Applicability of Simplified Models for the Estimation of Ion Exchange Diffusion Coefficients in Zeolites

The applicability of simplified models for the determination of ion exchange diffusion coefficients in zeolites is examined. The simplified models examined are Vermeulen's, Paterson's, and Nernst-Plank's approximations for isotopic and ion exchange processes, used in ion exchange systems analysis. Parameter analysis indicates the limits for fractional attainment of equilibrium U(t), the ratio of exchangeable ions in liquid to solid phase (w), and the ratio of surface diffusion coefficients of exchangeable ions (a), all clearly inter-related, within which the above-mentioned simplified models can be successfully used. Studies of the applicability of the isotopic exchange simplified models to experimental data for batch-type Na(+)-Pb(2+) exchange on clinoptilolite confirm the parameter analysis conducted. Copyright 2001 Academic Press.     

Determination of gas-liquid partition coefficients by automatic equilibrium headspace-gas chromatography utilizing the phase ratio variation method

Summary The new phase ratio variation method is described which represents a convenient way for the determination of gas-liquid partition coefficients for practical purposes, utilizing equilibrium headspace-gas chromatography (EHS-GC). This method is based on the relationship between reciprocal peak area and the phase ratio in the vial containing the sample solution; it involves regression analysis of the EHS-GC measurements of a number of sample vials containing the same sample solution but with a wide variation of phase ratios. Examples are given for both aqueous systems and systems consisting of a stationary (liquid) phase used as the solvent; comparison of the measured values with results obtained by other methods shows satisfactory agreement. A critical discussion of the conditions influencing the accuracy of the analytical results is given.Symbols which specifically refer to gas chromatography (GC), to equilibrium headspace sampling (EHS) and to EHS-GC are marked by the corresponding acronym.     

NaOH-NaAl(OH)4-H2O溶液体系渗透系数的测定及离子作用模型

用等压法测定了在303.15 K时总碱质量摩尔浓度mNaOH(T)从0.61 mol/kg到5.72 mol/kg, 苛性比αK从1.98到7.04的NaOH-NaAl(OH)4-H2O溶液体系的等压平衡浓度和渗透系数, 并得到该溶液体系的水活度. 用Pitzer模型对实验结果进行了参数化研究, 拟合求得了离子相互作用参数. 用Pitzer模型计算的渗透系数值与实验结果一致. 用获得的参数计算了NaOH和NaAl(OH)4在NaOH-NaAl(OH)4-H2O溶液体系中的活度系数, 其值随总碱质量摩尔浓度的增加呈增加的趋势.     

A thermodynamic approximation for the estimation of velocity correlation coefficients in binary liquid mixtures

An equation is derived using the relations of equilibrium thermodynamics to estimate limiting distinct diffusion coefficients, (or velocity cross-correlation coefficients) in binary non-electrolyte mixtures. It is tested against 13 mixtures. Good agreement is obtained with distinct diffusion coefficients derived experimentally in the case of near deal systems. For non-ideal mixtures the calculated values appear to follow the experimental coefficients to some extent. For this reason, the thermodynamic approximation is not as suitable for a reference equation as a structural approximation previously derived.     

Determination of Henry''s law coefficients by combination of the equilibrium partitioning in closed systems and solid-phase microextraction techniques

This paper describes the determination of Henry's law coefficients by means of the EPICS (equilibrium partitioning in closed systems) technique in combination with SPME (solid-phase microextraction). The use of solid-phase microextraction-sampling allowed us to extend the possibilities of the equilibrium partitioning in closed systems technique with respect to the range of Henry's law coefficients which can be measured. Whereas the equilibrium partitioning in closed systems technique is limited to determine air–water equilibrium partitioning of volatile compounds with Henry's law coefficients of at least 0.06 (dimensionless), the current method allowed to measure coefficients between 0.0023 and 13.5. In this way Henry's law coefficients of 20 compounds, being in a range covering five orders of magnitude, were measured with relative standard deviations between 1.0 and 19.8% (mean standard deviation: 5.7%; median of standard deviations: 4.8%, n=99). Several types of compounds were examined i.e. aliphatic hydrocarbons, monocyclic and polycyclic aromatic hydrocarbons, chlorinated and fluorinated compounds, ethers and esters, biphenyl and N-containing compounds, including compounds for which availability of experimental Henry's law coefficients is limited. Measurement of the equilibrium partitioning in the 2 to 25°C range allowed to establish relations of Henry's law coefficient as a function of temperature.     

