Diffusion and relaxation in glassy polymer powders: 2. Separation of diffusion and relaxation parameters

Gravimetric sorption measurements for organic vapours in monodisperse glassy polymer powders have shown widely varied non-Fickian kinetic behaviour. These varied kinetics are interpreted by a single mathematical model involving a linear superposition of one or two phenomenologically independent first order relaxation terms upon the ideal Fickian diffusion equation. Analysis of experimental data for submicron powders through this model yields kinetic and equilibrium parameters describing the individual contributions of the diffusion and relaxation processes. This analysis has been applied to both integral and incremental sorption data for vinyl chloride, acetone, and methanol in poly(vinyl chloride) and for n-hexane in polystyrene. Sorption by initially penetrant-free polymer samples is dominated by a rapid Fickian diffusion process, while incremental sorptions show larger relative contributions from slow relaxation processes. The relaxation processes appear to be related to slow redistribution of available free volume through relatively large scale segmental motions in the relaxing polymer. The diffusion—relaxation model seems to provide a meaningful analysis of several non-Fickian ‘anomalies’, including a very slow approach to apparent equilibrium, two-stage and sigmoidal sorption curves, and sorption curves involving an initial maximum followed by temporary desorption and subsequent resorption.     

Effect of the fiber orientation on the sorption kinetics of seawater in an epoxy/glass composite: A free-volume microprobe study

The conventional gravimetric method and positron lifetime spectroscopy have been used to investigate the effect of glass fiber orientation on the diffusion behavior of seawater in epoxy-based composite samples with glass fiber orientations of 0 and 45°. The equilibrium mass uptake of seawater in 45 and 0° orientation composites has been found to be 2.77 and 1.57%, respectively. The diffusion process is non-Fickian in a 45° fiber oriented composite, whereas it is Fickian in a 0° oriented composite. Free-volume data for 45° fiber oriented composites indicates swelling upon the sorption of seawater leading to structural relaxation, and hence the diffusion becomes non-Fickian. On the other hand, a 0° fiber orientation sample exhibits no swelling, and this suggests that water diffusion to the fiber–resin interface through the resin matrix is impeded by the large number of bonds. A polymer–fiber interaction parameter determined from these results also further supports the idea that interface interaction in a 45° fiber oriented composite is less than that in a 0° fiber oriented composite. Positron and gravimetric results support this argument. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

The effect of penetrant activity and temperature on the anomalous diffusion of hydrocarbons and solvent crazing in polystyrene part I: Biaxially oriented polystyrene

The effects of temperature and penetrant activity on the sorption kinetics and equilibria of a series of alkanes in glassy, biaxially oriented polystyrene were studied. Normal isomers of pentane, hexane, and heptane cause crazing of polystyrene film samples at high penetrant activities (> 0.85). Crazing kinetics are identical to the kinetics of Case II transport. Transport of these normal hydrocarbons in glassy polystyrene in the temperature range 25 to 50°C is markedly non-Fickian; limiting Case II transport is observed at activities in exces of 0.6. Sorption appears to be controlled by highly activated relaxation processes including primary bond breakage at these high penetrant activities. Fickian diffusion behavior is approached, however, as penetrant activity is reduced. Sorption of the branched isomers of these compounds does not result in polymer microfailure. The sorption kinetics of the branched isomers, although time dependent, appear to be controlled primarily by thermally activated diffusion rather than large scale polymer relaxations which control Case II transport.     

The effect of molecular orientation on the vapour sorption of cyclohexane in amorphous polyester fibres

The sorption and transport of cyclohexane in poly(ethylene terephthalate) (PETP) fibres with various molecular orientations below the glass transition have been studied. The results have been analyzed in terms of the dual sorption model which has been successfully employed for glassy polymers. It has been shown that the capacity of the Langmuir mode of sorption inherent to glassy polymers is connected with the molecular orientation in the fibres of PETP. The increase of molecular orientation in the fibres has caused the decrease of the Langmuir capacity of PETP. This postulates a decrease in the free volume as a consequence of gradually increasing molecular orientation. Observations on the diffusion coefficients and activation energies for cyclohexane-PETP fibres system have been discussed.     

Water in epoxy resins Part II. Diffusion mechanism

A model is proposed for the diffusion mechanism of water in glassy epoxy resins. The polymer network is assumed to consist of two regions in which water molecules possess different mobilities. By considering the distribution of water molecules among these regions it is possible to describe the concentration dependency of the diffusion coefficient in the sorption and resorption processes. The diffusion coefficient becomes constant when the sorption temperature is close to the effective glass transition temperature of the epoxy-water binary mixture. An explanation of this effect is also provided by the model.     

