Mathematical simulation of atomic hydrogen diffusion transfer through a multilayer metal membrane at finite pressures

Diffusion transfer of atomic hydrogen through multilayer metal membranes has been studied within the lattice model of an ideal gas, with the transfer being described by a set of nonlinear algebraic equations. It has been shown that, for multilayer membranes composed of less than four layers, an analytical expression describing a diffusion flux can be derived. Atomic hydrogen transfer through a membrane consisting of a vanadium layer, the surfaces of which are coated with palladium films, has been analyzed in detail. It has been found that the value of the flux may depend on the transfer direction. The effect of diffusion asymmetry arises at finite pressures of hydrogen on the outer membrane surfaces, when its dissolution in metals is described by nonlinear sorption isotherms. The degree of the diffusion asymmetry increases with a rise in hydrogen pressure and depends on the arrangement of the layers composing a membrane.     

Asymmetric transmembrane transfer caused by a difference in adsorption characteristics at interfaces

A surface adsorption mechanism is proposed for the effect of asymmetric diffusion permeability of a modified membrane. A model is developed to describe diffusion transfer through the modified membrane with regard to the finiteness of the rate of adsorption on external membrane surfaces. Expressions are derived for diffusion fluxes as functions of transfer direction, and asymmetry coefficient is calculated for the diffusion permeability of the membrane. It is shown that the difference in the kinetic properties of the external surfaces of the membrane, which results from the modification of one of the surfaces, may induce the effect of asymmetric diffusion permeability.     

Asymmetry of Hydrogen Transfer through a Composite Membrane

Hydrogen mass transfer through a composite membrane represented by a film of palladium (or its alloys) applied onto a porous substrate has been studied. The hydrogen flux through the composite membrane has been shown to be governed by the ratio between the diffusion permeabilities of the film and the porous substrate, the mechanism of the transfer through the film, and the external pressure. It has been found that the intensity of hydrogen transfer through the composite membrane may depend on the transfer direction. The transfer is most asymmetric when the diffusion permeabilities of both layers are close and the hydrogen transfer in the film is limited by diffusion. At the same time, the transfer asymmetry effect does not arise when the hydrogen transfer in the film is limited by adsorption processes on its surface.     

Electrotransport properties and morphology of MF-4SK membranes after surface modification with polyaniline

The method of template synthesis is used for the surface modification of MF-4SK membranes with polyaniline. The influence of the time of polyaniline synthesis in the surface layer of a perfluorinated MF-4SK membrane on its morphology and electrotransport properties is investigated. It is established that under the synthesis conditions, a gradient distribution of polyaniline develops across the thickness of the membrane, and as a result of this, an anisotropic composite structure is formed. It is shown that the specific electrical conductivity and the electroosmotic and diffusion permeability exhibit an extremal character as functions of the time of polyaniline synthesis. When the orientation of these composite membranes is changed with respect to electrolyte flow, an asymmetry effect in their diffusion characteristics is found. With the application of the bilayer fine porous membrane model, the modified-layer thickness is estimated, and the determining influence of the difference in absolute values of effective fixed-charge volume densities on the development of the asymmetry effect is found.     

Hydrogen diffusion transfer through an asymmetric three-layer vanadium membrane

Hydrogen diffusion transfer through a three-layer membrane has been studied within the framework of the lattice model under the Bragg?Williams approximation. A set of equations describing hydrogen transfer through a vanadium membrane coated with thin palladium layers has been derived taking into account the interactions of hydrogen atoms in the membrane layers. The obtained equations have been solved using the Mathcad-14 software package. It has been shown that the interaction between hydrogen atoms has a significant influence on hydrogen permeability at near-atmospheric pressures. It has been found that the permeability of the vanadium membrane is markedly higher than that of a palladium one at the same thickness. The effect of asymmetric vanadium membrane embrittlement has been shown to depend on the location of palladium layers with different thicknesses. The embrittlement of the vanadium membrane begins at higher pressures, when a thicker palladium layer is located at the inlet. It has been revealed that, for asymmetric membranes, the value of the diffusion flux of hydrogen atoms may depend on the transfer direction. At the same membrane thickness, the permeability of the asymmetric membrane is actually equal to that of a symmetrical membrane, provided that a thicker palladium layer is located at the inlet. At the opposite orientation, of the permeability of the asymmetric membrane is lower than that of the symmetric one.     

