A detailed study of the viscoelastic nature of vapor sorption and transport in a cellulosic polymer. I. Origin and physical implications of deviations from Fickian sorption kinetics

Various aspects of the kinetics of sorption of acetone vapor by cellulose acetate films at 30°C have been studied in detail, the principal aim being to understand more thoroughly the physical nature and causes of non-Fickian behavior in this and other similar polymer-micromolecular penetrant systems. Particular attention was given to the changes in sorption (including absorption, desorption, and resorption) kinetics caused by (a) systematic variation of the vapor pressure of acetone in different ways and (b) changes in membrane thickness. It has been shown that both viscous volume swelling relaxation and longitudinal differential swelling stress effects must be invoked, in order to explain fully the observed behavior. Detailed analysis of two-stage sorption kinetics indicated (1) reasonable agreement between estimates of the diffusion coefficient reported by different authors, as long as a consistent analysis of the first stage is used, although the significance of the values given is open to some doubt, because the said first stage is found not to be free of non-Fickian features; and (2) reasonable conformity of the second stage to a first-order volume relaxation process (except a long times), with a relaxation frequency strongly dependent on the width of the concentration interval covered by the sorption experiment (and hence on the applied “osmotic stress”). The close similarity of second-stage sorption to nonlinear viscoelastic creep behavior, previously found in the cellulose-water system was confirmed and is taken further here, by demonstrating semiquantitative agreement between the corresponding “elastic swelling” and mechanical bulk moduli. ©1995 John Wiley & Sons, Inc.     

Transport of water in polyvinyl alcohol films: Effect of thermal treatment and chemical crosslinking

Data on sorption and transport of water in polyvinyl alcohol films, modified by thermal treatment above T_g, or by chemical crosslinking with glutaraldehyde at different crosslinking degrees, are presented. Equilibrium swelling is constrained by both treatments, except for low degrees of crosslinking where the said reduction is counterbalanced by the partial loss of crystallinity. Analysis of the resulting water uptake kinetics indicates that viscous relaxation effects are, at least partly, responsible for the observed non-Fickian kinetic behavior. Thermodynamic diffusion coefficients of water, D_W, and relaxation frequencies of the swelling polymer, β_W, are determined by application of a theoretical model accounting for relaxation-dependent sorption kinetics in glassy polymers. The results indicate that the effect of both heat-treatment and chemical crosslinking is more intense on the macromolecular relaxation process than on the diffusion coefficient of water. Comparison of the release kinetics of a model drug from as-prepared, non-crosslinked and from crosslinked matrices indicate that the retardation of macromolecular relaxations process induced by crosslinking results in a more uniform release rate.     

A detailed study of the viscoelastic nature of vapor sorption and transport in a cellulosic polymer. II. Sorption and longitudinal swelling kinetic correlations

Longitudinal swelling kinetics of cellulose acetate films sorbing acetone vapor at 30°C were studied under various conditions and correlated with the corresponding sorption kinetic measurements reported in Part I. The results were analyzed in the light of (1) previous theoretical studies of simple viscoelastic polymer-penetrant model systems and (2) mechanical stress-strain data on the cellulose acetate-acetone system, which are also reported here. The conclusions drawn from this analysis confirm and/or amplify (particularly as regards the effect of longitudinal differential swelling stresses) our previous interpretations based on sorption kinetic analysis, concerning the physical nature and causes of various features of the non-Fickian kinetic behavior of cellulosic polymer-micromolecular penetrant systems. History-dependent long-term aging effects were also observed and investigated. © 1995 John Wiley & Sons, Inc.     

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.     

Selective water sorbents for multiple applications, 4. CaCl2 confined in silica gel pores: Sorption/desorption kinetics

This paper presents experimental data on water sorption/desorption kinetics on composite SWS-1L and SWS-1S materials, bulk aqueous CaCl₂ solutions and pure KSKG silica gel. Desorption kinetic curves are measured in the temperature range of 328–363 K at different vapor pressures. First order kinetics is found for both SWS materials and the bulk aqueous solution with the apparent activation energies of the water desorption equal to 23.5 kJ/mol and 48.6 kJ/mol, respectively. The difference in the kinetic behavior of the bulk and disperse systems is discussed.     

