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.     

Sorption and diffusion of toluene in highly oriented polypropylene

The sorption and diffusion of toluene vapor at 30°C in polypropylene with draw ratios from 1 to 18 have been studied. Drawing leads to the transformation of the initially spherulitic material into the fibrous structure, with many taut tie molecules lying mainly on the outer boundary of the microfibrils. The free volume and hence the sorption sites are thereby reduced, and the microfibrils become less and permeable as the draw ratio increases. As a result, the equilibrium concentration and the zero-concentration diffusion coefficient drop by factors of 4 and 30, respectively. The diffusion coefficient increases exponentially with toluene concentration but the concentration dependence becomes weaker with increasing draw ratio, indicating that the severely constrained chain segments in the drawn samples have much less freedom to mix with penetrant molecules. Annealing relaxes the tie molecules and thus restores the sorption and diffusion properties to values corresponding to completely relaxed amorphous component, i.e., to values even higher than those of the undrawn but quenched material.     

Sorption and diffusion of methyl substituted benzenes through cross-linked nitrile rubber/poly(ethylene co-vinyl acetate) blend membranes

The diffusion and sorption of methyl substituted benzenes through cross-linked nitrile rubber/poly(ethylene co-vinyl acetate) (NBR/EVA) blend membranes has been studied. The influence of blend composition, cross-linking systems, temperature and size of penetrants on the transport behaviour has been analysed. It was observed that as the EVA content increases in the blends, the solvent uptake decreases. An increase in the penetrant size also decreases the solvent uptake. The diffusion experiments were carried out in the temperature range 23–75 °C. As temperature increases the equilibrium uptake also increases. The transport coefficients namely diffusion coefficient, sorption coefficient and permeation coefficient have been calculated. The sorption data has been used to estimate the activation energies for permeation and diffusion. The van’t Hoff relationship was used to determine the thermodynamic parameters. The affine and phantom models for chemical cross-links were used to predict the nature of cross-links. Models for permeability were used and the theoretical values compared with the experimental results.     

Polyimide-epoxy alloys prepared via micro-modification: Water sorption and diffusion

A novel polyimide-epoxy or PI-EP alloys are prepared by the modification of polyamic acid in the concentration range of 1.54×10⁻⁶ to 1.54×10⁻² mol/L. The methanol sorption for these alloys at 24 hrs and at equilibrium conditions are determined and the residual solvent in fully cyclized polyimides were calculated. The presence of the residual solvent is visualized in fully imidized polymer and a structure containing partly imidized amic acid moiety is proposed and their concentration (in percentage) is calculated. The water sorption for these alloys at 24 hrs and at equilibrium conditions and the values of the water diffusion coefficient are determined from absorption isotherms. The PI-EP alloys have shown comparatively lower water sorption and higher diffusion coefficient than the unmodified polyimide. The mechanistic aspects of water sorption and diffusion are discussed.     

Inverse gas chromatography study on the effect of humidity on the mass transport of alcohols in an ethylene-vinyl alcohol copolymer near the glass transition temperature

Inverse gas chromatography (IGC) was used to study the effect of moisture on transport properties of three low molecular weight alcohols (methanol, ethanol, and 1-butanol) through high barrier copolymers of ethylene-vinyl alcohol with an ethylene content of 38%mol (EVOH38) at 40 degrees C. The value of the partition coefficient (K) was obtained by using two approaches: (a) the fit of the slope of sorption isotherms obtained through the method of Kiselev and Yashin; and (b) the solution to the model of Romdhane and Danner obtained by using the law of moments. The second method also allowed the estimation of the diffusion coefficient (D(p)) at the different humidity conditions. None of these two methods were applicable at low values of relative humidity. With the first method, the diffusion of the permeants through the copolymer was not fast enough to allow them to reach the core of the EVOH particles used as stationary phase resulting in sorption values unrealistically low. The fit of the chromatograms obtained by using the second method also suggested questionable values of the mass transport parameters. Although the theoretical curve perfectly described the chromatogram, the low extent of the interaction and the slow diffusion resulted in interdependent values of the coefficients K and D(p), with infinite pairs of values providing the same curve profile. As the relative humidity of the carrier gas increased, the diffusivity and the sorption of the alcohols also increased, making both methods applicable. In the case of the partition coefficient, the sorption of the biggest molecules (ethanol and 1-butanol) was the most affected, the increment of K for methanol being moderate. As regards the D(p) value, methanol was the most influenced compound and 1-butanol the least. Finally, a sharp increment of the D(p) of the three alcohols was observed between 35 and 47% RH and attributed to the plasticization of the copolymer.     

