Solute diffusion through swollen polymer membranes

Experiments were designed to study the role of the solvent in the transport of a solute through a solvent-swollen polymer membrane. A single solute (an organic dye), a single polymer (cross-linked natural rubber), and 24 different organic solvents were used for this purpose. The solute diffusion coefficient D was calculated from the measured permeability P and distribution coefficient K, and was compared to the diffusion coefficient of the solute in the pure solvent. The main parameters of the solvent were shown to be its viscosity and the degree it swells the polymer. At high swelling, the results are in agreement with a model that pictures the resistance to solute diffusion as hydrodynamic interaction with the solvent while the polymer acts as an obstruction that increases the tortuosity of the diffusion path. At very low swelling, the diffusion coefficient approaches an asymptotic limit which is independent of solvent viscosity. However, even with as low as 10% solvent, some effects of viscosity are still seen. These results are discussed in terms of a quantitative theory for the obstruction effect proposed by Meares and compared to other literature data.     

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.     

Permeability and partition coefficient of aqueous sodium chloride in soft contact lenses

Transport of physiologic saline through soft contact lenses is important to on‐eye behavior. Using a specially designed Stokes‐diaphragm cell, we measure aqueous NaCl permeabilities through commercial soft contact lenses at 35°C. The permeabilities increase exponentially with the water content of the lenses spanning a range from 10⁻⁷ to 10⁻⁵ cm²/s. Equilibrium partition coefficients are obtained by the back‐extraction of lenses initially immersed in 1M aqueous NaCl. Partition coefficients also increase with lens water content but over a smaller range, from 0.1 to 0.7. Because the partition coefficient values are smaller than the water content of the lenses, ideal theory is not followed. Donnan exclusion, bound water, and excluded volume are proposed explanations. The diffusion coefficients of aqueous NaCl through soft contact lenses increase with increasing lens water content following free‐volume theory. Aqueous NaCl diffusivities in the lower water‐content lenses are smaller than the diffusion coefficient of NaCl in water by factors up to 100 indicating very tortuous diffusion paths. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Measurement of the diffusion coefficient of aluminum in mercury

The diffusion coefficient of aluminum in mercury was measured over a concentration of 0.9 to 14 mM. It was found to increase with increasing concentration from 1.2 × 10^?5 to 1.9 × 10^?5 cm² sec ^?1. This unusual dependence of D on C was attributed to the formation of aggregates of several aluminum atoms in the amalgam.     

Concentration-induced stress effects in diffusion of vapors through polymer membranes

There are two types of anomalous diffusion of vapors in solid polymers which are held to be due to swelling. If the latter is seen as strain, then there must be an accompanying stress which can affect the nature and magnitude of diffusion. The theories of diffusion in polymers are examined in light of the network theory of Larché and Cahn. Their formalism is used to solve permeation and sorption in polymer membranes to illustrate the general features of the elastic effects, particularly the time-dependent nature of the solubility. That “anomalous” effects will be present is without doubt, considering the concurrent nature of the added elastic effects. However, the present calculations fail to unearth any behavior similar to the case II diffusion. An order of magnitude estimate has been provided which shows that the effects of elasticity are usually significant in rubbery or amorphous glassy polymers where the anomalous effects occur.     

Swelling and diffusion properties from elongation of two-phase polymer membranes

Experimental results were presented dealing with the water permeance and diffusion rate in two-phase membranes consisting of hydrophilic domains of polyacrylic acid chemically bound by grafting to hydrophobic matrices: these are either rigid crystalline (polypropylene) or elastomeric amorphous (EPDM). Permeance is higher in rigid matrices: this is attributed to the wide net of microfractures originated from swelling of the hydrophilic domains whose formation is only possible in the case of a rigid matrix. A calculation method was proposed, which allows the evaluation of the apparent diffusion coefficient of both water and salt, starting from dilatometric measurements of membranes contacted with water and salt water. The apparent diffusion coefficient of water in rigid membranes is of the order of 10^-8 cm² sec^-1, whereas in elastomeric membranes it appeared about 100 times lower. The apparent diffusion coefficient of salt is of the order of 10^-12 cm² sec^-1 for both rigid-matrix and elastomeric membranes when previously swollen.     