The effect of gas surface diffusion on the asymmetric permeability of two-layer porous membranes

The permeability is calculated for two-layer membranes composed of porous layers with nano- and microsized pores. It is found that, in nanosized pores, the gas transfer occurs in the free-molecular regime in the pore volume and via diffusion along the adsorption layer. The degree of adsorption layer filling is determined from the Langmuir isotherm. The dependence of the diffusion coefficient in the adsorption layer on the degree of surface coverage is taken into account. The transfer in the microsized pored is described in a hydrodynamic regime. The values of the membrane permeability are determined at different orientations with respect to the direction of a gas flow. It is shown that the difference between the permeability values may be as large as 60%.     

Asymmetry of diffusion permeability of bi-layer membranes

To reveal the reason of asymmetry of the diffusion permeability of bi-layer electrodialysis membranes the following problems have been solved using the model of "homogeneous porous membrane": - diffusion of non-electrolyte solutions across a bi-layer membrane; - diffusion of electrolyte solutions across a non-charged bi-layer membrane; - diffusion of electrolyte solutions across a charged single layer membrane; - diffusion of electrolyte solutions across a charged bi-layer membrane. It is shown that the main factor responsible for the asymmetry is the difference between absolute values of densities of fixed charges (or so called "exchange capacities") of different layers of a membrane under investigation. Only in this case the ratio of the thickness of the membrane layers as well as the ratio of ion diffusivities contributes also to the asymmetry of the diffusion permeability. In the present review we survey and generalize our previous investigations and propose a new theory of asymmetry of diffusion permeability of bi-layer membranes. We have deduced explicit algebraic formulas for the degree of asymmetry of diffusion permeability of bi-layer membranes under consideration.     

Studies of asymmetry of diffusion permeability of nanocomposite ion-exchange membranes: Model of charge density of fixed groups linear by membrane thickness

A new model of a fine-porous membrane with a linear distribution of charges of its fixed groups along its depth is suggested in the work to explain the effect of asymmetry of diffusion permeability of perfluorinated MF-4SK membranes surface-modified by polyaniline. The model allowed better describing the experimental data for the synthesized nanocomposite MF-4SK/PANI membranes than the earlier developed model of a bilayer membrane with constant fixed charge densities in layers, which points to its feasilibity.     

Effect of adsorption of bovine serum albumin on liposomal membrane characteristics

The effect of adsorption of bovine serum albumin (BSA) on the membrane characteristics of liposomes at pH 7.4 was examined in terms of zeta potential, micropolarity, microfluidity and permeability of liposomal bilayer membranes, where negatively charged L-alpha-dipalmitoylphosphatidylglycerol (DPPG)/L-alpha-dipalmitoylphosphatidylcholine (DPPC), negatively charged dicetylphosphate (DCP)/DPPC and positively charged stearylamine (SA)/DPPC mixed liposomes were used. BSA with negative charges adsorbed on negatively charged DPPG/DPPC mixed liposomes but did not adsorb on negatively charged DCP/DPPC and positively charged SA/DPPC mixed liposomes. Furthermore, the adsorption amount of BSA on the mixed DPPG/DPPC liposomes increased with increasing the mole fraction of DPPG in spite of a possible electrostatic repulsion between BSA and DPPG. Thus, the adsorption of BSA on liposomes was likely to be related to the hydrophobic interaction between BSA and liposomes. The microfluidity of liposomal bilayer membranes near the bilayer center decreased by the adsorption of BSA, while the permeability of liposomal bilayer membranes increased by the adsorption of BSA on liposomes. These results are considered to be due to that the adsorption of BSA brings about a phase separation in liposomes and that a temporary gap is consequently formed in the liposomal bilayer membranes, thereby the permeability of liposomal bilayer membranes increases by the adsorption of BSA.     

Mathematical simulation of atomic hydrogen diffusion transfer through a bimetallic membrane

Mathematical simulation of atomic hydrogen diffusion transfer through a bimetallic membrane is performed under the approximation of an ideal lattice gas. Analytical expressions are derived for diffusion fluxes at different membrane orientations. The intensity of diffusion transfer of hydrogen atoms through a bimetallic membrane depends on the direction of transfer, provided that they have different solubilities in metal layers. It is shown that the effect of diffusion asymmetry must be taken into account when developing and using bimetallic membranes.     

Synthesis and diffusion permeability of MF-4SK/polyaniline composite membranes with controlled thickness of the modified layer

A new method is proposed for the synthesis of anisotropic membranes based on F-4SF films, which ensures their modification with polyaniline in a layer with a fixed thickness. The concentration dependences of conductivity and diffusion permeability of the composite membranes are studied. These parameters decrease with increasing thickness of the polyaniline-modified layer. The quantitative correlation is revealed between the regularities of variations in both transport characteristics and the thickness of the modified layer. The absence of the asymmetry of the diffusion permeability of the examined composite membranes is explained in terms of the model of a charged bilayer membrane.     

