Permeation of water through polar and nonpolar polymers and copolymers: Determination of the concentration‐dependent diffusion coefficient

The diffusion and permeation properties of liquid water through different polar and nonpolar polymers and copolymers were studied with a highly sensitive permeameter. The transient permeation fluxes through the polar polymer films could be fitted well only with an exponential equation for the diffusivity concentration dependence; this empirical exponential equation represented the diffusion plasticization effect of water on the materials. For the hydrophobic polyolefins, this exponential equation was no longer valid, and another form of the equation was empirically found to account for the reduction of the water diffusivity with the extent of the permeation. Such a negative plasticization effect might be attributed to the formation of water clusters in the polyolefins. The values of the diffusion coefficient of water in the dry polar polymers were smaller than those in dry polyolefins, but the opposite behavior was found for the permeability because it was much more favorable for water sorption in the polar polymers than in the hydrophobic polyolefins. For the ethylene–vinylacetate copolymers, the plasticization effect of water on its own diffusion was negative for the sample with a low vinyl acetate (VA) content; it became nil at 19 wt % VA and positive at higher VA contents. This increase in the extent of the water sorption with the increase in the VA content led to a steady increase in the water permeability in the poly(ethylene‐co‐vinylacetate) copolymers. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1998–2008, 2000     

New methods for the determination of the parameters of a concentration‐dependent diffusion law for molecular penetrants from transient permeation or sorption data

New methods were developed for the determination of the plasticization parameters and the limit diffusion coefficient of a penetrant whose diffusivity varies exponentially with its concentration. No specific computer softwares is required for their use and they are user friendly. The method using differential permeation data is based on the correlations between the slope of the reduced permeation flux versus time plot at the inflexion point, and the two key parameters of the concentration‐dependent diffusivity laws. For the transient sorption method, the slope of the penetrant mass uptake versus square‐root of time curve leads to the same parameters of the diffusion law via similar correlations.     

A dynamic approach to diffusion and permeation measurements

A dynamic method for investigating the mechanism of permeation and diffusion through polymers has been explored. The permeation cell consists of two compartments separated by the membrane. The permeant (gas, vapor, or liquid) is introduced into one compartment; a carrier gas (helium) flows at constant rate through the other and sweeps the permeant which diffuses through the membrane to the thermal conductivity detector. Both compartments are at atmospheric pressure; thus no or little membrane support is required, and leakage problems are minimal. Moreover, the same membrane can be used over a wide temperature range and for diverse permeants. The detector signal is at any instant proportional to the permeation rate. A simple mathematical formalism for deriving the diffusion coefficient from the transient permeation rates has been developed. The measured diffusion and permeability coefficients of CO₂, O₂, and N₂ through low-density polyethylene closely agree with literature values. Permeation of hexane and benzene through polyethylene follows a complex diffusion law, and the rate depends on the thermal history of the system. The dynamic method is particularly suited to the study of transitions in polymers. Changes in permeation rates, usually occurring at transition points, can easily be discovered by slow temperature scanning of the system.     

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.     

Mobility-sensitive fluorescence probes for quantitative monitoring of water sorption and diffusion in polymer coatings

The fluorescent molecular rotor probes 4-tricyanovinyl-[N-(2-hydroxyethyl)-N-ethyl]-aniline, tricyano-4-(dimethylamino) benzylidene, and tricyanovinyljulolidene have been used as extrinsic fluorescence probes for quantitative monitoring of water uptake in polymeric coatings. The presence of water causes plasticization of the polymer, which results in increased local mobility within the film. The nonradiative decay pathways of the rotor probes are increased as local mobility increases, and the resulting decrease in fluorescence intensity of the probes is directly proportional to the amount of water sorbed. Beyond allowing for the characterization of sorbent content, this fluorescence technique can be used to determine the diffusion coefficient of water in a polymer film. The relative change in fluorescence fits well to a Fickian diffusion model, yielding a diffusion coefficient for water of 3 × 10^-8 cm²/s in poly(vinyl acetate), and a value of 6 × 10^-9 cm²/s in a room-temperature cured epoxypolyamide, in excellent agreement with diffusion coefficient values determined from gravimetric analysis. Preliminary studies also demonstrate the utility of molecular rotor probes to monitor water uptake in individual layers of multilayered polymer systems. © 1995 John Wiley & Sons, Inc.     