Direct rotating ring-disk measurement of the sodium borohydride diffusion coefficient in sodium hydroxide solutions

This paper presents the experimental determination of the diffusion coefficient of borohydride anion and solution kinematic viscosity for a large panel of NaOH + NaBH₄ electrolytic solutions relevant for use as anolyte in Direct Borohydride Fuel Cells (DBFC). The diffusion coefficients have been measured by the transit-time technique on gold rotating ring-disk electrodes, and verified using other classical techniques reported in the literature, namely the Levich method and Electrochemical Impedance Spectroscopy on a gold RDE, or chronoamperometry at a gold microdisk. The agreement between these methods is generally good. The diffusion coefficients measured from the RRDE technique are however ca. twice larger than those previously reported in the literature (e.g. ca. 3 × 10⁻⁵ cm² s⁻¹ in 1 M NaOH + 0.01 M NaBH₄ at 25 °C in the present study vs. ca. 1.6 × 10⁻⁵ cm² s⁻¹ in 1 M NaOH + 0.02 M NaBH₄ at 30 °C in the literature, as measured by chronoamperometry at a gold microsphere), which is thoroughly discussed. Our measurements using chronoamperometry at a gold microdisk showed that such technique can yield diffusion coefficient values below what expected. The origin of such finding is explained in the frame of the formation of both a film of boron-oxide(s) at the surface of the (static) gold microdisk and the generation of H₂ bubbles at the electrode surface (as a result of the heterogeneous hydrolysis at Au), which alter the access to the electrode surface and thus prevents efficient measurements. Such film formation and H₂ bubbles generation is not so much of an issue for rotating electrodes thanks to the convection of electrolyte which sweeps the electrode surface. In addition, should such film be present, the transit-time determination technique on a RRDE displays the advantage of not being very sensible to its presence: the parameter measured is the time taken by a perturbation generated the disk to reach the ring trough a distance several orders of magnitude bigger than the film thickness, thus minimizing its effect.     

Estimation of diffusion coefficient for solute–polymer systems

Diffusion coefficients are needed for the analysis of many mass transfer problems involving polymers. Since the diffusivity for such systems are strong functions of temperature and concentration, the analysis of these problems is greatly facilitated if predictive methods are available for the determination of the required diffusion coefficient. Because of the limitations of the theoretical approaches for estimating diffusivity, empirical correlation of solute–polymer diffusion coefficient data with physical properties of the solute were investigated. Chemical permeation measurements were made for several organic liquids through three elastomers (polychoroprene, butyl and nitrile rubber) at five different temperatures, ranging from 25 to 65°C. The collected diffusivities were correlated with liquid kinematic viscosity. Diffusivities (at different temperatures) depend mainly on the kinematic viscosity of solutes. The results also indicate a close relation between the variation of diffusivity and viscosity with temperature.     

Friction coefficient analysis of multicomponent solute transport through polymer membranes

A new analysis is presented of the relations between the multicomponent diffusion coefficients and the classical Kedem–Katchalsky coefficients which describe solute transport in membranes. This analysis is applied to binary and ternary systems and shows the importance of system nonideality in the calculation of solute diffusion coefficients. It is shown that the solute permeability coefficients can be calculated from independent knowledge of the nonideal thermodynamic activity coefficients and the multicomponent diffusion coefficients of the system. © 1996 John Wiley & Sons, Inc.     

Pressure-induced diffusion of organic liquids through highly swollen polymer membranes

The transport of twelve organic liquids through a highly swollen rubbery membrane has been studied. The transport was caused by a pressure applied to the liquid above the membrane (reverse osmosis). The flux was found to be a highly nonlinear function of the driving pressure. Detailed thermodynamic and diffusion theories are proposed to describe the transport in terms of the concentration gradient of the swelling liquid within the membrane induced by the applied pressure. The data and the theory appear to be in very good agreement. The diffusion coefficients deduced from the data are explained in terms of a hydrodynamic mechanism of diffusion. Highly swollen membranes can yield very high liquid fluxes at moderate pressure and consequently may have applications for performing certain separations.     

Concentration dependence of the diffusion coefficient in polymer solution and molecular weight distribution determined by the diffusion method

The effects of the concentration dependence of the diffusion coefficient of a polymer solution (polystyrene in benzene and cyclohexane) in determining molecular weight distribution by the diffusion method are briefly discussed. The value of the ratio D_m0/D_A0 in a good solvent was found to be close to 1.0 for a polydisperse polymer and less than 1.0 for monodisperse polymers. Molecular weight distribution curves of the polydisperse sample were obtained by the diffusion method in cyclohexane and benzene, respectively. The molecular weight distribution curve obtained for the polymer used in benzene solution looked as if the polymer had a narrow molecular weight distribution. The phenomena cited above were interpreted in the light of the concentration dependence of the diffusion coefficient of polymer solutions.     

An equation for estimating the diffusion coefficient of electrolytes in ion exchange membranes

When operating electrodialysis equipment with ion exchange membranes, the diffusion coefficient in the membrane must be predetermined. We derived an equation to estimate the diffusion coefficient with only one unknown factor by assuming that the mobility of counter-ions in the membrane was proportional to that in the solution.The diffusion experiments were studied by a stirring cell method. The value of an apparent permeability coefficient became constant after 7200 seconds. The value was approximately equal to that of the permeability coefficient in the membrane at 200 rpm. The diffusion coefficients in the membranes were obtained for various electrolytes. The unknown factor was determined by comparing the theoretical with the experimental value of the diffusion coefficient, and a final equation to estimate the diffusion coefficient was derived. The diffusion coefficient in the membrane increased slightly with the increase of the electrolyte concentration.     

