Concentration-dependent transport of gases and vapors in glassy polymers

The transport of gases and vapors in glassy polymers is analyzed on the basis of the “dual-sorption” model with partial immobilization and the assumption that the diffusion coefficient is an exponential function of concentration. Expressions are derived for the effective (apparent) permeability and diffusion coefficients, as well as for the diffusion timelag. These expressions reduce in limiting cases to forms reported by other investigators. The implications of these results to the separation of gas and vapor mixtures by permeation through glassy polymer membranes are discussed.     

Finite difference modeling of the gas transport process in glassy polymers

Finite difference modeling has been used to predict the results of gas transport experiments for a concentration-dependent diffusion coefficient. Experiments on the transport of CO₂ in poly(ethylene terephthalate) and poly(ethylene naphthalate) had previously shown a difference between the effective diffusion coefficients for absorption and desorption runs of a double-sided experiment, but this effect had not been seen for single-sided experiments. The finite difference calculations show that such results are to be expected, and the parameters included in the models that attempt to describe the diffusion process in glassy polymers, such as the dual-mode model, and which lead to concentration-dependent diffusion coefficients, can be found by fitting the experimental data for the double-sided experiment using finite difference modeling. The dependence of the effective diffusion coefficient on pressure for the single-sided experiment can be correctly predicted using results from the double-sided experiment for an identical sample. © 1996 John Wiley & Sons, Inc.     

A generalization of dual mode transport theory for glassy polymers

The polymer matrix, divided in a number of cells in which the penetrant molecules can be sorbed and migrate, is considered. Each cell has been assigned an effective energy value that obeys a particular distribution. The effective diffusion coefficient and its concentration and temperature dependence are determined. The origin of sorbed penetrant mobility is studied. Using a delta-Dirac distribution for the site's energetic values, the model is reduced in the appropriate limit (low pressure) to other formulations of the dual transport model. More general results, allowing the site's energetic values to be drawn from a Gaussian distribution, are also given. © 1994 John Wiley & Sons, Inc.     

Diffusion in glassy polymers

Two versions of the free‐volume theory of diffusion are compared by considering differences in the predictions for the activation energy for the diffusion process. A number of data‐theory comparisons for free‐volume theory are discussed and evaluated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 785–788, 2003     

The effect of plasticization on the transport of gases in and through glassy polymers

The effects of plasticization on the transport of gases and vapors in and through glassy polymers are examined from the viewpoint of the “dual-mode” sorption model with partial immobilization. The analysis assumes the existence of two penetrant populations with different mobilities in the Henry's law and Langmuir domains of the glassy polymers. These mobilities are characterized by their mutual diffusion coefficients D_D and D_H. The plasticization of the polymer by penetrant gases is reflected in the concentration dependence of D_D and D_H. Expressions for the effective (apparent) diffusion and permeability coefficients are derived assuming that D_D and D_H are exponential functions of the penetrant concentration in the polymers. The results of this study are compared with a similar analysis which assumed the existence of a single mobile penetrant population. The present analysis provides information on the effects of plasticization on the penetrant transport in the Henry's law and Langmuir domains separately. The effects of antiplasticization or clustering of penetrant molecules on the effective diffusion and permeability coefficients are also examined.     

Dynamic heterogeneities in glassy polymers

The photoinduced isomerization of molecules incorporated in a glassy polymer matrix exhibits a wide spectrum of quantum yields. The source of the spectrum is matrix heterogeneities. The kinetics of the photoisomerization of 1-naphthyl-p-azomethoxybenzene in poly(ethyl methacrylate) and poly(n-butyl methacrylate) films is first used to study the rearrangement of the environments of photochromic molecules. The nonequilibrium distribution of cis molecules over the spectrum is obtained via conversion of trans molecules with the highest quantum yield into the cis form with the use of 405-nm light. The kinetics of attainment of the photostationary ratio for concentrations of cis and trans isomers under the action of light with a wavelength of 546 nm is studied through variation in the pause between the conversion of molecules into the cis form and the beginning of the studied process. It is shown that reversible changes in the structure of polymer matrices occur at a high rate at temperatures much lower than the glasstransition temperature.     

Strain-induced fibrillation of glassy polymers

Literature data on structural rearrangements taking place in amorphous glassy polymers upon their plastic deformation are analyzed. This deformation is shown to be primarily accompanied by polymer self-dispersion into fibrillar aggregates composed of oriented macromolecules with a diameter of 1—10 nm. The above structural rearrangements proceed independently of the deformation mode of polymers (cold drawing, crazing, or shear banding of polymers under the conditions of uniaxial drawing or uniaxial compression). Principal characteristics of the formed fibrils and the conditions providing their development are considered. Information on the properties of the fibrillated glassy polymers is presented, and the pathways of their possible practical application are highlighted.     

