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A study is performed of the accuracy of free energy F of a vapor–liquid system, calculated with modified fluid models in the quasi-chemical approximation (QCA) of the lattice gas model. Two ways of modifying the fluid model are discussed: (1) allowing for the softness of the lattice, which alters its weighted average parameter according to the density of the fluid and (2) jointly considering the translational and vibrational molecular motions in a rigid lattice. The effect the model of introducing the weighted average parameter of a soft lattice has on the calculated characteristics is analyzed. Calculations of the free energy using the analytical QCA formula (which contains no such modifications) are compared to thermodynamic relationships obtained with a chemical potential that considers them. It is found that both modifications of the fluid model result in distinctions between the two ways of calculating the free energy that grow along the density of the system. These distinctions are apparent at high densities and on the concentration dependence of pressure. The analytical QCA expression quantitatively estimates F values when there are small contributions from model modifications.

Because of their toxicity, flammability, and chemical instability, the vapor–liquid equilibria of the group V hydrides, phosphine, arsine, and stibine are underexplored. Gibbs ensemble Monte Carlo ...

A unified description of three types of two-phase interfaces (vapor–liquid, solid–vapor, and solid–liquid) at a vapor–liquid meniscus inside a slit-like pore are considered on the basis of the lattice gas model. This approach allows equally accurate calculations of molecular distributions in heterogeneous distributed models of transitional regions at all interfaces. It is assumed that pore walls cannot be deformed, and they create an external field for a stratifying fluid. Adsorption films form at solid–mobile phase interfaces due to the potential of adsorbate–adsorbent interaction. The state of the coexisting vapor-in-a-pore and liquid-in-a-pore phases satisfy the equality of the chemical potential that excludes the appearance of metastable states. Conditions for distinguishing regions of the system that lie beyond solid–liquid–vapor three-phase contact are discussed. A procedure is discussed for introducing a contact angle into a liquid–vapor–solid pore wall system through molecular distributions of the adsorbate in a slit-like pore. Dependences of the width of the considered interfaces and the contact angle as a function of the pore width and pore wall potential are found.

The continuum quasichemical approximation is used to improve the accuracy of describing molecular distributions in a vapor–liquid system. It considers displacements of the molecular center of mass from the center of a cell within the lattice gas model. It also allows for (as in its discrete variant) direct correlations of interacting molecules. The probability density of a molecule being inside the cell is used as a continuous function of its coordinate. An algorithm for solving a system of integral equations is developed with respect to the pair distribution function. The effect the continuum description of the particle distribution has on the concentration dependences of the main thermodynamic functions is investigated. The approach is shown to explain the concentration dependence of the parameter of effective lateral interaction.

Expressions for calculating Gibbs vapor–liquid surface tension σ are generalized to allow for the interaction between comparable components of a mixture with an arbitrary radius of the interaction potential. Calculations are performed within a modified lattice gas model reflecting a discrete-continuous distribution of mixture components in space with allowance for direct correlations in a quasi-chemical approximation. The calculating of σ is associated with the rejection priority of mechanical characteristics over chemical potential, which is traditional in continuum mechanics. The chemical potential governs local equilibrium distributions of components in the transitional region of a boundary, resulting in the need to use microscopic Gibbs–Duhem equations in a deformed lattice structure of a substance to determine the average distance between molecules (as lattice structure parameters) and to consider effective one-particle motions of components in a dense phase that alter these parameters. Calculations of the surface tension of dense mixtures in models ignoring the existence of vacancies and structural deformation are discussed.

A procedure to calculate the surface tension is developed based on a modified lattice gas model (MLGM) for the vapor–liquid system in a strict correspondence to the thermodynamic Gibbs definition for any curvature of the boundary. It is shown that MLGM enables a calculation of molecular distributions in a layered model of the transition region of the interface with regard to the softness of a lattice structure. The state of coexisting phases must satisfy the Yang–Lee theory of condensation, and additional conditions for chemical, thermal, and mechanical equilibria are imposed on the properties of the transition region of an equilibrium droplet with any curvature in each layer. The new calculation procedure for the surface tension is compared with the existing calculation procedures for equilibrium and metastable droplets. A difference in size dependences of the surface tension σ(R) for equilibrium and metastable droplets with a radius R in vicinity of the line σ/σbulk = 1, where σbulk is the bulk surface tension, allows us to formulate the accuracy and reliability criterion for different modeling methods: if the mentioned line exceeds the calculation accuracy σ(R), then it indicates that the method does not correspond to the Gibbs definition.

In this study, the effect of copper nanoparticles on the interface properties of liquid–vapor argon is investigated by molecular dynamics simulation. Stoddard Ford potential function has been utilized to estimate the interactions of argon–argon and argon–copper particles. Simulation is done in the nanoscale computational domain to phase change of vapor to liquid at different saturated temperatures. Density values and surface tension for different cutoff radii are obtained. It is demonstrated that in the $$r_{\text{c}} = 4\sigma$$ calculated values are acceptable. Simulation results show that nanoparticles change the interface properties of liquid–vapor argon. With addition of nanoparticles, liquid density decreases and vapor density increases. Nanoparticles displace density distribution and cause fluctuations in the density profile. Also, surface tension increases with increase in nanoparticle concentration.

