Contribution of convection,diffusion and migration to electrolyte transport through nanofiltration membranes

Transport mechanisms through nanofiltration membranes are investigated in terms of contribution of convection, diffusion and migration to electrolyte transport. A Donnan steric pore model, based on the application of the extended Nernst-Planck equation and the assumption of a Donnan equilibrium at both membrane-solution interfaces, is used. The study is focused on the transport of symmetrical electrolytes (with symmetric or asymmetric diffusion coefficients). The influence of effective membrane charge density, permeate volume flux, pore radius and effective membrane thickness to porosity ratio on the contribution of the different transport mechanisms is investigated. Convection appears to be the dominant mechanism involved in electrolyte transport at low membrane charge and/or high permeate volume flux and effective membrane thickness to porosity ratio. Transport is mainly governed by diffusion when the membrane is strongly charged, particularly at low permeate volume flux and effective membrane thickness to porosity ratio. Electromigration is likely to be the dominant mechanism involved in electrolyte transport only if the diffusion coefficient of coions is greater than that of counterions.     

The determination of molecular diffusion coefficients by the barometric method

The binary molecular diffusion coefficients D _AB of a vaporizing liquid in gases under atmospheric conditions were measured by the new simple barometric method. A change in the pressure of a vapor-gas mixture in a closed cell was determined as a function of time. Under experimental conditions, one can also find partial saturated vapor pressures of substances. The deviations of the coefficients D _AB obtained by the new procedure from the literature values were within the spread of the experimental data. The D _AB coefficients (absent in the literature) were measured for mixtures of acetone, ethyl acetate, carbon tetrachloride, difluoroethanol, and cis and trans isomers of perfluorodecalin with argon. The saturated vapor pressures were determined for difluoroethanol and cis-and trans-perfluorodecalins under argon.     

Water transport coefficient distribution through the membrane in a polymer electrolyte fuel cell

The net water transport coefficient through the membrane, defined as the ratio of the net water flux from the anode to cathode to the protonic flux, is used as a quantitative measure of water management in a polymer electrolyte fuel cell (PEFC). In this paper we report on experimental measurements of the net water transport coefficient distribution for the first time. This is accomplished by making simultaneous current and species distribution measurements along the flow channel of an instrumented PEFC via a multi-channel potentiostat and two micro gas chromatographs. The net water transport coefficient profile along the flow channels is then determined by a control-volume analysis under various anode and cathode inlet relative humidity (RH) at 80 °C and 2 atm. It is found that the local current density is dominated by the membrane hydration and that the gas RH has a large effect on water transport through the membrane. Very small or negative water transport coefficients are obtained, indicating strong water back diffusion through the 30 μm Gore-Select^® membrane used in this study.     

Irreversible thermodynamics of transport across charged membranes : Part I — Macroscopic resistance coefficients for a system with nafion 120 membrane

The transport of aqueous NaCl solutions across the perfluorinated Nafion 120 membrane is studied on the base of irreversible thermodynamics. The straight resistance coefficients r_ii, partial frictions f_ik^p and diffusion indices RT/c?_ir_ii are presented and discussed. The results suggest that the main force, which impedes the flow of chloride ions across the membrane is not the friction of these ions with the negatively charged polymer network, but the friction with water. The diffusion indices RT/c?_ir_ii exceed self-diffusion coefficients found by some authors while using tracer technique. Following Meares' suggestion such results point out to the convective flow contribution to the transport of ions and water.     

A model for methanol transport through Nafion membrane in diffusion cell

The transport of methanol through Nafion^® membrane in diffusion cell is investigated using the open circuit potential method at different initial methanol concentration solutions. A simple mathematical model based on quasi-steady-state diffusion for the transport of methanol across the membrane in a diffusion cell is developed to simulate the experimental data in order to measure the methanol permeability. The influence of the diffusion cell parameters and thickness of the membrane on the methanol permeability measurement has been evaluated and analyzed. By means of Maclaurin expansion technique, this model can be used to predict the deviation of methanol permeability determined by steady-state diffusion model.     

The electrostatic and steric-hindrance model for the transport of charged solutes through nanofiltration membranes

Nanofiltration (NF) membranes possess the intermediate molecular weight cut-off between reverse osmosis membranes and ultrafiltration membranes, and also have rejection to inorganic salts. So one can assume that NF membranes have charged pore structure. We have developed the electrostatic and steric-hindrance (ES) model from the steric-hindrance pore (SHP) model and the Teorell-Meyer-Sievers (TMS) model (Wang et al., J. Chem. Eng. Japan, 28 (1995) 372) to predict the transport performance of charged solutes through NF membranes based on their charged pore structure. In this article, by doing the permeation experiments of aqueous solutions of neutral solutes and sodium chloride, the structural parameters (the pore radius and the ratio of membrane porosity to membrane thickness) and the charge density of NF membranes (Desal-S, NF-40, NTR7450 and G-20) were estimated on the basis of SHP model and the TMS model, respectively. Then, we selected an aqueous solution of different tracer charged solutes (sodium benzenesulfonate, sodium naphthalenesulfonate and sodium tetraphenyl-borate) and a supporting salt (sodium chloride) to verify the ES model. The prediction based on the ES model was in good agreement with the experimental results.     