Oxygen diffusion in poly(dimethyl siloxane) using fluorescence quenching. I. Measurement technique and analysis

The transport properties of oxygen in poly(dimethyl siloxane) have been measured using the method of quenching of fluorescence. This paper discusses the uniqueness of this method and its use in measuring the diffusion coefficient of oxygen in unfilled PDMS. The results show (1) a large value for the diffusion coefficient of oxygen in pure PDMS at 25°C, D = 3.55 × 10^?5 cm²/s, (2) a low value of the acitivation energy, E_D = 4.77 kcal/mole, which was not temperature dependent in the ranges evaluated, and (3) a large value of the preexponential term, D₀ = 0.115 cm²/s. The diffusion coefficient was found to be independent of both the oxygen concentration and fluorophor concentration in the pressure and temperature ranges used in these experiments. The import of these experiments lies in their application to a unique biomedical oxygen sensor which is fast, sensitive, and does not consume oxygen.     

Transport of water and gases through EVA copolymer films,EVA70/PVC,and EVA70/PVC/gluten blends

The transport of water vapor and gases (oxygen or carbon dioxide) through poly(ethylene‐co‐vinyl acetate) (EVA) films of different VA contents and through EVA₇₀/PVC and EVA₇₀/PVC/gluten blend films, was analysed by permeation measurements. In the case of water, a plasticization effect on the material is observed for EVA films with more than 33percnt; wt. of VA content and also for the EVA₇₀/PVC blend. For EVA of 19 wt.percnt; VA, there is no plasticization, while for LDPE (low density polyethylene) and EVA of 4.5 wt.percnt; VA, the water diffusion coefficient decreases with increasing the water content. A negative plasticization effect was accounted for by an empirical model and attributed to the formation of water clusters in the non polar polymers. The increase in water sorption extent with the VA content leads to a steady increase in the water permeability in the EVA copolymers while for the EVA₇₀/PVC blend, the reduced water permeability is explained by the interaction between chlorinated units and polar groups. In the case of gas permeation, both for O₂ and CO₂ and whatever the VA content of the copolymer used, the experimental curves are characterized by a constant diffusion coefficient. This result is not surprising as it is generally admitted that, gases sorb into rubbery polymers according to Henry's law. By mixing PVC with the EVA of 70percnt; wt. VA, the diffusion coefficients of CO₂ and O₂ are greatly reduced (6 times).     

Adsorption of Pesticides onto Granular Activated Carbon: Determination of Surface Diffusivities Using Simple Batch Experiments

The Homogeneous Surface Diffusion Model (HSDM) has been successfully used to predict the adsorption kinetics for several chemicals inside batch adsorber vessels. In addition to the adsorption equilibrium, this model is based on external mass transfer and surface diffusion. This paper presents the determination of the surface diffusion coefficient (D _s) using a differential column batch reactor (DCBR). The adsorption kinetics for three pesticides onto granular activated carbon have been established experimentally. Their corresponding three diffusion coefficients were determined by fitting the computer simulations to the experimental concentration-time data. The results show that this original apparatus increases by an order of magnitude the range of reachable diffusion coefficient compared to perfectly mixed contactors. Moreover the computed D _s values are more accurate because of the better assessment of the external mass transfer coefficient (k _f) for fixed beds.     

Transport of steroids in poly(etherurethane) and poly(ethylene vinyl acetate) membranes

The permeability of polymer membranes to steroids was studied as a function of both permeant and membrane properties, using nine steroids and copolymer membranes prepared from poly(etherurethanes) and poly(ethylene vinyl acetates). Permeabilities, diffusion coefficients, and solubilities of the steroids in the membranes were determined in sorption—desorption and permeation experiments. Steroids with higher melting points permeated more slowly. This relationship originated from the lower diffusivities and solubilities of higher-melting steroids in the polymer phase; the effect of solubility changes was predominant. Reducing the polyether content of poly(etherurethane)merebranes ten-fold decreased their permeability to androstenedione by four orders of magnitude (from 10^?10 to 10^?14 g steroid/cm-sec at 37°C), due largely to diffusivity decreases. In contrast, reducing the vinyl acetate content of poly(ethylene vinyl acetate) membranes from 40% to 9% produced only modest changes in bath steroid solubility and diffusion coefficient. The permeability to androstenedione within this series of copolymer membranes ranged between 10^?11 and 10^?12 g steroid/cm-sec at 37°C.     