The objective of this work was to study the behavior of the azeotropic points of the methanol + DMC system under elevated pressures. We obtained isothermal vapor–liquid equilibria (VLE) data for this system at 383.15, 403.15, and 413.15 K by a static method. The azeotropic points were determined from the experimental VLE data. The temperature and pressure dependencies of the determined azeotropic points are discussed and compared with ones measured at reduced pressure. The experimental VLE data were represented by two activity coefficient models (non-random two-liquid and Wilson models). We also tested the modified UNIFAC (Dortmund) model for prediction of the VLE and azeotropic points. The azeotropic points of this system could be obtained over the pressure range from reduced pressures to elevated ones.

Vapor-liquid equilibria (VLE) and distribution coefficients (K-values) of carbon dioxide (CO2) - ethanol - water ternary systems and CO2 - ethanol - water - flavonoid (flavone, 6-methoxyflavone or 7-hydroxyflavone) quaternary systems were measured with a flow type apparatus at (313 to 353) K and (10 to 20) MPa. CO2 - ethanol - flavonoid ternary systems were measured at a nominal range of temperatures and pressures. The K-values of all flavonoids increased with increasing pressure. It was also indicated that the K-values of relatively lipophilic components such as flavone and 6-methoxyflavone increased with increasing water composition in feed while those of relatively hydrophilic components such as 7-hydroxyflavone increased with increasing ethanol composition in feed. A simple dimensionless relationship in terms of the K-values of the solvents (KCO2, KEtOH, KH2O) and the entropy-based solubility parameters of the vapor and liquid phases was developed to correlate the K-values of the three solutes in the CO2 - ethanol - water systems over the full range of conditions studied.

Vapor-liquid phase equilibria of the H2S H2O mixture were correlated by use of a cubic EOS-GEX over temperature and pressure range of 0.1–30 MPa and 278–627K. Average absolute deviations (AAD%) between the modeling results and the experimental data taken from literature for both the H2S-rich and the aqueous phases were found less than 5%. The new sets of EOS-GEX model parameters for H2S H2O mixture were evaluated from the experimental data over the above-mentioned temperature and pressure range. The proposed model was compared with the three previous published models and we discussed the advantages and the disadvantages for each of them. This study demonstrated that the advantages of the cubic EOS-GEX model in calculating phase equilibria of H2S H2O mixture over currently available models, especially at high pressures. The hydrate equilibrium, the salt effect, and the chemical reactions in the aqueous phase were not considered during phase equilibrium calculation in this study.

The role of interatomic interactions on the solid-liquid and vapor-liquid equilibria of neon is investigated via molecular simulation using a combination of two-body ab initio, three-body, and quantum potentials. A new molecular simulation approach for determining phase equilibria is also reported and a comparison is made with the available experimental data. The combination of two-body plus quantum influences has the greatest overall impact on the accuracy of the prediction of solid-liquid equilibria. However, the combination of two-body + three-body + quantum interactions is required to approach an experimental accuracy for solid-liquid equilibria, which extends to pressures of tens of GPa. These interactions also combine to predict vapor-liquid equilibria to a very high degree of accuracy, including a very good estimate of the critical properties.

The isothermal vapor + liquid equilibria of carbon dioxide + (E)-2-hexenal (a key apple aroma) was measured using a visual equilibrium cell with an analytic methodology. The selected isotherms were (313.2, 323.2 and 333.2) K, and the pressures assessed ranged from (2.2–9.8) MPa. The thermodynamic consistency of the experimental data was verified, and the uncertainties of the molar fractions of the vapor and liquid phases were estimated. The density and dynamic viscosity of pure (E)-2-hexenal were measured at 101.13 kPa and temperatures from (292.2–353.2) K. Two equations of state were selected to model the vapor + liquid equilibria. The Peng-Robinson with two different mixing rules, and the Perturbed Chain - Statistical Associating Fluid Theory. The phase envelopes showed a critical pressure, detected at carbon dioxide molar fractions ≥ 95 % mol∙mol−1.

The aim of this study was to investigate phase equilibria in a water + poly(propylene glycol) [Mn = 425 g mol−1] system. Vapor-liquid equilibria (VLE) were determined ebulliometrically in the completely miscible region with higher water concentrations at isotherms 323.15, 333.15, 343.15, and 353.15 K. These data were correlated with the UNIQUAC free-volume (FV) model to be consistent with our previous studies. Liquid-liquid equilibrium (LLE) was determined using the cloud-point method at 320–350 K, and lower critical solution temperature was found at 320.2 K. LLE was correlated with the entropic FV-UNIQUAC segmental interaction model developed earlier, which is suited for correlation and calculation of LLE of polymer solutions. We estimated new binary segmental interaction parameters for interactions between propylene glycol and water segments.

