Alkane penetration in filled polystyrene sheets part II

An earlier study characterizing the penetration kinetics of alkanes in zeolite-loaded polystyrene sheets has been extended to include the effect of glass beads as well as zeolite fillers at various loadings over a broad range of temperature. As the temperature is increased, the accelerating effect of the filler is progressively decreased, and at temperatures above 60°C no effect of filler is observed. At temperatures in the range of 30-55°C, the fillers increase the rate of penetration and the effect varies directly and monotonically with filler volume fraction, essentially independent of filler type. The observed penetration is apparently controlled by a combination of relaxations at the observable boundary coupled with a diffusional resistance in the outer, continuous swollen shell. At a given temperature the relative contribution of diffusion and relaxation is independent of filler type and concentration. There is, however, a systematic decrease in the relative contribution of the relaxation process as temperature is increased, presumably because the relaxation processes are more highly activated than the diffusion-controlled contribution to the observed penetration. Therefore, as temperature is increased the diffusion through the swollen gel-layers becomes increasingly important. These data and complementary results suggest that the accelerating effect of the filler is confined to stress concentration which accelerates only the relaxation component of the overall penetration. As the relaxation component becomes less dominant, at the higher temperatures, the effect of filler tends to vanish.     

The swelling interface number as a criterion for prediction of diffusional solute release mechanisms in swellable polymers

When a glassy polymer containing a uniformly dispersed solute is brought in contact with a penetrant, solute diffusion will be associated with the transport mechanism and penetration velocity of the penetrant in the polymer. Analysis and prediction of mechanisms of diffusional solute release may be obtained through a new dimensionless number, the swelling interface number, Sw, which compares the relative mobilities of the penetrant and the solute in the presence of macromolecular relaxations in the polymer. It is shown that a sufficient and necessary criterion for time-independent diffusional solute release rates from these swellable systems is that the Sw be smaller than 10^?2. The swelling interface number Sw may be related to easily determined structural and thermodynamic parameters of the solute/polymer/penetrant system. Preliminary experimental results of dynamic water swelling of poly(2-hydroxyethyl methacrylate-co-methyl methacrylate) and diffusional release of theophylline from initially glassy copolymers show that decreasing values of Sw are related to increased pseudo-case-II transport kinetics of the solute.     

Transport of methylene chloride in poly(aryl-ether-ether-ketone) (PEEK)

The sorption of methylene chloride in neat PEEK was investigated as a function of temperature, sample thickness, surface treatment, and thermal history. The solubility of H₂CCl₂ in neat PEEK is 23 wt.% and is independent of thickness. Both surface treatment and thermal annealing strongly affect the rate of penetration; the as-Received material sorbs H₂CCl₂ more rapidly than abraded or annealed samples; however, the bulk solubility is independent of surface treatment. The sorption and desorption processes are considerably different, and the diffusion process is not simple Fickian Case I. The penetrant advances as a sharp front, suggesting a two-step, relaxation-controlled diffusion mechanism.     

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.     

Diffusion of organic vapors at low concentrations in glassy PVC, polystyrene, and PMMA

Diffusion coefficients of various C₁ to C₆ organic vapors, at concentrations 0.5 wt. percent, have been determined by gravimetric sorption rate measurements on emulsion and suspension-polymerized powder samples of PVC, polystyrene, and PMMA. Fickian diffusion kinetics were observed at the lowest concentrations, with a second-stage, relaxation-controlled sorption appearing at higher concentrations. In conjunction with published data for diffusivities of fixed gases in these polymers, the results indicate that diffusivity decreases exponentially, and that diffusion activation energy (E_D) increases linearly, with increasing diameter of “spherical” penetrant molecules (e.g., the noble gases, CH₄, SF₆, CCl₄, and neopentane). Much of the observed scatter in these correlations is attributable to uncertainty in the molecular diameters. For C₄ and larger n-alkanes and other elongated or flattened molecules, diffusivities are higher, and E_D lower, than for spherical molecules of similar molar volume. This finding suggests that anisometric molecules are oriented and move along their long axes during diffusion through the glassy polymer matrix. Correlations of diffusivities with molecular dimensions suggests that transport of anisometric molecules is governed by a diameter smaller than the mean (equivalent sphere) diameter but larger than the minimum dimension of their extended-chain conformation. Among the three polymers studied, diffusivity of each penetrant, at a given temperature, decreases in the order polystyrene> PVC ≥ PMMA.     

