Diffusion in glassy polymers. III

The diffusion studies of several solvents in epoxy polymer reported by Kewi and Zupko in Part I of this series are explained with the solution obtained from the generalized diffusion equation which includes the internal stress contribution. The rate of permeation of a penetrant through a polymer film and the time lag needed to reach steady state are also given for the generalized diffusion equation.     

Diffusion in inhomogeneous films and membranes

In a number of different contexts one is interested in the diffusion of a penetrant into an inhomogeneous film or membrane. We review exact results in the theory of permeation through membranes containing fixed inhomogeneities. We also present the available exact results on permeation, time lag, and sorption for a sufficiently dilute penetrant in an inhomogeneous slab or film. We discuss and compare the kind of information provided by permeation and sorption studies using a variety of examples of simple types of inhomogeneities.     

Estimation of gas transport coefficients from differential permeation, integral permeation, and sorption rate data

Experimental methods for studying the transport of gases in polymers may be divided into three categories: integral permeation rate measurement, in which the cumulative amount of a penetrant that has passed through a membrane is determined; differential permeation rate measurement, in which the rate of penetration through a membrane is measured directly; and sorption rate measurement, or determination of the cumulative amount of a penetrant absorbed in a polymer sample. This paper reviews commonly used techniques for estimating diffusion coefficients from transport data of all three types. Several new estimation formulas are presented, and the relative merits of different measurement and estimation methods are discussed. A general relationship between the traditional time lag method for integral rate data analysis and a recently developed moment method for differential rate data analysis is established, extending the applicability of the moment approach to the analysis of non-ideal transport in membranes of arbitrary geometry and composition.     

On the unusual solvent retention and the effect on the gas transport in perfluorinated Hyflon AD membranes

Dense membranes of Hyflon AD 60X were prepared by the solvent evaporation method and by melt pressing. The diffusion coefficient, solubility and permeability of the membranes were measured for six permanent gases using time lag and steady state permeation measurements. The thermal properties were determined by Differential Scanning Calorimetry (DSC) and the solvent content was measured gravimetrically and was estimated by the Fox equation. It was found that unusually strong solvent retention in the solution-cast membrane leads to considerable plasticization of the polymer, to possible foam formation upon drying and, most important, to significant changes in the permeation properties. The residual solvent increases the diffusion coefficient and permeability of the larger gas species up to almost one order of magnitude, and it reduces the permselectivity. For most gas species the solubility is about two times higher in the solvent-free melt-pressed film than in the solution-cast film. The relation between the residual solvent and the membrane properties is discussed.     

A note on generalised time-lags

Derivations of an expression for the generalised outgoing ‘adsorption’ time-lag pertaining to transport through a slab membrane made by [Rutherford and Do, Review of time lag permeation technique as a method for characterisation of porous media and membranes, Adsorption 3 (1997) 283] and by [Ash et al., Sorption and surface flow in graphitized carbon membranes. II. Time-lag and blind pore character, Proc. Roy. Soc. London, Ser. A, 304 (1968) 407] are not in agreement. Causes for the discrepancy are identified. Two extensions of the generalised procedure are given with particular attention being paid to ΔL, the time-lag difference.     

Simple technique for the simultaneous determination of solvent diffusion coefficient in polymer by Quantum Resistive Sensors and FT‐IR spectroscopy

A simple, quick and novel method for the determination of diffusion properties through polymer films, based on Quantum Resistive Sensors made of Conductive Polymer nanoComposites is presented. The integral time lag method is employed for the calculation of diffusion coefficient, and the results are compared simultaneously with that of Fourier transform infrared spectroscopy and sorption method. Two model polymers, a semi‐crystalline poly(lactic acid) and an amorphous poly(isobutylene‐co‐isoprene), are used to validate the study. A good correlation is established between the diffusion coefficient values derived from all techniques demonstrating the interest of such reliable, simple and cheap nanosensors for the quick determination (several minutes) of diffusion properties in polymer films. Our first results suggest that this technique is meaningful for the determination of barrier properties in nanocomposite membranes filled with platelets of graphene or clay. Copyright © 2013 John Wiley & Sons, Ltd.     