In this work, we have been carried out GEMC-NVT simulations in the temperature range 18 K–32 K for fluid hydrogen and in range 60 K–140 K for fluid fluorine using four our developed ab initio 5-site intermolecular potentials for dimers H2-H2 and F2-F2, respectively. The thermodynamic properties of vapor-liquid equilibria and the critical points of fluids hydrogen and fluorine were calculated with the obtained densities of coexisting phases and vapor pressures. The simulation results drived from ab initio pair potentials were compared with those from ab initio potential plus three-body Axilrod-Teller potential and experimental data as well as those from Monte Carlo simulation using Lennard-Jones potentials, Deiters equation of state (D1-EOS) and Benedict-Webb-Rubin equation of state (EOS) reported in the literature.

The Si nanowire growth can be well explained by the classical vapor–liquid–solid (VLS) process taking into account the respective Au–Si phase diagram. For oxide-based compound materials, no phase d...

In this study, the thermodynamic modeling of SO2 solubilities in 14 Deep Eutectic Solvents (DESs) of different nature was investigated for the first time in literature. This is a challenging mixture to model. The thermodynamic modeling approach of γ − ϕ for vapor-liquid equilibria was used. The Cubic Plus Association Equation of State (CPA EoS) was used to represent the vapor phase and the NRTL and UNIQUAC models were both investigated for the liquid phase. The DESs were considered as pseudo-components and their physical properties calculated. Both the CPA-UNIQUAC and CPA-NRTL models showed good agreement with experimental values, with total AARD% of 2.9% and 3.1%, respectively. CPA-UNIQUAC shows slightly better results, while CPA-NRTL is a simpler model. In addition to the γ − ϕ approach, the ϕ − ϕ approach was investigated for all of the systems. However, the results were not reliable, even when incorporating binary interaction parameters as adjustable parameters in the model.

The critical temperatures and pressures of diethyl esters of straight-chain saturated dicarboxylic acids C2H5OOC(CH2)n−2COOC2H5 with n = 5, 8, 10 have been measured. The data of this work and the results of the previous measurements have been analyzed and the recommended critical temperatures and pressures of diethyl esters from diethyl ethanedioate to diethyl decanedioate have been given. The internal consistency of the experimental data has been tested by considering the plot ( M / p c ) 1 / 2 versus n, where M is the molar mass, p c is the critical pressure. The acentric factors of dicarboxylic acid diethyl esters have been calculated.

The vapor–liquid partitioning of Si(OH)4, B(OH)3, Ge(OH)4, As(OH)3 and Sb(OH)3 in water at temperatures between 567.7 and 633.2 K was studied by sampling the coexisting vapor and liquid phases. For Ge(OH)4 and Sb(OH)3 the measurements in pure water have been made for the first time. Distribution constants for all hydroxides of metalloids, K D , are smaller than unity, i.e., these compounds strongly partition into the liquid phase. Correspondingly, the values of the Krichevskii parameter, A K r , the property that governs the thermodynamic properties of a solute close to the critical point of a solvent, for all these species are negative and equal (in MPa) to −178.6 ± 3.6 for Si(OH)4, −172.4 ± 5.5 for Ge(OH)4, −77.8 ± 1.3 for B(OH)3, −112.6 ± 4.6 for As(OH)3, and −160 ± 12 for Sb(OH)3, correspondingly. For indicated species the recommended values of K D are tabulated at T ≥ 523.15 K.

An automatic high-throughput computing (HTC) procedure is implemented for calculating vapor-liquid equilibrium (VLE) curves of binary systems using molecular dynamics simulation and coarse-grained force field. The HTC procedure builds simulation models, carries out the simulations, and validates the simulations automatically. The procedure is demonstrated by calculating the VLE curves for 16 binary mixtures of carbon dioxide and n-alkanes on 856 state points in the temperature range of 277.2–420.0 K and pressure range of 0.3–25.0 MPa. The averaged uncertainties in predictions are 0.119 MPa for pressure, 0.007 and 0.029 for liquid and vapor CO 2 molar fractions, and 0.005 and 0.010 for liquid and vapor densities respectively. The Validation against experiment data on 10 binary systems and 316 state points shows that the predictions are accurate with average deviation of about 5% for CO 2 mole fraction and 3.5% for saturated density at pressure range to P P c . This automatic procedure can only be used for the prediction of the vapor-liquid equilibrium. The computed data can be obtained from http://sun.sjtu.edu.cn/msd .

The vapor–liquid equilibrium (VLE) phase diagrams of Pb–Pd and Pb–Pt alloy systems in vacuum distillation were obtained based only on pure-component properties and the structures of the atoms. The interaction energies between pairs of atoms were calculated from ab initio methods and were used as the input energy parameters for the Wilson equation. The calculated activity data of the components, using energy parameters which were obtained by ab initio methods, are in good agreement with the experimental data. It is revealed that a cluster size of eight atoms, optimized using the NVT ensemble at 300 K, a time step of 1 femtosecond, and the simulation time 10 ps gives a good representation of the liquid phase systems. This approach can be used to obtain accurate VLE predictions for alloy systems in vacuum distillation. The VLE phase diagram has a significant advantage in guiding experiment and industrial production in vacuum metallurgy.

