Chapter 5 - Sorption thermodynamics of low molecular weight compounds in polymers

Towards a predictive thermodynamic description of sorption processes in polymers: The synergy between theoretical EoS models and vibrational spectroscopy

A very large amount of information is available in the open literature on the diffusion, or transport, of small molecules in polymers. A comprehensive discussion of this field would require an amount of space exceeding by far the confines of the present monograph. It is to be hoped that this herculean but extremely useful task will be undertaken by some enterprising investigator, or investigators, in the not-too-distant future. In the meantime, a review is presented here of some of the important and more recent work on the diffusion of small molecules in both rubbery and glassy polymers. The main purpose of the review is to outline the thrust of this work and thus provide a perception of possible new developments in the field.

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

Solubility of gases in polymers is an important property of polymeric materials relevant to many practical applications. Sorption of small molecules in polymers is a fundamental concern in such areas as food packaging, beverage storage, and polymer processing. However, by far the main interest in the solubility of gases in polymers, and especially in glassy polymers, is related to development of novel advanced materials for gas separation membranes. This is because the concentration gradient of a dissolved gas is the driving force of membrane processes. Development of these novel separation methods resulted in a rapid accumulation, in the recent literature, of thermodynamic data related to the solubility of gases in polymers at different temperatures and pressures. Polymers can be regarded as special cases of media intermediate between liquids and solids. As a consequence, modeling of gas sorption in polymers is very difficult and presents a permanent challenge to theoreticians and experimenters. The collection and critical evaluation of solubility data for various gas–polymer systems is relevant to both practical aspects of polymer applications and to fundamental studies of polymer behavior. This volume of the IUPAC-NIST Solubility Data Series summarizes the compilations and critical evaluations of the data on solubility of gases in glassy polymers. It is implied in this edition that “gases” are the components that are either permanent gases (supercitical fluids) or have saturated vapor pressure more than 1 atm at ambient conditions (298 K). The polymeric components of compilations and critical evaluations are primarily high molecular mass, amorphous, linear (noncross-linked) compounds that have the glass transition temperatures above ambient temperature. The data for each gas–polymer system have been evaluated, if the results of at least three independent and reliable studies have been reported. Where the data of sufficient accuracy and reliability are available, values are recommended, and in some cases smoothing equations are given to represent variations of solubility with changes in gas pressure and temperature. Referenced works are presented in the standard IUPAC-NIST Solubility Data Series format. Depending on the gas–polymer system, reported data are given in tabular form or in the form of sorption isotherms. The data included in the volume comprise solubilities of 30 different gases in more than 80 primarily amorphous homo and copolymers. Where available, the compilation or critical evaluation sheets include enthalpies of sorption and parameters for sorption isotherms. Throughout the volume, SI conventions have been employed as the customary units in addition to the units used in original publications.

The diffusion of small molecules in polymers above the glass transition temperature appears to be dominated by those factors which affect the Rouse segment mobility, e.g. the diffusion coefficient is strongly concentration dependent in accord with predictions of free-volume theories. The major complication arises due to dispersed homogeneities such as crystallinity. The effect of such inhomogeneities are not well described by simple two phase models. We shall review previous attempts to deal with crystallinity in rubbery polymers. While rubbery polymers respond rapidly to changes in their condition this is not the case with glassy polymers. Diffusion in such polymers is often dominated by finite rate relaxation effects which produce a whole range of anomolous behavior. We will discuss some recent attempts to describe the coupling of mass transport with relaxation behavior whose origin can be mechanical or structural.

Inverse-gas chromatography and the thermodynamics of sorption in polymers

A compressible lattice model with holes, the glassy polymer lattice sorption model (GPLSM), was used to model the sorption of carbon dioxide, methane, and ethylene in glassy polycarbonate and carbon dioxide in glassy tetramethyl polycarbonate. For glassy polymers, an incompressible lattice model, such as the Flory–Huggins theory, requires concentration‐dependent and physically unrealistic values for the lattice site volumes in order to satisfy lattice incompressibility. Rather than forcing lattice incompressibility, GPLSM was used and reasonable parameter values were obtained. The effect of conditioning on gas sorption in glassy polymers was analyzed quantitatively with GPLSM. The Henry's law constant decreases significantly upon gas conditioning, reflecting changes in the polymer matrix at infinite dilution. Treating the Henry's law constant as a hypothetical vapor pressure at infinite dilution, gas molecules in the conditioned polymer are less “volatile” than those in the unconditioned polymer. Flory–Huggins theory was used to model the sorption of carbon dioxide, methane, and ethylene in silicone rubber. Above the glass transition temperature, the criterion of lattice incompressibility for Flory‐Huggins theory was satisfied with physically realistic and constant values for the lattice site volumes. © 1992 John Wiley & Sons, Inc.

