Gas Diffusion in Glassy Polymers

The diffusion behavior of simple gases (i.e., gases above the critical temperature) in glassy polymers is often quite different from the behavior of the same gases in the same polymers but above the polymer glass transition temperature [64], In particular, gas solubUity shows negative deviations from Henry s law, and the dissolution process is much more exothermic in glassy polymers. These and other 

The basic premise of the dual-sorption theory is that a glassy polymer contains microvoids, or holes created during the process of cooling the polymer below its glass transition temperature. Therefore, gas molecules can either dissolve in the bulk polymer or go into these holes. Consequently, glassy polymers have a high gas solubility due to the availability of dual-sorption modes. It is found that gas dissolution in the matrix follows Henry s law, whereas that in the holes displays a Langmuir-type dependence. Thus, at equilibrium, the total gas concentration in the polymer can be separated into a normal sorption term c, and a hole contribution [65]  

In view of the foregoing, kjy can be obtained from the slope of the sorption isotherm at high pressures. A knowledge of then allows us to calculate from c, and this leads to an evaluation of the other two model parameters by recasting Eq. (13.7.3) as follows  

SO that c u and b can be determined from the slope and intercept of the straight-line plot of p/Cf] versus p. 

As far as the rate of penetrant transport through glassy polymers is coneemed, it is assumed that material contained in the microvoids or holes is completely immobilized and does not contribute to the diffusive flux. It is further assumed that diffusion of the mobile species follows Pick s first law in terms of the concentration gradient of and a constant diffusivity. Thus, the flux in the x direction is 

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Application of the dual mode concept to gas diffusion in glassy polymers was originally subject to the limitation that DT2 = OinEq. (6) ( total immobilization model )6-Later this simplifying assumption was shown to be unnecessary, provided that suitable methods of data analysis were used 52). Physically, the assumption DX2 = 0 is unrealistic, although it is expected that DT2 < DX1 52). Hence, this more general approach is often referred to as the partial immobilization model . 

Prediction of gas diffusivity in glassy polymers. CEDis useful as it can be estimated conveniently without experimental measurements. In contrast, Vf values require measurements of polymer density. Accordingly, we attempted to correlate CED and D for several families of glassy polymers. Figure 7 presents this correlation for polyimides(7-5), polycarbonates(77,33), polysulfones(3 ), polystyrenes(i9), and the polyimides which we have studied. Overall, a good correlation between log(D) and CED was observed. 

Dual-Mode Gas Sorption and Diffusion in Glassy Polymer Membranes. 97... 

Sefcik M. D., Raucher D. The Matrix Model of Gas Sorption and Diffusion in Glassy Polymers, to be published... 

Carbon-13 rotating-frame relaxation rate measurements are used to elucidate the mechanism of gas transport in glassy polymers. The nmr relaxation measurements show that antiplasticization-plasticization of a glassy polymer by a low molecular weight additive effects the cooperative main-chain motions of the polymer. The correlation of the diffusion coefficients of gases with the main-chain motions in the polymer-additive blends shows that the diffusion of gases in polymers is controlled by the cooperative motions, thus providing experimental verification of the molecular theory of diffusion. Carbon-13 nmr relaxation... 

In the following chapter we present the matrix model of gas sorption and diffusion in glassy polymers which is based on the observation that gas molecules interact with the polymer, thereby altering the solubility and diffusion coefficients of the polymer matrix. 

The concept of dual mode sorption was first dearly demonstrated and quantified by Michaels, Vieth and Barrie in 1963 The same authors also discussed its effect on the diffusion process itself. Vieth and his co-workers aibsequently extended these findings to a number of polymer-gas systems and elaborated the theoretical aspects of the problem In particular, a model for diffusion in glassy polymers, which has come to be known as the totd inunobilization model, was developed by Vieth and Sladek ... 

Thran, A. Kroll, G. Faupel, F. Correlation between fractional free volume and diffusivity of gas molecules in glassy polymers. J. Polym. Sci. Part B Polym. Phys. 1999, 37 (23), 3344-3358. 

The results of the delayed stress on radiation studies presented above (Figure 7) are also consistent with the mechanism of gas buildup within the polymer specimens as the cause of the accelerated creep. An additional interesting conclusion is that applied stress should increase the rate at which gases diffuse out of a polymer specimen. This is not unreasonable in view of the fact that this conclusion is reached for stress application during irradiation, when expansion of the polymer matrix by the internally generated gas would be expected to facilitate gas diffusion. (Actually, one would expect increased gas diffusion in stressed glassy polymers, even in the absence of radiation, owing to the low Poisson ratio in such materials.)... 

Earlier work on the application of the concept of dual mode sorption and diffusion to glassy polymer-gas systems has been reviewed in detail 6) and important aspects of more recent work have been dealt with in more recent reviews 7 10). Eq. (5) was first applied by Michaels et al U). Sorption in the polymer matrix and in the specific sorption sites was represented by linear (Henry s law) and Langmuir isotherms respectively so that Sj in Eq. (5) is given by... 

Nonlinear, pressure-dependent sorption and transport of gases and vapors in glassy polymers have been observed frequently. The effect of pressure on the observable variables, solubility coefficient, permeability coefficient and diffusion timelag, is well documented (1, 2). Previous attempts to explain the pressure-dependent sorption and transport properties in glassy polymers can be classified as concentration-dependent and "dual-mode models. While the former deal mainly with vapor-polymer systems (1) the latter are unique for gas-glassy polymer systems (2). 

Permeation of gases in glassy polymers can also be described in terms of the dual sorption model. One diffusion coefficient (Do) is used for the portion of the gas dissolved in the polymer according to the Henry s law expression and a second, somewhat larger, diffusion coefficient (DH) for the portion of the gas contained in the excess free volume. The Fick s law expression for flux through the membrane has the form... 

S. The diffusion coefficients of gases in glassy polymer membranes are strong functions of the penetrant gas concentration in the membranes (or of the gas pressure), and depend also on polymer morphology (crystallinity, orientation), crosslinking, and chain mobility. The chain mobility depends, in turn, on the polymer free volume, the... 

This paper reviews some of the more important models and mechanisms of gas diffusion in rubbery and glassy polymers in light of recent experimental data. 

STERN TROHALAKI Gas Diffusion in Rubbery and Glassy Polymers... 

Considerable effort has been made during the last two decades to develop a "microscopic" description of gas diffusion in polymers, which is more detailed than the simplified continuum viewpoint of Fick s laws. It has been known for a long time that the mechanism of diffusion is very different in "rubbery" and "glassy" polymers, i.e., at temperatures above and below the glass-transition temperature, Tg, of the polymers, respectively. This is due to the fact that glassy polymers are not in a true state of thermodynamic equilibrium, cf. refs. (1,3,5,7-11). Some of the models and theories that have been proposed to describe gas diffusion in rubbery and glassy polymers are discussed below. The models selected for presentation in this review reflect only the authors present interests. 

A phenomenological theory known as the "dual-mode sorption" model offers a satisfactory description of the dependence of diffusion coefficients, as well as of solubility and permeability coefficients, on penetrant concentration (or pressure) in glassy polymers (4-6,40-44). This model postulates that a gas dissolved in a glassy polymer consists of two distinct molecular populations ... 

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