Plasticized microporous poly(vinylidene fluoride) separators for lithium‐ion batteries. II. Poly(vinylidene fluoride) dense membrane swelling behavior in a liquid electrolyte—characterization of the swelling kinetics

Some microporous poly(vinylidene fluoride) (PVdF) separators for lithium‐ion batteries, used in liquid organic electrolytes based on a mixture of carbonate solvents and lithium salt LiPF₆, were characterized by the study of the swelling phenomena on dense PVdF membranes. Various aspects of the kinetics of the carbonate solvents and the solvent mixture sorption in dense PVdF slabs were studied at different temperatures. Non‐Fickian behavior, characterized by S‐shaped sorption curves, was highlighted, and a salt effect, which resulted in two‐stage sorption, was studied. Diffusion coefficients and activation energies were calculated for the Fickian portions of the sorption curves, that is, at short times and low swelling ratios. A strong influence of the different interaction parameters was shown for the swelling kinetics. This study proved that the swelling of microporous PVdF membranes could be considered instantaneous. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 544–552, 2004     

Analysis of the kinetics of vapor absorption/desorption in/from silicone rubber and cellulose acetate membranes in the presence of stagnant boundary layers

The application of an interferometric technique (optical thickness meter, OTM) to the measurement of vapor sorption kinetics in both rubbery and glassy polymers is presented. In this technique, the membrane is formed by casting on a suitable glass surface and interferometry is applied in situ. The use of a carrier gas loaded with penetrant vapor introduced a stagnant boundary layer (SBL) effect which had to be corrected, in order to determine true sorption kinetics. The said SBL effect was estimated, on the basis of existing theory for the silicone rubber–methylene chloride (SR/MC) system and found to be more pronounced in the case of desorption. Upon correction for this effect, Fickian sorption curves were obtained; which yielded nearly constant values of the diffusion coefficient, not materially different for absorption and desorption, in line with theoretical expectation.Cellulose acetate–methylene chloride (CA/MC) was then studied as an example of a glassy polymer–vapor system, where the SBL effect distorts the absorption kinetic curve in the same way as the non-Fickian mechanism of sorption inherent in this kind of polymer–penetrant system. Here, the vapor sorption data were corrected using the results obtained from the Fickian SR/MC system. The corrected results were checked by comparison with independent data reflecting the true kinetic behavior of CA/MC, obtained with a vacuum balance apparatus (VBA), which is free of SBL effects. It is shown that this novel method of applying the SBL correction was reasonably successful in favorable circumstances, while a criterion is provided to identify cases where reasonably reliable correction is not possible.     

Kinetics study of oil sorption with open‐cell polypropylene/polyolefin elastomer blend foams prepared via continuous extrusion foaming

The objective of the present work was to study the sorption kinetics of open‐cell polypropylene/polyolefin elastomer (PP/POE) blend foams. First, open‐cell PP/POE foams of different cell structures were prepared by controlling the foaming temperature via a continuous extrusion foaming process. Second, the effect of the cell structures on the sorption process, rate, and capacity was studied. Pseudo‐first order and pseudo‐second order models were applied to study the sorption kinetics of the PP/POE foams for cyclohexane. Third, the sorption rate and sorption capacity by both volume and weight of the PP/POE foam for different oils and solvents were studied to show how the intrinsic properties of the testing oils and solvents affected the sorption performance. The results showed that the sorption with the PP/POE foams followed the pseudo‐second order kinetics model. Both the cell structures of the foams and the intrinsic properties of the testing oils and solvents affected the sorption performance. For the same testing oil, a higher open‐cell content in the foam was favorable for a higher sorption rate, and a higher void fraction was favorable for a higher sorption capacity. For the same foam, a lower viscosity of the testing oil was favorable for a higher sorption rate. The sorption capacity by volume was closely related to the viscosity of the testing oil, while both the viscosity and the density of the testing oil determined the sorption capacity by weight.     