The two 5-site potentials from ab initio calculations at the theoretical level CCSD(T) with correlation consistent basis sets aug-cc-pVmZ (with m = 4, 34) have been constructed from oxygen. The extrapolation ab initio energies were approximated by the basis sets aug-cc-pVmZ (m = 3, 4). These two potentials were constructed by using the ab initio intermolecular energy values and a non-linear least-squares fitting method. The second virial coefficients of oxygen were determined to demonstrate the accuracy of these ab initio 5-site potentials. These ab initio potentials were employed to estimate the thermodynamic properties of the vapor���liquid equilibria by GEMC simulation. The influence of ab initio potential alone and plus 3-body interaction Axilrod-Teller potential was investigated within GEMC simulation from 80 K to 140 K. The discrepancy between them is insignificant. This showed that the two 2-body 5-site potential functions can also be used together with the 3-body interaction Axilrod-Teller potential to generate the accurate thermodynamic properties of the liquid���vapor equilibria.

In this work, the liquid-liquid equilibrium data of the system water + 1-butanol + 2-butanol was studied at 303.15 and 313.15 K. In addition, the vapor-liquid and vapor-liquid-liquid equilibrium at 101.3 kPa was also determined experimentally. The effect of the temperature on the binary water + 2-butanol system and on the ternary system was analysed. Several correlations were tested using the experimental data. The viability of using LLE correlations to calculate LLE on the one side and VLE on the other side and the viability of using the VLE correlation to calculate VLE and LLE were studied using UNIQUAC and NRTL models. A comparison of these result with the UNIFAC predictive model was performed. The authors wish to thank the Conselleria d'Educació, Investigació, Cultura i Esport (Generalitat Valenciana) of Spain for the financial support of project AICO/2015/052.

Properties of the vapor-liquid interface of the binary mixture cyclohexane + CO2 as well as for the two pure substances are reported. The data were obtained from pendant drop experiments (Exp), molecular dynamics (MD) simulation, and density gradient theory (DGT) in combination with the PCP-SAFT equation of state. The following interfacial properties were studied: surface tension (Exp, MD, DGT), relative adsorption (Exp, MD, DGT), enrichment (MD, DGT), and interfacial thickness (MD, DGT). The measurements were carried out at temperatures between 303.15 K and 373.15 K and pressures up to 6 MPa. Furthermore, bulk VLE properties were computed by MD and PCP-SAFT and compared to experimental data from the literature. Data from experiment, MD, and DGT were found to be in good agreement throughout.

A new Helmholtz free energy density functional is presented to predict the vapor-liquid interface of chainlike molecules. The functional is based on the last version of the statistical associating fluid theory for potentials of variable range for homogeneous Mie chainlike fluids (SAFT-VR Mie). Following the standard formalism, the density functional theory (SAFT-VR Mie DFT) is constructed using a perturbative approach in which the free energy density contains a reference term to describe all the short-range interactions treated at the local level, and a perturbative contribution to account for the attractive perturbation which incorporates the long-range dispersive interactions. In this first work, we use a mean-field version of the theory in which the pair correlations are neglected in the attractive term. The SAFT-VR Mie DFT formalism is used to examine the effect of molecular chain length and the repulsive exponent of the intermolecular potential on density profiles and surface tension of linear chains made up to six Mie (lr6) segments with different values of the repulsive exponent of the intermolecular potential. Theoretical predictions from the theory are compared directly with molecular simulation data for density profiles and surface tension of Mie chainlike molecules taken from the literature. Agreement between theory and simulation data is good for short-chain molecules at all thermodynamic conditions of coexistence considered. Once the theory has proven that is able to predict the interfacial properties, and particularly interfacial tension, the SAFT-VR Mie DFT formalism is used to predict the interfacial behavior of two new coarse-grained models for carbon dioxide and water recently proposed in the literature. In particular, the theoretical formalism, in combination with the coarse-grained models for carbon dioxide and water, is able to predict the interfacial properties of these important substances in a reasonable way., The authors thank helpful discussions with Carlos Avendaño andJosé Matías Garrido. We also acknowledge Centro de Supercom-putación de Galicia (CESGA, Santiago de Compostela, Spain) andMCIA (Mésocentre de Calcul Intensif Aquitain) of the Universitésde Bordeaux and Pau et Pays de l’Adour (France), for providingaccess to computing facilities and Ministerio de Economía, In-dustria y Competitividad through Grant with reference FIS2017-89361-C3-1-P co-financed by EU FEDER funds. Further financialsupport from Junta de Andalucía and Universidad de Huelva isalso acknowledged. J.A., J.M.M., and F.J.B. thankfully acknowl-edge the computer resources at Magerit and the technical supportprovided by the Spanish Supercomputing Network (RES) (ProjectQCM-2018-2-0042)., The authors thank helpful discussions with Carlos Avendaño and José Matías Garrido. We also acknowledge Centro de Supercomputación de Galicia (CESGA, Santiago de Compostela, Spain) and MCIA (Mésocentre de Calcul Intensif Aquitain) of the Universités de Bordeaux and Pau et Pays de l’Adour (France), for providing access to computing facilities and Ministerio de Economía, Industria y Competitividad through Grant with reference FIS2017- 89361-C3-1-P co-financed by EU FEDER funds. Further financial support from Junta de Andalucía and Universidad de Huelva is also acknowledged. J.A., J.M.M., and F.J.B. thankfully acknowledge the computer resources at Magerit and the technical support provided by the Spanish Supercomputing Network (RES) (Project QCM-2018-2-0042)

