Prediction of solvent diffusion coefficient in amorphous polymers based on an equation‐of‐state

This study develops a modified free‐volume model to predict solvent diffusion coefficients in amorphous polymers by combining the Vrentas–Duda model with the Simha–Somcynsky (S‐S) equation‐of‐state (EOS), and all the original parameters can be used in the modified model. The free volume of the polymer is estimated from the S‐S EOS together with the Williams‐Landel‐Ferry fractional free volume, and the complex process of determining polymer free‐volume parameters in the Vrentas–Duda model and measuring polymer viscoelasticity can be avoided. Moreover, the modified model includes the influence of not only temperature but also pressure on solvent diffusivity. Three common polymers and four solvents are employed to demonstrate the predictions of the modified model. The calculation results are generally consistent with the experimental values. It is reasonable to expect that the modified free‐volume model will become a useful tool in polymer process development. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1000–1009, 2006     

Prediction of infinite dilution solvent activity coefficient in rubbery polymer solutions using Engaged Species Induced Clustering (ENSIC) model

It is extremely important to predict infinite dilution solvent activity coefficients in rubbery polymers in design and operation of polymer‐related processes. Many models have been developed to predict the activity coefficients. However, the accuracies of these models are not satisfactory. This article advances a method for predicting the infinite solvent dilution activity coefficients in the rubbery polymers, using the Engaged Species Induced Clustering (ENSIC) model. It elucidates the physiochemical significance and mathematical meaning of the parameters in the ENSIC model. In this article, the ENSIC approach has been proven to agree extremely well with the experimental data in both correlating the finite dilution solvent activity coefficient and predicting the infinite dilution solvent activity coefficient for rubbery polymer/solvent systems. In other words, both the ENSIC equation and its derivative at extremely low solvent concentration are in good agreement with the experimental data. In addition, the article indicates that the ENSIC model is much more accurate than another kind of empirical models‐ the F–H and related models in predicting the infinite dilution solvent activity coefficients in polymer solutions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1668–1675, 2006     

A new model and extension of Wong–Sandler mixing rule for prediction of (vapour + liquid) equilibrium of polymer solutions using EOS/GE

The cubic equation of state (CEOS) is a powerful method for calculation of (vapour + liquid) equilibrium (VLE) in polymer solutions. Using CEOS for both the vapour and liquid phases allows one to calculate the non-ideality of polymer solutions based on a single EOS approach. However, the traditional mixing rules are not appropriate to extend the CEOS to non-ideal mixtures such as polymer solutions. Several authors have applied the EOS/G^E approach to predict (vapour + liquid) equilibria in polymer solutions, however, incorporating an appropriate excess Gibbs free energy for the new mixing rule is a major step. In this research, the NRTL-NRF model was extended in terms of volume fraction of polymer and solvent (instead of mole fraction), then equilibrium calculations were carried out using PRSV EOS and Wong–Sandler mixing rules. Using the adjustable parameters as a function of solution temperature, the NRTL-NRF model can be used as a predictive model. In comparison with NRTL model, the results of the new NRTL-NRF model show better accuracy.     

Totally inclusive cubic equation of state with five parameters for pure fluids

A totally inclusive cubic equation of state (cubic EOS) is proposed. Although, its form is fairly simple as compared with the present cubic equations, it can include all of them as special cases. The EOS has five parameters. By fitting the experimental critical isothermal for six typical substances combining the critical conditions, the generalized expressions for the five parameters at critical temperature are established. The temperature coefficients of the five parameters for 43 substances are determined by fitting the experimental data of vapor pressure and saturated liquid density. These coefficients are correlated with the critical compressibility factor and acentric factor to obtain the generalized expressions. The predicted saturated vapor pressure, saturated liquid density, critical isothermal and coexistence curve near the critical point show that the equation gives the best results when compared with the Redlich–Kwong–Soave (RKS) and Peng–Robinson (PR) EOS.     

Activity coefficients of single electrolytes in concentrated solutions derived from a quasi-lattice model

This paper describes a new model to calculate the mean activity coefficients of dissociated electrolytes in concentrated solutions. It is based on three assumptions: (i) a quasi-lattice arrangements of ions in solution; (ii) a contribution from ion-water interactions to the mean activity coefficients; (iii) a concentration dependence of the dielectric constant. The mean activity coefficients of thirteen strong electrolytes from moderately dilute solutions to saturated solutions are found to correlate well by this model. For dilute solutions, a limiting equation in which only ion-specific parameters are required is proposed. It is suggested that specific ionwater interactions might be the major source of the nonideality of strong electrolyte solutions at high concentrations.     

