Investigation of gas transport through porous membranes based on nonlinear frequency response analysis

Theoretical development of a new experimental method for investigation of mass transport in porous membranes, based on the principle of the modified Wicke-Kallenbach diffusion cell and the nonlinear frequency response analysis is presented. The method is developed to analyze the transport of a binary gas mixture in a porous membrane. The mixture is assumed to consist of one adsorbable and one inert component. Complex mass transfer mechanism in the membrane, where bulk or transition diffusion in the pore volume and surface diffusion take place in parallel, is assumed. Starting from the basic mathematical model equations and following a rather standardized procedure, the frequency response functions (FRFs) up to the second order are derived. Based on the derived FRFs, correlations between some characteristic features of these functions on one side, and the whole set of equilibrium and transport parameters of the system, on the other, are established. As the FRFs can be estimated directly from different harmonics of the measured outputs, these correlations give a complete theoretical basis for the proposed experimental method. The method is illustrated by quantifying the transport of helium (inert gas) and C₃H₈ and CO₂ (adsorbable gases) through a porous Vycor glass membrane.     

Micelle-mediated transport of vitamin K1 through porous membranes: contribution of phosphatidylcholine-bile salt mixed micelles

Diffusion of vitamin K1 solubilized by phosphatidylcholine-sodium deoxycholate mixed micelles through porous membranes having various pore characteristics was examined. The membranes include Nuclepore, Duragard and nitrocellulose membranes, which were intended to mimic the narrow channels in the vicinity of absorptive brush border. The diffusion coefficient of the mixed micelles was 4.6-5.5 x 10(-7) cm2/s, from which the hydrodynamic radius was calculated to be about 50 A. The dependence of the diffusivity on pore size showed that the transport of the micelles is hindered by pores having a radius ratio of the diffusate to the pore of about 0.05 or larger.     

Competitive facilitated transport through liquid membranes

A mathematical model is presented which solves the dimensionless, transient, non-linear partial differential equations governing the competitive facilitated transport of two gases through a liquid membrane. The model incorporates the mass transfer coefficients in the boundary conditions for the free gas concentrations. Several studies were carried out. A comparison of this model with a steady-state “equilibrium core” model was excellent. Through varying the dimensionless parameters, it was found that gas I would have a higher steady-state facilitation factor than gas 2 if k₁ >k₂ and k_-1k_-2. The boundary conditions and mass transfer coefficients were also varied to see their effects on the facilitation factors. The idea of pumping one of the gases against its concentration gradient was shown to be theoretically possible.     

Ion transport modelling through nanofiltration membranes

The aim of this work is to study the transport mechanism of ions through nanofiltration membranes. A model based on extended Nernst–Planck and film theory equations is reported. This model can be characterized by three transport parameters: the water permeability L_p, the salt transmittance Φ and the effective salt transfer coefficient K_eff. The knowledge of the feed and permeate concentration and of the permeate volumetric flux enable us to calculate these transport parameters. The model is used to estimate cadmium salts rejection by a NANOMAX 50 membrane. Experimental and calculated results are shown to be in good agreement. The model is then successfully extended to experimental data reported in the literature.     

Quantum model for transport through membranes

In the present paper a new model for the transport through membranes, introduced previously by Hosur, is considered. In this model, the membrane is assimilated to a potential barrier, and the material flow through the membrane is determined from the transmission coefficient of the barrier, assuming the existence of an energy difference among the molecules placed at both sides of the membrane. An equation for the transport, in the case of small energy differences, is obtained, which is particularized to the cases that the energy difference is caused by a temperature gradient, a concentration gradient, and both gradients acting together. In all cases, under certain limitations, formally identical equations to those of the thermodynamics of irreversible processes are obtained.     

Separation of mixed gases through porous polymeric membranes

The separation of a gas from a two component gas system was studied both theoretically and experimentally. Helium and argon as an inorganic gas pair, ethylene and butane as an organic gas pair, and air were used. The theory based on the free molecular flow could not be applied to all the combinations of the gases experimentally studied. Experiments showed that the permeability coefficient of each component in the mixture was very close to that of each single component, when the pressure in the low pressure side became zero, but those of the mixture approached one another rapidly as the pressure increased. In the case of the separation of one inorganic gas from another, there exists most suitable pressures both in the high and low pressure sides for the most efficient separation, as considered from the selectivity and permeability. In the cases of the mixed organic gases and the organic-inorganic gas combination, a rather high separation efficiency is expected for a very high pressure on the high pressure side.     