The PC-SAFT equation of state (EoS) was examined for the prediction of liquid–liquid equilibria (LLE) at high pressure on the basis of LLE data at 1 bar. New parameters set for 2-alkoxyethanol with the two-site association scheme were proposed. Mixtures of 2-alkoxyethanol with aliphatics, aromatics, alcohols, and water have been investigated. Different binary 2-methoxyethanol + alkanes systems at high pressure up to 4000 bars were also predicted using the PC-SAFT EoS. Satisfactory predictions of vapor-liquid equilibria and liquid-liquid equilibria can be achieved by using the same binary interaction parameter (k ij ) for a similar kind of mixtures. The results are finally compared to other association models.

Techniques have been developed to determine vapor-liquid phase boundaries and swelling factors of CO2-heavy oil systems and C3H8-n-C4H10-CO2-heavy oil systems under reservoir conditions. Experimentally, a pure substance of CO2 and a gas mixture consisting of 27.7 mol% C3H8, 23.9 mol% n-C4H10, and 48.4 mol% CO2 are respectively introduced to dilute the highly viscous heavy oil. A pressure-volume-temperature (PVT) setup is used to measure vapor-liquid phase boundaries (i.e., saturation pressures) and swelling factors at high pressures up to 11.1 MPa and elevated temperatures up to 373.35 K. Theoretically, the volume-translated Peng-Robinson equation of state (PR EOS) coupled with a recently modified alpha function is applied as the primary thermodynamic model to reproduce the experimental measurements. The heavy oil which is a complex mixture with unknown molecular structure is characterized as six pseudocomponents by using an exponential distribution splitting function and a logarithm-type lumping method. The optimal exponents in binary interaction parameter (BIP) correlations are obtained by best matching the measured saturation pressures. Subsequently, the comparisons have been performed between this work and a commercial simulator in terms of the overall prediction accuracy of saturation pressures for the quaternary C3H8-n-C4H10-CO2-heavy oil systems. It is found that the minimum absolute average relative deviation (AARD) of 6.7% is obtained by the methodology developed in this work, compared to the AARD of 35.6% obtained by running the commercial simulator.

Ionic liquids (ILs) have been extensively studied as replacements to sulfolane in the separation of aromatics from alkanes. The employment of ILs could reduce energy requirements and operating costs of the aromatic extraction unit as a result of their nonvolatile character. However, the ILs studied so far have shown mass-based aromatic distribution ratios lower than the sulfolane values, which would increase the solvent-to-feed ratio in the extractor. To overcome this drawback, we tested the performance of the 1-butyl-3-methylimidazolium tricyanomethanide ([bmim][TCM]) and the 1-butyl-4-methylpyridinium tricyanomethanide ([4bmpy][TCM]) in the separation of toluene from n-heptane, exhibiting the [4bmpy][TCM] mass-based toluene distribution ratios and toluene/n-heptane selectivities higher than those of sulfolane. We also studied the vapor-liquid recovery of the extracted hydrocarbons from the ILs, obtaining relative volatilities of n-heptane from toluene substantially higher in the presence ILs than those without ILs. A thermophysical characterization of the ILs was also made by measuring their densities, viscosities, thermal stabilities, and estimating their maximum operation temperatures. Finally, the regeneration and reuse of the ILs was studied on successive recovery cycles. After five recovery cycles, ILs have shown the same extractive capacity.

Experimental measurement of vapor-liquid equilibria (VLE) was performed for 2,3,3,3-tetrafluoropropene (HFO-1234yf) + 1,1,1,2,2-pentafluoropropane (HFC-245cb) system. The VLE data were measured by a static-analysis apparatus at temperatures ranging from (283.15–313.15) K. Within the experimental temperature range, the binary system was slightly non-ideal; no azeotropic behavior was observed. Experimental results were correlated based on equations of state (EOS) method. Peng-Robinson EOS and van der Waals mixing rules were used to calculate both vapor and liquid phase fugacity coefficient. Correlation deviation was acceptable and thermodynamic consistency was well satisfied.