An extension of cubic equations of state to vapor-liquid equilibria in polymer-solvent mixtures

Cubic equations of state (EOS) are extended to describe polymer-solvent vapor-liquid equilibria (VLE). The solvents are described the conventional way using critical parameters. To describe the pure polymers, only the weight-average molecular weight is necessary, though number-average molecular weight, polydispersity and melt density can be incorporated if desired. To extend the model to mixtures, a mixing rule that combines EOS with excess energy models is used. In this formulation, the excess Gibbs energy term is considered in two parts: the classical Flory term for the entropic contributions and a residual term that takes care of specific interactions between the solvent and the polymer. For athermal mixtures that exhibit no such interactions, the residual term drops out and the model becomes completely predictive. Otherwise, for residual contributions, depending upon the complexity of specific molecular interactions anticipated in the mixture, either a single parameter Flory expression or a two-parameter NRTL equation can be used. We conclude that the simple cubic EOS approach presented here is easy to use, yet competes successfully with more sophisticated EOS models developed particularly for polymer solutions. Moreover, it offers more flexibility if one or more parameters are to be tuned to the process data.     

Simulation of polymer--polymer interdiffusion using the dynamic lattice liquid model

In this paper, we present computer simulation results concerning interdiffusion of fully compatible components in symmetric binary (AB) polymer mixtures in solutions. The simulation is performed in two dimensions using the algorithm based on the dynamic lattice liquid model. The solvent molecules are taken into account explicitly. The evolution of the concentration profiles in time at an interface is studied for chain lengths N=2,4,8,16 for three polymer concentrations phi=0.1,0.5,0.9. The tracer diffusion coefficients for polymer chains and for the solvent are obtained by monitoring the mean square displacements of their center of mass. The relationships between coefficients of interdiffusion and self-diffusion are tested.     

Modelling of high-pressure phase equilibria using the Sako–Wu–Prausnitz equation of state: II. Vapour–liquid equilibria and liquid–liquid equilibria in polyolefin systems

Phase equilibria in binary and ternary polyolefin systems are calculated using the cubic equation of state proposed by Sako–Wu–Prausnitz (SWP). Calculations were done for high-pressure phase equilibria in ethylene/polyethylene (LDPE) systems and for liquid–liquid equilibria (LLE) in systems containing either high-density polyethylene or poly(ethylene-co-propylene). The calculations for the copolymer/solvent systems are compared with those using the SAFT EOS. The two equations of state can describe UCST, LCST as well as U-LCST behaviour with similar accuracy. Whereas, the binary interaction parameter is temperature-independent for SAFT, it is found to be a function of temperature for the SWP model. Moreover, the influence of an inert gas on the LCST of the polyethylene/hexane system is investigated using the SWP EOS. The polydispersity of the different polyethylenes is considered in the phase equilibrium calculations using pseudocomponents chosen by the moments of the experimental molecular weight distributions.     

Numerical values of individual activity coefficients of single-ion species in concentrated aqueous electrolyte solutions and the attempt of a qualitative interpretation on a model of electrostatic interaction

Individual activity coefficients of single-ion species can be achieved by the factorizing of a new concentration function for the mean activity coefficient to the required power applying a purely mathematical method. These single-ion activity coefficients, calculated in this manner, are listed for some aqueous strong electrolytes. The reasons for the magnitude and variation of the activity coefficients as a function of the concentration are, without a doubt, of complex nature. Activity coefficients have their meaning as practical values. In relation to the analytical concentration, the individual activity coefficients represent the macroscopic effectiveness of the single-ion species in solution an easy manner. However, with increasing deviations from Debye–Hückel conditions of an infinitely diluted electrolyte solution, a physically correct interpretation of the macroscopically visible activity coefficient is becoming more and more difficult, if not impossible to find. On the basis of a model of electrostatic interaction, an attempt has been made to create a qualitative interpretation of the individual ion activity coefficients in concentrated aqueous electrolyte solutions which were calculated applying the purely mathematical method by Ferse.     

Vapor–liquid equilibria for the ternary mixture of carbon dioxide + 1-propanol + propyl acetate at elevated pressures

Vapor–liquid equilibrium (VLE) data for the ternary mixture of carbon dioxide, 1-propanol and propyl acetate were measured in this study at 308.2, 313.2, and 318.2 K, and at pressures ranging from 4 to 10 MPa. A static type phase equilibrium apparatus with visual sapphire windows was used in the experimental measurements. New VLE data for CO₂ in the mixed solvent were presented. These ternary VLE data at elevated pressures were also correlated using either the modified Soave–Redlich–Kwong or Peng–Robinson equation of state (EOS), and by employing either the van der Waals one-fluid or Huron–Vidal mixing model. Satisfactory correlation results from both EOS models are reported with temperature-independent binary interaction parameters. It is observed that at 318.2 K and 10 MPa, 1-propanol may probably be separated from propyl acetate into the vapor phase at the entire concentration range in the presence of high pressure CO₂.     