Diffusion effects in the oxidative degradation of vulcanized rubbers. II. Transient rate of chain scission

The effect of diffusion in the oxidative degradation of cis-1,4-polyisoprene vulcanizates was estimated by the analysis of the transient state of diffusion and oxidative degradation. An expression for the number of network chain scissions was obtained by solving the diffusion equation, which takes into account first-order oxygen consumption as well as constant scission efficiency. A practical method was proposed to analyze the transient process, which makes it possible to estimate diffusion coefficient and first-order rate constant independently. It was shown that the same analytical procedure would be applicable to the concentration jump method. The diffusion coefficient thus obtained was somewhat lower than the extrapolated value from the low-temperature data which was obtained in the absence of oxidation. Possible reasons responsible for this discrepancy were discussed.     

Combined sorption/transport of sodium dodecyl sulfate and hydrochloric acid in a blend of cellulose acetate butyrate with cellulose acetate hydrogen phthalate

The transport of hydrochloric acid (0.001-0.1 M) and sodium dodecyl sulfate (0.001-0.1 M) has been measured through a membrane consisting of a blend of cellulose acetate butyrate and cellulose acetate hydrogen phthalate. The cellulose derivative blend is suggested to suffer an alteration in the degree of hydrophobicity when in equilibrium with sodium dodecyl sulfate (SDS) through hemimicelle formation. An increase in surface hydrophobicity of the blend when in equilibrium with SDS solution was observed by fluorescence measurements using the vibronic bands of the probe pyrene, as well as by water desorption kinetics; a decrease of the effective diffusion coefficients from 1.2 × 10⁻¹¹ m² s⁻¹ in the absence of SDS to approximately 2 × 10⁻¹³ m² s⁻¹ in its presence was found. The value obtained for the mutual diffusion coefficient of HCl in the concentration range 0.001-0.1 M (D=4.2×10⁻¹⁴ m² s⁻¹) shows also that the membrane presents hydrophobic features. The flux of SDS in the blend membrane at different pH values shows two distinct permeation rates depending on the cmc. However, from the calculation of permeability coefficients at SDS concentrations below the cmc a clear decrease in P is found, whilst, at concentrations above the cmc the permeability coefficients are nearly constant, only showing a slightly increase. The diffusion coefficients of SDS in the blend increase over the whole SDS concentration range analysed and show an effective diffusion coefficient 2-3 orders of magnitude below the diffusion coefficients of SDS in aqueous solutions. This fact suggests that the only diffusing species are SDS unimers. The presence of HCl in the SDS bulk solution has the effect of increasing the permeability and diffusion coefficients. Mutual analysis of permeation and diffusion coefficients and sorption isotherms shows that, on decreasing the pH, the interactions between SDS and the polymer network decrease. This is also reflected in a clear decrease of the hydrophobic interactions between the diffusing and polymeric species, provoked by a decrease in the unimer-unimer association.     

Characterization of water vapor transport in glassy polyacrylonitrile by combined permeation and sorption techniques

Diffusion time lags, steady state permeabilities and sorption/desorption kinetics are reported for water vapor in biaxially oriented, solvent cast polyacrylonitrile (PAN) films. A wide range of vapor activities was studied at 15°C, 30°C, and 45°C. The transient and steady state permeation behavior at low and intermediate upstream vapor activities suggests that Fickian transport occurs under most of the conditions studied. Specifically, time lags predicted by Fick's law using the concentration-dependent diffusion coefficient derived from steady state permeation measurements agree reasonably well with experimentally measured values in most cases. p]Integral sorption/desorption kinetics at low and intermediate vapor activities also appear to be Fickian with a concentration-dependent diffusion coefficient. The form of the concentration dependency, evaluated from the “long time” solution of the diffusion equation for sorption experiments, is consistent with the form established for the diffusion coefficient from the steady-state permeation data. The diffusion coefficient exhibits a maximum near the concentration at which clustering is initiated. Presumably, the effective diffusion coefficient of water increases initially due to plasticizing or dual mode sorption effects associated with gap filling in the glassy matrix. As clustering becomes significant, the effective mobility of water is substantially reduced; therefore, the diffusion coefficient decreases at higher activities as clustering becomes the dominant mode of sorption. p]A tendency of the “early time” sorption/desorption kinetic data to exhibit concavity to the square root time axis at high activities suggests that time-dependent reductions in the diffusion coefficient may be occurring. Such reductions could be related to the kinetics of cluster formation at the higher vapor activities during sorption and to slow polymer consolidation during desorption. Any such non-Fickian effects, related to chain segment relaxations occurring over time scales similar to those of a diffusional jump, appear to be of importance only at short times. The short time nature of any such processes is suggested by the fact that diffusion coefficients evaluated from the “long time” solution to the diffusion equation for sorption are consistent with coefficients evaluated from steady state permeation data, in which case all time-dependent relaxation phenomena should be absent.     