Diffusion in glassy polymers. III

The diffusion studies of several solvents in epoxy polymer reported by Kewi and Zupko in Part I of this series are explained with the solution obtained from the generalized diffusion equation which includes the internal stress contribution. The rate of permeation of a penetrant through a polymer film and the time lag needed to reach steady state are also given for the generalized diffusion equation.     

Solvent diffusion in amorphous glassy polymers

In this article, a mathematical model is proposed for predicting solvent self‐diffusion coefficients in amorphous glassy polymers based on free volume theory. The basis of this new model involves consideration of the plasticization effects induced by small molecular solvents to correctly estimate the hole‐free volume variation above and below the glass‐transition temperature. Solvent mutual‐diffusion coefficients are calculated using free volume parameters determined as in the original theory. Only one parameter, which can be predicted by thermodynamic theory, is introduced to express the plasticization effect. Thus, this model permits the prediction of diffusion coefficients without adjustable parameters. Comparison of the values calculated by this new model with the present experimental data, including benzene, toluene, ethyl benzene, methyl acetate, and methyl ethyl ketone (MEK) in polystyrene (PS) and poly(methyl methacrylate) (PMMA), has been performed, and the results show good agreement between the predicted and measured values. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 846–856, 2000     

The thermoelastic effect in glassy polymers

The thermoelastic effect has been measured in compression on four glassy polymers; namely, polystyrene, poly(methyl methacrylate), polycarbonate, and epoxy resin. Quantitative results have been obtained for the first time on three of these polymers. It has been shown that by paying attention to specimen geometry and instrumentation results can be obtained to a high degree of accuracy (better than ±1.5% on a given set of measurements). The polymers are shown to obey the classical Thompson equation for thermoelasticity in solids over the temperature range studied (ca. 220–350°K). By inference such materials can be expected to behave classically in general. The results have been used, as first suggested by Trainor and Haward, to obtain values for the linear thermal expansion coefficient and the values so obtained are shown to be in excellent agreement, in general, with literature values obtained by more conventional methods. Results are given for a range of stress from 5 MN m^?2 to between 25 and 50 MN m^?2 according to ambient temperature. The method affords a measurement of parameters, in particular, linear thermal expansion coefficient. Values of specific heat for the four plastics have been measured by differential scanning calorimetry and the results compared with published data.     

Diffusion in glassy polymers. I

Synopsis The diffusion of six solvents in three crosslinked, glassy epoxy polymers is studied. Case II swelling and Fickian sorption are observed as two simple limiting cases. The mechanism of diffusion changes from one limit to another as the nature of the solvent or the crosslink density of the polymer is altered. With mixed solvents, properly chosen, a superposition of Fickian diffusion and case II swelling is observed.     

Diffusion in glassy polymers. II

The Fickian diffusion coefficient of methylene chloride in a glassy epoxy polymer is calculated with the use of Crank's model of discontinuous change of D with concentration C. The diffusion constant is obtained as 1.93 × 10^?6 cm²/sec. The swollen layer behind the advancing solvent front is essentially in the rubbery state of the same polymer. The case II swelling by benzene is discussed in terms of a convective transport arising from the partial stress (internal) tensor of the penetrant. The superposition of Fickian and case II diffusion found with mixtures of methylene chloride and benzene is also discussed briefly.     

Diffusion of small molecules in glassy polymers

Small molecules in glassy polymers are considered to occupy sites with a distribution of free energies of dissolution. Then their diffusivity depends on concentration and temperature in the same way as it has been derived for hydrogen atoms in metallic glasses. For hydrogen it was shown that the tracer diffusion coefficient is proportional to the activity coefficient of the solute atoms. The latter can be evaluated from measured data of sorption of the small molecules in the polymer. Knowing this quantity, the thermodynamic factor can be calculated and the concentration dependence of the mutual diffusion coefficient is obtained in excellent agreement with published experimental results. New experimental results are presented for the diffusion coefficient of CO₂ in Kapton and four polycarbonates (BPA-PC, BPZ-PC, TMBPA-PC, and TMC-PC) in the low CO₂ pressure range of a few mbar up to 1 bar. The results are in agreement with the model developed for hydrogen. The reference diffusion coefficient, which is a fitting parameter of the model that is independent of the distribution of free energies is smallest for the polycarbonate BPZ-PC having a high γ-relaxation temperature. This correlation between the diffusion coefficient and the dynamics of the polymer can be found for other substituted polycarbonates as well. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 2397–2408, 1997     

Statistical mechanical model for diffusion of simple penetrants in polymers. II. Applications—nonvinyl polymers

The theory developed in Part I of this series is applied to a number of nonvinyl “smooth” chained homopolymers. The agreement between predicted and observed activation energies of diffusion for simple penetrants is generally good, particularly for polyethylene. Discrepancies observed for the smallest penetrants, He and H₂, in some polymers may be rationalized in terms of atomic scale irregularities on the polymer chain surface. It is shown that in favorable cases the theory may permit diffusion data to be used as an additional check on the accuracy of conformational energy maps for polymers.