-123, CF3CHCl2, was measured by adiabatic calorimetry over the temperature range 8.55–297.52 K. The temperature of the λ-anomaly, Ttrs=125.5±0.1 K, the triple point temperature, Ttp=145.68±0.02 K, and the enthalpy and entropy of fusion, ΔfusHm=5.51±0.01 kJ mol−1 and ΔfusSm=37.83±0.05 J mol−1 K−1 were determined. The main thermodynamic functions of CF3CHCl2: S°m(T), (H°m(T)−H°m(0)), and (G°m(T)−H°m(0)) were calculated at T=298.15 K. The low-temperature differences between the heat capacities of ideal gas and liquid, ΔCp,m=C°p,m(g)−Cp,m(l), were used for simultaneous treatment with the saturated vapor pressure data of R-123 [Int. J. Thermophys. 13 (1992) 999], which had been measured from 256.4 to 453.8 K, in order to extrapolate the saturation vapor pressure from T=256 K down to Ttp.

International audience; A review of experimental data of several fluids shows that their coexistencecurve follows a power law in reduced temperature at the approach of the critical point, with an universal exponent equal to 0.325, their capillaryconstant a power law with an universal exponent equal to 0.925 and their surfacetension a power law with an universal exponent equal to 1.26. In the critical region, the concept of two-scale-factor universality was used to predict the density difference amplitude, the capillaryconstant amplitude, and the surfacetension amplitude between near critical vapor and liquid phases. A comparison with amplitudes determined from experimental data is given. In order to extend this universality all along the liquid-gas coexistencecurve from the triple point to the critical point for n-alkanes, a mean field approximation was used far away from TC. We show that the density difference, the capillaryconstant and the surfacetension can be calculated with a reasonable accuracy by generalized scaled equations adding only two empirical constants. A comparison between calculated and experimental data is presented.

The recent development of a new excess Gibbs function GE by Twu, Sim and Tassone allows infinite-pressure cubic of equations of state/AE (CEOS/AE) mixing rules to transition smoothly to the conventional van der Waals one-fluid mixing rules. The incorporation of their proposed GE model into a cubic equation-of-state allows an equation-of-state to describe both van der Waals fluids and highly non-ideal mixtures over a broad range of temperatures and pressures in a consistent and unified framework. We continue our work to develop a versatile excess Gibbs free energy function for zero-pressure CEOS/AE mixing rules, in addition to the infinite-pressure CEOS/AE mixing rules. An optimal two-parameter cubic equation-of-state TST (Twu–Sim–Tassone) has been found to allow better prediction of liquid densities for heavy hydrocarbons and polar components. The alpha function of the TST cubic equation-of-state is generalized here. The generalized alpha function is a linear function of the acentric factor at a constant reduced temperature, not a fourth-order or a sixth-order function as suggested by Soave and other researchers. The advantage of a linear function in the acentric factor is obvious in the extrapolation of the alpha function to heavy hydrocarbons, petroleum fractions, and gas condensates. The new generalized alpha function, when used with the TST, allows very accurate prediction of the vapor pressure from the triple point to the critical point of hydrocarbons. The performance of SRK, PR and TST is examined using the versatile excess Gibbs free energy function in the zero-pressure CEOS/AE mixing rules for the prediction of high pressure and high temperature phase equilibria of highly non-ideal systems.

Using a similar approach as Lencka and Anderko [AIChE J. 39 (1993) 533], we developed an equation of state for hydrogen fluoride (HF), which can correlate the vapor pressure, the saturated liquid and vapor densities of it from the triple point to critical point with good accuracy. We used an equilibrium model to account for hydrogen bonding that assumes the formation of dimer, hexamer, and octamer species as suggested by Schotte [Ind. Eng. Chem. Process Des. Dev. 19 (1980) 432]. The physical and chemical parameters are obtained directly from the regression of pure component properties by applying the critical constraints to the equation of state for hydrogen fluoride. This equation of state together with the Wong–Sandler mixing rule as well as the van der Waals one-fluid mixing rule are used to correlate the phase equilibria of binary hydrogen fluoride mixtures with HCl, HCFC-124, HFC-134a, HFC-152a, HCFC-22, and HFC-32. For these systems, new equation of state with the Wong–Sandler mixing rule gives good results.