Blended silicone-ionic liquid membranes: Transport properties of butan-1-ol vapor

This paper is focused on modeling of sorption and desorption kinetics as well as on equilibrium butan-1-ol vapor sorption in blended poly(dimethylsiloxane)-benzyl-3-butylimidazolium tetrafluoroborate membranes. Based on the generalized Fick’s second law, on time-dependent boundary conditions and on two models of equilibrium sorption, the diffusion coefficients of butan-1-ol were calculated from the experimental data using the finite difference modeling. Although anomalous sorption occurred at higher concentrations of butan-1-ol, the diffusion coefficients calculated from the data on sorption and desorption kinetics were in a good agreement. The increase of the ionic liquid content in poly(dimethylsiloxane) elevated the butan-1-ol equilibrium concentration in the membrane, and, at the same time, decreased the values of butan-1-ol diffusion coefficient.     

Diffusion of 137Cs in compacted bentonite: Effect of pH and concentration

The effect of pH and concentration on the diffusion of ¹³⁷Cs in the compacted bentonite is studied with capillary method at the ionic strength of 0.1M NaClO₄. The apparent diffusion coefficient increases with increasing concentrations if the sorption of radionuclides is largely dependent on the radionuclide concentrations. The apparent diffusion coefficient decreases with increasing pH because most of the radionuclide sorption on the bentonite increases with increasing pH. The interlaminary space contributes significantly to the radionuclide diffusion and sorption in compacted bentonite. The relationship of the apparent diffusion coefficient and the effective diffusion coefficient of ¹³⁷Cs is also discussed.     

Sorption of strontium by Mexican erionite

The apparent diffusion coefficient of Sr²⁺ in natural Mexican erionite from Sonora at different pH and concentrations were determined. Neutron activation was applied to measure the sorption of strontium. The apparent diffusion coefficient values showed that the mobility of Sr²⁺ through the cavities of the erionite depended on the concentration of strontium and the pH of the solution. As a consequence the sorption of this ion by the erionite was affected by these parameters and the maximum sorption of Sr²⁺ was at pH higher than 3 and 0.0094 mol·l^–1 strontium nitrate solution.     

Measurement of sorption in polymer membranes with a quartz crystal microbalance

An application of the oscillating quartz crystal microbalance (QCM) in the measurements of sorption rates and equilibria in polymer—vapor systems is presented. The sorption isotherms of methanol, ethanol and n-heptane in cellulose acetate and poly(hexamethylene adipamide) were measured with the QCM at 298K. The results agree reasonably with the Flory model except at low absorbate activities where appreciable deviations due to localized absorption were observed, as verified with IR spectroscopy. The diffusion coefficient of methanol in cellulose acetate was also calculated from the sorption rate data measured with the QCM. The values obtained at different methanol concentrations correlate well with the published diffusion coefficients.     

Toluene diffusion in butyl rubber

The sorption isotherm and the polymer mass-fixed diffusion coefficients, D, for toluene in butyl rubber have been measured by the incremental sorption method to concentrations of 130%, corresponding to a solvent volume fraction of 0.578. The increase in D with concentration is strongly exponential to a concentration of 30% and then begins to level out. Since the nature of the dimensional change occurring in vapor sorption was not known, the values of D were converted to solvent self-diffusion coefficients, D₁, assuming both swelling in the thickness direction (1D) and isotropically (3D). The free volume (FV) theory of Fujita was fitted to the resulting D₁ with the zero concentration diffusion coefficient and the self-diffusion coefficient of toluene as limiting values leaving only a single arbitrary parameter. In this form the FV theory was able to describe the trend of the experimental D₁ for the 1D and 3D cases equally well. Values of D were back-calculated from the FV relations for the 1D and 3D cases for comparison with the experimental results and with the diffusion coefficient determined by immersion in toluene. These comparisons favor the assumption that swelling is isotropic. It appears that the simple free volume relation is capable of providing a satisfactory representation of the experimental data with only a single fitting parameter, although there are moderate quantitative discrepancies. © 1994 John Wiley & Sons, Inc.     

