Influence of concentration on the activation energy for diffusion in polymer-solvent systems

The self-diffusion of benzene, toluene, and ethylbenzene in polystyrene have been analyzed using the Vrentas/Duda free-volume diffusion model. Diffusion coefficient predictions suggest an exponential concentration dependence of the activation energy required to overcome attractive forces, E. Without the use of any diffusion data approximating E as zero over the entire concentration range yields self-diffusion coefficient predictions which are in good agreement with experimental data. © 1992 John Wiley & Sons, Inc.     

Light scattering measurement and theoretical interpretation of mutual diffusion coefficients in binary liquid mixtures

Mutual diffusion coefficients for eleven binary systems of simple organic liquids have been measured by laser light scattering. By separating the mutual diffusion coefficient into a kinetic diffusion coefficient and a thermodynamic factor, we have been able to analyze the dynamical information contained in the kinetic coefficient in terms of a simple hard sphere theory of molecular motion. The hard sphere model of the kinetic diffusion coefficient is shown to be accurate for ideal and moderately nonideal solutions, and for both spherical and very nonspherical molecules. Only for extremely nonideal solutions were we unable to interpret diffusion coefficient data by our methods of analysis.     

Effect of molecular weight on the diffusion coefficient of carbon dioxide in polystyrene

The permeability and time lag at pressures below 1 atm were measured for carbon dioxide in five polystyrene samples with different molecular weights at 25 to 40°C. The apparent permeability coefficient decreases with increasing carbon dioxide pressure and also decreases with increasing molecular weight of polystyrene, whereas the apparent diffusion coefficient calculated from time lag increases with pressure and is independent of molecular weight. Parameters for the partial-immobilization model were determined from the apparent diffusion and permeation coefficients by using a nonlinear least-squares optimization program without using sorption data. The results suggest that the void-saturation constant C′_H decreases as the molecular weight of the polymer increases or as the chain-end free volume decreases. The significance of these observation and their interpretation is discussed in terms of free-volume theory for glassy polymers.     

(Liquid + liquid) equilibria of binary polymer solutions using a free-volume UNIQUAC-NRF model

In this work, a modified free-volume (FV) model based on the UNIQUAC-Nonrandom factor (UNIQUAC-NRF) model developed by Haghtalab and Asadollahi was proposed. While the combinatorial part of the proposed model for activity coefficient takes the same form as that of the entropic free-volume (entropic-FV) model, the residual part is similar to that of the UNIQUAC-NRF model. The proposed model, i.e., the FV-UNIQUAC-NRF model overcomes the main shortcoming of the original UNIQUAC-NRF model in predicting the lower critical solution temperature (LCST) for polymer solutions. The appearance of the LCST is believed to be attributed to the existence of the free volume differences between polymer and solvent molecules. Thus, the models without considering such differences fail to predict the LCST behavior of polymer solutions. The proposed model was applied to correlate the experimental data of (liquid + liquid) equilibria (LLE) for a number of binary polymer solutions at various temperatures. The values for the binary characteristic energy parameters for the proposed model and the FV-UNIQUAC model along with their average relative deviations from the experimental data were reported. It should be stated that the binary polymer solutions studied in this work were considered as monodisperse. The results obtained from the FV-UNIQUAC-NRF model were compared with those obtained from the FV-UNIQUAC model. The results of the proposed model show that the FV-UNIQUAC-NRF model can accurately correlate the experimental data for LLE of polymer solutions studied in this work. Also the error produced from the FV-UNIQUAC-NRF model show the slightly better accuracy in comparison with that from the FV-UNIQUAC model. The clear advantage of the proposed model, contrary to the original UNIQUAC-NRF model, is its capability in predicting the LCST for binary polymer solutions.     