Thermodynamic properties were predicted for two groups of pure fluids, along the saturation curve and in the single-phase region: IUPAC pure fluids (propylene, chlorine, oxygen and nitrogen) and halogenated hydrocarbons (R11, R12, R21, R22, R152a). A new form of equation GEOS, named GEOS3C, was used. A wide comparison with literature recommended data, as well as with results of other six cubic equations of state (Soave-Redlich-Kwong, Peng-Robinson, Stryjek-Vera, Schmidt-Wenzel, Freze et al. and Salim and Trebble) was made. The GEOS3C equation has three parameters estimated by matching three points on the saturation curve (vapor pressures and the corresponding liquid volumes). The three fixed temperatures are the triple point, the boiling point and the reduced temperature Tr=0.7. The GEOS3C equation leads to the best results in predicting vapor pressure and volumes at saturation. It also gives reasonable deviations for the other thermodynamic properties in the saturation range, but this do not lead necessarily to similar best predictions of all properties in the single-phase region.

Extensive examination of the anisotropic interaction potential of chlorine by Rodger et al. [P.M. Rodger, A.J. Stone, D.J. Tildesley, J. Chem. Soc., Faraday Trans. 2, 83 (1987) 1689–1702] (with interaction sites located at the positions of atoms in a molecule and the electrostatic part found by ab initio calculations) for its predictive power has been performed. We have calculated (i) the second virial coefficient by using a non-product algorithm, (ii) a series of liquid-phase state points in the temperature and pressure ranges of 200 to 400 K and 0 to 6.2 MPa, respectively, by the constant pressure–constant temperature molecular dynamics simulations, (iii) vapor–liquid equilibrium and heat of vaporization from the triple point (172 K) to 300 K by the Gibbs–Duhem integration method combined with simultaneous (but independent) constant pressure–constant temperature molecular dynamics simulations of the vapor and liquid phases, and (iv) the properties of the zero-pressure crystal structures by molecular dynamics technique due to Parinello and Rahman [M. Parrinello, A. Rahman, Phys. Rev. Lett. 45 (1980) 1196–1199]. Generally, good to excellent agreement of the calculated properties with the corresponding values for real chlorine was observed. The results obtained from the investigated interaction potential are equivalent to (or even better than) those reported for a more complicated potential by Wheatley and Price [R.J. Wheatley, S.L. Price, Mol. Phys. 71 (1990) 1381–1404].

Recommended data on vapour pressures are presented for all dichlorobenzenes, all trichlorobenzenes, and pentachlorobenzene in the temperature range from the triple point up to the normal boiling point. For some chlorobenzenes where reliable sublimation pressures and solid heat capacities are available (1,4-dichlorobenzene, 1,2,3-trichlorobenzene, 1,3,5-trichlorobenzene, and pentachlorobenzene), recommended sublimation pressures are also given that cover the range from about −40°C (with the exception of 1,4-dichlorobenzene where there are no experimental sublimation pressures below the phase transition at −1.38°C) up to the triple point temperature. The data were developed by a simultaneous multi-property correlation of vapour or sublimation pressures and the related thermal data (heat capacities in the liquid or the solid phase, heat capacities of the ideal gas, enthalpies of vaporisation or sublimation). The data are presented as parameters of the Cox correlation equation which has an identical form for description of vapour–solid (v–s) and vapour–liquid (v–l) equilibria and are consistent at the triple point. Recommendations are based mostly on new experimental vapour and sublimation pressures obtained recently by the authors. Solid and liquid heat capacities required for the simultaneous correlation were provided by merging new experimental data measured using a C80 Setaram heat conduction calorimeter over approximate temperature range from 30 to 160°C (depending on the compound) with the data critically selected from the literature.

An equation of state for HFC-143a has been developed based on available experimental data. The equation of state presented here for HFC-143a is valid both in the superheated gaseous phase and compressed liquid phase at pressures up to 35 MPa, densities to 1327 kg/m3, and temperatures from the triple point temperature of 161.34 K to 433 K. Correlations of the ideal gas heat capacity, vapor pressure and saturated liquid density are also presented.

The adsorption of a binary liquid mixtures onto a weakly attractive substrate has been studied in the vicinity of bulk liquid phase separation. A wetting transition between two different kinds of wetting films has been found. Below the wetting transition temperature, homogeneous films of one liquid phase wet the substrate. Above the wetting temperature, the wetting films contain both liquid phases. The surface phase transition line associated with this wetting transition is found to extend to both sides of the bulk phase separation line. On one side it is a prewetting line, and on the other side it becomes a line of triple point induced dewetting transitions. The experimental system used to study this behavior was liquid helium mixtures on a cesium substrate.