A semi-empirical approach for predicting the performance of mixed matrix membranes containing selective flakes

A successful model for mixed matrix membrane performance must address the complex geometry of the problem and accurately treat the diffusion behavior of the host–guest systems being considered. Detailed calculations based on the Maxwell–Stefan equations provide a widely accepted means of treating the diffusion of gases within zeolites. However, a full numerical solution of these equations for a complex mixed matrix membrane geometry does not offer the convenience and transparency that comes with an analytical treatment. At the same time, existing analytical equations which were formulated specifically to address mixed matrix geometry do so under the assumption of very simplistic models for diffusion. Here, an approach is presented for predicting the permeability and selectivity of mixed matrix membranes containing zeolite flakes that combines well-known analytical expressions for mixed matrix membrane performance with Maxwell–Stefan modeling for zeolite diffusion. The constant permeabilities required by the analytical models are calculated by the Maxwell–Stefan equations as a function of operating conditions, and these calculated effective permeabilities are used to predict mixed matrix membrane performance at corresponding operating conditions. The method is illustrated through two case studies: normal- and iso-butane separation by a membrane containing silicalite-1 flakes and carbon dioxide/methane separation by membranes containing CHA-type zeolites. Predictions are compared to experimental results found in the literature for both cases. Also, the applicability of the Maxwell and Cussler analytical models for mixed matrix membrane performance is explored as a function of flake loading and aspect ratio.     

Mechanism of diffusion and sorption of carbon dioxide in poly(vinyl acetate) above and below the glass transition temperature

The pressure dependence below 1 atm of the apparent diffusion and permeation coefficients were observed by using the permeation time lag method for carbon dioxide in poly(vinyl acetate), which has a glass transition near room temperature, at temperatures ranging from 8 to 50°C. Above the glass transition temperature, pressure dependence of the diffusion and permeation coefficient has not been observed; hence, Fick's law with a concentration independent diffusion coefficient applies. On the other hand, in the glassy state, the apparent diffusion coefficient shows pressure dependence. Moreover, the behavior of the pressure dependence does not show a clear curve in the ranges between 30°C to 17°C. Above 17°C, the apparent diffusion coefficients show discontinuities, but below 17°C increase with pressure is regular. Using the theoretical prediction of Paul, a computer was used in the numerical calculation to determine the true diffusion coefficient and other dual sorption parameters. p]The compensated diffusion coefficients controlled only by Henry's law dissolution was described by three straight lines with two intersection in the form of Arrhenius plots, which give good agreement with both our results for He and Ar and those of Meares. It is assumed that beside the dual sorption mechanism, another effect, for instance some relaxation effect may also contribute to the diffusion for carbon dioxide in poly(vinyl acetate) near the glass transition temperature region.     

Analysis of Dual Diffusion and Non-linear Adsorption Isotherm with a Time Lag Method

This paper presents an application of the time lag method in the analysis of an adsorption system, where dual diffusion mechanism is assumed to exist and the equilibrium relationship between the fluid and adsorbed phases is non-linear. The derived time lag is expressed in terms of system parameters and operating conditions in the form of a quadrature. The feature of this solution is that the relative contribution of the pore and surface diffusions is a strong function of upstream pressure when the time lag experiment is operated over the non-linear range of the adsorption isotherm. It is this nice feature that we take advantage of to determine the pore and surface diffusivities without resorting to isolation of the pore diffusion by using non-adsorbing gas as a reference, as usually done in many other work. This advantage is not manifested in linear systems where the relative contribution of the pore and surface diffusions is a constant, rendering the delineation of these two processes impossible. Effects of various parameters on the utility of this time lag method are discussed in this paper, and application of the method is demonstrated with experimental data of sulfur dioxide adsorption onto Carbolac carbon (Proc. Roy. Soc., A271, 1–18, 1963).     

Non-equilibrium molecular dynamics simulation study on permeation phenomena of LJ particles in slit-shaped membranes with periodic belt-like heterogeneous surfaces

In order to make clear the relationship between the pore structure and the diffusivity, we have carried out permeation simulations of pure gases through simple model membranes by using the external-field non-equilibrium molecular dynamics method. As the membrane, we model slit-shaped pores with periodic belt-like heterogeneous pore surfaces which are caused by the upheaval of surface atoms. Applying simulation results for membranes with several upheaval interval distances to Maxwell–Stefan (MS) theory, we calculate the effects of the molecular loading of permeating molecules in the pores on MS diffusivity (D_MS). In addition, the permeation potential barrier is estimated as the difference between the maximum and minimum permeation potential energies. The effect of the molecular loading on the permeation potential barrier and the D_MS are in inverse proportion. It is noted that, when the width of the adsorption area in the permeation direction is not common multiples of the molecular diameter, the permeation potential barrier decreases with the increase in the molecular loading. This is because the positive force against the permeation direction is caused to the permeating molecules by interactions with permeating molecules in the adsorpton area between adjacent upheavals. Therefore, we could suggest that the key factor for controlling diffusion property is the structural relationship between the adsorption area and the permeating molecules.     