Sorption and diffusion of aliphatic hydrocarbons into crosslinked natural rubber

The sorption and transport of four aliphatic hydrocarbons into natural rubber crosslinked by different vulcanization systems [conventional (CV), efficient (EV), peroxide (DCP) and a mixed system consisting of sulfur and peroxide (mixed)] were investigated in the temperature interval of 28–60°C. Of the four systems, natural rubber vulcanized by DCP exhibited lowest penetrant uptake. It was observed that the kinetics of liquid sorption in every case deviates from the regular Fickian trend, characteristic of sorption of liquids by rubbers. The diffusion coefficient, activation energy of sorption, enthalpy, entropy, and the rubber-solvent interaction parameter were evaluated for the four systems from the swelling data. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 725–734, 1997     

Transport of hexane vapor in polystyrene at 25°C I. Analysis of integral sorption data

A series of measurements of integral n-hexane vapor sorption at 25°C and moderate activity, in polystyrene microspheres of varying radii, exhibits typical non-Fickian behavior: nonoverlap of curves of fractional uptake versus (square root of time)/radius. The data are examined in light of a sorption isotherm indicating hexane solubility in excess of that predicted by the Flory–Huggins equation, up to the hexane activity at which the glass transition apparently occurs. A transport analysis is developed based on the assumption that below the transition temperature T_g the rate of sorption is limited by the rate of polymer chain relaxations induced by the penetrant, which facilitate hexane entry into, and immobilization in, glassy microvoids.     

Ethylbenzene solubility,diffusivity, and permeability in poly(dimethylsiloxane)

The pure‐gas sorption, diffusion, and permeation properties of ethylbenzene in poly(dimethylsiloxane) (PDMS) are reported at 35, 45, and 55 °C and at pressures ranging from 0 to 4.4 cmHg. Additionally, mixed‐gas ethylbenzene/N₂ permeability properties at 35 °C, a total feed pressure of 10 atm, and a permeate pressure of 1 atm are reported. Ethylbenzene solubility increases with increasing penetrant relative pressure and can be described by the Flory–Rehner model with an interaction parameter of 0.24 ± 0.02. At a fixed relative pressure, ethylbenzene solubility decreases with increasing temperature, and the enthalpy of sorption is −41.4 ± 0.3 kJ/mol, which is independent of ethylbenzene concentration and essentially equal to the enthalpy of condensation of pure ethylbenzene. Ethylbenzene diffusion coefficients decrease with increasing concentration at 35 °C. The activation energy of ethylbenzene diffusion in PDMS at infinite dilution is 49 ± 6 kJ/mol. The ethylbenzene activation energies of permeation decrease from near 0 to −34 ± 7 kJ/mol as concentration increases, whereas the activation energy of permeation for pure N₂ is 8 ± 2 kJ/mol. At 35 °C, ethylbenzene and N₂ permeability coefficients determined from pure‐gas permeation experiments are similar to those obtained from mixed‐gas permeation experiments, and ethylbenzene/N₂ selectivity values as high as 800 were observed. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1461–1473, 2000     

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.     

Transport of organic vapors and liquids in poly(vinyl chloride)

This paper reviews research since 1980 on the equilibria and kinetics of transport of small organic molecules in rigid and plasticized PVC. The forms of both the solubility isotherms and the sorption kinetics are shown to change as the PVC/penetrant system undergoes a glass-rubber transition with an increase of either temperature or penetrant concentration. The isotherms are of “dual-mode” form (concave to the activity axis) for the glassy state, and show an inflection to Flory-Huggins form when the penetrant concentration exceeds C_g, the transition composition at the experimental temperature. The solubility at a given penetrant activity is governed primarily by the PVC/penetrant interaction parameter, χ. Sorption kinetics are Fickian for conditions producing small changes of concentration in either the glassy or rubbery state. For sorption into initially unplasticized PVC, kinetics are anomalous if the final penetrant concentration is between about C_g/2 and C_g, and Case II if C_g is exceeded. The magnitude of the Fickian diffusion coefficients depends largely on the geometric factors of molecular size and shape of the penetrant; this dependence is much steeper in the glassy than in the rubbery state. Recent results show that carbon dioxide displays both high diffusivity and substantial solubility in PVC under high pressure; this combination makes compressed CO₂ uniquely useful in accelerating the absorption of low-molecular-weight additives into PVC.     