Water sorption and diffusion coefficients of protons and water in PVDF-g-PSSA polymer electrolyte membranes

Water sorption properties, proton NMR spectra, and diffusion of water and protons in poly(vinylidene fluoride)-graft-polystyrene sulfonic acid (PVDF-g-PSSA) polymer electrolyte membranes were studied. Sorption curves for the membranes with different degrees of grafting in protonated and Na⁺ form were measured by equilibrating the membranes over saturated salt solutions. The membrane water content was found to be sensitive to changes in relative humidity (RH). The water/sulfonic acid ratio λ for the protonated samples was around 2 at 20% RH and increased to λ ∼ 30 at 100%. Proton NMR, pulsed field gradient proton NMR (PFG-NMR), and impedance measurements were made on membranes with different λ. In the proton NMR spectra only one peak was found, originating from the water in the membrane. The chemical shift of the peak was found to be dependent on the counterion and the water content. The water self-diffusion coefficients D_H2O, measured by PFG-NMR, increased with degree of grafting and water content of the membranes. The proton conductivity and the calculated proton mobility decreased more steeply than the D_H2O with decreasing water content. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2893–2900, 1999     

Chronopotentiometric method for the assessment of ionophore diffusion coefficients in solvent polymeric membranes

A chronopotentiometric method is proposed for the determination of the diffusion coefficients of free ionophores in solvent polymeric membranes. For the pH sensitive chromoionophore ETH 5294, the method was shown to give diffusion coefficients that correlate well with those assessed by both optical and chronoamperometric methods. The limit of applicability of the chronoamperometric and chronopotentiometric methods in terms of membrane composition and experimental parameters has been identified. The chronopotentiometric method was successfully used to determine the diffusion coefficients of eight ionophores and proved to be more robust and more widely applicable than the previously reported chronoamperometric and optical methods. An erratum to this article can be found at     

Efficient determination of diffusion coefficients by monitoring transport during recovery delays in NMR

A novel NMR approach allows one to efficiently determine translational diffusion coefficients of macromolecules in solution. This method for Signal Optimization with Recovery in Diffusion Delays (SORDID) monitors transport occurring during the recovery times between consecutive scans so that the duration of the measurements can be reduced approximately by a factor two.     

Differential permeation — Part I: A method for the study of solvent diffusion through membranes

We describe the differential permeation method for the study of the diffusion of solvents from a liquid (or liquid mixture) through flat or tubular membranes. This method consists of measuring the transient permeation rates through the membrane when one of its faces is suddenly put into contact with the liquid medium. The change in the transient rate with time is analyzed by numerical best fitting methods to determine the Fickian diffusion coefficient. A simplified equation is proposed for the fitting of the response of a tubular membrane. Deviations from the Fickian transport mechanism with concentration-independent diffusion coefficient can be evidenced and eventually analyzed by using other mechanistic models.     

Irreversible thermodynamics of transport across charged membranes : Part III - efficiency of energy conversion in separation processes with nafion 120 membrane from phenomenological transport coefficients

In separation processes with charged membranes, as in electrodialysis units or electrochemical cells, the efficiency of conversion of electrical energy into the concentration gradient of an electrolyte is depressed by the immediate flow of water in the direction opposite to the solute flow. The equations for energy conversion in transport of ions and water across a cation-exchange membrane are derived in the present paper treating the system as a three-flow process and employing phenomenological transport equations. With these equations, the two-flow (q_1E, q_wE, q_1w and overall (q̃_E) degrees of coupling and the total (η) and component (η_1E,η_wE) efficiencies of energy conversion have been computed for the system sodium chloride/Nafion 120 membrane at temperatures of 298 and 333 K and for solute concentrations between 0.05 and 4 M. Considering the continuous separation processes, the so-called “driving region” and the energy requirement to keep the concentration difference in the adjacent compartments constant (static head) have been calculated and discussed.     

