Modeling the phase behavior of H2S+n-alkane binary mixtures using the SAFT-VR+D approach

A statistical associating fluid theory for potential of variable range has been recently developed to model dipolar fluids (SAFT-VR+D) [Zhao and McCabe, J. Chem. Phys. 2006, 125, 104504]. The SAFT-VR+D equation explicitly accounts for dipolar interactions and their effect on the thermodynamics and structure of a fluid by using the generalized mean spherical approximation (GMSA) to describe a reference fluid of dipolar square-well segments. In this work, we apply the SAFT-VR+D approach to real mixtures of dipolar fluids. In particular, we examine the high-pressure phase diagram of hydrogen sulfide+n-alkane binary mixtures. Hydrogen sulfide is modeled as an associating spherical molecule with four off-center sites to mimic hydrogen bonding and an embedded dipole moment (micro) to describe the polarity of H2S. The n-alkane molecules are modeled as spherical segments tangentially bonded together to form chains of length m, as in the original SAFT-VR approach. By using simple Lorentz-Berthelot combining rules, the theoretical predictions from the SAFT-VR+D equation are found to be in excellent overall agreement with experimental data. In particular, the theory is able to accurately describe the different types of phase behavior observed for these mixtures as the molecular weight of the alkane is varied: type III phase behavior, according to the scheme of classification by Scott and Konynenburg, for the H2S+methane system, type IIA (with the presence of azeotropy) for the H2S+ethane and+propane mixtures; and type I phase behavior for mixtures of H2S and longer n-alkanes up to n-decane. The theory is also able to predict in a qualitative manner the solubility of hydrogen sulfide in heavy n-alkanes.     

Predicting mixture phase equilibria and critical behavior using the SAFT-VRX approach

The SAFT-VRX equation of state combines the SAFT-VR equation with a crossover function that smoothly transforms the classical equation into a nonanalytical form close to the critical point. By a combinination of the accuracy of the SAFT-VR approach away from the critical region with the asymptotic scaling behavior seen at the critical point of real fluids, the SAFT-VRX equation can accurately describe the global fluid phase diagram. In previous work, we demonstrated that the SAFT-VRX equation very accurately describes the pvT and phase behavior of both nonassociating and associating pure fluids, with a minimum of fitting to experimental data. Here, we present a generalized SAFT-VRX equation of state for binary mixtures that is found to accurately predict the vapor-liquid equilibrium and pvT behavior of the systems studied. In particular, we examine binary mixtures of n-alkanes and carbon dioxide + n-alkanes. The SAFT-VRX equation accurately describes not only the gas-liquid critical locus for these systems but also the vapor-liquid equilibrium phase diagrams and thermal properties in single-phase regions.     

Solid-liquid equilibrium using the SAFT-VR equation of state: Solubility of naphthalene and acetic acid in binary mixtures and calculation of phase diagrams

A solid-liquid equilibrium (SLE) thermodynamic model based on the SAFT-VR equation of state (EOS) is presented. The model allows for the calculation of solid-liquid phase equilibria in binary mixtures at atmospheric pressure. The fluid (liquid) phase is treated with the SAFT-VR approach, where molecules are modelled as associating chains of tangentially bonded spherical segments interacting via square-well potentials of variable range. The equilibrium between the liquid and solid phase is treated following a standard thermodynamic method that requires the experimental temperature and enthalpy of fusion of the solute. The model is used to calculate the solubilities of naphthalene and acetic acid in common associating and non-associating organic solvents and to determine the solid-liquid phase behaviour of binary mixtures with simple eutectics. The SAFT-VR pure component model parameters are determined by comparison to experimental vapour pressure and saturated liquid density data with the choice of association models according to the nature of the molecule; in addition, an unlike adjustable parameter (k_ij) is used to model the solutions. The solubility data of naphthalene and acetic acid in both associating and non-associating solvents are reproduced essentially within the accuracy of the experimental measurements. The phase boundaries and the position of the eutectic points in the binary mixtures considered are, in most cases, reproduced with the accuracy commensurate with the industrial applications. Overall, the results presented show that the SAFT-VR EOS can be used with confidence for the prediction of the SLE of binary systems at atmospheric pressure.     

Equation of state modeling of the phase equilibria of ionic liquid mixtures at low and high pressure

Accurate design of processes based on ionic liquids (ILs) requires knowledge of the phase behavior of the systems involved. In this work, the truncated perturbed chain polar statistical associating fluid theory (tPC-PSAFT) is used to correlate the phase behavior of binary and ternary IL mixtures. Both non-polar and polar solvents are examined, while methyl imidazolium ILs are used in all cases. tPC-PSAFT accounts explicitly for weak dispersion interactions, highly directive polar interactions between permanent dipolar and quadrupolar molecules and association between hydrogen bonding molecules. For mixtures of non-polar solvents, tPC-PSAFT predicts accurately the binary mixture data. For the case of polar solvents, a binary interaction parameter is fitted to the experimental data and the agreement between experiment and correlation is very good in all cases.     