β Relaxations in polyethylenes and their anisotropy

Measurements have been made of the anisotropy of viscoelastic behavior in specially oriented sheets of low-density polyethylene. The results for the cold-drawn sheets show a β relaxation process of very characteristic anisotropy. The annealed sheets show two relaxations in this region of temperature. The lower relaxation (about ?10°C) is identified as an interlamellar shear process. The higher relaxation (about 70°C) has a very similar anisotropy to the β relaxation in cold-drawn samples. Isotropic sheets of low-density polyethylene have been also investigated. Two β relaxations are found in these materials.     

Sorption and transport of linear alkane hydrocarbons in biaxially oriented polyethylene terephthalate

Equilibrium sorption and uptake kinetics of n‐butane and n‐pentane in uniform, biaxially oriented, semicrystalline polyethylene terephthalate films were examined at 35 °C and for pressures ranging from 0 to approximately 76 cmHg. Sorption isotherms were well described by the dual‐mode sorption model. Sorption kinetics were described either by Fickian diffusion or a two‐stage model incorporating Fickian diffusion at short times and protracted polymer structural relaxation at long times. Diffusion coefficients increased with increasing penetrant concentration. n‐Butane solubility was lower than that of n‐pentane, consistent with the more condensable nature of n‐pentane. However, n‐butane diffusion coefficients were higher than those of n‐pentane. Infinite‐dilution, estimated amorphous phase diffusion and solubility coefficients were well correlated with penetrant critical volume and critical temperature, respectively. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 1160–1172, 2001     

Sorption of organic vapors into drawn and undrawn polyethylene

Drawing of linear polyethylene at 60°C. to an extension ratio of ten drastically reduces the sorption and diffusion of n-pentane, benzene, methylene chloride, and tetrachloroethylene. Methylene chloride was chosen for more detailed study. The sorption is of the normal Fickean type. It is also fully reversible in the temperature range between 25 and 45°C. if the sorbed amount is kept to below 0.5%. At higher concentrations the sample relaxes so that sorption irreversibly increases. The reversible sorption per gram of amorphous component is about 1/6 of that in undrawn polyethylene. The diffusion constant has a larger temperature and concentration dependence than in the undrawn material. At zero concentration the activation energy for diffusion is 34.4 kcal./mole and the diffusion constant at 25°C. is 8 × 10^?11 cm.²/sec. as compared with 14.4 kcal./mole and 1.5 × 10^?8 cm.²/sec. in undrawn PE. Cold drawing reduces the sorption sites without changing their energy content, but drastically cuts down diffusion and increases the activation energy. A smaller part of the increase of the latter is a consequence of the lower enthalpy of the amorphous material and a larger part is probably due to the increased distance between sorption sites.     

Analysis of transport behavior in polymer powders

Vapor sorption studies on powder samples of glassy polymers have provided data which supplement results obtained on conventional film specimens and aid in the elucidation of glassy-state transport mechanisms. For uniform spherical particles of sub-micron size, sorption kinetics at very low activities of organic vapors follow a simple Fickian diffusion model. The short diffusion path in such samples allows determination of the very low diffusivities characteristic of the glassy state in experiments of conveniently short duration. Deviations from the Fickian, uniform-sphere model are observed in several circumstances: Particle size non-uniformity retards the approach to diffusion equilibrium. Sorption data at substantial vapor activities show an apparently similar slow approach to equilibrium which can be related to the contribution of a relaxation-controlled mode of sorption. The effects of particle non-uniformity and of relaxation processes can be distinguished by appropriate experimental design, and models for both have been developed. Sorption rate data obtained under Fickian diffusion conditions can be used to characterize particle size distribution. Sorption kinetics on uniform-sphere powders, conversely, can be analyzed through a diffusion-plus-relaxation model to distinguish and quantify the roles of the two transport modes more clearly than is possible with polymer film specimens. Polymer powder vapor solubility isotherms show significant variations with sample history which can be interpreted in terms of free volume changes and glassy state relaxations. This discussion, based on a study of vapor sorption by poly(vinyl chloride) samples, indicates that powder sorption measurements are also likely to be of general value in the study of other glassy polymers.     