Pervaporative transport modelling in a ternary system: ethyltertiarybutylether/ethanol/polyurethaneimide

The study deals with the analysis of diffusion and mass transfer modelling during pervaporation in a true ternary system involving a polar liquid mixture (ETBE/EtOH) and a polar block copolymer (polyurethaneimide or PUI). A survey of methods of pervaporative transfer modelling in ternary systems is first developed. From differential permeation experiments carried out with both pure liquids, it appears that both permeants obey a Fickian law. Moreover, the diffusional behaviour is consistent with Long's model, which has thus been assumed for the related ternary system. An extension of the Brun's model is then derived, which takes into account the diffusion coupling as well the significant deviation from sorption ideality. From a practical point of view, the calculated values of fluxes show generally good agreement with the experimental results, although a small deviation occurs for mixtures of low ethanol content. Diffusion coefficients of both pure solvents corresponding to transient or steady state are compared. A very good agreement is found for the aprotic permeant (ETBE). whereas the diffusion coefficient of ethanol in transient state is only the quarter of the value corresponding to steady state. The results are discussed in comparison with related investigations in the literature, involving specific liquid-polymer interactions.     

CO2-induced plasticization phenomena in glassy polymers

A typical effect of plasticization of glassy polymers in gas permeation is a minimum in the relationship between the permeability and the feed pressure. The pressure corresponding to the minimum is called the plasticization pressure. Plasticization phenomena significantly effect the membrane performance in, for example, CO₂/CH₄ separation processes. The polymer swells upon sorption of CO₂ accelerating the permeation of CH₄. As a consequence, the polymer membrane loses its selectivity. Fundamental understanding of the phenomenon is necessary to develop new concepts to prevent it.In this paper, CO₂-induced plasticization phenomena in 11 different glassy polymers are investigated by single gas permeation and sorption experiments. The main objective was to search for relationships between the plasticization pressure and the chemical structure or the physical properties of the polymer. No relationships were found with respect to the glass-transition temperature or fractional free volume. Furthermore, it was thought that polar groups of the polymer increase the tendency of a polymer to be plasticized because they may have dipolar interactions with the polarizable carbon dioxide molecules. But, no dependence of the plasticization pressure on the carbonyl or sulfone density of the polymers considered was observed. Instead, it was found that the polymers studied plasticized at the same critical CO₂ concentration of 36±7 cm³ (STP)/cm³ polymer. Depending on the polymer, different pressures (the plasticization pressures) are required to reach the critical concentration.     

Diffusion in dilute aqueous acetic acid solutions at 25°C

A conductimetric technique has been used to measure diffusion coefficients for aqueous solutions of acetic acid at concentrations from 0.002 to 0.02 mol-dm^–3 at 25°C. The acetic acid component diffuses more rapidly at lower concentrations where a higher proportion of the slower acid molecules are converted by dissociation to acetate ions and highly mobile hydrogen ions. The observed concentration dependence of the diffusion coefficient verifies the limiting law for weak electrolyte diffusion. A new type of conductimetric diffusion cell with several practical advantages over earlier designs is described together with an improved procedure for the conductimetric determination of accurate diffusion coefficients for weak electrolyte systems.     

Fourier transform infrared/attenuated total reflectance analysis of water diffusion in poly[styrene‐b‐isobutylene‐ b‐styrene] block copolymer membranes