A simple currentless method of determination of ion fluxes to and within electroactive ion-exchange membranes

A simple protocol applicable for the determination of ion fluxes from a solution to an ion-exchange membrane and within it was proposed. Advantages of this method include the application of a simple typical potentiometric set-up, as the method uses open circuit potential measurements; thus, the membrane state is not biased by external polarization. The proposed approach is based on the analysis of potential vs. time dependences in the course of building up or disappearance of a diffusion layer in a solution, controlled by solution stirring. Using equations describing diffusion processes, both ion fluxes from a solution to a membrane and within the membrane can be calculated. Experimental studies were carried out on examples of electrodes coated by two different kinds of membranes: (i) poly(vinyl chloride)-based silver-selective membrane and (ii) polypyrrole film doped by poly(4-styrenesulfonate) ions, in solutions of silver ions. The results obtained for non-saturated silver-selective membranes highlight the role of membrane thickness and conditioning time as well as confirm the role of diffusion in the membrane as a rate-determining step. For polypyrrole layers, the ion flux results from silver deposition in the surface part of a conducting polymer film, and the flux value was found consistent with silver deposition rate determined earlier.     

Stationary electrodiffusion–adsorption processes in membranes including diffuse double layer effects: A network approach

Ion transport across membranes with surface charge due to ion adsorption, including the diffuse double layer effects, is analysed using the network simulation method. The membrane system under study is a multilayer one constituted by a membrane and two diffusion boundary layers on both sides of the membrane. The ion transport processes are described by the Nernst–Planck and Poisson equations not only in the membrane–solution interfaces, but also in the membrane bulk and in the two diffusion boundary layers. The membrane has a negative surface charge due to an anion adsorption process. The structure of the equilibrium diffuse double layers and the steady-state current–voltage characteristic have been analysed for the case of an adsorption process described by a Langmuir-type adsorption isotherm. The evolution of the electric potential difference across the membrane system in the equilibrium state of the system as a function of the bathing concentrations, have been also analysed.     

MICROPOROUS INORGANIC MEMBRANES

Recent development in microporous inorganic membranes represents a significant advance in materials for separation and chemical reaction applications. This paper provides an in-depth review of synthesis and properties of two groups (amorphous and crystalline) of microporous inorganic membranes. Amorphous microporous silica membranes can be prepared by the sol-gel and phase separation methods. Flat sheet, tubular and hollow fiber amorphous carbon membranes have been fabricated by various pyrolysis methods from polymer precursors. A large number of synthesis methods have been developed to prepare good quality polycrystalline zeolite membranes. Several techniques, including vapor and liquid approaches, are reviewed for pore structure modification to prepare microporous inorganic membranes from mesoporous inorganic membranes. Chemical, microstructural and permeation properties of these microporous membranes are summarized and compared among the several microporous membranes discussed in this paper. Theory for gas permeation through microporous membranes is also reviewed, with emphasis on comparison of theoretical with the experimental data. These inorganic microporous membranes offer excellent separation properties by the mechanisms of preferential adsorption, selective configurational diffusion or molecular sieving.     

Microfiltration of protein solutions at thin film composite membranes

An experimental study of the interaction of the enzyme yeast alcohol dehydrogenase (YADH) with polysulfone thin film composite microfiltration membranes (Dow-Danmark) has been carried out. It was found that the membranes adsorbed only 3/4 of a monolayer of the enzyme under the conditions studied. Even so, under filtration conditions, the membrane permeation rate decreased continuously with time. This decrease in permeation rate was due neither to concentration polarisation nor to protein adsorption alone. However, it could be quantified using the standard blocking filtration law, which describes a decrease in pore volume due to deposition of protein in the interior structure of the membrane. Reversal of the membrane, so that the supporting matrix faced the feed solution, gave more stable permeation rates. Implications for the microfiltration of industrial fermentation broths are discussed.     

On the permeation time lag for different transport equations by Frisch method

A constructive application of Frisch method for deriving permeation time lags for different transport equations is shown. Two main classes, i.e. parabolic and hyperbolic diffusional mass transport equations, are presented and compared. An influence of drift and chemical reaction terms on the time lag is discussed.     