Empirical Multicomponent Equilibrium and Film-Pore Model for the Sorption of Copper,Cadmium and Zinc onto Bone Char

The adsorption of three metal ions onto bone char has been studied in both equilibrium and kinetic systems. An empirical Langmuir-type equation has been proposed to correlate the experimental equilibrium data for multicomponent systems. The sorption equilibrium of three metal ions, namely, cadmium (II) ion, zinc (II) ion and copper (II) ion in the three binary and one ternary systems is well correlated by the Langmuir-type equation. For the batch kinetic studies, a multicomponent film-pore diffusion model was developed by incorporating this empirical Langmuir-type equation into a single component film-pore diffusion model and was used to correlate the multicomponent batch kinetic data. The multicomponent film-pore diffusion model shows some deviation from the experimental data for the sorption of cadmium ions in Cd-Cu, Cd-Zn and Cd-Cu-Zn systems. However, overall this model gives a good correlation of the experimental data for three binary and one ternary systems.     

Measurements of molecular and thermal diffusion coefficients in ternary mixtures

Thermal diffusion coefficients in three ternary mixtures are measured in a thermogravitational column. One of the mixtures consists of one normal alkane and two aromatics (dodecane-isobutylbenzene-tetrahydronaphthalene), and the other two consist of two normal alkanes and one aromatic (octane-decane-1-methylnaphthalene). This is the first report of measured thermal diffusion coefficients (for all species) of a ternary nonelectrolyte mixture in literature. The results in ternary mixtures of octane-decane-1-methylnaphthalene show a sign change of the thermal diffusion coefficient for decane as the composition changes, despite the fact that the two normal alkanes are similar. In addition to thermal diffusion coefficients, molecular diffusion coefficients are also measured for three binaries and one of the ternary mixtures. The open-end capillary-tube method was used in the measurement of molecular diffusion coefficients. The molecular and thermal diffusion coefficients allow the estimation of thermal diffusion factors in binary and ternary mixtures. However, in the ternaries one also has to calculate phenomenological coefficients from the molecular diffusion coefficients. A comparison of the binary and ternary thermal diffusion factors for the mixtures comprised of octane-decane-1-methylnaphthalene reveals a remarkable difference in the thermal diffusion behavior in binary and ternary mixtures.     

Soret coefficients of mixed electrolytes

Practical equations are developed which relate the Soret coefficients of mixed electrolytes to the entropies and enthalpies of transport. The derived equations together with published binary thermal diffusion data can be used to estimate the Soret coefficients of mixed electrolytes. The procedure is illustrated for the systems NaCl+HCl+ water and NaCl+MgCl₂+ water. Aqueous NaCl, like most salts, diffuses to the cold plate in binary Soret experiments. In aqueous HCl solutions, however, NaCl can diffuse to the warm plate, and the magnitude of its Soret coefficient can take values twice as large as those for binary solutions. The thermal diffusion of trace amounts of a salt in a solution containing a large excess of another salt is discussed. Exceptionally large Soret effects are predicted for traces of strong acids in aqueous salt solutions.     

Diffusion in polyacrylate aqueous systems at 25°C. Role of reference frame choice in interpreting diffusion coefficient data

Diffusion coefficients have been measured for the binary systems sodium polyacrylate-water and polyacrylic acid-water at 25°C as a function of concentration. Diffusion coefficients have been also measured for the ternary system sodium chloride-sodium polyacrylate-water at constant NaCl concentration and varying polyacrylate concentration. The experimental results have been compared with some limit expressions, available in literature, for the four D _ik diffusion coefficients of systems containing two electrolytes with a common ion. The ternary system shows strong interaction between flows: as the polyelectrolyte concentration, C₂, approaches zero, the main diffusion coefficient D₂₂ and the cross coefficient D₂₁ approach zero, while the cross coefficient D₁₂ reach quite high values. The water motion during the diffusion process is also discussed.     