Swelling behaviors of thermoresponsive hydrogels cross-linked with acryloyloxyethylaminopolysuccinimide

Based on a biodegradable cross-linker, acryloyloxyethylaminopolysuccinimide (AEA-PSI), a series of looser cross-linked poly(N-isopropylacrylamide-co-acrylic acid) [P(NIPAAm-co-AAc)] hydrogels were prepared, and their water content, swelling/deswelling kinetics, and the morphology of the gels were investigated. The swelling behaviors of AEA-PSI-cross-linked P(NIPAAm/AAc) hydrogels were investigated in Dulbecco’s phosphate-buffered saline (pH = 7.4), in the distilled water, and in the simulated gastric fluids (pH = 1.2), respectively. The water contents of the hydrogels were controlled by the monomer molar ratio of NIPAAm/AAc, swelling media, and the temperature. In the swelling kinetics, all the dried hydrogels exhibited fast swelling behavior, and the swelling ratios were influenced significantly by the amounts of AEA-PSI and AAc content. The deswelling kinetics of the hydrogel were independent of the content of AAc and cross-linker. Lastly, the morphology of the hydrogels was estimated by the field scan electron microscopy.     

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.     

Simulation of experimentally observed dilation phenomena during integral gas sorption in glassy polymers

A molecular modeling investigation of dilation effects induced by sorbed gas molecules in two glassy polymers is presented. As experimental reference, integral sorption of CO₂ and CH₄ was measured for polysulfone (PSU) and a polyimide (6FDA‐TrMPD, PI4) at 308 K and a pressure of 10 bar. Simultaneously, the gas induced swelling effect was measured with a dilatometer based on a capacitive distance sensor recorded. The experimental evidence of the (on the observed time scale and concentration levels) elastic nature of the gas induced dilation is supported by the dilation and contraction behavior observed in molecular dynamics (MD) simulations of respective detailed atomistic packing models. These models were constructed in accordance with gas concentration levels obtained from the experimental sorption results. Quantitative deviations between simulated and measured dilations are discussed as a consequence of an anelastic response of the polymer matrix which is too fast to be resolved in the experiments whose kinetics is dominated by diffusional processes. In the simulation, the initial insertion of penetrant molecules into equilibrated packing models “circumvents” the slow diffusional process of the experiment and allows a reasonable representation of the dilation process as well as a closer investigation. Our simulation approach reveals a different behavior for PSU and PI4 on the corresponding time scale. Most likely, the different chain mobility of the two polymers is responsible for the respective response to the inserted amount of gas molecules which is discussed in terms of the different chain mobilities of the two polymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 59–71, 2008     

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.     

Test of a model of stress-dependent diffusion by means of combined colored tracer and birefringence profile measurements

In the present paper we further test a model of stress-dependent diffusion previously used with success to simulate the variation from Case I to Case II penetration kinetics in the system liquid methylene chloride-uniaxially oriented cellulose acetate film, according to whether penetration occurs across or along the axis of preferred macromolecular orientation. Data on penetration rates, optical density profiles (using a colored tracer), and the corresponding birefringence profiles, characteristics of these penetration modes in the aforesaid system, are presented and compared with appropriate model uptake kinetic curves and penetrant concentration and compressive differential swelling stress profiles. It is shown that the salient features of the observed experimental behavior are in general accord with model predictions based on physically realistic assumptions.     

Induction and measurement of glassy-state relaxations by vapor sorption techniques