An experimental and theoretical analysis of molecular separations by diffusion through ultrathin nanoporous membranes

Diffusion based separations are essential for laboratory and clinical dialysis processes. New molecularly thin nanoporous membranes may improve the rate and quality of separations achievable by these processes. In this work we have performed protein and small molecule separations with 15 nm thick porous nanocrystalline silicon (pnc-Si) membranes and compared the results to 1- and 3- dimensional models of diffusion through ultrathin membranes. The models predict the amount of resistance contributed by the membrane by using pore characteristics obtained by direct inspection of pnc-Si membranes in transmission electron micrographs. The theoretical results indicate that molecularly thin membranes are expected to enable higher resolution separations at times before equilibrium compared to thicker membranes with the same pore diameters and porosities. We also explored the impact of experimental parameters such as porosity, pore distribution, diffusion time, and chamber size on the sieving characteristics. Experimental results are found to be in good agreement with the theory, and ultrathin membranes are shown to impart little overall resistance to the diffusion of molecules smaller than the physical pore size cutoff. The largest molecules tested experience more hindrance than expected from simulations indicating that factors not incorporated in the models, such as molecule shape, electrostatic repulsion, and adsorption to pore walls, are likely important.     

Experimental studies in relation to a new theoretical description of the permeation of dilute adsorbable gases through porous membranes

Precise data on the permeability of porous silica and alumina membranes to dilute gases are reported as a function of the nature of the gas and of temperature. It is shown that the unusual permeability behaviour previously observed only in “Vycor” porous glass at high temperatures [8-10] is a more general phenomenon. These results cannot be accounted for by conventional “surface diffusion” theory [1, 2] even qualitatively, but can be understood on the basis of recent, more advanced, theoretical treatments [3, 4, 7]. The present data provide an experimental test (not possible on the basis of previous data) of the general correlation between permeability and extent of sorption (including both the nature of the gas and temperature) predicted by the new theoretical approach, which is shown to be remarkably successful. Differences in the detailed permeability behaviour noted here, and in the previous porous glass study [8-10], are also satisfactorily accounted for in terms of differences in the mean effective pore size of the respective membranes.     

Transient behaviour of facilitated transport through liquid membranes

During the transient period of facilitated transport of a permeant across a thin liquid film, the ratio of the concentrations of the carrier at the two ends of the film as a function of time has a shape which is sensitive to the values of the physicochemical parameters. In certain systems involving ionic carriers, the above concentration ratio can be related to a conveniently measurable electrical potential difference, ΔV, across a pair of electrodes attached to the two faces of the liquid film. Bdzil et al. measured ΔV vs. time for NO FeCl₂FeCl₃—formamide system and observed that it goes through a maximum (ΔV_max), before reaching the asymptotic value corresponding to the steady state, ΔV_s.In the present paper, we solve numerically the species conservation equations, which describe the transients of the facilitated transport in the film, when the reversible reaction occurring in the film is of the form: A↑ + B = P (where A is the permeant and B and P are the carrier and permeant—carrier complex, respectively). The analysis takes into account: (i) the electrical effects which arise when B and P are ions of different diffusion coefficients and (ii) the effect of a second electrolyte added to the film to provide the cations which participate in an electrode reaction with the carrier ions. On this basis, an explanation is provided for the overshoot observed experimentally by Bdzil et al. in the ΔV vs. time curve. Such a maximum is exhibited by systems for which the time scales of diffusion and backward reaction in the film are of comparable magnitude. (Of course, for viable facilitation, the characteristic times of the forward and backward reactions should also be comparable.)The profile of ΔVvs. time is very sensitive to the values of the kinetic constants as well as the diffusion coefficients of the species A, B, and P. Therefore, measurements of ΔV vs. time (or equivalently the ratio of concentrations of the carrier on the two sides of the film as a function of time) can provide a more accurate method of determining the above parameters than those based on flux measurements.     

Kinetic analysis of coupled transport of thiocyanate ions through liquid membranes at different temperatures

Non-steady-state kinetics of coupled transport of thiocyanate ions through liquid membrane (trichloromethane), containing hexadecyl trimethyl ammonium chloride as a carrier, was examined at different temperatures. The kinetics of thiocyanate transport could be analyzed in the formalism of two, consecutive, irreversible first order reactions. The influence of temperature on the kinetic parameters (k_1d, k_2m, R_m^max, t_max, J_d^max, J_a^max) have been also investigated. The membrane entrance rate, k_1d, and the membrane exit rates, k_2m and k_2a, increase with temperature. For maximum membrane entrance and exit fluxes, J_d^max and J_a^max, the activation energies were found from the slopes of the two linear relationships: 7:75 and 8.30 kcal/mol, respectively. The values of the found activation energy indicate that the process is controlled by species difussion.     