A novel method for the determination of diffusion coefficients in amorphous poly(3-hydroxybutyrate)

A novel approach is proposed for the determination of the diffusion coefficient of certain drugs in amorphous poly(hydroxybutyrate) (PHB), which can be a reliable alternative to the conventional permeation based measurements. The method requires the preparation of PHB films with various concentrations of the drug and if the latter absorbs in the visible wavelength range, its concentration gradient in the polymer film as well as the time dependence of the latter can be analyzed quantitatively by following changes in color. Color can be converted into concentration with the help of adequate calibration and thus the dependence of additive concentration on space (x) and time (t), i.e. the c(x,t) function, can be determined relatively easily. The fitting of the numerical solution of Fick's second law onto the measured values provides directly the targeted diffusion coefficient. The comparison of diffusion coefficients obtained by the proposed approach to values published in the literature proved that the new method provides reliable results and requires reasonable time and effort at the same time.     

Estimation of diffusion and permeability coefficients of CO2 in polymeric membranes by FTIR method

Infrared spectra of CO₂ sorbed in rubbery and glassy polymeric membranes were measured to examine the relationships between the spectroscopic data and the physical properties of the membranes. The two peaks observed in the spectra of CO₂ were attributed to the R branch and P branch of CO₂ sorbed in the membranes based on the consideration that both peaks were observed at a temperature above the glass transition temperature of the membranes. Apparent diffusion coefficients of CO₂ in the membranes were measured from the desorption kinetics of CO₂ detected by FTIR spectroscopy. The solubility coefficients of CO₂ were also estimated from absorbance spectra of CO₂ sorbed in the membranes using Lambert-Beer's rule. The permeability, solubility, and diffusion coefficients estimated by the FTIR method were found to correlate well with the coefficients obtained by conventional methods such as vacuum-pressure or sorption isotherm methods. © 1996 John Wiley & Sons, Inc.     

Electrophoretic method for the determination of diffusion coefficients of ions in aqueous solutions*

The electrophoretic method was recently developed for the determination of diffusion coefficients of ions in aqueous solution. By solving the Fick's second law in the presence of unlimited media and constant quantity of diffusing species we obtain a relationship between the diffusion coefficient and the standard deviation of the distribution profile. The diffusion coefficients of Cd(II), In(III), Zr(IV), Hf(IV), Pu(VI) and [InDTPA]^2– in nitric acid solution were determined as well as the effective charge of In-DTPA complex at pH 4.50.     

Conditions for purely diffusional transport of charged reactant and charged product in the absence of supporting electrolyte

Steady-state currents of charged reactants, at a hemispherical ultramicroelectrode, are independent of the concentration of supporting electrolyte if the relationship z_R/z_P=D_R/D_P (R=ionic reactant, P=ionic product) is satisfied. Under the above conditions no electric field gradient is present in the solution and no migrational transport takes place. Also, there should be no distortion of the results caused by ohmic drop. The paper presents the theoretical derivation of appropriate equations.     

A new method of determination of diffusion coefficients using capillary zone electrophoresis (peak-height method)

Summary A new method of the determination of the diffusion coefficients,D, called “the peak-height method” has been developed. When the zone broadening of a species is solely caused by axial molecular diffusion, its diffusion coefficient can be calculated. The diffusion coefficients of L-cysteine and glutathione in a neutral phosphate buffer were measured by this method. Comparison between the experimental diffusion coefficient and the one calculated by the Wilke-Chang equation shows that the method gives good results.     

Mathematical modelling of low-frequency oscillations in solute transport by diffusion through a membrane

Low-frequency oscillations of concentration could occur in the case of substance diffusion through a membrane under stable external conditions. This phenomenon had been experimentally observed. A theoretical explanation of the phenomenon was given and the results of mathematical modelling were presented in the present paper. Models considering dependence of local conductivity of a membrane on concentration of a solution were studied. Emergence of positive feedback between fluctuations of flows and concentrations was shown. This determines an appearance of oscillations in the process of substance diffusion.     

A new method for determining membrane diffusion coefficients from their response to regular forced concentration waves

It is shown that when a membrane separates two permeant solutions, initially at equilibrium, and subsequently one of the solutions is forcibly oscillated, the concentration waves detected on the other side will show reduced amplitude and a change in phase angle. Using mathematical models it is shown that these may be expressed as explicit functions of the permeability and diffusion coefficient of the permeant, respectively. Solutions for cosine and square concentration waves are given. An experimental system was devised to exploit these effects and measure diffusion coefficients directly from the phase shift of the emergent waves. Input waves were generated using alternating sprays (concentrated and dilute) from two artists' air brushes. In preliminary experiments, diffusion coefficients for salt through test membranes were easily obtained to a precision of 5%.     

A New optical liquid membrane study technique : II. A Holographic interferometric study of transport through a liquid membrane

A liquid membrane consisting of a crown ether carboxylic acid dissolved in chloroform placed between a basic source aqueous solution and an acidic receiving aqueous solution was observed in a holographic interferometer to transport potassium ion by coupled counter-ion transport. Steady-state transport was achieved and quite precise measurements of the rate of transport made. The evolution of concentration gradients as a function of time was directly observed.