PSRK模型的修正混合规则及其应用于聚合物溶液汽液平衡的预测

To extend the PSRK (predictive Soave-Redlich-Kwong equation of state) model to vapor-liquid equilibria of polymer solutions, a new EOS-gE mixing rule is applied in which the term ∑xiln(b/bi) in the PSRK mixing rule for the parameter a, and the combinatorial part in the original universal functional activity coefficient (UNIFAC) model are cancelled. To take into account the free volume contribution to the excess Gibbs energy in polymer solution, a quadratic mixing rule for the cross co-volume bij with an exponent equals to 1/2 is applied [bij^1/2=1/2(bi1/2 bj1/2)]. The literature reported Soave-Redlich-Kwong equation of state (SRK EOS) parameters of i3 - 2- pure polymer are employed. The PSRK model with the modified mixing rule is used to predict the vapor-liquid equilibrium (VLE) of 37 solvent-polymer systems over a large range of temperature and pressure with satisfactory results.     

CORRELATION OF DIFFUSION COEFFICIENTS FOR LIQUIDS AND DENSE FLUIDS WITH TEMPERATURE AND PRESSURE

On the basis of the free volume theory and activation energy concept,a fundamental equation whichtakes into account the effects of temperature and pressure has been developed.By introducing differentexpressions for the free volume and activation energy,several equations for fluid diffusion coefficients were derivedaccordingly.With the van der Waals free volume and intermal energy formula,a three-parameter model for fluiddiffusion coeffficients at moderate pressure was obtained.The grand average absolute deviation percent of 345data points (44 systems)for self-and infinite dilute inter-diffusivities is 2.32,against the results of the model ofCohen and Turnbull,4.13.In particular,by means of the modified Carnahan-Starling free volume equation,afour-parameter model with average abosolute deviation percent 2.64(30 systems,644 data points)for theestimation of dense fluid inter-and self-diffusivities at high pressures and in supercritical conditions was derived.The derived model is superior to the method of L     

Analogy between adsorption and sorption:An elementary mechanistic approach.I.Monolayer adsorption and sorption without solvent cluster formation

The elementary mechanistic model of adsorption and sorption is based on a simple hypothesis:the adsorption sites are uniformly distributed on the surface of the pore walls in the adsorbent,the sorption sites are uniformly distributed in the volume of the polymer.In this first paper we will analyze the simple case where one solute mol-ecule is only allowed to occupy a single adsorption or sorption site.A common elementary occupation law of the free sites is assumed:the differential increase of the number of the adsorbed/sorbed molecules is proportional to the differential increase of the activity of the solute and the concentration of the free(non-occupied)sites in the solid.The proportionality coefficient is called affinity coefficient depending on the solid/solute couple and on the temperature and independent of the concentration of the solute.In adsorption the concentration of the free sites is a surface concentration on the pore walls and in sorption it is expressed by the molarity.The simple mono-layer adsorption law of Jovanovi?is obtained:n=n0(1?e?KP)where n is the number of moles adsorbed when the pressure is P. n0is the total number of adsorption sites and K the affinity coefficient for adsorption.The sorption law writes:a= 1k? ?1??]+1?rk ln?1+1r?1??]where?,r and k hold respectively for the volume fraction of the solvent in the polymer,for the ratio of the molar volumes of the solvent to the elementary polymer chain containing one single adsorption site and for the sorption affinity coefficient.The confrontation of these equations to experimental isotherms is satisfactory in comparison with the classical Langmuir and Flory-Huggins equations:the best results are obtained for adsorption of vapors on a 5A zeolite and for all analyzed sorption results.     

Study on the Diffusion Coefficient of Sodium Chloride at Infinite Dilution in Supercritical Water

The molecular dynamics (MD) was employed to simulate the diffusion coefficient of sodium chloride at infinite dilution in supercritical water from 703.2 K to 763.2 K and from 30 MPa to 45 MPa. Based on the simulated data and the Patel-Teja(PT) equation of state and the Liu-Ruckenstein equation, an equation for calculating the diffusion coefficient of NaCl at infinite dilution in supercritical water is proposed. Both the agreement between the simulated and correlated data, and that between the simulated and predicted data of diffusion coefficients for NaCl in supercritical water ranging from 703.2K to 803.2 K and from 25 MPa to 50 MPa show that this equation is applicable for the calculation of diffusion coefficients.     