Liquid mixtures of xenon with fluorinated species: xenon + sulfur hexafluoride

The vapor-liquid equilibrium of binary mixtures of xenon + SF6 has been measured at nine temperatures from 235.34 to 295.79 K and pressures up to 6.5 MPa. The mixture critical line is found to be continuous between the critical points of the pure components, and hence, the system can be classified as type I phase behavior in the scheme of van Konynenburg and Scott. The excess Gibbs free energies have been calculated, and the experimental results have been interpreted using the statistical associating fluid theory for potentials of variable range (SAFT-VR). Additionally, the SAFT-VR equation has been used to model other systems involving SF6 and alkanes, illustrating the predictability of the approach and further demonstrating the transferability of parameters between binary mixtures involving alkanes and xenon.     

Predicting thermophysical properties of biodiesel fuel blends using the SAFT-VR approach

Modeling of thermophysical properties and phase equilibria of long-chain methylesters mixtures are presented, using the SAFT-VR approach for mixtures. Molecules are represented as chains of spherical segments that can associate due to the presence of short-ranged attractive sites, using previous molecular parameters obtained for pure fatty acid methyl esters. These attractive sites as well as the intermolecular interactions between monomers segments are modeled via variable-ranged square-well potentials. The cross-energy binary-interaction parameter of the extended Berthelot combining rule was fitted to liquid densities and speed of sound. Very good predictions are obtained for isochoric heat capacities and for binary and ternary phase diagrams.     

Consideration of dipole–quadrupole interactions in molecular based equations of state

The thermodynamic behaviour of a number of real substances is determined by dipolar as well as quadrupolar interactions of the molecules. In equations of state (EOS) like, e.g. BACKONE separate contributions to the Helmholtz energy for the dipolar and the quadrupolar interactions are considered but no cross contributions. Here, the concept of effective dipole and quadrupole contributions is suggested in which the effective dipole strength μ_e is influenced by the quadrupole cross interaction. Similarily, the effective quadrupole strength Q_e takes into account the dipole cross interaction. In order to arrive at these effective dipolar and quadrupolar strengths, molecular simulations are performed. From the simulation results correlation equations are derived which are used in combination with BACKONE for the calculation of vapour–liquid equilibria (VLE) of real mixtures. By using these effective moments, the only required binary mixing rule parameter k_ij tends to small values of about 0.01 and becomes temperature-independent. Moreover, the VLE pressures are predicted now considerably better than without consideration of the cross contributions.     

Thermodynamic modeling of hydrogen sulfide solubility in ionic liquids using modified SAFT-VR and PC-SAFT equations of state

Equations of state based on the statistical associating fluid theory for potentials of variable range (SAFT-VR) and the perturbed chain statistical associating fluid theory (PC-SAFT) have been used to model the PVT behavior of ionic liquids and the solubility of H₂S in six imidazolium-based ionic liquids. The studied systems included [bmim][PF6], [hmim][PF6], [bmim][BF4], [hmim][BF4], [bmim][NTF2] and [hmim][NTF2] at various temperatures and pressures.For pure components, parameters of the models have been obtained by fitting the models to experimental data on liquid densities; the average relative deviation between the calculated and experimental densities for ionic liquids is less than 2.42% in the PC-SAFT model and 5.44% in the SAFT-VR approach, the latter which incorporates the square-well potential for short-range interactions. In both models an additional term has been added to account for dipole-dipole interactions between solute molecules resulting from the permanent charges on the chain molecules of the solvents. The model parameters have also been correlated as functions of the molecular weight of the solvents. For binary mixtures of ionic liquids and H₂S, the association interactions between H₂S molecules and between the ionic liquids and H₂S molecules have also been taken into account in both approaches, using binary interaction coefficients. The results show an average deviation of less than 5% in the calculation of the mole fraction of H₂S in the ionic liquids. The effect of inclusion of the polar term has been studied for binary systems in both models.     

Application of the Perturbed-Chain SAFT equation of state to polar systems

The Perturbed-Chain SAFT (PC-SAFT) equation of state is applied to pure polar substances as well as to vapor–liquid and liquid–liquid equilibria of binary mixtures containing polar low-molecular substances and polar co-polymers. For these components, the polar version of the PC-SAFT model requires four pure-component parameters as well as the functional-group dipole moment. For each binary system, only one temperature-independent binary interaction k_ij is needed. Simple mixing and combining rules are adopted for mixtures with more than one polar component without using an additional binary interaction parameter. The ability of the model to accurately describe azeotropic and non-azeotropic vapor–liquid equilibria at low and at high pressures, as well as liquid–liquid equilibria is demonstrated for various systems containing polar components. Solvent systems like acetone–alkane mixtures and co-polymer systems like poly(ethylene-co-vinyl acetate)/solvent are discussed. The results for the low-molecular systems also show the predictive capabilities of the extended PC-SAFT model.     