Vapor pressure measurements on nonaqueous electrolyte solutions. Part 6. Some remarks on integral equations

Various combinations of the hypernetted chain (HNC) equation with the mean spherical approximation (MSA) and the Percus-Yevick (PY) equation are compared both for a well-known aqueous 2-2 electrolyte model solution and for real acetonitrile solutions. Belloni's self-consistency test shows that classical HNC calculations yield the best compressibility data for the two systems despite an apparently unrealistic g₊₊ maximum in the case of the aqueous solution. Effective concentration-dependent potentials making use of the dependence of the solution permittivity on electrolyte concentration are used for HNC calculations of osmotic coefficients for methanol solutions.     

Modified McKay–Perring Equation and Its Two Particular Solutions

Zdanovskii’s rule is the simplest isopiestic molality relation of mixed electrolyte aqueous solutions and the McKay–Perring equation is a differentio-integral equation particularly suitable for calculating solute activity coefficients from isopiestic measurements. However, they have two unsolved problems, which have puzzled solution chemists for several decades: (1) Zdanovskii’s rule has been verified by precise isopiestic measurements. But, several scientists suggested that the rule contradicts the Debye–Hückel limiting law for extremely dilute unsymmetrical mixtures. (2) In the McKay–Perring equation, a solute activity coefficient is multiplied by a solute composition variable. Different scientists have suggested that the composition variable may be the total ionic strength, common ion concentration, total ionic concentration, or an additive function with arbitrary proportionality constants. But, the different choices of the composition variable may lead to different activity coefficient results. Here, I derive a modified McKay–Perring equation in which the composition variable has the exclusive physical meaning of total ionic concentration for mixed electrolyte solutions (or of total solute particle concentration for the mixed solutions containing nonelectrolyte solutes). I also demonstrate that Zdanovskii’s rule is consistent with the Debye–Hückel limiting law for extremely dilute unsymmetrical mixtures. I derive two particular solutions of the modified McKay–Perring equation: one for the systems obeying Zdanovskii’s rule and another for the systems obeying a limiting linear concentration rule. These theoretical results have been verified with literature experiments and model calculations.     

Modeling hydrate formation conditions in the presence of electrolytes and polar inhibitor solutions

In this paper, a new predictive model is proposed for prediction of gas hydrate formation conditions in the presence of single and mixed electrolytes and solutions containing both electrolyte and a polar inhibitor such as monoethylene glycol (MEG), diethylene glycol (DEG) and triethylene glycol (TEG). The proposed model is based on the γ–φ approach, which uses modified Patel–Teja equation of state (VPT EOS) for characterizing the vapor phase, the solid solution theory by van der Waals and Platteeuw for modeling the hydrate phase, the non-electrolyte NRTL-NRF local composition model and Pitzer–Debye–Huckel equation as short-range and long-range contributions to calculate water activity in single electrolyte solutions. Also, the Margules equation was used to determine the activity of water in solutions containing polar inhibitor (glycols). The model predictions are in acceptable agreement with experimental data. For single electrolyte solutions, the model predictions are similar to available models, while for mixtures of electrolytes and mixtures of electrolytes and inhibitors, the proposed model gives significantly better predictions. In addition, the absolute average deviation of hydrate formation pressures (AADP) for 144 experimental data in solutions containing single electrolyte is 5.86% and for 190 experimental data in mixed electrolytes solutions is 5.23%. Furthermore, the proposed model has an AADP of 14.13%, 5.82% and 5.28% in solutions containing (Electrolyte + MEG), (Electrolyte + DEG) and (Electrolyte + TEG), respectively.     

Development of a new equation of state for mixed salt and mixed solvent systems,and application to vapour–liquid and solid (hydrate)–vapour–liquid equilibrium calculations

An equation of state that can be used for phase equilibrium and other thermodynamic property calculations at high pressures is developed for systems that contain aqueous solutions of strong electrolytes and molecular species. The proposed equation of state is based upon contributions to the Helmholtz free energy from a non-electrolyte term and three electrolyte terms. The non-electrolyte term comes from the Trebble–Bishnoi equation of state and the electrolyte terms consist of a Born energy term, a mean spherical approximation term and a newly developed hydration term. The application of the proposed equation of state to aqueous systems containing mixed salts and mixed solvents is illustrated by calculating the vapour–liquid equilibrium (VLE) and solid (Clathrate hydrate)–vapour–liquid equilibrium (SVLE) conditions for several systems. The solubility of CO₂ in salt water systems is examined at elevated pressures. As well, the new equation of state is used in conjunction with the model of van der Waals and Platteeuw to predict the SVLE conditions for gas hydrate forming systems in the presence of single salts, mixed salts and a mixture of aqueous salts and methanol. It is found that the new equation of state is able to accurately represent the experimental data over a wide range of pressure, temperature and salt concentration.     