The concentration dependence of the diffusion and permeability in a homogeneous membrane

For the sorption and diffusion coefficient dependence on the concentration of the penetrant the transport properties of a homogeneous medium are calculated. The diffusion current is assumed to be proportional to the negative gradient of the chemical potential. This is in contrast with the first Fick's law that assumes this current to be proportional to the negative gradient of the concentration of the penetrant. The difference between the two cases depends on the concentration dependence of the sorption coefficient. In a homogeneous membrane the chemical potential formulation leads to an equation which is very similar to the Fickian expression. The apparent diffusion coefficient, however, depends not onlly on the transport resistance but also on the deviation of the sorption coefficient from constancy.     

Diffusion in ethylene–propylene rubber

A study of sorption in a copolymer of ethylene and propylene is presented. Long-time sorption and desorption measurements provided the actual diffusion coefficient in the limit of zero concentration gradient. An analysis of the diffusion–sorption data reinforced the Frisch hypothesis about diffusion in a polymer matrix. The better solvent deforms the microstructure, allowing a more marked dependence of the diffusivity upon concentration.     

Temperature and concentration dependence of diffusion coefficients in ethylene–propylene-diene copolymers

Self-diffusion and partition coefficients were measured for two commercial ethylene–propylene-diene copolymers (EPDM) and five solvents at infinite dilution using inverse gas chromatography. Mutual diffusion coefficients for solvents in EPDM also were measured for finite concentration using gravimetric sorption for three of the solvents. From the inverse gas chromatography experimental values for self-diffusion coefficients were obtained. Free-volume parameters were obtained through regression of the self-diffusion coefficient as a function of temperature. Mutual diffusion coefficients as a function of concentration were predicted using free volume theory and compared with experimental data obtained using gravimetric sorption. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1713–1719, 1998     

Diffusion of water vapour in polymethyl methacrylate

Certain aspects of the concentration dependence of the diffusion coefficient and on the mechanism of sorption of water vapour in PMMA are investigated. Early time integral sorption kinetics follow the Fickian pattern of initial linearity. Diffusion coefficients deduced from the slopes of these lines are independent of concentration and satisfactorily agree with those obtained from late-time analysis; however, desorption values are higher throughout the whole range of activities than the corresponding absorption ones. On the contrary, typical “non-Fickian” features are discerned in differential absorption kinetics on membranes of different thickness. These anomalies are attributed to rate-determining relaxation processes concurrent with diffusion, whereas other sorption models are incompatible with the general behaviour of this system. General trends of the equilibrium and kinetic data are compared with those of other polymer—water systems and the observed differences are interpreted in terms of the molecular relaxation model.     

Equilibrium, kinetics, mechanism, and process design for the sorption of methylene blue onto rice husk

Batch experiments were carried out for the sorption of methylene blue onto rice husk particles. The operating variables studied were initial solution pH, initial dye concentration, adsorbent concentration, and contact time. Equilibrium data were fitted to the Freundlich and Langmuir isotherm equations and the equilibrium data were found to be well represented by the Langmuir isotherm equation. The monolayer sorption capacity of rice husks for methylene blue sorption was found to be 40.5833 mg/g at room temperature (32 degrees C). The sorption was analyzed using pseudo-first-order and pseudo-second-order kinetic models and the sorption kinetics was found to follow a pseudo-second-order kinetic model. Also the applicability of pseudo second order in modeling the kinetic data was also discussed. The sorption process was found to be controlled by both surface and pore diffusion with surface diffusion at the earlier stages followed by pore diffusion at the later stages. The average external mass transfer coefficient and intraparticle diffusion coefficient was found to be 0.01133 min(-1) and 0.695358 mg/g min0.5. Analysis of sorption data using a Boyd plot confirms that external mass transfer is the rate limiting step in the sorption process. The effective diffusion coefficient, Di was calculated using the Boyd constant and was found to be 5.05 x 10(-04) cm2/s for an initial dye concentration of 50 mg/L. A single-stage batch-adsorber design of the adsorption of methylene blue onto rice husk has been studied based on the Langmuir isotherm equation.     