Computer simulation studies of anisotropic systems XXIX. Quadrupolar Gay-Berne discs and chemically induced liquid crystal phases

Liquid crystal phases can be induced chemically by mixing compounds whose specific interactions are such that the transition temperature for the induced phase is higher than the melting points of the two compounds. A particularly dramatic example of such behaviour is the creation of a columnar nematic and a hexagonal columnar phase on mixing discotic multiynes with 2,4,7-trinitrofluorenone. Although the intense colour of the mixture indicates a strong charge-transfer band, it is uncertain as to whether the charge-transfer interaction between unlike molecules is enough to stabilize the induced liquid crystal phases. An alternative explanation for the formation of such phases involves an electrostatic quadrupolar interaction between the components,whose quadrupole moments differ in sign. This interaction weakens the face-to-face attraction for like particles while strengthening it for unlike particles. We have explored this possible explanation for chemically induced liquid crystal phases in discotic systems by modelling the basic interaction between discs with a Gay-Berne potential, to which is added a point quadrupolar interaction. We have determined the phase behaviour of the pure systems and their binary mixtures with constant pressure Monte Carlo simulations. It would seem that the quadrupolar interaction can account for many of the features of chemically induced liquid crystals.     

Model phase diagrams of binary nematic mixtures. A comparative study between linear and crosslinked polymers

Model calculations of phase diagrams of side chain liquid crystal polymers (SCLCP) and low molecular weight liquid crystals (LMWLC) are presented. The polymer is assumed to have grafted side chain units characterized by a nematic‐isotropic transition temperature T_{NI 2}, and the LMWLC presents also a similar transition at a temperature T_{NI 1} . The model calculations can accommodate for the cases where the latter two temperatures are comparable or widely different. For the sake of illustration, the case T_{NI 1} = 60°C and T_{NI 2} = 80°C is adopted here. The main point of interest here is to perform a comparative study of the equilibrium phase diagrams of SCLCP made either of linear free chains or crosslinked chains forming a single network. To our knowledge this is the first comparative study of the phase behavior of binary nematic mixtures involving linear and crosslinked polymer matrices which permits to clearly identify the effects of crosslinks present in the polymer matrix. The crosslinks attribute elasticity to the polymer constituent which induces important distortions in the phase diagram. To highlight these distortions, examples of hypothetical binary nematic mixtures are chosen involving both linear and crosslinked polymers with side chain mesogen units. The quadrupole interaction parameter between the two nematogens is related to individual parameters via a geometric average ν²₁₂ = κν₁₁ν₂₂ with a coupling parameter κ. Different values of this parameter are considered and the impact of coupling strength on the phase diagram is discussed for crosslinked and linear polymers.     

Electric polarization effects on the electronic spectral shift of centrosymmetric compounds

The classic dielectric dipolar Onsager model was extended to include quadrupolar interactions between solute molecules and solvents with different polarities. A multiparametric solvatochromic expression, based on the point quadrupole moment inside a spherical cavity embedded in a dielectric continuum, is applied to centrosymmetric sulfonamide porphyrins, zinc tetraphenyl porphyrin, squaraine and 9,10-dicyanoanthracene, in order to account for the quadrupolar polarization effect of solute molecules. The reaction field polarity functions created respectively by dipole and quadrupole moments are compared and found to be linearly correlated.     

Efficient prediction of thermodynamic properties of quadrupolar fluids from simulation of a coarse-grained model: the case of carbon dioxide

Monte Carlo simulations are presented for a coarse-grained model of real quadrupolar fluids. Molecules are represented by particles interacting with Lennard-Jones forces plus the thermally averaged quadrupole-quadrupole interaction. The properties discussed include the vapor-liquid coexistence curve, the vapor pressure along coexistence, and the surface tension. The full isotherms are also accessible over a wide range of temperatures and densities. It is shown that the critical parameters (critical temperature, density, and pressure) depend almost linearly on a quadrupolar parameter q=Q(*4)T*, where Q* is the reduced quadrupole moment of the molecule and T* the reduced temperature. The model can be applied to a variety of small quadrupolar molecules. We focus on carbon dioxide as a test case, but consider nitrogen and benzene, too. Experimental critical temperature, density, and quadrupolar moment are sufficient to fix the parameters of the model. The resulting agreement with experiments is excellent and marks a significant improvement over approaches which neglect quadrupolar effects. The same coarse-grained model was also applied in the framework of perturbation theory in the mean spherical approximation. As expected, the latter deviates from the Monte Carlo results in the critical region, but is reasonably accurate at lower temperatures.     

Prediction of thermodynamic behavior of binary mixtures by applying the crossover approach to Soave–Redlich–Kwong equation of state

Thermodynamic analysis of binary mixtures near the critical region is essential for many chemical process designs. In this research, based on isomorphism principle and incorporating general crossover approach the original Soave–Redlich–Kwong (SRK) equation of state (EOS) was developed for the binary mixtures. We have introduced an additional term in the crossover function in order to take into account the difference between the classical critical parameters and the real critical parameters. The applicability of this crossover EOS was verified against methane–ethane mixture to describe their thermodynamic properties over a wide range of thermodynamic states, because of their wide applications. It is shown that based on this approach we can received too much more accuracy for predicting thermodynamic properties in comparison with classical form of SRK EOS.