Calculation of the stability and of the phase equilibrium in the system polystyrene+cyclohexane+carbon dioxide based on equations of state

In order to calculate spinodals for polymer systems with an equation of state (EOS), we developed a stability theory using continuous thermodynamics. Here, the mixture considered consists of a polydisperse polymer and two monodisperse components as for example a solvent and a gas. We derived the spinodal equation on the base of the segment-molar Helmholtz energy of the mixture. As a result, a determinant similar to that of the monodisperse case is obtained, but the polydisperse polymer is identified by its weight average of the molecular weight. Furthermore, our paper provides the equations for the cloud-point curve derived with the aid of continuous thermodynamics. The final equations are applied to the system polystyrene+cyclohexane+carbon dioxide using the EOS of Sako, Wu and Prausnitz (SWP-EOS). For parameter fit and to prove the accuracy of the treatment, experimental data of the high-pressure equilibrium of the binary subsystems and of the ternary system were taken from literature.     

Modeling of three-phase vapor–liquid–liquid equilibria for a natural-gas system rich in nitrogen with the SRK and PC-SAFT EoS

In this work, we present the modeling of three-phase vapor–liquid–liquid equilibria for a mixture of natural gas (Hogback gas) containing high concentrations in nitrogen (51.8 mol%) with the SRK and PC-SAFT equations of state. The interest of studying this mixture is due to the experimental evidence of the occurrence of multiple equilibrium liquid phases for this mixture over certain ranges of temperature and pressure. The calculation of the multiphase equilibria was carried out by using an efficient numerical procedure based on the minimization of the system Gibbs energy and thermodynamic stability tests to find the most stable state of the system. The results of the calculated vapor–liquid–liquid equilibria (VLLE) show that the PC-SAFT equation of state predicts satisfactorily the phase behavior that experimentally exhibits this mixture, whereas the SRK equation of state predicts a three-phase region wider than the experimentally observed. The two-phase boundary for this mixture was also calculated through flash calculations, and the results showed that this mixture does not present any gas-liquid critical point.     

Computer simulation of non-linear preparative chromatography processes

Summary A theory of non-linear chromatography based on the mass balance equation is presented. The model is a system of partial differential equations and it includes axial dispersion in the mobile phase, flow in the mobile phase and mass transfer between phases. In the case of the injection of a mixture competition between components for places in the stationary or the mobile phase is taken into account. In the paper are discussed: numerical calculations of concentration and volume overloading and the effect of the mutual influence of the components of the injected mixture on the process of mass transfer between phases. Additionally, results of experiments for convex and concave adsorption isotherms are presented. In both cases the results obtained qualitatively confirm the theoretical analyses.     

Self-Consistency of the Theory of Elementary Stage Rates of Reversible Processes and the Equilibrium Distribution of Reaction Mixture Components

An analysis is presented of one of the key concepts of physical chemistry of condensed phases: the theory self-consistency in describing the rates of elementary stages of reversible processes and the equilibrium distribution of components in a reaction mixture. It posits that by equating the rates of forward and backward reactions, we must obtain the same equation for the equilibrium distribution of reaction mixture components, which follows directly from deducing the equation in equilibrium theory. Ideal reaction systems always have this property, since the theory is of a one-particle character. Problems arise in considering interparticle interactions responsible for the nonideal behavior of real systems. The Eyring and Temkin approaches to describing nonideal reaction systems are compared. Conditions for the self-consistency of the theory for mono- and bimolecular processes in different types of interparticle potentials, the degree of deviation from the equilibrium state, allowing for the internal motions of molecules in condensed phases, and the electronic polarization of the reagent environment are considered within the lattice gas model. The inapplicability of the concept of an activated complex coefficient for reaching self-consistency is demonstrated. It is also shown that one-particle approximations for considering intermolecular interactions do not provide a theory of self-consistency for condensed phases. We must at a minimum consider short-range order correlations.     

多元气-液-固复杂体系相平衡

石油流体中含有气相、液相及可能遇到的固相包括水合物、石蜡和沥青质等,涉及多元气-液-固复杂体系的相平衡问题.为防止这些沉积物堵塞造成安全隐患,需要确定水合物、石蜡、沥青质沉积起始条件以及沉积量.本文针对化学热力学理论在含水合物、石蜡和沥青质的多元-多相平衡研究中的应用进行了综述.水合物相平衡模型较为成熟,主要有两类,其一为基于等温吸附理论的van der Waals-Platteeuw型热力学模型;其二为基于双过程水合物生成机理的Chen-Guo水合物热力学模型.石蜡沉积一般采用活度系数法、状态方程法及多固相模型描述.沥青质絮凝、沉积则可采用溶解度参数模型、状态方程法、胶体模型和标度理论模型进行计算.同时对多元气-液-固复杂体系的相平衡研究发展方向进行了展望.     

Statistical thermodynamics of polydisperse polymer blends with strong interaction

A statistical thermodynamics theory of polydisperse polymer mixtures with strong interaction between dissimilar components based on a lattice fluid model is formulated. Expressions for the free energy, equation of state, phase stability and spinodal for a polydisperse, binary polymer mixture with strong interaction are derived.     