Recent gravimetric studies of the sorption of organic vapors by poly(vinyl chloride) and polystyrene powders have demonstrated several features which promise to be generally useful in studying the structure and properties of the glassy state. The uptake of vapor can be significantly altered by prior thermal or vapor treatment of the polymer, apparently reflecting changes in the microvoid content or free volume of the polymer. Fickian sorption in sufficiently fine powders proceeds to equilibrium in a few minutes. Upon exposure of a polymer powder to an appreciable pressure of vapor, both a rapid Fickian sorption and a slower, relaxation-controlled sorption are observed. Superposition of these processes leads to widely varied sorption kinetics; a model comprising Fickian diffusion and first-order relaxation terms accurately describes the data and allows estimation of equilibrium and rate constants for both processes. After prolonged exposure, removal of a swelling vapor induces a slow reconsolidation of the polymer structure; this deswelling relaxation can be monitored by the decreasing amounts of vapor sorbed in repeated brief exposures to low vapor pressures, and can also be described by a first-order relaxation model. In this regard, the penetrant vapor serves as a molecular probe, monitoring glassy-state relaxation occurring in the absence of penetrant. The same, presumably true equilibrium is ultimately reached both by swelling from a low free-volume state and by consolidation from a preswollen state of high free volume. The rates of both swelling and consolidation relaxations appear to be retarded by the presence of low concentrations of vapor in the polymer, suggesting that vapor molecules may preempt some of the free volume required for relaxation.     

Kinetics and equilibria associated with the absorption and desorption of water and lithium chloride in an ethylene—vinyl alcohol copolymer

Sorption and desorption equilibria and kinetics for LiCl and H₂O in an ethylene—vinyl alcohol copolymer film containing 70 mole percent vinyl alcohol were investigated at 25°C. The swelling behavior of water in the polymer was characterized by vapor and liquid sorption experiments over a range of water activities. p]The effects of LiCl content on the water sorption kinetics and equilibria in the films are presented and discussed. The kinetics and mechanism of LiCl sorption have also been studied. The amount of salt sorbed into the polymeric films increases linearly with the salt concentration in the external aqueous solutions. Both the rate and the amount of sorbed water increase significantly as the LiCl content increases. p]The desorption of LiCl, previously sorbed into the polymer, was characterized for different salt loadings. The rate of fractional salt release is independent of LiCl concentration in the film. Initially, the salt release is controlled by the nearly constant-rate absorption of water. The salt release, at long times, lags behind the swelling-controlled water uptake, indicating that the salt release is not completely controlled by the water sorption and that diffusion in the swollen polymer matrix contributes significantly to the long term elution of LiCl. Independent thermal analysis experiments suggest the formation of a metal salt—poly(ethylene—vinyl alcohol) complex.     

Water sorption in silicone foam containing diatomaceous earth

Room temperature vulcanizing (RTV) silicone foams are commonly used for compression sealing, structural support, packaging, and damping applications. The presence of sorbed water in foams can affect the mechanical and chemical properties of these materials. In order to investigate water sorption behavior, a silicone foam containing diatomaceous earth filler was synthesized and studied for water uptake characteristics at 20, 50, and 80 degrees C. Type II equilibrium and bimodal kinetic behavior that was governed by a rapid initial uptake followed by a prolonged sorption over a larger time scale was observed. In order to explain this bimodal behavior, the major components of this foam-the silicone polymer and the diatomaceous earth-were independently studied for their water equilibrium behavior and uptake kinetic characteristics. Type II equilibrium was observed for both components. The kinetic behavior of the silicone polymer was governed by a very rapid uptake of water. The kinetic behavior of the diatomaceous earth was governed by a rapid initial uptake followed by a prolonged sorption over a larger time scale. A physically based and thermodynamically consistent mathematical model describing the water equilibrium and kinetics in diatomaceous earth and silicone polymer components, was employed to characterize the data. This model formed the basis of a predictive model for estimation of water sorption in filled silicone foam. The predictive model was tested against sorption and desorption data yielding favorable results for a range of temperatures.     