Experimental and theoretical studies of asymmetry of transport properties of modified ultrafiltration membranes

Ultrafiltration membranes based on polyamide and polysulfone modified by polyelectrolytes are produced. The effect of the nature of a polymer matrix and modifier on the rejection ability and diffusion permeability of membranes is studied. The effect of the asymmetry of transport properties, which is manifested at different orientations of membrane with respect to the flow of electrolyte, is quantitatively evaluated. It was demonstrated that the asymmetry of substance transport is more pronounced in the ultrafiltration regime than in the diffusion of sodium chloride solutions. A mathematical model that describes the filtration of binary electrolyte solutions on partially charged two-layer membranes is proposed and the corresponding boundary-value problem is solved analytically. The qualitative correspondence between theoretical calculations and experimental data on the asymmetry effect of the rejection ability of two-layer system is revealed.     

Effects of lysozyme and bovine serum albumin on membrane characteristics of dipalmitoylphosphatidylglycerol liposomes

The effects of adsorption of two kinds of proteins on the membrane characteristics of liposomes were examined at pH 7.4 in terms of adsorption amounts of proteins on liposomes, penetrations of proteins into liposomal bilayer membranes, phase transition temperature, microviscosity and permeability of liposomal bilayer membranes, using positively charged lysozyme (LSZ) and negatively charged bovine serum albumin (BSA) as proteins and negatively charged L-alpha-dipalmitoylphosphatidylglycerol (DPPG) liposomes. The saturated adsorption amount of LSZ was 720 g per mol of liposomal DPPG, while that of BSA was 44 g per mol of liposomal DPPG. The penetration of LSZ into DPPG lipid membranes was greater than that of BSA. The microviscosity in the hydrophobic region of liposomal bilayer membranes increased due to adsorption (penetration) of LSZ or BSA, while the permeability of liposomal bilayer membranes increased. The gel-liquid crystalline phase transition temperature of liposomal bilayer membranes was not affected by adsorption of LSZ or BSA, while the DSC peak area (heat of phase transition) decreased with increasing adsorption amount of LSZ or BSA. It is suggested that boundary DPPG makes no contribution to the phase transition and that boundary DPPG and bulk DPPG are in the phase-separated state, thereby increasing the permeability of liposomal bilayer membranes through adsorption of LSZ or BSA. A possible schematic model for the adsorption of LSZ or BSA on DPPG liposomes was proposed.     

Thickness dependent penetrant gas transport properties and separation performance within ultrathin polysulfone membrane: Insights from atomistic molecular simulation

Simulation technique has been employed to elucidate the effect of thickness upon confinement to gas transport properties in pure and binary mixtures within ultrathin polysulfone membranes. It is found that the gas diffusivity, solubility, and permeability are improved with increment in membrane thickness, which can be rationalized through bigger free volume in thicker polymeric membranes attributed to diminishing chains relaxation. The effect is found to be exceptionally perceptible in thinner polymeric films beneath 400 Å. Accuracy of the simulation methodology has been validated by demonstrating good accordance with actual gas permeability data. As for binary condition, the gas transport properties are demonstrated to be comparatively lower than its pure counterpart due to competitive sorption and barrier for diffusion in the presence of secondary gas molecules. In addition, quantitative re‐evaluation of published correlations and establishment of new empirical models have been conducted to associate membrane thickness effect to gas transport characteristics. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 131–158     

Diffusion of electrolytes of different natures through the cation-exchange membrane

Diffusion of different electrolytes through a negatively charged (cation-exchange) membrane into distilled water has been studied. It has been established theoretically (with no regard to the presence of diffusion layers) that the integral diffusion permeability coefficient of an electrolyte depends on the diffusion coefficients and the ratio between the charge numbers of a cation–anion pair, the ratio between the density of charges fixed in the membrane and electrolyte concentration, and the averaged coefficient of equilibrium distribution of cation?anion ion pairs in the membrane matrix. It has been found that, when co-ions have a higher mobility, the dependence of diffusion permeability on electrolyte concentration passes through a maximum. Derived equations have been compared with experimental dependences of the diffusion permeability of an MC-40 membrane with respect to different solutions of inorganic 1: 1 and 2: 1 electrolytes. The developed method has been shown to be applicable for describing diffusion of any electrolytes (including asymmetric ones) through arbitrary uniformly charged membranes.     