Calculation for liquid-liquid equilibria of quaternary alkane-ethyl acetate-methanol-water systems used in counter-current chromatography

The calculation of liquid-liquid equilibrium compositions of solvent systems is very important for the work on counter-current chromatography (CCC), especially the phase composition and volume ratio obtained from liquid-liquid equilibrium calculation. In this work, liquid-liquid equilibria of quaternary Arizona solvent systems, alkane-ethyl acetate-methanol-water, and related ternary systems are correlated and predicted using the non-random two-liquid model (NRTL). Hexane, heptane and isooctane are the used alkanes. The parameters in the model are regressed only with the special systems considered. Detailed comparison with experimental data shows that liquid-liquid equilibria of these systems can be predicted with greatly improved accuracy as compared to the group contribution method (UNIFAC).     

Phase-equilibrium calculations for n-alkane + alkanol systems using continuous thermodynamics

A new association model based on continuous thermodynamics is introduced and applied to six systems of the type n-alkane (n-hexane, n-heptane, n-octane) + alkanol (methanol, ethanol). The alkanol is considered to be a mixture of chain associates with the composition described by a continuous distribution function. This distribution function is derived as an analytical expression from the mass action law applied to the association equilibrium. To consider the entropic contribution originating from the size differences of the molecules (associates) activity coefficients based on Flory–Huggins model are included in the mass action law. Unlike the molecular-mass distribution of a polymer the chain-length distribution of the associates depends on the temperature and on the mole fraction of the alkanol. The treatment of vapor–liquid equilibrium and liquid–liquid equilibrium is similar to that of an oil system or of a polymer solution using continuous thermodynamics. Different to other chemical models of association there is no additive split into a physical and a chemical contribution. The equilibrium constants of association were fitted to vapor-pressure data of methanol and ethanol. The model needs only one interaction parameter being independent of temperature and taking the same value for all systems studied. Considering the simplicity of the model, both the liquid–liquid equilibrium of the three methanol systems and the vapor–liquid equilibrium of all six systems are predicted with reasonable accuracy.     

Transport Coefficients of Two-temperature Lithium Plasma for Space Propulsion Applications

Lithium has been proposed as an attractive metal propellant for advanced electric propulsion. In our current work, transport coefficients including the viscosity, thermal conductivity, and electrical conductivity of lithium plasma under both the equilibrium and non-equilibrium conditions are calculated based on a two-temperature model. The collision integrals used in calculating the transport coefficients are significantly more accurate than values used in previous theoretical studies, resulting in more reliable values of the transport coefficients. Results are computed for different degrees of thermal non-equilibrium, i.e. the ratio of electron to heavy particle temperatures, from 1 to 15, with the electron temperature ranging from 300 to 60,000 K in a wide pressure range from 0.0001 to 100 atm. We compare our calculated results with existing published results and discrepancies are found and explained.     

Phase equilibria for binary systems of octane boosters with 2,2,4-trimethylpentane

Isobaric vapor–liquid equilibrium data at 95.96 kPa for the three binary systems of 2,2,4-trimethylpentane with methyl tert-butyl ether, di-isopropyl ether and dimethoxymethane are determined. A Swietoslawski type ebulliometer is used for the measurements. The experimental T–x data are used to estimate Wilson parameters and the parameters, in turn, are used to calculate vapor phase compositions and activity coefficients. All the systems studied here do not exhibit azeotropes and behave like non-ideal solutions.     

Partition Equilibria for Alcohols in Reverse Micellar AOT-Oil-Water Systems Studied by PGSE-FT NMR. A Comparison Between AOT-containing and the Corresponding AOT-free Systems

Microemulsions of the reverse micellar type were investigated by determining the self-diffusion coefficients of the components using the Pulsed Field Gradient Spin Echo – Fourier Transform NMR method (PGSE-FT NMR). The microemulsions were composed of the surfactant AOT, water and an oil (either benzene or cyclohexane), forming a water core in an oil continuum. The primary alcohols ranging from methanol to 1-decanol were added to the microemulsions as a fourth component. The degree of binding, p, of the alcohol to the micelles was determined from the measured self-diffusion coefficients for this component. Partition equilibrium constants were calculated from the values of p. Thermodynamic partition equilibrium constants, K _c , calculated from the partition coefficients are presented and compared with values based on literature data for AOT-free systems. Similarities and differences between these cases are revealed and interpreted.     