A Fourier transform infrared/attenuated total reflectance technique was used to study the diffusion of water through poly(styrene‐b‐isobutylene‐b‐styrene) block copolymers (BCPs), as well as sulfonated (H⁺) and Na⁺‐sulfonated ionomer versions. Diffusion data were collected and interpreted for these membranes versus polystyrene block composition, degree of sulfonation, Na⁺ ion content in the ionomers, and the effect of initially dry versus prehydrated conditions. An “early time” diffusion coefficient, D, decreased with increasing percent polystyrene for a series of unmodified BCPs. D decreased with increasing degree of sulfonation, and with increasing ion content for the Na⁺‐exchanged samples and this was interpreted in terms of diffusion limitations caused by a strong tendency for ion hydration. The method also yielded information relating to the time evolution of water structure from the standpoint of degree of intermolecular hydrogen bonding. Membrane prehydration causes profound increases in D for both the unmodified BCP and sulfonated samples, as in plasticization. The simultaneous acquisition of information relating to interactions between water molecules and interactions of water molecules with functional groups on the host polymer matrix offers more information than conventional diffusion measurement techniques that simply count transported molecules. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 764–776, 2005     

In situ migration of tritiated water and iodine in Grimsel granodiorite,part II: assessment of the diffusion coefficients by TDD modelling

Diffusive transport of iodine (I) and tritiated water (HTO) in granodiorite is studied in the framework of the long term diffusion project (LTD) at the Grimsel Test Site, Switzerland. In this paper we modelled the tracer profiles measured in a long term (780 days) in situ diffusion test was carried out as part of LTD. The main outcome of the modelling tends to prove that the in situ apparent diffusion coefficients of I and HTO are close to the reference apparent diffusion coefficient determined in the laboratory (D _a = 3 × 10⁻¹⁰ m² s⁻¹).

     

Transport and mechanical properties of blends of poly(ϵ‐caprolactone) and a modified montmorillonite‐ poly(ϵ‐caprolactone) nanocomposite

The structural characterization and transport properties of blends of a commercial high molecular weight poly(?‐caprolactone) with different amounts of a montmorillonite‐poly(?‐caprolactone) nanocomposite containing 30 wt % clay were studied. Two different vapors were used for the sorption and diffusion analysis—water as a hydrophilic permeant and dichloromethane as anorganic permeant—in the range of vapor activity between 0.2 and 0.8. The blends showed improved mechanical properties in terms of flexibility and drawability as compared with the starting nanocomposites. The permeability (P), calculated as the product of the sorption (S) and the zero‐concentration diffusion coefficient (D₀), showed a strong dependence on the clay content in the blends. It greatly decreased on increasing the montmorillonite content for both vapors. This behavior was largely dominated by the diffusion parameters. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1118–1124, 2002     

Ultrafiltration of sodium dodecylsulfate solutions

The present paper is devoted to ultrafiltration (UF) of aqueous solutions containing micellized sodium dodecylsulfate (NaDS) through zircon membranes, following permeation data of cetyltrimethylammonium bromide (CTABr), which we have reported recently.The experimental results are analyzed using the same model of diffusion in the membrane matrix based on the thermodynamics of irreversible processes (TIP). A comparison with the classical model of resistances in series leads to a new analysis of the measured resistances in terms of membrane–permeant and permeant–permeant interactions. NaDS micelles being able to cross the membrane as permeants, in contrast with CTABr micelles, the comparison of the behaviors of anionic and cationic surfactants is worthwhile. The resistance of the membrane strongly depends on the composition of the feed. The TIP approach allows us to relate the membrane resistance to the concentrations of all the species present in the feed, namely free ions, spherical micelles and rod-like aggregates. It is shown that the resistance is highly influenced by free ions (dodecylsulfate (DS⁻) and sodium (Na⁺)), very slightly by negatively charged spherical micelles, and weakly by rod-like aggregates, also negatively charged.     

Water absorption of a diglycidyl ether of bisphenol A/1,3-bisaminomethylcyclohexane (DGEBA/1,3-BAC) epoxy resin system

The diffusive and dynamic mechanical behavior of the DGEBA/1,3-BAC epoxy resin system was studied during water absorption. The diffusion of water was investigated at 100% relative humidity, by immersion of specimens in water at 60, 80 and 100°C. In all absorption experiments, water diffusion followed Fick's law. Diffusion coefficients and saturated water concentrations are given for these temperatures. The activation energy for diffusion was determined from the relationship between the diffusion coefficient and the reciprocal of the absolute temperature. The value obtained was 31.2 kJ mol^–1. Dynamic mechanical analysis of samples immersed in 100°C water and with various water contents showed both a shift of T_g, defined by thetan peak, to lower temperatures and a slight decrease in the dynamic modulus in the presence of water. These effects are probably a result of plasticization.This work was supported by the Xunta de Galicia through grant XUGA-17201A92.