Transport behavior of carbon disulfide into poly aryl ether ether ketone

The sorption/desorption of carbon disulfide into/from PEEK as a function of crystallinity and temperature was investigated. The sorption curves of carbon disulfide into PEEK show only two major regions: (a) an increase of penetrant weight with time, and (b) a limiting equilibrium value (solubility). This is in contrast to the sorption of toluene into PEEK which shows three regions. The solubility of carbon disulfide decreases with increasing crystallinity, but temperature has little effect on the solubility in the temperature range of 25–40°C. An acceleration in penetration rate at the later stage of diffusion is observed for PEEK films whose crystallinity is greater than 13.4%, suggesting Supercase II diffusion. Carbon disulfide can be desorbed completely from PEEK in contrast to other fluids, such as toluene or methylene chloride, which are difficult to desorb. The normalized weight loss of carbon disulfide during desorption is an exponential function of square-root time. Solvent-induced crystallization was observed. Crystallinity was estimated from both the measured density and microhardness of the desorbed polymer and polymer which had undergone a sorption/desorption/resorption/desorption cycle. © 1996 John Wiley & Sons, Inc.     

Diffusion of methyl ethyl ketone in polyisobutylene: Comparison of spectroscopic and gravimetric techniques

In this study, vapor sorption FTIR–ATR (Fourier Transform Infrared Attenuated Total Reflectance) spectroscopy was combined with a conventional gravimetric sorption balance to examine diffusion in polymers. Mutual diffusion coefficients of methyl ethyl ketone in polyisobutylene were measured using both methods at various penetrant activities and temperatures in the range 40–60°C. Actual penetrant concentrations were determined from the sorption balance. The diffusion coefficients from the two techniques agree very well with each other. In addition, the diffusivity data from both techniques could be correlated successfully as a function of temperature and concentration with the Vrentas and Duda free-volume model. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1261–1267, 1997     

Dual-mode analysis of subatomspheric-pressure CO2 sorption and transport in Kapton H polyimide film

Sorption kinetics and equilibria as well as permeabilities and diffusion time lags for CO₂ in Kapton polyimide film have been studied at temperatures from 35 to 55°C and pressures up to 0.78 atm. The sorption/desorption cycles indicate that the diffusivity of CO₂ increases with increasing local penetrant concentration in the polymer. Both the permeability and time lag decrease with increasing upstream CO₂ pressure. All of these results are described well by theoretical expression based on the dual-mode theory of sorption and transport in glassy polymers.     

Diffusion in atactic polystyrene above the glass transition point

Diffusivities and solubilities in the system n-pentane-polystyrene were measured for low penetrant concentrations at several temperatures above the glass transition temperature. The relatively sharp changes in the activation energy of diffusion and the heat of solution near 150°C. are interpreted tentatively as indicating that a second-order transition exists in atactic polystyrene above the glass transition temperature. Evidence indicating the existence of this transition has been obtained by other techniques and the effects observed in this study should also be present in the diffusion of other penetrants in polystyrene. Correlation of these and other available data for diffusion in polystyrene as a function of the molecular size of the penetrant indicates that specific thermodynamic interactions between polymer and penetrant have little influence on the diffusion process.     

Diffusion in polymers with varying accessibility

This paper considers the problem of describing quantitatively the process of diffusion in polymers attended by plasticization of their amorphous phase. A consequence of such plasticization is that the volume accessible to the penetrant molecules continuously increases during the course of their sorption. Assuming that the rate of relaxation processes is far greater than that of diffusion, an equation has been generated to describe the sorption in a matrix with varying accessibility. A numerical solution of this equation, using experimental data for a polyamide-water system, demonstrates that sorption in a matrix with increasing accessibility is slower than sorption in a hypothetical matrix with constant accessibility and with the same proportion of the amorphous phase. At the same time, the concentration of the penetrant in the former case proves to be higher at any point in the polymer specimen. The results obtained are important for calculating the rate constants for chemical reactions that proceed in a polymer matrix in the diffusion-kinetic mode.