Transport phenomena in gas permeation through glassy polymer membranes with concentration-dependent sorption and diffusion parameters

The modified dual-mode mobility model for permeation of a gas in glassy polymer membranes was combined with the extended dual-mode sorption model to take account of the plasticization effect of sorbed gas molecules on both sorption and diffusion processes. The combined model was further simplified by the introduction of a concentration of the mobile gas species. However, the observed pressure dependence of mean permeability coefficients of carbon dioxide in methylmethacrylate-n-butyl acrylate copolymer and polymethylmethacrylate films at 30°c and also that of oxygen in a polycarbonate film at 50°C and 60°C showed that a plasticization action of sorbed gas species has an influence on the diffusion process rather than on the sorption process, that is, were simulated by the modified dual-mode mobility model combined with the conventional dual-mode sorption model.     

INFLUENCE OF RHEOLOGICAL PROPERTIES IN MASS TRANSFER PHENOMENA: SUPER CASE II SORPTION IN GLASSY POLYMERS

The sorption rate of swelling penetrants in glassy polymers has been considered as controlled both by the swelling kinetics and the penetrant diffusion through the swollen layer. The stress exerted on the glassy core at the moving boundary is the driving force for the swelling, and results from an osmotic stress and a differential swelling stress contribution. During the sorption process, the osmotic stress at the moving boundary decreases, due to the increasing diffusion resistance; the differential swelling stress, on the contrary, increases giving rise to an acceleration of the front velocity (Super Case II).

The particular case of negligible diffusion resistance in the swollen region is here considered in more detail. It is shown that the rheological properties of both swollen and glassy phases crucially enter the mass transport problem; thestress relaxation in the swollen region must be taken into account in order to obtain a thickness dependent Super Case 11 effect     

Gas sorption and transport in poly(phenylene oxide) and comparisons with other glassy polymers

The sorption and transport of several gases in poly(phenylene oxide) were measured at 35°C, and the results have been analyzed in terms of the dual sorption/mobility models which have been successfully employed for this purpose for other glassy polymers. Both the extent of sorption and rate of permeation of gases are quite large for poly(phenylene oxide) compared to other glassy polymers with rigid chain backbones. It is shown that the high extent of sorption is owing to the high glass transition temperature of this polymer, but this is not a significant factor in its high permeability to gases. The latter stems from large diffusion coefficients. It is shown that the capacity of the Langmuir mode of sorption inherent to glassy polymers is related to the value of the glass transition temperature in a general way for a wide variety of polymers. Observations about the diffusion coefficients for numerous gas–polymer pairs are discussed.     

Sorption and transport of water vapor in glassy poly(acrylonitrile)

Sorption data for H₂O in glassy poly(acrylonitrile)(PAN) are presented for a range of relative vapor pressures at temperatures from 20 to 50°C. Simple dual mode sorption, involving “hole-filling” and molecular solution appears to dominate the low activity region of sorption. Based on the clustering analysis suggested by Zimm and Lundberg, pronounced clustering of penetrant appears to occur above a relative pressure of 0.6. The form of the effective concentration-dependent diffusion coefficient for H₂O in PAN, determined by analysis of steady state permeation data, suggests that water in the microvoids and clusters has a lower mobility than the molecularly dissolved water in the polymer matrix. Time lag measurements at high upstream relative water vapor pressures suggest that the transient state permeation has a non-Fickian character due to relaxations which occur slowly to accommodate the clustering process.     

Heat effects in sorption of organic vapors in rubbery polymers

During supposedly isothermal sorption/desorption of gases or vapors by solid polymers, latent heat effects alter local temperatures with the result that diffusion behavior may appear to be non-Fickian. Even when sorption curves are seemingly Fickian, spurious values of the diffusion coefficient, D, may still be inferred. These phenomena are examined in an experimental and theoretical study of incremental sorption/desorption of acetone vapor in the fluoroelastomer, vinylidene fluoride/hexafluoropropylene copolymer. A theoretical analysis developed earlier to model water vapor sorption in wool and cellulose is shown to successfully reconcile measured mass transfer rates and temperature changes. © 1996 John Wiley & Sons, Inc.     

Equilibrium Swelling Characterization and Dye Uptake Studies of Acrylamide-co-Methylenesuccinic Acid Hydrogels and Semi-IPNs with PEG

A novel semi-interpenetrating network hydrogel, composed of acrylamide with methylenesuccinic acid as comonomer, with poly (ethylene glycol) and trimethylolpropane triacrylate was prepared. Highly swollen hydrogels were synthesized by free radical polymerization. Swelling experiments were performed in water and dye solutions at 25°C. The hydrogels were used in experiments on sorption of Basic Blue 12. Water and Basic Blue 12 diffusion into hydrogels was found to be non-Fickian in character. For sorption of BB 12 into the hydrogels was studied by batch sorption technique at 25°C. The adsorption capacity, removal effiency and partition coefficient of the hydrogels was investigated.     