A diffusion model of the pervaporation separation of ethylene glycol-water mixtures through crosslinked poly(vinyl alcohol) membrane

The pervaporation separation of ethylene glycol-water mixtures was carried out over the full range of compositions at temperatures varying from 60 to 80°C, using chemically crosslinked PVA dense membrane which had been developed in our laboratory. A new thermodynamic diffusion coefficient equation is derived based on the modified Vigne equation. Combining Lee-Thodos equations, Wilke-Chang equations, Vrentas-Duda's free volume theory, diffusion equations and swelling equilibrium equations, the permeation fluxes of individual components in ethylene glycol-water mixture through crosslinked poly(vinyl alcohol) (PVA) dense membrane have been calculated and showed to be in agreement with the experimental values.     

Thermodynamic equilibrium of adsorbed phases

The types of phase equilibrium behavior for adsorbed binary mixtures that can be predicted by an equation of state (EOS) based on the lattice gas theory are investigated. The equilibrium conditions were obtained by solving the isofugacity equations between adsorbed phases. It is observed that the investigated EOS can predict complex behavior for adsorbed phases such as the existence of azeotropes, and retrograde and double retrograde phase transition phenomena, that are analogous to those found in bulk phase equilibrium. Furthermore, it was possible to find systems that presented phase equilibrium between two dense adsorbed phases, analogously to liquid–liquid equilibrium for bulk phases. Experimental data would be necessary to confirm the types of adsorbed phase behavior predicted by the calculations presented.     

Concentration dependences of the transport coefficients of rod-like molecules in narrow slit-shaped pores

The concentration dependences of the label transport and shear viscosity coefficients for rod-like molecules in slit-shaped pores were studied. The calculations were carried out using the lattice gas model, which describes a broad range of fluid concentrations (from the gaseous to the liquid state) and temperatures (including the critical region). In the calculation of the local distributions of mixture components in the equilibrium states, lateral interactions were taken into account. The translational and rotational motions of molecules were described in terms of the transition state theory for nonideal reaction systems, which took into account the influence of neighboring molecules on the height of the activation barrier. The model equations reflect the pronounced anisotropy of the distribution of system components along the normal to the pore wall surface and ordering effects of molecules along various directions. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1485–1494, September, 2006.     

Thermal equation for the adsorption of a binary gas mixture

Conclusions An equation proposed previously has been generalized to the case of the adsorption of binary gas mixtures. Based on this equation, the partial thermal equations of adsorption of the components of a mixture have been derived, and the critical parameters of the adsorbed phase have been calculated.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2418–2421, November, 1987.     

The problem of a self-consistent description of the equilibrium distribution of particles in three states of aggregation

The possibility of unified self-consistent calculations of equilibrium distributions of molecules in three states of aggregation within the framework of the lattice gas model is considered. The corresponding approach was generalized to arbitrary pressures with including the compressibility of lattice structures. Closed equations were obtained for calculating thermodynamic functions (including an equation for the chemical potential of mixture components) in the continuum quasi-chemical approximation. Their use ensures equally accurate calculations of interphase equilibria in gas-liquid-solid systems and the determination of the triple and critical points. Possibilities for simplifying the equations by passing to the effective pair interaction potential, which takes into account averaged vibrations and volume accessible to the translational motion of molecules of commensurate sizes, are considered.     

Estimation of solubility and interaction parameters in binary liquid mixtures by reversed-flow gas chroamtography

Summary A new method, called reversed-flow gas chromatography, is presented for the measurement of the gaseous equilibrium concentrations of all the components under study, both in the pure state and in binary liquid mixtures. From the equilibrium concentrations, activities, activity coefficients and volume fraction activity coefficients were determined. Using various empirical equations relating activity with the molecular interactions between the components of a binary liquid mixture, the solubility parameters of ethanol, 1-propanol, acetone and methylethylketone in water were calculated. The total interaction parameters and the partial contributions of the dispersion, orientation and residue forces on the van der Waals attraction between the organic compounds and water were also computed. The variation of the interaction parameters with the composition of organic component in the binary mixture was investigated. The successful application of reversed-flow gas chromatography to the estimation of polymer solubility parameters is also reported. Finally, the solubility parameters found by the present method are compared with those determined by other techniques or calculated theoretically.     

Equations for describing liquid-vapor phase equilibria in binary mixtures

Three forms of equations for describing experimental data on liquid and vapor pressures, depending on temperature and composition at phase equilibria in binary mixtures, are proposed and evaluated. It is determined that the form of equation depends on the relationship between the temperature of a mixture and the critical temperatures of the components of the mixture. Exact data on the phase equilibria in nitrogenoxygen, nitrogen-argon, and oxygen-argon mixtures [1] are approximated to assess the effectiveness of the equations’ forms. It is found that the equations also allow us to determine the phase composition at a given temperature and pressure and temperatures of phases at a given pressure and composition.     

Thermodynamic properties of chain liquid mixtures with strong,local interactions

This paper addresses the effect in chain liquids on thermodynamic behavior of a large charge in the strength of local interactions on mixing. We classified real systems according to the ability of the Flory equation of state (FES) theory to prodict the excess volume. The FES theory enables reliable estimates provided the mixture is nearly athermal and the pure components obey the Flory equation of state. These requirements arise from Flory's approximations for the lattice part of the configuration integral, Z_L, and the cell part, Z_C, respectively. We revised Z_L without adding adjustable parameters by the quasichemical perturbation method to account for local ordering in the mixture because of a large change in the strength of binary interactions on mixing. The modification improves the predictions of the thermodynamic functions for systems where Flory's Z_L is inadequate.