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.     

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。     

Molecular thermodynamics for some applications in biotechnology

As biotechnology sweeps the world, it is appropriate to remember that the great virtue of thermodynamics is its broad range of applicability. As a result, there is a growing literature describing how chemical thermodynamics can be used to inform processes for old and new biochemical products for industry and medicine. A particular application of molecular thermodynamics concerns separation of aqueous proteins by selective precipitation. For this purpose, we need phase diagrams; for constructing such diagrams, we need to understand not only the qualitative nature of phase equilibria of aqueous proteins but also the quantitative intermolecular forces between proteins in solution. Some examples are given to show how aqueous protein–protein forces can be calculated or measured to yield a potential of mean force and how that potential is then used along with a statistical thermodynamic model to establish liquid–liquid and liquid–crystal equilibria. Such equilibria are useful not only for separation processes but also for understanding diseases like Alzheimer’s, cataracts and sickle-cell anemia that appear to be caused by protein agglomeration.

     

FROM UNIT OPERATIONS TO SEPARATION PROCESSES 1

The Arthur D. Little concept of unit operations embodied a number of different methods of separating mixtures and represented a major advance in chemical engineering. Over time, those and subsequent concepts have evolved into a unified field of separation processes. The ways in which this happened are traced. The more unified view of separations enables more coherent and powerful approaches for process selection and design, reducing energy requirements, for selecting separating agents, understanding the complex interactions of mass transfer and phase equilibria, and identifying new methods for separating complex mixtures. As such, separation processes provide one of the most effective vehicles for teaching and understanding the engineering of chemical processes.     

Molecular surface electrostatic potentials of anticonvulsant drugs

The computed molecular surface electrostatic potentials of a group of anticonvulsants of various chemical types were investigated with the objective of identifying common features that may be related to their activities. The calculations were carried out with the density functional B3P86/6-31G* procedure, using HF/STO-3G*-optimized geometries. Analysis of several statistically based properties of the surface potentials indicates that the negative regions are of primary importance and that an optimum intermediate level of local polarity, or internal charge separation, is required. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 1137–1143, 1998     

On the thermodynamics of alcohol solutions. Phase equilibria of binary and ternary mixtures containing any number of alcohols

Nagata, I., 1985. On the thermodynamics of alcohol solutions. Phase equilibria of binary and ternary mixtures containing any number of alcohols. Fluid Phase Equilibria, 19: 153–174.Binary vapor—liquid and liquid—liquid equilibrium data for alcohol solutions includin one or two alcohols are correlated with the UNIQUAC associated solution theory (Nagata and Kawamura). The theory uses pure liquid association constants determined by the method of Brandani and a single value of the enthalpy of the hydrogen bond equal to ?23.2 kJ mol ^?1 for pure alcohols. For alcohol-active nonassociating component mixtures and alcohol—alcohol mixtures the theory involves additional solvation constants. The theory is extended to contain ternary mixtures with any number of alcohols. Ternary predictions of vapor—liquid and liquid—liquid equilibria are performed using only binary parameters. Good agreement is obtained between calculated and experimental results for many representative mixtures.     

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.     

Thermodynamics of mixtures containing a very strongly polar compound: IV – application of the DISQUAC,UNIFAC and ERAS models to DMSO+ organic solvent systems

Binary mixtures of dimethylsulfoxide (DMSO) with alkane, benzene, toluene 1-alkanol, or 1-alkyne have been investigated in terms of DISQUAC. The corresponding interaction parameters are reported. ERAS parameters for 1-alkanol + DMSO mixtures are also given. ERAS calculations were developed considering DMSO as a not self-associated compound.

DISQUAC represents fairly well a complete set of thermodynamic properties: molar excess enthalpies, molar excess Gibbs energies, vapor–liquid equilibria, natural logarithms of activity coefficients at infinite dilution, or partial molar excess enthalpies at infinite dilution. DISQUAC improves UNIFAC calculations for H ^E . Both models yield similar results for VLE. In addition, DISQUAC also improves, ERAS results for 1-alkanol + DMSO mixtures. This may be due to ERAS cannot represent the strong dipole–dipole interactions present in such solutions.     