Stability and permeability of amphiphile bilayers

In this review the rupture and permeability of bilayers are considered on the basis of a mechanism of the formation of microscopic holes as fluctuations in the bilayers. The hole formation is treated as a nucleation process of a new phase in a two-dimensional system with short-range intermolecular forces. Free rupture and deliberate rupture (by α-particles) of foam bilayers (Newtonian black films) are discussed. A comparison is made between the rupture of foam and emulsion bilayers. Experimental methods for obtaining foam and emulsion bilayers from thin liquid films are considered. Methods for investigating the stability and permeability of foam bilayers, which are based on a microscopic model allowing the use of amphiphile solutions with very low concentrations, are described. Experimental dependences of the lifetime of bilayers, the probability of observing the foam bilayer in a foam film, the gas permeability of bilayers, etc. on the concentration of amphiphile molecules in the solution are reported. The influence of temperature and external impact (e.g. α-particle irradiation) have also been experimentally studied. A good agreement between theory and experiment is established, allowing determination of several characteristics of foam and emulsion bilayers obtained from ionics or non-ionics: the specific edge energy of bilayer holes, equilibrium surfactant concentration below which the bilayer is thermodynamically metastable, work for the formation of a nucleus hole, number of vacancies in the nucleus hole, coefficient of gas diffusion through the bilayer, etc. On the basis of the effect of temperature on the rupture of foam bilayers the binding energy of a surfactant molecule in the bilayer is determined. The adsorption isotherm of surfactant vacancies in the foam bilayer is obtained which shows a first-order phase transition. Some applications to scientific, technological and medical problems are considered. The foam bilayer is used as a model for investigating short-range forces in biological structures, the interaction between membranes and cell fusion. It is also shown that the foam bilayer is a suitable model for studying the alveolar surface and stability. On that basis a clinical diagnostic method is developed for assessment of the human foetal lung maturity.     

Adsorption of amylase enzyme on ultrafiltration membranes

A method to measure the static adsorption on membrane surfaces has been developed and described. The static adsorption of amylase-F has been measured on two different ultrafiltration membranes, both with a cutoff value of 10 kDa (a PES membrane and the ETNA10PP membrane, which is a surface-modified PVDF membrane). The adsorption follows the Langmuir adsorption theory. Thus, the static adsorption consists of monolayer coverage and is expressed both as a permeability drop and an adsorption resistance. From the adsorption isotherms, the maximum static permeability drops and the maximum static adsorption resistances are determined. The maximum static permeability drop for the hydrophobic PES membrane is 75%, and the maximum static adsorption resistance is 0.014 m2.h.bar/L. The maximum static permeability drop for the hydrophilic surface-modified PVDF membrane (ETNA10PP) is 23%, and the maximum static adsorption resistance is 0.0046 m2.h.bar/L. The difference in maximum static adsorption, by a factor of around 3, affects the performance during the filtration of a 5 g/L amylase-F solution at 2 bar. The two membranes behave very similarly during filtration with almost equal fluxes and retentions even though the initial water permeability of the PES membrane is around 3 times larger than the initial water permeability of the ETNA10PP membrane. This is mainly attributed to the larger maximum static adsorption of the PES membrane. The permeability drop during filtration exceeds the maximum static permeability drop, indicating that the buildup layer on the membranes during filtration exceeds monolayer coverage, which is also seen by the increase in fouling resistance during filtration. The accumulated layer on the membrane surface can be described as a continually increasing cake-layer thickness, which is independent of the membrane type. At higher concentrations of enzyme, concentration polarization effects cannot be neglected. Therefore, stagnant film theory and the osmotic pressure model can describe the relationship between flux and bulk concentration.     

“Superpermeability” and “pumping” of atomic hydrogen through palladium membranes

Permeation of atomic as well as molecular hydrogen through palladium membranes has been investigated experimentally in the temperature range from room temperature to 200 °C and at a higher incident flux of hydrogen atoms on palladium surface than in previous studies. The results demonstrate that phenomena of ‘superpermeability’ and ‘pumping’ of atomic gases through metal membranes are of a common nature. A theoretical model based on chemical thermodynamics and diffusion theory adequately describes the quantitative relationships observed in experiments. It was found that permeability of atomic hydrogen depends strongly on the magnitude of surface incident flux and membrane temperature.     

Rhodopsin in a new model bilayer membrane

In search of a planar and uniform model membrane presenting a wide interaction-surface for the study of photobiological processes, we have succeeded in depositing lipid bilayer on a single face of a porous disc. Using a method that combines the Langmuir-Blodgett dipping and the touching procedures, a symmetrical or asymmetrical bilayer membrane has been obtained. The illumination of rhodopsin-containing membranes appears to increase the permeability to K⁺, Na⁺, and Ca²⁺ with a high selectivity for Ca²⁺. The bilayer adsorption on the porous disc is discussed and an attempt is made to explain the failure of the dipping method in our experimental conditions for preparing an artificial membrane. A comparative look at model membranes is also presented.