Isobaric vapour–liquid equilibria for the binary systems of fuel oxygenates with aromatic hydrocarbons

Isobaric vapour–liquid equilibrium data at 720?mm?Hg for the binary systems of diisopropyl ether with o-xylene and m-xylene and dimethoxymethane with benzene and toluene are determined. A Swietoslawski type ebulliometer is used for the measurements. The experimental T?x data are used to estimate Wilson parameters and the parameters in turn are used to calculate the vapour compositions and activity coefficients. The activity coefficients are used to calculate molar excess Gibbs free energy (G ^E). All the systems studied here do not exhibit azeotropes. Excess Gibbs free energy values are positive over the entire range of composition for all the systems.     

Synthesis and characterization of thermoresponsive isopropylacrylamide-acrylamide hydrogels

In this study, hydrogels of poly(N-isopropylacrylamide-co-acrylamide) having a thermoresponsive character were prepared by a redox polymerization method. NIPAM-co-AAm hydrogels with different thermoresponsive properties were obtained by changing the initial NIPAM/AAm mole ratio and crosslinker concentration.Equilibrium-swelling ratio, dynamic swelling ratio and dynamic deswelling ratio were evaluated for all hydrogel systems. The fast shrinking was observed with all gels. The time required for equilibrium shrinking increased with the increase of acrylamide content in the gel.     

Evaluation of liquid-liquid extraction process for separating acrylic acid produced from renewable sugars

In this article, the separation and the purification of the acrylic acid produced from renewable sugars were studied using the liquid-liquid extraction process. Nonrandom two-liquids and universal quasi-chemical models and the prediction method universal quasi-chemical functional activity coefficients were used for generating liquid-liquid equilibrium diagrams for systems made up of acrylic acid, water, and solvents (diisopropyl ether, isopropyl acetate, 2-ethyl hexanol, and methyl isobutyl ketone) and the results were compared with available liquid-liquid equilibrium experimental data. Aspen Plus (Aspen Technology, Inc., version 2004.1) software was used for equilibrium and process calculations. High concentration of acrylic acid was obtained in this article using diisopropyl ether as solvent.     

Phase equilibrium and insulin partitioning in aqueous two-phase systems containing block copolymers and potassium phosphate

In this work, phase diagrams of aqueous two-phase systems (ATPS) containing PEO–PPO–PEO block copolymers and potassium phosphate as well as the partitioning behavior of insulin in these systems are presented. Experiments aimed at the identification of the effects of copolymer structure (by varying the number of EO units per polymer molecule), temperature (283.15 and 298.15 K) and pH (5.0 and 7.0) on the phase behavior of these systems were carried out. The results indicated the enlargement of the two-phase region upon increasing the temperature, pH and copolymer hydrophobicity (expressed as the PO/EO ratio in the copolymer molecule). Experimental measurements of the partitioning of human insulin in these ATPS also indicated the dependency of the partition coefficients on temperature, pH, and copolymer hydrophobicity, with the latter being the most influential factor. Finally, experimental data on the phase behavior and insulin partitioning were correlated using an excess Gibbs energy virial-type model modified in order to account for coulombic interactions and ionization equilibrium between the various forms of the phosphate ion.     

Nonrandom factor model for the excess Gibbs free energy of weak electrolytes including phosphoric acid

The Electrolyte Nonrandom Two Liquid-Nonrandom Factor (NRTL-NRF) model of Haghtalab and Vera was modified to determine the excess Gibbs free energy of weak electrolyte systems. The model was applied to the phosphoric acid solution as a weak and complex electrolyte. Its thermodynamic behavior was investigated in a wide range of concentration by choosing an appropriate equilibrium reaction between molecular and ionic species. The model contains four adjustable parameters which were determined using osmotic experimental data. The results of dissociation and of activity coefficients are presented separately.     

Correlation and prediction of liquid-liquid distribution coefficients in aqueous systems using a modified Wilson model

A modified Wilson model is tested for its ability to correlate and predict distribution coefficients in two representative systems: 1-butanol-water and cyclohexanewater. The model is fitted to ternary equilibrium data for various solutes in these systems using a procedure involving minimization of the least-squares distance between calculated and experimental logarithmic distribution ratios. In addition, benzene-water, hexane-water, and cyclohexane-water distribution coefficients for infinitely diluted liquid solutes are predicted using only binary system information. All computations involve using both van der Waals and molar volumes as structural parameters to account for the geometry of the molecules studied. Satisfactory representations of experimental distribution ratios and fairly accurate distribution coefficients at infinite dilution are obtained for both systems. However, in a number of cyclohexane-water systems, miscibilities of constituent binary mixtures are poorly predicted from ternary system information when van der Waals volumes are used. Replacement of van der Waals volumes by molar volumes has little influence on the fit, but significant improvement is observed for the prediction of both binary miscibility properties and for distribution coefficients at infinite dilution in all the solvent-water systems considered.Presentation to First International Symposium on Solubility Phenomena, University of Western Ontario, London, Ontario, August 21–23, 1984.     