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.     

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.     

Liquid Structure and Thermodynamics of Alkane Mixtures

Spectroscopic investigations and light scattering experiments with saturated, liquid hydrocarbons and their mixtures indicate a specific and distinct influence of the constitution, conformation, and flexibility of the molecule on the structure and macroscopic behavior of such liquids. Orientational order present in pure liquid n-alkanes, for example, characteristically affects the thermodynamic mixing properties, such as the enthalpy of mixing ΔH_M and the entropy of mixing ΔS_M , when these liquids are mixed with each other, or with other liquids. Nowadays it is possible to determine thermodynamic mixing properties experimentally with such precision that systematic investigations of these properties allow the behavior of liquids to be studied qualitatively and–with molecular theories of liquids–to some extent also quantitatively. The latest results in this respect, exemplified by mixtures of alkanes, are discussed. These results not only demonstrate the progress made in understanding the relations between molecular (microscopic) and macroscopic properties, but are also of importance for industrial applications (e.g. separation processes) in which mixtures of hydrocarbons are involved.     

Thermodynamics of associated mixtures of the Mecke—Kempter type

A chain-forming associated solution theory based on the UNIQUAC equation is presented for alcohol-unassociated active component liquid mixtures of the Mecke—Kempter type. The capability of the theory in reproducing the excess Gibbs free energy and excess enthalpy data for many binary mixtures is successfully shown. Ternary extension of the theory is presented in the calculations of vapor—liquid and liquid—liquid equilibria and excess enthalpy data from binary data.     

Surface phase separation in complex mixed adsorbing systems: an interface-bulk coupling effect

The interfacial thermodynamics and structure of ternary mixtures of the type A+B+solvent are investigated. According to the Gibbs phase rule, the coupling between the bulk phase and the interfacial region-which is related to the reversibility of the adsorption of the corresponding species-is a determinant as to whether phase separation can be observed at the interface. For an n-component adsorbing solution, at least one of the species has to adsorb irreversibly over the experimental time scales in order not to fix more intensive variables than those required to observe surface phase separation. We present results for a lattice model planar interface consisting of the ternary mixture A+B+solvent. The solvent molecules and the type A molecules have fixed chemical potentials at the interface since they are equilibrated with a bulk solution. In contrast, the type B molecules are irreversibly adsorbed at the interface and do not equilibrate with the bulk. Mean-field theory is compared with Monte Carlo simulation. Interestingly, the spinodal line in the interaction-composition plane shows a reentrant on the B-rich phase side. We discuss the implications of these results for surface phase separation of adsorbing mixtures of proteins and low-molecular-weight surfactants.     

Polydispersity Effects on the Demixing Behavior of Poly(Vinyl Methyl Ether)/Polystyrene Blends

Phase equilibrium calculations for solutions or mixtures of synthetic polymers become considerably more difficult when there is polydispersity of the polymers. To simplify the calculations, polydispersity is often neglected in the calculations or accounted for in a summary way only, and often only relatively simple free energy relations are applied. For example, Halary et al. published experimental demixing data on poly(vinyl methyl ether)/polystyrene blends. In evaluating the data the following assumptions were made: 1) the minimum of the demixing curve equals the critical point, 2) the X-parameter is independent of concentration and molecular weight, 3) the polydispersity may be roughly taken into account by using the formulas for monodisperse polymers and using the weight-average molecular weight. Continuous thermodynamics proves to be a suitable method to overcome the difficulties caused by polydispersity. Therefore, this method permits one to obtain detailed information on the phase equilibria in polymer solutions and in polymer blends in a relatively easy way. To show this, the data of Halary et al. are reanalyzed by means of continuous thermodynamics. In this way, more profound knowledge may be obtained from the experimental material, e.g., a more precise determination of the critical point and a more correct location of the spinodal.     