Liquid trifluoromethane has been studied for several temperatures between triple point and critical point by Monte Carlo computer simulations. The molecules were modelled as 5-center Lennard–Jones particles with partial charges and anisotropic polarizability. All model parameters were treated as constants; no density or temperature dependences were used. The simulations were carried out in the NPT ensemble by means of a modified Metropolis algorithm. The simulation results for the dielectric constant, density, heat of vaporization, and liquid structure agree well with experimental data over the whole temperature range. The dipole–dipole correlation function, coordination numbers and heat capacity could also be obtained from the simulations.

A new, simple, accurate three-parameter enthalpy-of-vaporization equation is constructed consistent with the renormalization-group theory of critical phenomena. The proposed equation is valid over the entire range from the triple point to the critical point for various pure compounds and reproduces data within the experimental accuracy. Since the correct near-critical behavior is built in, the new equation is often better than existing enthalpy-of-vaporization equations in that it can be used to not only accurately correlate but also effectively extrapolate from the usual range in which data are available both to the critical point and to the triple point. Fitted parameters are given for 30 pure substances. The result is compared with experimental data and previous equations.

A new simple viscosity-temperature equation with only three adjustable parameters is proposed that is valid over the entire saturated liquid curve for a chemically diverse set of compounds. This equation can incorporate the correct near-critical behavior and satisfies the need for a reliable equation for fitting and predicting the viscosity of saturated liquids. It reproduces data within the experimental uncertainty over the entire saturated liquid region. Compared with the previous viscosity-temperature equations, the new equation not only more accurately correlates experimental data but also more effectively extrapolates values from the usual range in which data are available both to the critical point and to the triple point.

An accurate, generalized orthobaric density equation is proposed for refrigerants R-11, R-12, R-13, R-14, R-22, R-23, R-32, R-123, R-123a, R-124, R-134a, R-141b, R-142b, R-143, R-143a and R-152a. The fitting parameter for the new equation has been obtained from experimental saturated liquid densities. The triple point density, while observable, is unknown for the substances in this work and also must be obtained from the fit of the data. The density equation is based on a combination of asymptotic behavior in the critical region and the rule of rectilinear diameters. This equation describes the entire saturated liquid density curve within the estimated accuracy of the experimental measurements. Although a saturated vapor equation would also result from the current analysis, we do not address the vapor in this paper.

A new generalized isothermal equation of state for liquid is obtained from the law of corresponding state. Only one temperature-independent parameter is needed for the density calculations from triple point up to the critical point for both nonpolar and polar liquids including strongly associating liquids such as alcohols and water. The parameter has an obvious physical significance and it can be obtained from generalized correlations. The equation can be applied to polymers also if an isothermal compressibilily datum or one density value is known.

An accurate correlation to predict the thermal pressure coefficients of normal paraffins, including polyethylene, is obtained. Only the number of carbon atoms is needed for the prediction of thermal pressure coefficients at densities from triple point up to critical point. The relationship between the thermal pressure coefficients of branched paraffins and their molecular structures is also discussed based on the graph theory. Two topological indexes, the Wiener index and polarity number, were used to develop a correlation which can predict the thermal pressure coefficients for branched paraffins satisfactorily.

Values of the enthalpy of vaporization from the critical to the triple point are correlated by an empirical equation. The equation contains parameters which characterize each substance: the critical and triple point temperatures and the enthalpy of vaporization at the triple point, and for all substances the same universal critical ratio. This work suggests that a wide class of fluids with the exception of quantal liquids shows an universal behavior along the coexistence curve.

This paper contains parameters for a universal vapor pressure equation describing methane, ethane, propane, n-butane, i-butane, R-11, R-12, R-22, R-23, R-32, R-123, R-124, R-125, R-134a, R-141b, R-142b, R-143a and R 152a. These parameters have been generated using experimental vapor pressures reported in literature. The vapor pressure equation, based upon asymptotic behavior at the triple and critical points, has three adjustable fluid-dependent parameters. This equation describes the entire vapor pressure curve within the apparent accuracy of the experimental values.

An improved correlation to estimate the thermal pressure coefficients of liquids over a wide temperature range from the triple point to the critical point is presented: γ = ( 0.569R b ∗ ) exp ( b ∗ V ) , where b ∗ is a substance-dependent constant whose value can be evaluated from one reliable experimental γ value of from group contribution. The calculation shows that the precision of both methods is far higher than that of the hard-sphere method.