文物冷冻干燥水蒸气扩散系数的测量

采用聚乙二醇(PEG)溶液进行预处理,然后加以冷冻干燥,是保护出土饱水木质文物的有效方法。在自制的冷冻干燥装置上进行了仿木质文物的冻干实验,根据实验数据拟合得到了干燥区的水蒸气扩散系数。该数据将为文物冻干过程的时间预测和控制优化提供帮助。     

Block polymer nonionic surfactants in textiles

Block polymer surfactants have wide acceptance in the textile industry. These products are characterized by low-to-moderate foam, low levels of toxicity, and a variety of other desirable physical properties. This paper reviews their use as lubricants, texturizers, antistats, softeners, dyes, rayon processing agents, emulsifiers, defoamers and bleaching agents.     

Measurement of binary diffusion coefficient of gases and organic vapours by chromatography

The binary diffusion of organic vapours such as benzene, nitrobenzene, aniline, n-hexane, acetone, ethyl alcohol and toluene in H₂, Ar and N₂ at different temperatures and the diffusion coefficients of the gas pairs; Ar-O₂, Ar-N₂, Ar-SO₂, N₂-NH₃, N₂-O₂, N₂-CO₂ & N₂-SO₂ at 25°C have been studied using a gas chromatograph (GCHF-18). Good agreement was found between observed and theoretically calculated values of diffusion coefficients.     

The diffusion of nonionic penetrants in polyamide

The diffusion behavior of nonionic penetrants in aqueous solution into nylon 6 was examined in the temperature range 5°–95°C. The Arrhenius plot of the diffusion coefficients is linear and its slope changes at 30–40°C higher than the glass transition temperature in water, as determined by dilatometry and viscoelastic measurements. The results are discussed in relation to the molecular size of the penetrant and the segmental motion of polymer chains.     

Development of a predictive model for polymer/solvent diffusion coefficient calculations

A new calculation procedure for free‐volume parameters is considered in this work by using viscosity prediction methods and the Levenberg‐Marquardt calculation scheme. All parameters used in the Vrentas–Duda free‐volume theory can be estimated from pure component properties. The prediction results are compared with experimental data for some polymer/solvent systems. The diffusion coefficient calculated by Vrentas–Duda theory can be used in the modeling of membrane separation processes. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Measuring oxygen, carbon monoxide and hydrogen sulfide diffusion coefficient and solubility in Nafion membranes

A Devanathan-Stachurski type diffusion cell made from a fuel cell assembly is designed to evaluate the gas transport properties of a proton exchange membrane as a function of cell temperature and gas pressure. Data obtained on this cell using the electrochemical monitoring technique (EMT) is used to estimate solubility and diffusion coefficient of oxygen (O₂), carbon monoxide (CO) and hydrogen sulfide (H₂S) in Nafion membranes. Membrane swelling and reverse-gas diffusion due to water flux are accounted for in the parameter estimation procedure. Permeability of all three gases was found to increase with temperature. The estimated activation energies for O₂, CO and H₂S diffusion in Nafion 112 are 12.58, 20 and 8.85 kJ mol⁻¹, respectively. The estimated enthalpies of mixing for O₂, CO and H₂S in Nafion 112 are 5.88, 3.74 and 7.61 kJ mol⁻¹, respectively. An extensive comparison of transport properties estimated in this study to those reported in the literature suggests good agreement. Oxygen permeability in Nafion 117 was measured as a function of gas pressures between 1 and 3 atm. Oxygen diffusion coefficient in Nafion 117 is invariant with pressure and the solubility increases with pressure and obeys Henry's law. The estimated Henry's constant is 3.5 × 10³ atm.     

Rotational diffusion coefficient of rod-like polymer with a slight flexibility in semidilute and concentrated solutions

Summary A confined stiff chain model is suggested for the prediction of the rotational diffusion coefficient of a rigid rodlike polymer with a slight flexibility above the region of dilute solution (c1/L³). It shows a fairly good agreement with the experimental data of various polymers. Among them, PBLG and PBT with more rigidity are more consistent with the model when the log-jamming effect is considered. The predicted rotational diffusivity shows approximately the inverse seventh-power of length, which is less than 9 of Doi-Edwards tube model, but larger than the experimental value 5.7 of M-virus, while it shows the inverse power of concentration is a little larger than the value 2 of tube model except for the rodlike virus M-13.