Attachment of Hydrogen Molecules to Atomic Ions (Na+, Cl−): Examination of an Adiabatic Separation of the H2 Rotational Motion

Interactions between molecular hydrogen and ions are of interest in cluster science, astrochemistry and hydrogen storage. In dynamical simulations, H₂ molecules are usually modelled as point particles, an approximation that can fail for anisotropic interactions. Here, we apply an adiabatic separation of the H₂ rotational motion to build effective pseudoatom-ion potentials and in turn study the properties of (H₂)_nNa⁺/Cl⁻ clusters. These interaction potentials are based on high-level ab initio calculations and Improved Lennard-Jones parametrizations, while the subsequent dynamics has been performed by quantum Monte Carlo calculations. By comparisons with simulations explicitly describing the molecular rotations, it is concluded that the present adiabatic model is very adequate. Interestingly, we find differences in the cluster stabilities and coordination shells depending on the spin isomer considered (para- or ortho-H₂), especially for the anionic clusters.     

Effect of temperature on acid–base equilibria in separation techniques. A review

Studies on the theoretical principles of acid–base equilibria are reviewed and the influence of temperature on secondary chemical equilibria within the context of separation techniques, in water and also in aqueous-organic solvent mixtures, is discussed. In order to define the relationships between the retention in liquid chromatography or the migration velocity in capillary electrophoresis and temperature, the main properties of acid–base equilibria have to be taken into account for both, the analytes and the conjugate pairs chosen to control the solution pH. The focus of this review is based on liquid–liquid extraction (LLE), liquid chromatography (LC) and capillary electrophoresis (CE), with emphasis on the use of temperature as a useful variable to modify selectivity on a predictable basis. Simpli?ed models were evaluated to achieve practical optimizations involving pH and temperature (in LLE and CE) as well as solvent composition in reversed-phase LC.     

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.     

Influence of carrier gas on the prediction of gas chromatographic retention times based on thermodynamic parameters

We present an investigation into the influence of carrier gas on the thermodynamics governing a capillary gas chromatographic separation. Thermodynamic parameters are estimated for a series of alkanes and alcohols on three common stationary phases using helium, hydrogen, and nitrogen carrier gases. It is shown that the substitution of carrier gases for one another results in a change in the thermodynamic parameters governing the separation. The effect of the carrier gas on the thermodynamic parameters is large enough to compromise the accuracy of the retention time calculations based on thermodynamic parameters collected in a carrier gas other than the one actually in use in a specific gas chromatographic system. A possible kinetic explanation for these observations is also investigated.     

New statistical mechanical model for calculating Kirkwood factors in self-associating liquid systems and its application to alkanol+cyclohexane mixtures

A new statistical mechanical model for calculating Kirkwood factors in self-associating molecular liquids and their mixtures with nonassociating components has been developed in a consistent way which is based on an extended version of the Flory-Huggins model taking into account chemical association equilibria. The majority of molecular parameters involved into the theory has been fixed by independent quantum mechanical ab initio calculations of associated molecular clusters. The model is also able to predict other thermodynamic mixture properties such as the enthalpy of mixing and also the infrared absorbance of monomer alcohol species as function of concentration. Experimental results of nine alcohol+cyclohexane mixtures taken from the literature have been used to test the new model. The Kirkwood correlation factor gK, the molar enthalpy of mixing HmE, and the monomer IR absorbance can be described simultaneously in excellent agreement with experimental data covering the whole range of mole fraction including temperature dependence of gK, HmE, and the IR absorbance. Two parameters have been adjusted freely for each system. A third parameter for the nonspecific intermolecular dispersion interactions has been adjusted within a limited range of possible values given by physical arguments. The model opens a new way of a more reliable understanding of structures and equilibrium properties of hydrogen bonded systems in the condensed liquid state.