基于化学缔合统计理论的链状流体状态方程

基于化学缔合统计理论的链状流体状态方程(EOS)能够反映实际分子的形状、链节成链、缔合等具体信息,在实际流体热力学性质计算中有着广泛应用.一般的链状流体EOS仅考虑相邻链节间的相关性,我们则借助统计力学和计算机模拟结果在模型中纳入了相间链节间的相关性,获得的硬球链流体(HSCF)模型能够更好地预测模型流体的压缩因子和第二维里系数.以HSCF为参考,引入方阱色散微扰项获得了实际方阱链流体(SWCF)EOS;结合根据黏滞球模型导得的缔合项,进一步构建了缔合流体EOS.最近,我们根据微扰理论和积分方程方法又开发了一新的变阱宽方阱链流体(SWCF-VR)模型.SWCF和SWCF-VREOSs可很好地用于计算小分子、聚合物、离子液体等纯流体及混合物的相行为、热焓、表面张力、黏度等热力学及传递性质,显示了模型良好的工程应用价值.本文就本课题组多年来在自由空间范畴内基于化学缔合统计理论开发链状流体EOS及其实际应用作系统的总结.     

A thermochemical study of aqueous solutions of sodium naproxene

The enthalpies of solution of sodium naproxene and dilution of its aqueous solutions were measured on an isoperibolic calorimeter at 293.15, 298.15, 303.15, 308.15, 313.15, and 318.15 K. The maximum content of the electrolyte was determined by its solubility at the given temperature (0.038–0.083 mol/kg solvent). The Pitzer model was used to obtain the virial coefficients for calculations of many excess thermodynamic properties of both solutions and their components. Changes in these characteristics depending on the concentration and temperature are considered.     

Measurement and prediction of solubilities and diffusion coefficients of carbon dioxide in starch–water mixtures at elevated pressures

The solubility and diffusion coefficient of carbon dioxide in intermediate‐moisture starch–water mixtures were determined both experimentally and theoretically at elevated pressures up to 16 MPa at 50 °C. A high‐pressure decay sorption system was assembled to measure the equilibrium CO₂ mass uptake by the starch–water system. The experimentally measured solubilities accounted for the estimated swollen volume by Sanchez–Lacombe equation of state (S‐L EOS) were found to increase almost linearly with pressure, yielding 4.0 g CO₂/g starch–water system at 16 MPa. Moreover, CO₂ solubilities above 5 MPa displayed a solubility increase, which was not contributed by the water fraction in the starch–water mixture. The solubilities, however, showed no dependence on the degree of gelatinization (DG) of starch. The diffusion coefficient of CO₂ was found to increase with concentration of dissolved CO₂, which is pressure‐dependent, and decrease with increasing DG in the range of 50–100%. A free‐volume‐based diffusion model proposed by Areerat was employed to predict the CO₂ diffusivity in terms of pressure, temperature, and the concentration of dissolved CO₂. S‐L EOS was once more used to determine the specific free volume of the mixture system. The predicted diffusion coefficients showed to correlate well with the measured values for all starch–water mixtures. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 607–621, 2006     

Comments on “Solubility and Dissolution Thermodynamic Data of Cefpiramide in Pure Solvents and Binary Solvents”

Errors are found in the mathematical correlation based on the combined Jouyban–Acree and Modified Apelblat models for describing the variation in the mole fraction solubility of cefpiramide with temperature and solvent composition for the binary aqueous–ethanol solvent system. The equation coefficients given by Tang and coworkers, when substituted into the model equation, do not yield the authors’ calculated mole fraction solubilities of cefpiramide.     

Vapor pressure measurements on nonaqueous solutions. Part IV. HNC calculations using Friedman's cosphere overlap model

Vapor pressure data for solutions of various alkali metal and tetraalkylammonium salts in methanol at 25° and NaI solutions in ethanol, 2-propanol, and acetonitrile at 25° in the concentration range 0.04–1]<0.75 are used to show the applicability of the HNC integral equation method to nonaqueous electrolyte solutions. Friedman's model of overlapping cospheres is used to express the non-electrostatic part of the ion-interaction potential. Data analysis is based on the Rasaiah-Friedman algorithm for the calculation of g₊₊ and g_+– functions. After conversion from Lewis-Randall to the McMillan-Mayer system the measured osmotic coefficients of all electrolyte solutions can be reproduced with the help of the calculated correlation functions.