Effects of mechanical and chemical properties on transport in fluoropolymers. I. Transient sorption

This is the first part of a study of chemical structure-physical property-performance relationships among several fluoropolymers and liquid penetrants, focusing on their diffusivities and solubilities. Transient sorption experiments conducted with perfluoroalkoxy, fluorinated ethylene propylene, and ethylene tetrafluoroethylene exhibited Fickian diffusion. The first two exhibited concentration-independent diffusivity, while the last displayed concentration-dependent diffusivity. Conversely, polyvinylidene fluoride (PVDF) and ethylene chlorotrifluoroethylene (ECTFE) exhibited non-Fickian behavior, including acceleration as saturation approached. Suspected causes for the unusual sorption behavior were structural characteristics due to processing (e.g., skin or orientation with respect to processing direction), intrinsic chemical structure, and morphological deformation induced by swelling. Stress-strain tests indicated that mechanical properties depend similarly on the presence of penetrants to transport properties. Weak swelling agents exhibited Fickian transport and a negligible change of mechanical properties. In contrast, strong swelling agents induced non-Fickian diffusion and caused significant changes of mechanical properties. A new kinetic model fit the transient sorption results, particularly the observed acceleration in PVDF and ECTFE. The model accounts for structural changes due to swelling and relaxation resulting from free-volume creation, which is assumed to be proportional to the amount of liquid sorbed. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 64: 455–476, 1997     

Kinetics and mechanisms of water sorption in hydrophobic,ionizable copolymer gels

The aqueous kinetic swelling properties of a class of cross-linked hydrophobic polyamine copolymer gels based on n-alkyl esters of methacrylic acid (nAMA) and N,N-dimethylaminoethyl methacrylate (DMA) have been studied as a function of solution ionic composition (pH, ionic strength, and buffer content), gel composition, and temperature. Water uptake and swelling in these gels are driven by ionization of the DMA amine groups, which overcomes the hydrophobic tendency of these gels to exclude water in the unionized state. Sorption kinetics in initially glassy gel disks are generally biphasic, characterized by an initial phase of relatively slow water uptake followed by an accelerated phase during which significant volume expansion of the gel occurs. This sorption/swelling behavior strongly suggests a moving penetrant front mechanism. The initial rate of water sorption increases markedly as (1) solution pH decreases, (2) gel nAMA comonomer content decreases, (3) gel nAMA side-chain length decreases, and (4) temperature increases. Furthermore, the initial phase of sorption in initially glassy gels is generally non-Fickian and approaches zero-order behavior as (1) pH increases, (2) nAMA content increases, and (3) temperature decreases. In direct contrast, sorption in initially dry, rubbery gels is monophasic, but non-Fickian, and approaches zero-order behavior as temperature increases. This behavior is contrary to the Fickian sorption behavior normally observed in polymers above their glass transition temperatures. Finally, sorption kinetics critically depend upon the nature of the ions in solution: Kinetics are significantly faster in the presence of weak electrolytes than that of strong electrolytes. We discuss the importance of the rate of ion transport in determining the overall sorption kinetics and how sorption kinetics can be non-Fickian in rubbery gels. Also, we propose a mechanism for the observed enhanced kinetics in the presence of weak electrolytes.     

Swelling Characterization and Adsorptive Features of Acrylamide/Itaconic Acid Hydrogels and Semi-IPNs for Uranyl Ions

A novel semi-interpenetrating network (semi-IPNs) hydrogel, composed of acrylamide (AAm) with itaconic acid (ITA) as co-monomer, with poly (ethylene glycol)(PEG) and trimethylolpropane triacrylate (TMPTA) was prepared. Hydrogels and semi-IPNs were synthesized by free radical solution polymerization. Swelling experiments were performed in water and aqueous solutions of uranyl acetate. Diffusion behavior was investigated and their diffusion into hydrogels was found to be non-Fickian in character. Sorption of uranyl ion onto the polymeric system was studied by a batch sorption technique at 25°C. The sorption capacity, removal effiency and partition coefficient of the hydrogels were investigated.     

Transport properties of dichloromethane in glassy polymers. VI. Poly(ethylene terephthalate)

Sorption and diffusion of dichloromethane vapor in amorphous poly(ethylene terephthalate) (PET) were investigated, with the aim of studying how aging phenomena, at different temperatures, influence the transport properties. It has been found that aging produces the appearance of non-Fickian behavior in the sorption curves as well as the reduction of the diffusion coefficients. Furthermore, aging at 60°C reduces the sorption of vapor at low activity, and this led to the hypothesis of the presence of ordered domains in the aged samples. In this case, the process of solvent-induced crystallization is favored, and it appears at lower activity. © 1996 John Wiley & Sons, Inc.     