In this work, interaction energies between pairs of atoms for the Ag–Pb, Cu–Pb and Sn–Pb systems have been calculated using ab initio methods. These energies are then used as the interaction energy parameters in the Wilson equation. Phase diagram of vapor–liquid equilibria (VLE) for the Pb-based alloy systems in vacuum distillation are obtained based on the calculated parameters. The results indicate that this approach can lead to accurate VLE predictions for alloy systems in vacuum distillation based only on properties of pure components and the structure of the clusters. The comparisons show the computational results are in good agreement with the experimental data.

Supercritical fluid extraction (SFE) is one of the techniques used to obtain Illicium verum volatile oil, however, solubility of the volatile oil in CO2, one of the most important process variables from the SFE, is still unknown. In this work, vapor liquid equilibria experiments (VLE) were conducted in order to verify solubility of the major compound in the I. verum volatile oil, E-anethole, in CO2. In addition, SFE was carried with 750 g/h and 1500 g/h of CO2 at 308.15 K and 8000 kPa, 9000 kPa, 10,000 kPa and the antioxidant activity of the volatile oil accessed by the DPPH method. The VLE experimental data was modeled using the Peng–Robinson EOS (PR-EOS) with three mixing rules (vdW1, vdW2 and MKP). Moreover, SFE process was simulated using the equation proposed by Sovova and solubility data was compared with the values obtained by the PR-EOS.

This paper presents the measurements of isothermal vapor-Liquid equilibria (VLE) data for two binary systems of 2,3,3,3-tetrafluoropropene (HFO-1234yf) + 2-chloro-3,3,3-trifluoropropene (HCFO-1233xf) and 2-chloro-3,3,3-trifluoropropene (HCFO-1233xf) + 2-chloro-1,1,1,2-tetrafluoropropane (HCFC-244bb). The measurements were performed with an apparatus based on the static-analysis method. The HFO-1234yf + HCFO-1233xf system was measured at three temperatures from (293.15 to 313.15) K, and the HCFO-1233xf + HCFC-244bb system was measured at three temperatures from (303.15 to 323.15) K. The system of HFO-1234yf + HCFO-1233xf shows a small deviation from Raoult's law and dose not exhibit azeotropic behavior, while the system of HCFO-1233xf + HCFC-244bb exhibits near azeotropic behavior within the complete range of composition. All of the experimental data were correlated with the Peng–Robinson equations of state with the van der Waals mixing rules. Good consistency was obtained between the experimental data and correlated values for the both systems in the experimental temperature range. Thermodynamic consistency testing was also performed by the data-reduction method for the observed experimental data.

The role of cohesive r−4 interactions on the existence of a vapor phase and the formation of vapor–liquid equilibria is investigated by performing molecular simulations for the n-4 potential. The cohesive r−4 interactions delay the emergence of a vapor phase until very high temperatures. The critical temperature is up to 5 times higher than normal fluids, as represented by the Lennard-Jones potential. The greatest overall influence on vapor–liquid equilibria is observed for the 5–4 potential, which is the lowest repulsive limit of the potential. Increasing n initially mitigates the influence of r−4 interactions, but the moderating influence declines for n > 12. A relationship is reported between the critical temperature and the Boyle temperature, which allows the critical temperature to be determined for a given n value. The n-4 potential could provide valuable insight into the behavior of non-conventional materials with both very low vapor pressures at elevated temperatures and highly dipolar interactions.

In this work, the equilibrium of the system water + 1-butanol + 2-pentanol is studied. Data for isobaric vapor–liquid (VLE) and vapor-liquid-liquid (VLLE) equilibria are obtained at a constant pressure of 101.3 kPa. The equipment used to carry out the experiments is an all-glass dynamic recirculating still, with an ultra-sonic homogenizer coupled to the boiling flask. In addition, liquid-liquid equilibrium (LLE) data at a constant temperature of 303.15 and 313.15 K are analyzed. All the data are found to be thermodynamically consistent and have been correlated by means of different activity coefficients models such as NRTL and UNIQUAC. The results are compared with UNIFAC predictions. The authors wish to thank the Conselleria d’Educació, Investigació, Cultura i Esport (Generalitat Valenciana) of Spain for the financial support of project AICO/2015/052.

The effect of interface curvature on phase equilibrium has been much more studied for single-component than multicomponent systems. We isolate the effect of curvature on multicomponent vapor-liquid equilibrium (VLE) phase envelopes and phase composition diagrams using the ideal system methanol/ethanol and the nonideal system ethanol/water as illustrative examples. An important finding is how nanoscale interface curvature shifts the azeotrope (equal volatility point) of nonideal systems. Understanding of the effect of curvature on VLE can be exploited in future nanoscale prediction and design.