Sorption and diffusion of oxygen in plasticized ethyl cellulose films of varying degrees of substitution

Plasticized films cast from ethyl cellulose were examined to evaluate the effect of the degree of substitution, DS, and the plasticizer content on the sorption and diffusion of oxygen. Sorption and permeation measurements were performed over a temperature range of 25–65°C on three different types of ethyl cellulose in the DS range 1.7–2.5 that had been plasticized with organic esters of comparatively low molecular weight. Sorption coefficients were determined by the pressure decay method, and permeability coefficients were measured independently according to ASTM D-1434-66. The diffusion coefficients were calculated assuming Fickian transport, and were compared to the values directly obtained from the evaluation of the sorption kinetics. The permeability coefficient indicates that there is a significant improvement of the barrier properties of the materials when the DS is reduced and when the plasticizer content is at the absolute minimum required. It was found that the variation in the magnitude of the permeability coefficient is related to the value of the diffusion coefficient, which is governed by the chemical composition of the mixtures. In contrast, the solubility of oxygen was determined by the physical state of the polymer matrix and increased rapidly at temperatures significantly below the glass transition temperature. Using an ergodic model, the diffusion coefficients obtained were related to the size distribution of microvoids in the materials and relative values for the diffusion coefficient were computed as a function of DS and temperature. The model calculates the concentration (number per volume) of voids that are large enough to be occupied by a penetrant molecule. It was assumed that the unoccupied volume fraction as a function of the cohesive energy density follows a Boltzmann distribution. The cohesive energy density and the unoccupied volume fraction of the polymer-plasticizer mixtures were calculated by fitting the Simha-Somcynsky equation of state to pressure-volume-temperature data. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys, 35: 639–653, 1997     

Study of Sorption of 2,4‐D on Outer Peristaltic Part of Waste Tire Rubber Granules

From this study it was evident that outer peristaltic parts of waste tire granules gave the highest removal. Film and pore diffusions are the major factors controlling rates of sorption from solution by porous adsorbents. For sorption of 2,4‐D on waste tire rubber granules, the sorption rate coefficient of second‐order kinetic equation was utilized indirectly to determine the rate‐limiting step. The diffusion coefficient lies in the scale of 10^?8 cm²/s, and the pore diffusion coefficient is in the range of 10^?9–10^?10 cm²/s. So both film and pore diffusion are rate limiting. Considering external mass transfer from fluid to particle, using the effect of initial concentration, and using the effect of adsorbent size, no conclusion was reached regarding rate‐controlling steps. It is apparent from the study that external mass transfer (film diffusion) as well as intra‐particle diffusion (pore diffusion) play significant roles in the sorption process for 2,4‐D removal from water onto rubber granules.     

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.     

Non-Fickian diffusion of amyl acetate in polypropylene packaging: Experiments and modelling

In this paper, we present the methodology and the results obtained by the gravimetric and the FTIR methods to study the sorption of amyl acetate in polypropylene packaging. The influence of the concentration of amyl acetate and the temperature of aging on the sorption is discussed. A non-Fickian model is used to determine the diffusion coefficient and the surface mass transfer coefficient and their evolution with the amyl acetate concentration and the temperature of aging. The effect of the diffusion of amyl acetate on the polypropylene is studied by means of thermal properties.     

Intraparticle phosphorus diffusion in a drinking water treatment residual at room temperature

Phosphorus (P) has been recognized as one of the major limiting nutrients that are responsible for eutrophication of surface waters, worldwide. Efforts have been concentrated on reducing P loads reaching water bodies, via surface runoff and/or leaching through a soil profile. Use of drinking water treatment residuals (WTRs) is an emerging cost-effective practice to reduce soluble P in poorly P-sorbing soils or systems high in P. Literature suggests that WTRs have huge P sorption capacities. We hypothesized that P sorption would be limited by diffusional constraints imposed by the WTR particles. Selected chemical and physical (specific surface area, particle size distribution) characteristics of an iron-based WTR were measured. Sorption P isotherms at room temperature were constructed, and sorption kinetics were monitored. An intraparticle diffusion model was utilized to fit the kinetic data. Results showed that the WTR dramatically reduced soluble P, showing nonequilibrium characteristics, even after 80 d of reaction. Specific surface area (SSA) measured with CO2 gas was significantly greater than the traditional BET-N2 value (28 versus 3.5 m2 g(-1)), suggesting that a large amount of internal surfaces might be present in the WTR. The intraparticle P diffusion model was modified to include the wide particle size distribution of the WTR. The intraparticle diffusion model fitted the data well (r2 = 0.83). We calculated a maximum apparent P diffusion coefficient value of 4 x 10(-15) cm2 s(-1), which agrees with published values for intraparticle diffusion in microporous sorbents. This work may be useful for predicting long-term sorption characteristics of WTRs, since WTRs have been suggested as potential long-term immobilizers of sorbed P in P-sensitive ecosystems.