Fabrication and evaluation of molecularly imprinted regenerated cellulose composite membranes via atom transfer radical polymerization

A simple and effective method for surface molecularly imprinted composite membranes （MICMs） for artemisinin （Ars） based on regenerated cellulose membranes was first prepared through surface- initiated atom transfer radical polymerization （ATRP）, and the as-prepared MICMs were then evaluated as adsorbents for selective recognition and separation of Ars molecules. Batch rebinding studies were conducted to determine the specific adsorption equilibrium, kinetics and selective permeation performance. The adsorption capacity of MICMs toward Ars by the Langmuir isotherm model was 2.008 mgg-1, which was nearly 5.0 times higher than non-molecularly imprinted composite membranes （NICMs）. The kinetic property of MICMs was well-fitted by the pseudo-second-order rate equation. The selective permeation experiments were successfully investigated to prove the excellent selective permeation performance for Ars than the competitive analog （artemether）.     

High-speed protein purification by adsorptive cation-exchange hollow-fiber cartridges

Novel cation-exchange adsorptive membranes were assessed according to their protein adsorption capacity and permeation flowrate. Maximum static adsorption capacities for the three main egg-white proteins, lysozyme, ovoalbumin and conalbumin, were 140, 88 and 66 mg/ml, respectively. However, membranes showed an inverse relationship between permeation flowrate and static protein adsorption capacity. Two size cartridges (membrane volume of 0.42 and 3.5 ml) were built using the selected membrane. An adsorptive cross-flow cartridge was tested to recover and purify lysozyme from an egg-white solution. Breakthrough curves developed using a pure lysozyme solution showed a dynamic-to-static capacity ratio of 0.6, which was reduced to 0.4 during lysozyme recovery from egg-white solution in cross-flow mode. Total process cycle for the enzyme recovery and purification was in the range of 10–15 min for both cartridges. In both cases high-purity lysozyme (95%) was recovered with a productivity of 150 g/(l h) and no size-exclusion effect was detected.     

Zeolite Membranes: From the Laboratory Scale to Technical Applications

Current trends and novel concepts in R&D of zeolite membranes like the seeding supported crystallization and the preparation of Al-containing zeolite membranes are discussed. The influences of adsorption and diffusion on the permeation properties of zeolite membranes are considered. Dehydration of ethanol by steam permeation and pervaporation as the first zeolite membrane based industrial separation is presented. Membrane supported dehydrogenation and esterification are discussed as possible applications of a catalytic membrane reactors. In memoriam Wolfgang Schirmer.     

Correlations between types of absorbed water molecules and water permeability in swollen polymer membranes

A series of poly(vinyl formal) membranes was synthesized by formalization of poly(vinyl alcohol) membranes. Representative pieces were selected for this study. Some cellulose acetate membranes cast from dioxane were used for comparison. The main experimental techniques employed included water absorption measurements and direct osmosis measurements. Aqueous solutions of sodium chloride at various concentrations were used for the studies of permeation through the membranes by direct osmosis. The plot of water permeability coefficient P_w versus volume fraction V_w of water absorbed in a membrane was interpreted in terms of the effect of two different types of absorbed water molecules. The individual diffusion coefficients were evaluated from asymptotic slopes of the curves. Similar analyses applied satisfactorily to data found in the literature.     

Separation of gas mixtures using a range of zeolite membranes: a molecular-dynamics study

Gas separation efficiencies of three zeolite membranes (Faujasite, MFI, and Chabazite) have been examined using the method of molecular dynamics. Our investigation has allowed us to study the effects of pore size and structure, state conditions, and compositions on the permeation of two binary gas mixtures, O(2)N(2) and CO(2)N(2). We have found that for the mixture components with similar sizes and adsorption characteristics, such as O(2)N(2), small-pore zeolites are not suited for separations, and this result is explicable at the molecular level. For mixture components with differing adsorption behavior, such as CO(2)N(2), separation is mainly governed by adsorption and small-pore zeolites separate such gases quite efficiently. When selective adsorption takes place, we have found that, for species with low adsorption, the permeation rate is low, even if the diffusion rate is quite high. Our results further indicate that loading (adsorption) dominates the separation of gas mixtures in small-pore zeolites, such as MFI and Chabazite. For larger-pore zeolites such as Faujasite, diffusion rates do have some effect on gas mixture separation, although adsorption continues to be important. Finally, our simulations using existing intermolecular potential models have replicated all known experimental results for these systems. This shows that molecular simulations could serve as a useful screening tool to determine the suitability of a membrane for potential separation applications.