Comprehensive time-lag measurement as a diagnostic and analytical tool for non-Fickian transport studies: a salient porous barrier-gaseous permeant test case

Concentration-independent permeation of He, Ne and N2 through a porous barrier, specially constructed by multistep compaction of fine "Carbolac" carbon powder, has been studied. Emphasis was placed on measuring a variety of time lags, supplemented with transient permeation and sorption kinetics. Previous time-lag data, restricted to values of a single time-lag parameter, were instrumental in revealing deviations from Fick's law in similar solid barrier-penetrant systems; however, they could only provide indirect evidence as to the nature of the underlying causes, namely, time- or spatial dependence of the relevant transport parameters. Thus, an interpretation in terms of time-dependence (induced by the presence of blind pores) was proposed, predicated on calculations indicating that, in theory, spatial dependence (induced by non-uniform compaction) could be reduced to insignificance by adoption of a suitable multistep powder compaction technique. The comprehensive time-lag analysis approach applied here is a general diagnostic and analytical tool, previously successfully tested on graphite barriers, that can discriminate rigorously between the aforementioned non-Fickian functional dependences, as well as provide additional substantial information in either case. This capability is well illustrated by the results obtained in the system under study here, which provide unequivocal evidence of substantial spatial dependence. Furthermore, it is shown that the predicted functional form of the detected spatial dependence (i) can, in conjunction with an adequate physical model and with the results of a previous theoretical parametric study, account fully for all aspects of the observed non-Fickian time-lag behaviour and (ii) correlates satisfactorily with variation of local porosity across the barrier, detected by a suitable X-ray imaging technique. On the other hand, there is no evidence, from time lags or transient kinetics, of any significant time-dependence attributable to slow filling or emptying of blind pores or to other causes.     

Photopolymerization of poly(ethylene glycol) dimethacrylates: The influence of ionic liquids on the formulation and the properties of the resultant polymer materials

The photo‐initiated polymerization of poly(ethylene glycol)dimethacrylates [PEGDM(n)] in the presence of various ionic liquids (ILs) is reported. The influence of ILs concentrations as well as of their nature upon the photopolymerization kinetics was studied in detail. It was found that according to reactive ability in bulk and in solution photopolymerization, the investigated monomers can be divided into two groups: PEGDM(1)–PEGDM(2)–PEGDM(3) and PEGDM(4)–PEGDM(7‐8). ILs slightly influence the photopolymerization of monomers from the first group and greatly change kinetics of those from the second. Such behavior was explained by the theory of “kinetically favorable or unfavorable monomer associations.” It was demonstrated that certain ILs accelerate the photopolymerization of the highest PEGDMs and offer access to the polymers derived from low reactive monomers. Relying on the obtained data, the attempt to predict the structure of the “best” ionic additive for the given monomer photopolymerization was performed and proved. Finally, the influence of both residual and specially added ILs quantities upon the properties of obtained polymer materials was investigated. It was revealed that ILs can physically interact with polymer networks increasing their thermal stability, plasticizing films, and blocks, imparting ionic conductivity equal up to 3.62 × 10^?3 Sm/cm at 25 °C. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 2388–2409, 2010     

The effect of film thickness and sample history on the parameters describing transport in glassy polymers

The effect of a characteristic dimension of a glassy polymeric specimen on the kinetic mechanism controlling unidirectional absorption of organic vapors and liquids in glassy polymers is demonstrated by comparing n-alkane absorption experiments in microspheres, spheres, films, and sheets of polystyrene. Absorption in submicron microspheres is controlled by Fickian diffusion whereas, under otherwise identical boundary conditions, films (ca. 75μm thick) and spheres (ca. 184 μm in diameter) sorb according to Case II absorption kinetics. Thinner films (35 μm thick) sorb by Super Case II kinetics and relatively thick sheets (2000 μm thick) sorb initially by Case II kinetics but, at long times, diffusion through the outer swollen region contributes significantly to the overall resistance to mass transfer and the rate of absorption decreases progressively with time. p]The rather short experimental times, afforded by the exceedingly small mean diameter of the narrowly distributed microsphere powder sample, permitted convenient characterization of the effects of preswelling, sorption-desorption cycling, and annealing on the kinetics and apparent equilibria of sorption. History effects were quite dramatic and were related to glassy state relaxations initiated by the various thermal and swelling histories imposed upon the glassy microspheres. p]Prediction of sorption and permeation behavior in membranes, from kinetic and equilibrium parameters determined experimentally on film and powder samples, requires explicit recognition of these dimensional and history effects. These effects do not appear to be related to any special properties of this polymer-penetrant system.