The approach described in the previous paper (Twu, C.H., Coon, J.E. and Cunningham, J.R., 1994a. A new generalized alpha function for a cubic equation of state. Part 1. Peng-Robinson equation. Fluid Phase Equilibria, 105: 49–59) is applied to the Redlich-Kwong cubic equation of state (RK CEOS) to develop a new generalized alpha function for this equation. The new generalized alpha function for the RK CEOS reproduces the vapor pressure for hydrocarbons from the triple point to the critical point with almost identical accuracy to the generalized alpha function used for the Peng-Robinson CEOS in the previous paper. This indicates that the approach developed should be a general one, applicable to any cubic equation of state. The alpha function has been generalized in terms of the reduced temperature and acentric factor, so it can be used for any hydrocarbons and petroleum fractions, with no additional characterization to the standard methods required (Twu, 1984). The new alpha function is more appropriate for the RK CEOS than Soave's alpha function, which has been widely used in phase behavior calculations in the petroleum production and refinery industries over the last twenty years.

Most non-associated organic and inorganic compounds are shown to obey the principle of corresponding states with regard to the orthobaric or saturated densities. The compounds are divided into two classes: one class containing those substances which behave like the perfect gases (Ar, Kr, Xe) with respect to this principle; the other consists of all other non-associated species. Each class follows its own temperature-density relation. These relations contain only two parameters, specific for the compounds: the critical temperature and a critical density, calculated from a reference density. For the liquids the useful range of reduced temperatures is between the triple point and about 0.96; for the gases from approximately 0.7 or 0.8 to 1. Average absolute percentage deviations in predicted liquid densities are about 0.7% (less than 1%) for some 150 compounds and in predicted gas densities less than 10% for about 50 compounds. For practical applications the equations can satisfactorily be used to predict liquid densities within 1%, starting from a given density at ambient temperature.

Correlation equations are recommended for expressing the temperature dependence of the heat of vaporization of pure substances, providing reliable extrapolation to both the critical and triple point. These equations have been used to treat heat of vaporization data for 56 substances.

Twu, C.H., Coon, J.E. and Cunningham, J.R., 1994. A generalized vapor pressure equation for heavy hydrocarbons. Fluid Phase Equilibria, 96: 19-31. Pitzer's acentric factor is widely used in physical property estimations; one important area is that of generalized vapor pressure correlations. Since Pitzer's acentric factor is defined in terms of the vapor pressure at a reduced temperature equal to 0.7, using this approach to generalize a vapor pressure equation gives excellent accuracy at reduced temperatures between 0.7 and 1.0, but predicts vapor pressures less accurately at lower reduced temperatures. To improve the vapor pressure prediction of hydrocarbons at low reduced temperatures, the definition of the acentric factor is re-examined and a modified acentric factor is proposed. Two sets of generalized vapor pressure equations are presented, with Pitzer's acentric factor and the modified acentric factor, respectively, as the third corresponding states parameter. These two equations are applied from the triple point to the critical point. Both correlations give more accurate vapor pressure predictions than the Lee-Kesler (1975) 2 correlation, especially at low reduced temperatures, with the correlation using the modified acentric factor as the third parameter being the most accurate. Additionally, an internally consistent approach is proposed for estimating the normal boiling point, critical temperature and critical pressure of petroleum fractions using a single low temperature vapor pressure data point. The procedure proposed uses either correlation from this work and gives an accurate estimation of the normal boiling point and acentric factor for heavy petroleum fractions for use in equations of state.

Salim P.H. and Trebble M.A., 1994. Modelling of solid phases in thermodynamic calculations via translation of a cubic equation of state at the triple point. Fluid Phase Equilibria 93; 75-99 A simple methodology is demonstrated by which a cubic equation of state (EOS) can be modified to allow calculation of equilibria involving solid phases as well as thermodynamic properties of the solid phase itself. Volume translation of the EOS at the triple point is performed using experimental values of solid density. Temperature-dependent parameters of the translated equation (TEOS) are then regressed to vapour pressure data at temperatures below the triple point if data are available. A generalized procedure for calculation of temperature-dependent parameters in the translated equation is also described (for instances where data are unavailable) which requires the heat of sublimation at the triple point and the isobaric heat capacity of the solid. The translated equation can then be utilized to describe solid phases at temperature above the triple point temperature by extrapolation, with the result that the entire pressure-temperature space for a pure component can be accurately reproduced. The methodology is successfully applied to the Trebble-Bishnoi-Salim EOS and is used to calculate both pure component phase behaviour and binary solid-liquid and solid-vapour equilibria. Criteria are also discussed to ensure that the translated equation does not violate thermodynamic consistency.