A description of phase equilibria in nonideal systems with the use of integral equation theory

Integral equation theory for partial distribution functions was used to consider a method for calculations of vapor-liquid phase equilibrium conditions in binary Lennard-Jones systems with substantial deviations from the Berthelot-Lorentz mixing rules. Possible sources of errors in pressure and chemical potential values and methods for refining the results were analyzed. The required accuracy of calculations can be reached using two parameters only, one in the closure to the Ornstein-Zernike equation and the other in the equation for the chemical potential. These parameters are determined independently from two thermodynamic equations.     

Phase separation of model adsorbates in random matrices

The liquid-liquid phase behavior of binary mixtures in random pores is investigated with non-additive hard spheres using both ROZ (Replica Ornstein-Zernike) integral equations and cavity biased grand canonical Monte Carlo simulations. The critical densities of the coexistence phase envelopes are determined as function of the non-additivity parameter Delta, varying from Delta = 0.2, 0.4, 0.6, up to 0.8. The matrix is made of quenched hard spheres. Its porosity is varied to ascertain the effects of confinement, with packing densities rho(0) ranging from 0.1, 0.3, to 0.5. To obtain fiduciary results from ROZ, we use the accurate ZSEP closure relation proposed earlier with and without thermodynamic consistency. The ZSEP closure is known to enforce the zero-separation theorems via special adjustable parameters in the bridge function. Two versions of this closure are used to assess their accuracies (vis-à-vis the Monte Carlo data): first ZSEP-T, namely, the ZSEP closure with added thermodynamic consistency (the Gibbs-Duhem relation); and second purely ZSEP without adding thermodynamic consistency. It is found that both closures give correct qualitative trend, with errors of ZSEP falling within 8-9%, while ZSEP-T, being more accurate, to within 1-2%. As non-additivity is increased, both versions become more accurate. The critical density rho(c) is found to decrease with decreasing porosity. In addition, rho(c) also decreases with increasing Delta, in a non-monotone fashion.     

Fluid-phase diagrams of binary mixtures from constant pressure integral equations

A new algorithm for solving integral equations of the theory of liquids at fixed pressure is introduced. Combining this technique with the Lee's star function approximation for the chemical potentials, we obtain an efficient method to investigate fluid-phase diagrams of binary mixtures. We have tested the capabilities of such technique to study symmetric and asymmetric phase diagrams in nonadditive hard spheres and Lennard-Jones mixtures. We find that the integral equation theories, although approximate, can provide a flexible tool to determine the fluid-phase diagrams whose accuracy is critically dependent on the quality of the closure and of the resulting chemical potentials.     

Thermodynamic consistency of experimental VLE data for asymmetric binary mixtures at high pressures

A thermodynamic consistency of isothermal vapor–liquid equilibrium data for 9 non-polar and 8 polar binary asymmetric mixtures at high pressures has been evaluated. A method based on the isothermal Gibbs–Duhem equation was used for the test of thermodynamic consistency using a Φ–Φ approach. The Peng–Robinson equation of state coupled with the Wong–Sandler mixing rules were used for modeling the vapor–liquid equilibrium (VLE) within the thermodynamic consistency test. The VLE parameters calculations for asymmetric mixtures at high pressures were highly dependent on bubble pressure calculation, making more convenient to eliminate the data points yielding the highest deviations in pressure. However the results of the thermodynamic consistencies test of experimental data for many cases were found not fully consistent. As a result, the strategies for solving these problems were discussed in detailed.     

A molecular theory for the thermodynamic behavior of polar mixtures. II. Development of an equation of state based on the local composition mixing rules

In this study, the essential features of a molecular theory developed earlier for the local composition model in solution thermodynamics is used as the basis for more applied calculations of vapor-liquid equilibria for mixtures of molecules vastly different in size, polarity, and strength of interaction. An accurate equation of state is introduced into the method by incorporating the Helmholtz free energy through the Gibbs-Helmholtz relation. In the local composition mixing rules, the interaction energy effects are represented by a multifluid model, while molecular size effects are represented by a one-fluid model, which in spirit corresponds to a mean density approximation for the molecular pair distribution functions. Calculations of the vapor-liquid equilibria of a wide variety of binary mixtures including nonpolar hydrocarbons, hydrogen-bonding alcohols, water, ammonia , and carbon dioxide show good agreement with experimental data.     

Effect of three-body interactions on the vapor-liquid phase equilibria of binary fluid mixtures

Gibbs-Duhem Monte Carlo simulations are reported for the vapor-liquid phase coexistence of binary argon+krypton mixtures at different temperatures. The calculations employ accurate two-body potentials in addition to contributions from three-body dispersion interactions resulting from third-order triple-dipole interactions. A comparison is made with experiment that illustrates the role of three-body interactions on the phase envelope. In all cases the simulations represent genuine predictions with input parameters obtained independently from sources other than phase equilibria data. Two-body interactions alone are insufficient to adequately describe vapor-liquid coexistence. In contrast, the addition of three-body interactions results in very good agreement with experiment. In addition to the exact calculation of three-body interactions, calculations are reported with an approximate formula for three-body interactions, which also yields good results.     