一个基于NRTL方程的液体混合物表面张力模型

A new equation for predicting surface tension is proposed based on the thermodynamic definition of surface tension and the expression of the Gibbs free energy of the system. Using the NRTL equation to represent the excess Gibbs free energy, a two-parameter surface tension equation is derived. The feasibility of the new equation has been tested in terms of 124 binary and 16 multicomponent systems(13-ternary and 3-quaternary) with absolute relative deviations of 0.59~0 and 1.55~0 respectively. This model is also predictive for the temperature dependence of surface tension of liquid mixtures. It is shown that, with good accuracy, this equation is simple and reliable for practical use.     

超临界水中NaCl无限稀释扩散系数的研究

The molecular dynamics(MD) was employed to simulate the diffusion coefficient of sodium chloride at infinite dilution in supercritical water from 703.2K to 763.2K and from 30 MPa to 45 MPa ,Based on the simulated data and the Patel-Teja(PT) equation of state and the Liu-Ruckenstein equation,an equation for calculating the diffusion coefficient of NaCl at infinite dilution in supercritical water is proposed,Both the agreement between the simulated and correlated data,and that between the simulated and predicted data of diffusion coefficients for NaCl in supercritical water ranging from 703.2K to 803.2K and from 25 MPa to 50MPa show that this equation is applicable for calculation of diffusion coefficients.     

空气在二甲基硅油和液压油中扩散系数的测量

A piston-cylinder apparatus was established to measure the solubility and diffusivity of air in dimethyl silicone oils and in hydraulic oils based on the PVT state equation of air and the solution of unsteady one-dimensional diffusion equation. The measured diffusivity-temperature relation can be well fitted by the Arrhenius equation for engineering applications. The correlation between the solute diffusivity D and solvent viscosity  is examined. In terms of Eyring’s activation theory, the activation in the air-silicone-oil diffusion process is quite different from that in the momentum transport of the silicone oil: the activation entropy of the former is positive while that of latter is negative. However, the activation enthalpies of the two processes are in the same order of magnitude, which leads to the observation that D/T is roughly constant.     

Correlation of the mean activity coefficient of aqueous electrolyte solutions using an equation of state

Accurate calculation of thermodynamic properties of electrolyte solution is essential in the design and optimization of many processes in chemical industries.A new electrolyte equation of state is developed for aqueous electrolyte solutions.The Carnahan–Starling repulsive model and an attractive term based on square-well potential are adopted to represent the short range interaction of ionic and molecular species in the new electrolyte EOS.The long range interaction of ionic species is expressed by a simplified version of Mean Spherical Approximation theory(MSA).The new equation of state also contains a Born term for charging free energy of ions.Three adjustable parameters of new e EOS per each electrolyte solution are size parameter,square-well potential depth and square-well potential interaction range.The new e EOS is applied for correlation of mean activity coefficient and prediction of osmotic coefficient of various strong aqueous electrolyte solutions at 25 °C and 0.1 MPa.In addition,the extension of the new e EOS for correlation of mean activity coefficient and solution density of a few aqueous electrolytes at temperature range of 0 to 100 °C is carried out.     

Effect of Tetrachloroethylene on Sphalerite Leaching

The effects of tetrachloroethylene (C2Cl4) on sphalerite leaching in FeCl3-HCl were investigated in view of simultaneous mass transfer and reaction, and the leaching models with and without organic solvent C2Cl4 were derived. The leaching experiments and the SEM results show that C2Cl4 is an effective organic solvent for sphalerite leaching in FeCl3-HCl system to be accelerated and for the sulfur to be separated. Adding C2Cl4 in the FeCl3-HCl medium will turn the kinetic model controlled by sulfur layer diffusion with process activation energy of 67.9 kJ/mol into mixed diffusion with the energy reduced to 55.1 kJ/mol when 20 ml of C2Cl4 was added.     