Effect of macromolecular polydispersity on diffusion coefficients measured by Rayleigh interferometry

Rayleigh interferometry has been extensively used for the precise determination of diffusion coefficients for binary and ternary liquid mixtures. For ternary mixtures, the 2x2 matrix of multicomponent diffusion coefficients is obtained. Polydispersity adds complexity to the meaning of these measured diffusion coefficients. Here we discuss three important issues of polydispersity regarding the diffusion measurements extracted from this interferometric technique. First, we report novel equations for the extraction of diffusion moments from the Rayleigh interferometric pattern. These moments are used to define polydispersity parameters for macromolecular systems. We have experimentally determined mean diffusion coefficients and polydispersity parameters for aqueous solutions of poly(ethylene glycol) and poly(vinyl alcohol) at 25 degrees C. Aqueous solutions of poly(ethylene glycol) mixtures were used to examine the accuracy of the polydispersity parameters. Second, we compare Rayleigh interferometry to dynamic light scattering. Specifically, we have performed diffusion measurements on the same system using both techniques. To our knowledge, no direct experimental comparison between dynamic light scattering and classical methods for the measurements of diffusion coefficients has been previously reported in relation to polydispersity. We find that substantial discrepancies (i.e., 1 order of magnitude) between the mean diffusion coefficients obtained from these two different techniques can be observed when polydispersity is large. Third, for two-solute mixtures with one polydisperse solute, we report a novel corrective procedure for extracting accurate ternary diffusion coefficients from Rayleigh interferometry. Computer simulations were used to examine the accuracy of the extracted ternary diffusion coefficients.     

Permeation of pure carbon dioxide and methane and binary mixtures through cellulose acetate membranes

Steady-state permeation rates for pure CO₂ and CH₄ and their binary mixtures through homogeneous dense cellulose triacetate membranes have been measured at three temperatures between 20 and 40°C and pressures up to 2.8 MPa. The pressure dependence of the mean permeability coefficient for CO₂ can be described by the total immobilization model in conjunction with a modified free-volume model. No appreciable pressure dependence of the permeability coefficient for CH₄ is observed, while the permeability coefficients for CH₄ in binary mixture of CO₂ and CH₄ depend on applied gas pressure. The pressure dependences of the mean permeability coefficients for the components in the binary mixture are discussed in terms of the above mobility model. Membrane plasticization induced by CO₂ affects permeation by both gases.     

Diffusion in aqueous copper sulfate and copper sulfate-sulfuric acid solutions

Diffusion coefficients of copper sulfate-water and copper sulfate-sulfuric acid-water solutions have been determined at 25°C using conductimetric and diaphragm-cell techniques. The ternary diffusion measurements indicate that diffusion of sulfuric acid can produce large counterflows of copper sulfate and vice versa. If diffusion of copper sulfate in aqueous sulfuric acid solutions is treated as a binary process, the measured apparent diffusivities of copper sulfate can be 1 to 8% lower than the salt's true diffusivity. Equations are developed to predict transport coefficients from the concentrations and mobilities of the diffusing species.     

Characterization of thermal diffusion of polystyrene in binary mixtures of THF/dioxane and THF/cyclohexane

The thermal diffusion coefficient (D_τ) was determined for three polystyrene standards of different molecular masses in binary mixtures of tetrahydrofuran/dioxane and tetrahydrofuran/cyclohexane of various compositions. The D_τ values were obtained by combining retention data from thermal field-flow fractionation measurements with diffusion data from dynamic light scattering experiments. In agreement with earlier work of Schimpf and Giddings, the thermal diffusion coefficient was found to be virtually independent of the molecular mass of the polymers. In the binary mixtures of tetrahydrofuran and dioxane, both good solvents for polystyrene, the D_τ value was approximately equal to the average of the D_τ values in the pure solvents, weighted according to the mole fractions of the solvents in the mixture. However, for polystyrene in binary mixtures of tetrahydrofuran and cyclohexane this linear behavior of the thermal diffusion phenomenon was not observed. The addition of cyclohexane to tetrahydrofuran has initially only a minor effect on the molecular and thermal diffusion coefficients of the polystyrene standards. Because cyclohexane is a theta solvent for polystyrene, the preferential solvation of polystyrene by tetrahydrofuran could be an explanation for these results. © 1996 John Wiley & Sons, Inc.     