Molecular Thermodynamics for Chemical Process Design

Thermodynamic properties are essential for quantitative process design to produce chemical products. Caloric properties are required for heat balances, but these properties are usually available or estimated easily. More important—and often much more difficult to estimate—are the chemical potentials of components in mixtures; it is these potentials which determine phase equilibria, as required for separation operations, and chemical equilibria, as required for chemical reactors and for separation operations based on chemical reactions. Molecular thermodynamics is an engineering-oriented science for calculating the desired chemical potentials from a minimum of experimental data. This applied science, based on classical and statistical thermodynamics, yields chemical potentials through models that are based on molecular physics and physical chemistry. Selected examples are cited to illustrate the applicability of molecular thermodynamics: group-contribution methods for obtaining chemical potentials in highly nonideal mixtures as required for distillation-column and process-safety design; equation of state for precipitation of uniform-sized crystals from supercritical fluids; molecular-orbital calculations to guide process development for alternatives to environmentally dangerous chlorofluorohydrocarbons; molecular-simulation calculations for separation of gas mixtures with porous adsorbents; equilibria in two-phase aqueous systems for separation of protein mixtures; and, finally, extended polymer-solution thermodynamics to guide synthesis of hydrogels suitable for protein recovery from soybeans and for novel drug-delivery devices.     

A modification of Newton-Raphson algorithm for phase equilibria calculations using numerical differentiation of the gibbs energy

Deiters, U.K., 1985. A modification of Newton-Raphson algorithm for phase equilibria calculations using numerical differentiation of the Gibbs energy. Fluid Phase Equilibria, 19: 287-293.For the solution of the system of nonlinear equation describing the phase equilibrium conditions in fluid mixtures a modified Newton-Raphson method is proposed, which uses numerical differentiation to obtain the chemical potentials. For binary mixtures the new algorithm a little faster, because the same intermediate results that are required for the chemical potentials are also used for the construction of the Jacobian matrix.     

The special features of molecular transport in nanosized channels

The molecular theory of the transport of pure substances and mixtures of molecules of different shapes in narrow slit-like pores, in which the potential of surface forces creates a strongly anisotropic distribution of molecules across pores and thereby makes the hydrodynamics equation inapplicable, is considered. The new microhydrodynamic approach is based on the lattice gas model, which takes into account the intrinsic volume of molecules and intermolecular interactions in the quasi-chemical approximation. Self-consistent calculations of dissipative coefficients taking nonlocal fluid properties into account were performed on the basis of the transition state model including information about equilibrium adsorbate distribution. Changes in fluid concentrations from the gaseous to liquid state and a broad temperature range, including the critical region, are analyzed. This allows vapor, liquid, and vapor-liquid fluid flows to be considered in the presence of capillary condensation. An increase in the size of pores transforms the equations of the theory into hydrodynamic transfer equations for gas or liquid flows, while preserving the relation of transfer coefficients to intermolecular potentials. The use of microhydrodynamic approach equations in numerical calculations and the possibility of applying this approach are discussed.     

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

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

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.     

室温离子液体混合物的相平衡研究进展

室温离子液体混合物的相平衡数据是设计和优化涉及离子液体的化学反应与分离工程的重要基础。本文综述了近年来室温离子液体混合物,特别是室温离子液体＋有机物体系的气－液平衡、液－液平衡和固－液平衡的研究进展,总结了这些混合物相行为的基本热力学规律以及对萃取分离工程的指导作用。     

The calculation of vapor-liquid coexistence curve of Morse fluid: application to iron

The vapor-liquid coexistence curve of Morse fluid was calculated within the integral equations approach. The critical point coordinates were estimated. The parameters of Morse potential, fitted for elastic constants in solid phase, were used here to apply the results of present calculations to the determination of iron binodal. The properties of copper and sodium were considered in an analogous way. The calculations of pair correlation functions and isobars at liquid phase have shown that only for sodium these potential parameters allow one to obtain agreement with the measurements data. For iron another parameters are necessary to get this agreement in liquid phase. However, they give rise to very low critical temperature and pressure with respect to the estimates of other authors. Consequently, one can suppose that Morse potential is possibly inapplicable to the calculation of high temperature properties of non-alkali metals in disordered phases.     

Computer simulation study of the global phase behavior of linear rigid Lennard-Jones chain molecules: comparison with flexible models

The global phase behavior (i.e., vapor-liquid and fluid-solid equilibria) of rigid linear Lennard-Jones (LJ) chain molecules is studied. The phase diagrams for three-center and five-center rigid model molecules are obtained by computer simulation. The segment-segment bond lengths are L = sigma, so that models of tangent monomers are considered in this study. The vapor-liquid equilibrium conditions are obtained using the Gibbs ensemble Monte Carlo method and by performing isobaric-isothermal NPT calculations at zero pressure. The phase envelopes and critical conditions are compared with those of flexible LJ molecules of tangent segments. An increase in the critical temperature of linear rigid chains with respect to their flexible counterparts is observed. In the limit of infinitely long chains the critical temperature of linear rigid LJ chains of tangent segments seems to be higher than that of flexible LJ chains. The solid-fluid equilibrium is obtained by Gibbs-Duhem integration, and by performing NPT simulations at zero pressure. A stabilization of the solid phase, an increase in the triple-point temperature, and a widening of the transition region are observed for linear rigid chains when compared to flexible chains with the same number of segments. The triple-point temperature of linear rigid LJ chains increases dramatically with chain length. The results of this work suggest that the fluid-vapor transition could be metastable with respect to the fluid-solid transition for chains with more than six LJ monomer units.     

