The glassy polymer lattice sorption model (GPLSM) is a lattice-based activity coefficient model that has been developed for gas sorption in glassy polymers. The model recognizes the presence of holes on the lattice and determines how the number of holes changes by taking into account swelling due to penetrant gas molecules. The GPLSM equation has a composition-dependent energy term similar to that in the Flory-Huggins theory and an entropic term based on the mixing of gas molecules and holes. The utilization of sorptive dilation data for the determination of the number of holes gives a physically realistic interpretation of the local free volume in a glassy polymer. A good representation of the experimental data is obtained for the carbon dioxideand methane-polycarbonate systems.
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.
Sorption-desorption isotherms for carbon dioxide in polycarbonate, tetramethylpolycarbonate, hexafluoropolycarbonate, and poly (vinyl benzoate) were fitted using the glassy polymer lattice sorption model (GPLSM). The model requires sorptive dilation data to account properly for lattice compressibility. Using polymer segment-segment interaction energies from the sorption isotherms, the desorption isotherms were fitted with only a single adjustable parameter, the Henry's law constant. Differences in Henry's law constants between sorption and desorption were explained in terms of the unoccupied volume before and after the sorption-desorption process and the "volatility" of the gas in the local polymer environment at infinite dilution.
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.
Carbon dioxide sorption and dilation data were fitted with the glassy polymer lattice sorption model (GPLSM) to obtain segment-segment interaction parameters for poly(2,6-dimethyl-1,4-phenylene oxide) (PPO), polystyrene (PS), and two PPO/PS miscible blends. These interaction parameters were then used to calculate the enthalpy of mixing for the two polymers. The resulting enthalpies were -0.2 and -1.1 cal/cm 3 for PPO/PS blends of 50/50 and 75/25 by weight, respectively, which compare favorably to those determined from measured heats of solution and from calorimetry with low molecular weight analogs.
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