Diffusion in microstructured block copolymer solutions

This work explores the effect of heterogeneity of chemical composition on tracer diffusion, when the characteristic size of the heterogeneities approaches that of the diffusing molecule. A heterogeneous environment is created by the self-assembly of diblock copolymers in solution. The system chosen for this study is polystyrene-polyisoprene diblock copolymers in toluene, which is a common solvent for the two blocks. Above a certain critical concentration, these systems are known to microphase separate into swollen domains of polystyrene and polyisoprene. Diffusion of homopolystyrene through the microstructure is measured in this work. The characteristics of the microstructure are varied by studying block copolymers of different molecular weights and compositions. The tracer diffusion coefficients of the labelled polystyrenes are measured by forced Rayleigh scattering, while the microstructure of the matrix is inferred from small angle X-ray scattering measurements. In this paper, we report results for the diffusion of polystyrenes (molecular weights 3.2 × 10⁴ and 9.0 × 10⁴) in microstructured solutions of three copolymers. Two copolymer samples forming lamellae of alternating polystyrene and polyisoprene microphases and one sample forming polystyrene cylinders embedded in a polyisoprene matrix have been examined. The data indicate that the tracer diffusion coefficient of 3.2 × 10⁴ molecular weight polystyrene in lamellar and cylindrical solutions is comparable to that of the homopolymer in a homogeneous solution of the same concentration. In contrast, the diffusion of 9.0 × 10⁴ molecular weight polystyrene is substantially slower in the structured solutions than in unstructured solutions of the same concentration. For example, the diffusion coefficient of 9.0 × 10⁴ molecular weight polystyrene in a 47% block copolymer solution with cylindrical microstructure is lower than its value in a homogeneous solution of the same concentration by a factor of 30.     

Thermodynamic studies of drug-alpha-cyclodextrin interactions in water at 298.15 K: promazine hydrochloride/chlorpromazine hydrochloride + alpha-cyclodextrin + H(2)O systems

Data on osmotic coefficients have been obtained for a binary aqueous solution of two drugs, namely, promazine hydrochloride (PZ) and chlorpromazine hydrochloride (CPZ) using a vapor pressure osmometer at 298.15 K. The observed critical micelle concentration (cmc) agrees excellently with the available literature data. The measurements are extended to aqueous ternary solutions containing fixed a concentration of alpha-cyclodextrin (alpha-CD) of 0.1 mol kg(-1) and varied concentrations (approximately 0.005-0.2 mol kg(-1)) of drugs at 298.15 K. It has been found that the cmc values increase by the addition of alpha-CD. The mean molal activity coefficients of the ions and the activity coefficient of alpha-CD in binary as well as ternary solutions were obtained, which have been further used to calculate the excess Gibbs free energies and transfer Gibbs free energies. The lowering of the activity coefficients of ions and of alpha-CD is attributed to the existence of host-guest (inclusion)-type complex equilibria. It is suggested that CPZ forms 2:1 and 1:1 complexed species with alpha-CD, while PZ forms only 1:1 complexed species. The salting constant (ks) values are determined at 298.15 K for promazine-alpha-CD and chlorpromazine-alpha-CD complexes, respectively, by following the method based on the application of the McMillan-Mayer theory of virial coefficients to transfer free energy data. It is noted that the presence of chlorine in the drug molecule imparts better complexing capacity, the effect of which gets attenuated as a result of hydrophobic interaction. The results are discussed from the point of view of associative equilibria before the cmc and complexed equilibria for binary and ternary solutions, respectively.     