Ab-initio calculations on large molecules and solids by desirable computational procedures

Desirable computational procedures developed here recently for ab-initio calculations on large molecules are outlined. Effective core model potentials (MODPOT) permit calculations of valence electrons only explicitly, yet accurately; a charge-conserving integral prescreening evaluation to decide whether a block of integrals will be larger than a preset threshold and thus be calculated explicitly is effective for spatially extended systems; an efficient MERGE technique to save and reuse common invariant skeletal integrals is useful for geometry variations and for adding basis fcuntions, substituent groups and molecules; and an effective configuration interaction (CI) Hamiltonian into which are folded the effects of the occupied molecular orbitals from which no excitations are allowed is useful for molecular decompositions and intermolecular reactions. These techniques have been extended for CI calculations on breaking a chemical bond in a molecule in a crystal or solid; atom-class/atomic-class potential functions and dispersion calculations have been added. In a new program, POLY-CRYST, all the integral strategies for large molecules are meshed.     

Prediction of the thermophysical properties of pure neon, pure argon, and the binary mixtures neon-argon and argon-krypton by Monte Carlo simulation using ab initio potentials

Gibbs ensemble Monte Carlo simulations were used to test the ability of intermolecular pair potentials derived ab initio from quantum mechanical principles, enhanced by Axilrod-Teller triple-dipole interactions, to predict the vapor-liquid phase equilibria of pure neon, pure argon, and the binary mixtures neon-argon and argon-krypton. The interaction potentials for Ne-Ne, Ar-Ar, Kr-Kr, and Ne-Ar were taken from literature; for Ar-Kr a different potential has been developed. In all cases the quantum mechanical calculations had been carried out with the coupled-cluster approach [CCSD(T) level of theory] and with correlation consistent basis sets; furthermore an extrapolation scheme had been applied to obtain the basis set limit of the interaction energies. The ab initio pair potentials as well as the thermodynamic data based on them are found to be in excellent agreement with experimental data; the only exception is neon. It is shown, however, that in this case the deviations can be quantitatively explained by quantum effects. The interaction potentials that have been developed permit quantitative predictions of high-pressure phase equilibria of noble-gas mixtures.     

The QCHB model of fluids and their mixtures

The essentials of the QCHB (quasi-chemical hydrogen-bonding) equation-of-state model are presented along with some applications for calculations of phase equilibria and interfacial properties of fluids and their mixtures. This is a model applicable to non-polar systems as well as to highly non-ideal systems with strong specific interactions, to systems of small molecules as well as to macromolecules, including polydisperse polymers, glasses, and gels, to liquids as well as to vapours including supercritical systems, to homogeneous as well as to inhomogeneous systems. A quasi-thermodynamic approach of inhomogeneous systems is used for modeling the fluid–fluid interface. Consistent expressions for the interfacial tension and interfacial profiles for various properties are presented. A satisfactory agreement is obtained between experimental and calculated surface tensions. Extension of the approach to mixtures is examined along with the associated problems for the numerical calculations of the interfacial profiles. A new equation is derived for the chemical potentials in the interfacial region, which facilitates very much the calculation of the composition profiles across the interface. The relation of the model with the COSMO-RS approach is also discussed.     

Surface tension of quantum fluids from molecular simulations

We present the first molecular simulations of the vapor-liquid surface tension of quantum liquids. The path integral formalism of Feynman was used to account for the quantum mechanical behavior of both the liquid and the vapor. A replica-data parallel algorithm was implemented to achieve good parallel performance of the simulation code on at least 32 processors. We have computed the surface tension and the vapor-liquid phase diagram of pure hydrogen over the temperature range 18-30 K and pure deuterium from 19 to 34 K. The simulation results for surface tension and vapor-liquid orthobaric densities are in very good agreement with experimental data. We have computed the interfacial properties of hydrogen-deuterium mixtures over the entire concentration range at 20.4 and 24 K. The calculated equilibrium compositions of the mixtures are in excellent agreement with experimental data. The computed mixture surface tension shows negative deviations from ideal solution behavior, in agreement with experimental data and predictions from Prigogine's theory. The magnitude of the deviations at 20.4 K are substantially larger from simulations and from theory than from experiments. We conclude that the experimentally measured mixture surface tension values are systematically too high. Analysis of the concentration profiles in the interfacial region shows that the nonideal behavior can be described entirely by segregation of H(2) to the interface, indicating that H(2) acts as a surfactant in H(2)-D(2) mixtures.