Tetrahydrofuran (THF) is a popular thermodynamic promotor for gas hydrates. Nonetheless, the phase equilibrium calculations of THF hydrates are limited given the abundant experimental data. In this work, we successfully applied the Chen–Guo hydrate model to the THF/CH4/N2 system with different compositions of CH4/N2 gas mixtures. In consideration of various reaction conditions, we proposed the vapor–hydrate two-phase and vapor–liquid–hydrate three-phase models for the equilibrium separations of THF/CH4/N2 via hydrate formation. The hydrate formation condition and equilibrium separation of CH4/N2 in 6 mol% THF solution were calculated and compared with experimental results. The average absolute relative deviations between the experimental and calculated data for hydrate formation pressure and equilibrium separation compositions are 6.86% and 7.56%, respectively. This demonstrates that the Chen–Guo model has relatively high accuracy for the equilibrium calculation of THF/CH4/N2 hydrates. This work provides an effective approach to predict the thermodynamic phase behavior of hydrates containing promotors or inhibitors.

Vapor–liquid nucleation is a ubiquitous process that has been widely researched in many disciplines. Yet, case studies are quite scattered in the literature, and the implications of some of its basic concepts are not always clearly stated. This is especially noticeable for heterogeneous nucleation, which involves a solid surface in touch with the liquid and vapor. The current review attempts to offer a comprehensive, though concise, thermodynamic discussion of homogeneous and heterogeneous nucleation in vapor–liquid systems. The fundamental concepts of nucleation are detailed, with emphasis on the role of the chemical potential, and on intuitive explanations whenever possible. We review various types of nucleating systems and discuss the effect of the solid geometry on the characteristics of the new phase formation. In addition, we consider the effect of mixing on the vapor-liquid equilibrium. An interesting sub-case is that of a non-volatile solute that modifies the chemical potential of the liquid, but not of the vapor. Finally, we point out topics that need either further research or more exact, accurate presentation.

At any given temperature, pressure, and composition, a compound or a mixture of compounds will exist either in a single phase, whether solid, liquid, or vapor, or in a combination of these phases coexisting in equilibrium. For multiphase systems, it is known that the geometry of the interface impacts the equilibrium state; this effect has been well-studied in single component systems with spherical interfaces. However, multicomponent phase diagrams are usually calculated assuming a planar interface between phases. Recent experimental and theoretical work has started to investigate the effect of curved interfaces on multicomponent phase equilibrium, but these analyses have been limited to isothermal conditions or to a portion of the isobaric phase diagram. Herein, we consider complete vapor-liquid phase diagrams (both bubble and dew lines) under isobaric conditions. We use Gibbsian composite-system thermodynamics to derive the equations governing vapor-liquid equilibrium for systems with a spherical interface separating the phases. We validate our approach by comparing the predicted nitrogen/argon dew points with reported literature data. We then predict complete isobaric phase diagrams as a function of radius of curvature for an ideal methanol/ethanol system and for a nonideal ethanol/water system. We also determine how the azeotropic composition of ethanol/water changes. The effect of curvature on isobaric phase diagrams is similar to that seen on isothermal phase diagrams. This work extends the study of curved-interface multicomponent phase equilibrium to isobaric systems, expanding the conditions under which nanoscale systems, such as nanofluidic systems, shale gas reservoirs, and cloud condensation nuclei, can be understood.

The critical temperatures and pressures have been measured by the pulse-heating method for fifteen compounds: benzoic acid, 2-methylbenzoic acid, 3-methylbenzoic acid, 4-methylbenzoic acid, benzaldehyde, 4-methylbenzaldehyde, phenylmethanol, (4-methylphenyl)methanol, 2-carboxybenzaldehyde, 1,3-propanediol, 2,2-dimethyl-1,3-propanediol, methyl tetradecanoate, methyl hexadecanoate, methyl octadecanoate, and (Z)-9-methyl octadecenoate. The experimental critical properties have been compared with those estimated by the Wilson/Jasperson and Marrero/Gani methods.

The high-pressure vapor–liquid equilibria of butane/ethanol system and isobutane/ethanol system were measured by a minimum continuous flow method using a process gas chromatography at 313–403 K. Experimental PXY data were compared with references. The modified RK EOS parameters were regressed and PXY data were also compared with PSRK EOS.

In this work, the recently proposed Functional-Segment Activity Coefficient (F-SAC) model is revised and extended in order to simultaneously represent infinite dilution activity coefficient (IDAC), vapor–liquid (VLE), and liquid–liquid (LLE) equilibrium data. For this investigation, systems involving aromatics, alkanes, cycloalkanes, alkenes and n-Formylmorpholine were selected for the tests. The behavior of these mixtures vary from nearly ideal to partially miscible. A new parameter per group was introduced in order to better represent LLE data in wide temperature ranges. The revised model was calibrated with experimental IDAC and LLE (binary and ternary systems) data. F-SAC correlation results and predictions of VLE experiments were compared with different UNIFAC parametrizations available in the literature. For the systems tested, the proposed approach showed to be more general; there were good IDAC and LLE correlations as well as VLE predictions, all with a single parameter set.