A GE/Equation of State Mixing Rule for Vapor-Liquid Equilibria

A new excess Gibbs free energy/equation of state type mixing 0rule was derived byremoving the infinite pressure boundary condition imposed by Wong and Sandler.The mixing rulewas extensively tested in terms of a comprehensive data base,consisting of 52 simple nonpolar-nonpolar,carbon dioxide containing,hydrocarbon-hydrocarbon,CFC,polar-polar,nonpolar-polarbinary and multicomponent systems.Focused on the complete predictive capability,a comparisonbetween the Wong-Sandler and the mixing rule proposed was conducted.The results indicate that thenew mixing rule is in general superior to the Wong-Sandler's,and the binary interaction parameteras required by the latter is removed,which reduces computing effort and is reliable in predictions ofvapor-liquid equilibria from low pressures to high pressures.     

Prediction of solvent‐diffusion coefficient in polymer by a modified free‐volume theory

Several versions of free‐volume theory have been proposed to correlate or predict the solvent diffusion coefficient of a polymer/solvent system. The quantity of free volume is usually determined by the Williams–Landel–Ferry (WLF) equation from viscosity data of the pure component in these theories. Free volume has been extensively discussed in different equation‐of‐state models for a polymer. Among these models, the Simha–Somcynsky (SS) hole model is the best one to describe the crystalline polymer, because it describes it very approximately close to the real structure of a crystalline polymer. In this article, we calculated the fractions of the hole free volume for several different polymers at the glass transition temperature and found that they are very close to a constant 0.025 by the SS equation of state. It is quite consistent with the value that is determined from the WLF equation. Therefore, the free volume of a crystalline polymer below the glass transition temperature (T_g) is available from the SS equation. When above the T_g, it is assumed that the volume added in thermal expansion is the only contribution of the hole free volume. Thus, a new predictive free‐volume theory was proposed. The free volume of a polymer in the new predictive equation can be estimated by the SS equation of state and the thermal expansion coefficient of a polymer instead of by the viscosity of a polymer. The new predictive theory is applied to calculate the solvent self‐diffusion coefficient and the solvent mutual‐diffusion coefficient at different temperatures and over most of the concentration range. The results show that the predicted values are in good agreement with the experimental data in most cases. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 428–436, 2000     

3种芳香烃在聚乙烯膜中的无限稀释扩散系数

基于Hadj-Romdhane和Danner色谱过程的数学模型 ,采用反相气相色谱法在 348.2～ 36 3.2K温度范围内测定了苯、甲苯和乙苯 3种芳香烃溶剂在聚乙烯膜中的无限稀释扩散系数 .实测数据的关联结果表明 ,采用空穴自由体积替代Vrentas-Duda自由体积理论方程中自由体积项的修正方程 ,能很好地描述溶剂分子的无限稀释扩散系数随温度的变化关系 .同时在修正方程的基础上建立了一般化自由体积方程 ,并对该方程的预测能力进行了探讨     

A diffusion coefficient model for polymer devolatilization

Polymer devolatilizers are in widespread use in the polymer industry for removing solvents and monomers from polymer melts prior to product fabrication. Design equations for describing the solvent flux usually include both the diffusion coefficient of the solvent in the polymer melt and the equilibrium concentration of the solvent at the polymer-vapor interface. Several models make the as sumption that the solvent diffusivity is constant over the ranges of solvent concentrations and temperatures in the devolatilizer. This is a critical assumption that may be difficult to check without obtaining diffusivity data at the operating temperatures and concentrations of the process equipment. There are three models that can be used for diffusion coefficients in devolatilizer design: the free volume model developed by Duda, Vrentas, and coworkers; a new linear model proposed in this study; and a constant diffusivity model, The linear model is obtained by combining a new correlation for solvent activity coefficients in molten polymers with free volume theory and linearizing the resulting equation. The error between using the complete free volume theory and using the linear model, or alternatively, using a constant diffusion coefficient, is calculated for several solvent-polymer systems. The linear model is convenient to use for determining the effects of the solvent activity coefficient on the diffusion coefficient. A method is presented for determining whether the complete model, the linear model, or the constant diffusivity model is appropriate for a given devolatilizer design.     