Osmotic and activity coefficients in the binary solutions of 1-butyl-3-methylimidazolium chloride and bromide in methanol or ethanol at T = 298.15 K from isopiestic measurements

Osmotic coefficients of the binary solutions of two room-temperature ionic liquids (1-butyl-3-methylimidazolium chloride and bromide) in methanol and ethanol have been measured at T = 298.15 K by the isopiestic method. The experimental osmotic coefficient data have been correlated using a forth-order polynomial in terms of (molality)^0.5, with both, ion interaction model of Pitzer and electrolyte non-random two liquid (e-NRTL) model of Chen. The values of vapor pressures of above-mentioned solutions have been calculated from the osmotic coefficients. The model parameters fitted to the experimental osmotic coefficients have been used for prediction of the mean ionic activity coefficients of those ionic liquids in methanol and ethanol.     

A comparative study between cosolvent and cononsolvent ternary polymer systems through the preferential adsorption coefficient

Sorption equilibrium of polystyrene and poly (dimethyl siloxane) in mixed solvents has been monitored by means of the preferential adsorption coefficient experimentally determined from intensity light scattering measurements. The pairs of solvents used to dissolve each polymer sample have been selected for the purpose to perform cosolvent and cononsolvent ternary polymer systems. Flory-Huggins formalism including ternary interactions has been used to predict the sorption equilibrium for the cosolvent system and, for the first time, for cononsolvent ones. Moreover, the proportionality between binary and ternary interactions, recognized by Pouchly, is also corroborated for both ternary polymer systems. From a thermodynamic standpoint, the sorption equilibrium has been described by approaching the behavior of the bulk solvent to the binary liquid mixture through the excess Gibbs free energy.     

Modeling of size-exclusion chromatography of electrolytes on non-ionic nanoporous adsorbents

A dynamic model has been developed for chromatographic separation of mixed electrolyte solutions with non-ionic nanoporous adsorbents. The thermodynamic equilibrium condition at the pore entrance is written in terms of mixing, electrostatic and size-exclusion effects. The model is tested against experimental data measured with three binary mixtures on hypercrosslinked polystyrene and nanoporous carbon. The selectivity of the nanoporous adsorbents can be explained by the size-exclusion of the electrolytes and enrichment of both electrolytes in frontal chromatographic runs can be correlated satisfactorily with the proposed model. The model is also used to demonstrate continuous separation in a simulated moving-bed (SMB) system.     

Determination of Diffusion Coefficients for Binary Nonelectrolyte Mixtures. A Free-Volume Predictive Approach

A diaphragm cell has been used to measure mutual diffusion coefficients at 25°C for four binary nonelectrolyte mixtures: ethylbenzene + n-hexane, carbon tetrachloride + ethylbenzene, cyclohexane + p-xylene, and 1,2-dichloroethane + cyclohexane. A free-volume predictive approach for binary mutual diffusion coefficients was developed and tested. Only infinite dilution diffusion coefficients, some readily available pure substance data, and UNIFAC group contribution parameters are used in the model. No binary equilibrium thermodynamic information is required. For 73 binary systems with an overall average absolute deviation of 5.2%, it has been shown that the developed method is better than two commonly available reference methods for the prediction of liquid diffusion coefficients.     

On the interpretation of ternary diffusion measurements in low-molecular weight fluids by dynamic light scattering

Dynamic light scattering (DLS) allows for efficient measurement of physical transport properties in fluids. It is now a well established technique for determination of mutual mass diffusion coefficients in binary mixtures and multicomponent macromolecular solutions. More recently, ternary systems of low-molecular weight compounds have been analyzed by DLS where it was found that only one of the two mass diffusion modes can be observed. In this work, a theoretical interpretation of these findings is provided. For this purpose, a simple theory is developed that describes the observed signals. Thereby, it can be shown that both diffusion modes contribute to the signal but one mode is strongly enhanced for situations typically encountered in DLS experiments. The developed theory thus clarifies the relationship between ternary DLS measurements and other diffusion experiments. It provides the practical basis for quantitative analysis of DLS experiments in ternary low-molecular weight fluids.