Swelling and plasticization of PDMS and PTMSP in methanol and dimethyl carbonate vapors and liquids: Volume, mechanical properties, Raman spectra

The main objective of this study is to assess the validity of a free-volume model of gas permeation through rubbery polymer membranes. Such information is of importance for the development of new membrane processes for the separation of gas mixtures. Steady-state permeability coefficients for N/sub 2/O in polyethylene between 20 and 50/sup 0/C and at pressures up to 15 atm were found to be 45% higher (on the average) than values predicted by the free-volume model. The difference between the experimental and theoretical permeability coefficients for N/sub 2/O is about twice as large as observed with many other gases in polyethylene. Permeability, diffusion time-lags, and absorption measurements were made with n-C/sub 4/H/sub 10/ in poly(eta-butyl methacrylate) at 30/sup 0/C and subatmospheric pressures. The experimental time-lags agreed satisfactorily with values predicted by the free-volume model, using model parameters obtained from gas absorption measurements. However, the experimental permeability coefficients were substantially higher than the theoretical values. This may be due to a non-Fickian transport component because the measurements were made at only 3/sup 0/C above the glass transition temperature of the polymer. This study was recently extended to the solution and transport of gases and vapors in glassy polymers. Satisfactory agreement betweenmore » experiment and theory was found for the solution, permeation, and diffusion of acetone, benzene, and methanol in ethyl cellulose and water vapor in poly(acrylonitrile) and for the solution of vinyl chloride monomer in poly(vinyl chloride). A generalized model of transport of small molecules in polymers has been developed. The model incorporates free-volume and dual-mode sorption concepts, and should be applicable both to rubbery and glassy polymers.« less

Chapter 6 - Mass transport of low molecular weight compounds in polymers

Comparison of transport properties of rubbery and glassy polymers and the relevance to the upper bound relationship

A theoretical approach has been developed to describe the processes of gases diffusion and sorption in rubbery and glassy polymers. Various models (Flory-Huggins, dual-mode sorption, gas-polymer-matrix) used for interpreting the sorption-diffusion experiments are discussed within this approach framework. Experimental data on carbon dioxide sorption in glassy and rubbery polymers have been considered using the proposed approach. The comparison of the experimental and theoretical data has permitted to make the conclusion on the developed concepts adequacy. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1339–1348, 1997

The influence of penetrant concentration on the diffusion and permeation of small molecules in polymers above tg

Sorption thermodynamics of water in two glassy polymers, polyetherimide (PEI) and polyetheretherketone (PEEK), is investigated by coupling gravimetry and on line FTIR spectroscopy in order to gather information on the total amount of sorbed water as well as on the different species of water molecules absorbed within the polymers, addressing the issue of cross- and self-interactions occurring in the polymer/water systems. Water sorption isotherms have been determined at temperatures ranging from 30 to 70°C while FTIR spectroscopy has been performed only at 30°C. The experimental analysis provided information on the groups present on the polymer backbones involved in hydrogen bonding interactions with absorbed water molecules. Moreover, it also supplied qualitative indications about the different “populations” of water molecules present within the PEEK and a quantitative assessment of these “populations” in the case of PEI. The results of the experimental analysis have been interpreted using an equation of state theory based on a compressible lattice fluid model for the Gibbs energy of the polymer-water mixture, developed by extending to the case of out of equilibrium glassy polymers a previous model intended for equilibrium rubbery polymers. The model accounts for the non-equilibrium nature of glassy polymers as well as for mean field and for hydrogen bonding interactions, providing a satisfactory quantitative interpretation of the experimental data.

Theories and models are presented for gas sorption in polymers above and below the glass transition temperature. With the exception of predictive theories that do not represent the data well, the models are fit to data for the carbon dioxide/silicone rubber and carbon dioxide/polycarbonate systems for the purposes of comparison. During the past decade, a number of new models and theories have been proposed specifically for gas sorption in glassy polymers. Each new model attempts to incorporate aspects of the gas sorption process that are unique to polymers below the glass transition temperature. This review discusses these recent advances, the assumptions used in their development and their advantages and disadvantages.