丙烯酸聚氨酯涂料成膜过程(Ⅰ)溶剂扩散系数的估算

采用傅里叶变换红外光谱（FTIR）测定了不同时间下丙烯酸聚氨酯涂料体系成膜聚合物的固化度及固化反应速率常数,并将该体系按二元聚合物-溶剂体系进行简化处理,在Vrentas-Duda自由体积理论模型的基础上,利用Di-Benedetto方程关联了溶剂的扩散系数与涂膜的固化度,建立了涂膜中溶剂扩散系数的预测模型.结果表明,本涂膜体系中溶剂扩散系数是溶剂浓度、干燥时间的函数.     

Hydraulic permeation of liquids through swollen polymeric networks. III. A generalized correlation

An approximate equation was developed that permits calculation of the solvent tracer diffusion coefficient in a homogeneous swollen membrane from the measured hydraulic permeability coefficient. This relation was applied to data for 28 polymer–solvent systems that included 15 different organic solvents and 5 hydrocarbon polymer networks whose equilibrium swellings ranged from 16.1 to 91.5% polymer on a volume basis. The calculated tracer diffusion coefficient divided by the pure solvent self-diffusion coefficient for these systems formed a unique correlation when plotted versus the polymer volume fraction in the membrane. This relation agreed well with tracer diffusion coefficient data in the literature for the benzene–natural rubber system measured by radioactive tagging. Discussion centers on the evidence for the validity of the equation developed and the role of hydrodynamics on diffusion in swollen membranes.     

Solvent diffusion in molten polyethylene

Diffusivity data are presented for the o-xylene–polyethylene system in the temperature range 125–175°C. The diffusion coefficient increases slightly as the solvent concentration increases near the pure polymer limit. Although the concentration and temperature dependences of the diffusivity for this system are different from what are typically observed for polymer–solvent systems, they are consistent with the free-volume theory of diffusion.     

Solvent and temperature effects on diffusion in polymer–solvent systems

The temperature dependence of the mutual diffusion coefficient at zero solvent concentration for a number of polystyrene–solvent systems is satisfactorily represented by an equation derived from a new version of the free-volume theory of molecular transport. The free-volume parameter which governs the temperature dependence of the diffusion rate is linearly related to the size of the solvent as estimated by its molar volume at OK. Data taken on various polystyrene–solvent systems are used to deduce information on the mechanism of solvent transfer in polymeric systems.     

Solvent‐induced crystal formation in polymers: Experimental studies and theoretical modeling of poly(vinyl alcohol) based on free‐volume concepts

A model has been developed to describe the simultaneous diffusion and solvent‐induced crystal formation in polymers based on the idea that crystal formation is governed by polymer chain mobility and a thermodynamic driving force. The polymer chain mobility is described based on solvent and polymer physical characteristics using the free‐volume theory of transport. The semicrystalline polymer‐solvent system is treated as a ternary system consisting of crystalline polymer, amorphous polymer, and solvent. The addition of solvent to the amorphous phase is assumed to increase the local free volume and facilitate movement of polymer chains, thereby enabling crystal formation. Diffusion of the solvent is assumed to occur solely in the amorphous polymer phase. The species continuity equations are formulated in volume‐averaged coordinates and give rise to a convective term due to the density change accompanying transformation of the amorphous polymer to the crystalline polymer. Accurate modeling of this problem requires that a moving boundary be considered. The model was tested using gravimetric sorption data for the poly(vinyl alcohol)‐water system. In the experimental studies, the water was initially absorbed and then a high percentage of it was expelled. The proposed model accurately describes this behavior. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 45171.     

Acetic Acid Extraction by Solvent Membrane

Abstract

Solvent extraction of acetic acid at low concentrations from aqueous solutions was studied. Decalin was found to be the optimal solvent and trioctyl phosphine oxide an effective carrier species. Phase equilibrium constants were measured and the results agree with the theoretical equation in the low carrier concentration range. The polymer supported solvent membranes carrying the same solvent and carrier, under various physical and chemical conditions, were prepared and the apparent diffusion coefficients of acetic acid through these membranes were measured and the results were discussed. The apparent diffusion coefficient of acetic acid in these tests was not interfered with by the existence of hydrochloric acid in the feed stream.