A simple procedure has been proposed to estimate the Wilson parameters from molecular structures and pure-component properties. To evaluate the interaction energies due to attractive force between unlike molecules, the interaction parameters are required. These parameters can be obtained by using the empirical equations developed in this study with normal boiling points and solubility parameters. The procedure has been applied to binary mixtures containing various esters including isomers (ester + hydrocarbon and ester + alcohol) and it is found that vapor–liquid equilibria of the mixtures can successfully be predicted from pure-component properties alone.

In order to improve osseointegration for biomedical implants, it is crucial to understand the interactions between nanostructured surfaces and cells. In this study, TiO₂ nanowires were prepared via Vapor-Liquid-Solid (VLS) process with Sn as a metal catalyst in the tube furnace. Nanowires were grown with N₂ heat treatment with their size controlled by the agglomeration of Sn layers in various thicknesses. MC3T3-E1 (pre-osteoblast) were cultured on the TiO₂ nanowires for a week. Preliminary results of the cell culture showed that the cells adhere well on the TiO₂ nanowires.

This document describes the results of an investigation on the variation of the so-called fundamental derivative of gas dynamics, Γ, in the vapor–liquid critical region of well-measured substances, namely methane, carbon dioxide and water, for which accurate, scaled fundamental equations are available. The results demonstrate that for a pure fluid in the single-phase thermodynamic regime, Γ diverges to +∞ independent of the direction of approach of the vapor–liquid critical point. Furthermore, in the two-phase thermodynamic regime, Γ diverges to −∞ independent of the direction of approach of the vapor–liquid critical point. These two qualitative results, as well as the value of the exponent giving the power-law dependence of Γ along the critical isochore as a function of |T − TC|/T (T is the temperature and “C” indicates its critical point value), namely ≈−0.89, are similar for all pure, non-ionized fluids belonging to the class of 3-dimensional Ising-like systems, i.e., systems governed by short-range forces.

The main purpose of this study was to employ the algorithm of vapor–liquid–liquid–hydrate multiphase equilibrium to the multicomponent mixtures containing hydrogen. The Patel–Teja equation of state was used to perform the vapor–liquid–liquid (V–L HC –L W ) three-phase flash calculation and the Chen–Guo two-step hydrate model was employed to calculate the vapor–hydrate phase equilibria. This method is rather simple due to avoiding the complexity of simultaneous solution of the sophisticated equation group. The proposed algorithm was tested on gas-emulsion systems. The comparisons of calculated results with experimental data show that the proposed algorithm is very stable and effective.

Using canonical Monte Carlo simulations, the vapor-liquid phase diagrams of a square-well fluid confined in hard and weakly attractive cylindrical pores are calculated. The critical temperature shows a maximum as a function of the attraction strength between the fluid particle and the pore wall. This maximum is located where the fluid–fluid equals the wall–fluid interaction strengths. With the aid of combined density profiles in the axial and radial directions the maximum of the critical temperature is correlated with the structure of the confined fluid.

Vapor–liquid equilibrium (VLE) data for ternary systems of benzene + ethylbenzene, benzene + methylcyclohexane, toluene + methylcyclohexane, toluene + 1-hexene, toluene + cyclohexane, and toluene + ethyl benzene with ionic liquid of 1-methyl 3-octylimidazolium thiocyanate [Omim][SCN], were measured using headspace gas chromatography. The temperature was set at 323.15 K. The experimental data shows that the presence of ionic liquid improves the separation factors of these systems significantly. The VLE data of ternary systems were correlated using the Non Random Two Liquid (NRTL) model with a good accuracy.

Combining Peng–Robinson (PR) equation of state (EOS) with Liu et al.’s association contribution derived from shield-sticky model (SSM), a new cubic-plus-association (CPA) EOS is proposed to describe the thermodynamic properties of pure associating fluids and their mixtures. The CPA-SSM EOS contains five molecular parameters (a0, c1, b, ω and δɛ/k) for the pure associating fluids, while for non-associating fluids it reduces to PR EOS with three molecular parameters (a0, c1, b). The molecular parameters are obtained by fitting the saturated pressures and/or liquid molar volumes at wide temperature ranges. The overall average absolute deviations (AADs) of 58 pure associating fluids and 20 non-associating fluids are 0.74% and 0.54% for saturated vapor pressure, 2.00% and 1.85% for liquid molar volumes respectively. The enthalpies of vaporization for 13 pure associating fluids are well predicted by using these molecular parameters. The molecular parameter b for homologous substances shows a good linear relationship with respect to their corresponding molecular weights. Using one temperature-independent binary adjustable parameter kij, satisfactory results of vapor–liquid equilibria (VLE) for both self- and cross-associating systems are obtained. The overall AADs of the equilibrium temperatures, pressures and vapor phase mole fractions are 1.46 K, 1.26 kPa and 0.0197 respectively for 25 self-associating systems, and 0.75 K, 0.50 kPa and 0.0155 respectively for 29 cross-associating systems. Other caloric properties such as the excess molar enthalpies of mixing are also successfully computed. The CPA-SSM EOS proposed has been proved to have comparable accuracy as other models but with much simpler form.