A method for measuring infinite-dilution partition coefficients of volatile compounds between the gas and liquid phases of aqueous systems

Vejrosta, J., Novák, J. and Jönsson, J.Å., 1982. A method for measuring infinite-dilution partition coefficients of volatile compounds between the gas and liquid phases of aqueous systems. Fluid Phase Equilibria, 8: 25–35.A method has been developed for measuring the partition coefficients of volatile compounds between the gas and liquid phases of aqueous systems, based on the direct analysis of both phases. A gas mixture containing a known proportion of a volatile compound is drawn through the liquid (water) until equilibrium is established. A defined volume of the liquid phase is then withdrawn through a porous-polymer trap while maintaining the system at equilibrium. The residual water in the trap is then expelled by a stream of nitrogen gas, and the deposit remaining is thermally desorbed and analyzed by gas chromatography. This approach, together with an experimental technique for producing gas mixtures containing an accurately known concentration of hydrocarbon at low values, makes it possible to determine accurately the partition coefficients of low-solubility compounds, such as for hydrocarbons in aqueous systems, at very low solute concentrations in the system. The method has been verified by measuring the partition coefficient of hexane between the gas and liquid phases of an aqueous system at various concentrations and temperatures.     

硝酸盐型卤水体系的综合热力学模型与多温相图预测

硝酸盐型卤水是盐湖卤水、 硝酸盐工业、 废水处理中普遍遇到的电解质溶液体系. 硝酸盐具有极高的溶解度, 实现硝酸盐型复杂电解质体系物性和相平衡的精准热力学表达依然具有挑战性. 以煤化工废水的典型体系Na⁺//NO₃^- , Cl^-, SO₄^{2 -} -H₂O为对象, 以改进的eNRTL模型为基础, 由活度系数模型、 溶液物性模型、 物种热力学模型和固液相平衡模型构成了电解质体系的综合热力学模型. 利用二元体系的冰点、 饱和蒸汽压、 等压摩尔热容、 活度系数和渗透压系数等物性数据和三元体系等温相平衡数据, 采用多目标优化方法, 获得了表达研究体系的多温特性的12组液相特征参数和7个固相物种的热力学参数. 据此完成了3个二元体系、 3个三元体系等温相平衡的准确计算和三元、 四元完整相图的预测, 适用温度达到实验所及的全部温度范围(254.65~543.15 K); 适用浓度达到饱和程度, 其中NaNO₃的浓度高达226.88 mol/kg. 三元、 四元体系的多温相图预测结果与实验数据相吻合, 并给出了9个三元、 5个四元体系零变点的完整信息.     

Evaporation of Lennard-Jones fluids

Evaporation and condensation at a liquid/vapor interface are ubiquitous interphase mass and energy transfer phenomena that are still not well understood. We have carried out large scale molecular dynamics simulations of Lennard-Jones (LJ) fluids composed of monomers, dimers, or trimers to investigate these processes with molecular detail. For LJ monomers in contact with a vacuum, the evaporation rate is found to be very high with significant evaporative cooling and an accompanying density gradient in the liquid domain near the liquid/vapor interface. Increasing the chain length to just dimers significantly reduces the evaporation rate. We confirm that mechanical equilibrium plays a key role in determining the evaporation rate and the density and temperature profiles across the liquid/vapor interface. The velocity distributions of evaporated molecules and the evaporation and condensation coefficients are measured and compared to the predictions of an existing model based on kinetic theory of gases. Our results indicate that for both monatomic and polyatomic molecules, the evaporation and condensation coefficients are equal when systems are not far from equilibrium and smaller than one, and decrease with increasing temperature. For the same reduced temperature T/T(c), where T(c) is the critical temperature, these two coefficients are higher for LJ dimers and trimers than for monomers, in contrast to the traditional viewpoint that they are close to unity for monatomic molecules and decrease for polyatomic molecules. Furthermore, data for the two coefficients collapse onto a master curve when plotted against a translational length ratio between the liquid and vapor phase.