A novel laser desorption/ionization method using through hole porous alumina membranes

Rationale

A novel matrix‐free laser desorption/ionization method based on porous alumina membranes was developed. The porous alumina membranes have a two‐dimensional (2D) ordered structure consisting of closely aligned straight through holes of sub‐micron in diameter that are amenable to mass production by industrial fabrication processes.

Methods

Considering a balance between the ion generating efficiency and the mechanical strength of the membranes, the typical values for the hole diameter, open aperture ratio and membrane thickness were set to 200 nm, 50% and 5 μm, respectively. The membranes were coated with platinum on a single side that was exposed to the laser. Evaluation experiments were conducted on the feasibility of this membrane structure for an ionization method using a single peptide and mixed peptides and polyethylene glycol samples and a commercial matrix‐assisted laser desorption/ionization (MALDI) time‐of‐flight mass spectrometer in the positive ion mode.

Results

Results showed a softness of ionization and no sweet spot nature. The capillary action of the through holes with very high aspect ratio enables several loading protocols including sample impregnation from the surface opposite to the laser exposure side.

Conclusions

The feasibility study indicates that the through hole porous alumina membranes have several advantages in terms of usefulness over the conventional surface‐assisted laser desorption ionization (SALDI) methods. The proposed novel ionization method is termed Desorption Ionization Using Through Hole Alumina Membrane (DIUTHAME).

     

Preferential glycerol transport by electroosmosis through ionic membranes

This paper describes a process in which glycerol is preferentially sorbed relative to water by an ionic membrane and transported into the product solution by electroosmosis at a significantly higher concentration than that in the feed solution. Direct measurement of the membrane distribution coefficient demonstrated preferential glycerol sorbtion for Neosepta CL-25T and AV-4T membranes. Both DC and AC electric currents significantly increase glycerol transport over that of a concentration difference alone.     

Gas transport through homogeneous and asymmetric polyethersulfone membranes

Both homogeneous and asymmetric polyethersulfone (PES) membranes were prepared by solvent casting. The sorption and permeation behavior of CO₂, O₂, and N₂ using these two kinds of cast PES membranes and commercially available homogeneous PES film was investigated to extract the pressure dependence of gas permeability and the permselectivity for CO₂ relative to N₂, and to confirm the validity of the working assumption that a skin layer in an asymmetric membrane can be essentially replaced by a thick homogeneous dense membrane. The pressure dependence of the mean permeability coefficient to CO₂ in homogeneous membranes obeys the dual-mode mobility model. The ideal separation factor for CO₂ relative to N₂ at an upstream pressure of 0.5 MPa attains ca. 40, while the permeability to CO₂ is about 2.7 Barrer at the same upstream pressure. The same separation factor in asymmetric membranes amounts to 35. The diffusion behavior for the skin layer in an asymmetric membrane with a thin skin layer can be simulated approximately by that in a homogeneous dense membrane. © 1993 John Wiley & Sons, Inc.     

Evaporation of alcohol/water mixtures through hydrophobic porous membranes

The evaporation of methanol/water, ethanol/water and propanol/water mixtures across hydrophobic porous membranes (Gore-Tex polytetrafluoroethylene membranes) with different nominal pore radii was studied at ambient temperatures. The evaporation process leads to a higher concentration of the alcohols in the vapor phase. There exists only a limited composition range (dilute solutions of alcohols in water) in which evaporation experiments are possible. The experimental results are interpreted in terms of the average pore diameter of the membranes, the vaporliquid equilibrium data of the systems and the measured contact angles between methanol/water, ethanol/water and n-propanol/water mixtures and polytetrafluoroethylene, respectively.     

Carrier-mediated transport of rare earth elements through liquid membranes

Transport of tervalent REEs — Sc, Y, Ce, Eu, Gd, Tm, Yb — from nitrate medium through a liquid membrane containing TBP in n-dodecane, impregnated on a flat-sheet nucleoporous support, has been studied as a function of time and initial metal concentration, salting-out agent concentration and pH of the feed phase. Influences of various complexing agents dissolved in the strip phase was investigated, too. Adding a suitable amount of EDTA into the feed phase, separation of binary mixtures of REEs was experimentally achieved.