Sorption and transport of benzene in poly(ethylene terephthalate)

The kinetics and equilibria of benzene sorption in poly(ethylene terephthalate) were measured at 40°C, 50°C, and 60°C, with benzene activities ranging from 0.02 to 0.3. At most experimental conditions, diffusion was found to be Fickian; however, evidence of non-Fickian transport was found at the highest activity levels. Values of the diffusion coefficient of benzene range from 10^-14 cm²/s at 40°C to 10^?12 cm²/s at 60°C in the limit of low concentrations. Nonlinear isotherms observed for benzene sorption were successfully interpreted in terms of the dual mode model for sorption in glassy polymers, whereby the sorbed penetrant exists as two populations: one sorbed according to Henry's law and the other following a Langmuir isotherm. Non-Fickian transport data were correlated with a model that superimposes diffusion of both the Henry's law and Langmuir populations (the “partial immobilization” model) upon first-order relaxation of the polymer matrix.     

Solvent sorption and swelling in poly(ethersulphone)

The sorption of carbon disulphide, methanol and chloroform by poly(ethersulphone), PES, has been studied on a time-scale which excludes the crystallization effects reported previously. The thermal history of this glassy polymer has a marked effect on the sorption kinetics which are non-Fickian. Ancillary measurements concern the dimensional changes undergone by specimens of PES during solvent sorption and desorption. Each solvent has a constant partial specific volume in mixtures with PES.     

Implications of Weak Donnan Potential in Ion-Exchange Reactions. An Alternate Strategy for Modeling Sorption Processes

ABSTRACT

Donnan potential generated during an ion-exchange process is conventionally believed to play an important role in partitioning co-ions in the resin and solution phases; most earlier studies implied near total exclusion of co-ions from the resin pores. The present work attempts to investigate implications of weak Donnan potential with specific reference to the sorption of acids on weak base resins. An alternate mathematical treatment has been proposed to describe the sorption behavior of any type of acid by assuming diffusion and sorption of single species, the composite acid molecule, in the resin pores. Fick's law is then used to characterize the diffusion process. The proposed model is validated using data reported in the literature for the sorption of a strong monobasic acid (HCl) and also for a weak monobasic acid (HCOOH). The fit of the model is excellent, and the regressed values of the effective diffusion coefficient are shown to be reasonable and correct to the order of magnitude. The model is expected to offer a simpler and unified approach for modeling sorption behavior of different types of acids and will be more useful in problems of acid separation from mixtures.     

Diffusion and relaxation in glassy polymer powders: 1. Fickian diffusion of vinyl chloride in poly(vinyl choride)

A model is presented for diffusion-controlled sorption in polymer powders consisting of uniform spherical particles. Gravimetric sorption-rate data for vinyl chloride in PVC powders are found to obey this Fickian model for certain types of samples over limited ranges of vinyl chloride pressure increment or temperature. Superficially similar deviations from the model are caused by particle non-uniformity and by the onset of a relaxation-controlled transport mode. These two causes can be distinguished by appropriate choice of sample type and experimental conditions. A simple modification of the model satisfactorily accounts for the effect of particle non-uniformity upon sorption kinetics for conditions under which transport is diffusion-controlled. The use of powder samples in vapoursorption experiments seems to afford several advantages over conventional film specimens, including more convenient measurement of the very low diffusivities characteristic of the glassy state, and more definitive separation of the contributions of diffusion and relaxation processes to the overall transport mechanism.     

Water sorption and diffusion through saturated polyester and their nanocomposites synthesized from glycolyzed PET waste with varied composition

A new system of saturated polyester and their nanocomposites synthesized from glycolyzed PET with varied composition is investigated for the sorption and diffusion studies in water. The kinetics of sorption is studied by using the equation of transport phenomena. The values of ‘n’ from transport equation are found to be below ‘0.5’, showing the non-Fickian or pseudo-Fickian transport in the polymer. The dependence of diffusion coefficient on composition and temperature has been studied for all polymeric samples. The diffusion coefficient of saturated polyester samples decreases with an increase in glycolyzed PET contents. The nanocomposite samples show less diffusion coefficient than pristine polymer and it decreases with an increase in nano-filler up to 4 wt%. The diffusion coefficient increases with an increase in temperature for all the samples. The sorption coefficient shows a little change with variation in composition as well as temperature for all the samples and it is in a range of 1. The activation energy for diffusion and permeation is positive for all the samples. The heat of sorption is also positive for all the samples, indicating Henry type mode of sorption.