Model glassy polymers, matrix

The sorption isotherms for ethanol and methanol reported in Figure 4 and 5 cannot be interpreted on the basis of the well known dual mode model (/,2). This model assumes that the penetrant content in the glassy polymer matrix may be expressed as fimction of pressure through the sum of two contributions the first refers to the penetrant molecules which are considered to be adsorbed onto the surface of microvoids in the interior of the solid polymer, and the second represents the contribution due to penetrant molecules which are strictly dissolved into the solid phase. In the original formulation of the dual mode model the first contribution is expressed as fimction of pressure in terms of the Langmuir equation and the second through Henry s law. 

In glassy polymers tire interactions of tire penetrant molecules witli tire polymer matrix differ from one sorjDtion site to anotlier. A limiting description of tire interaction distribution is known under tire name of tire dual-soriDtion model [, 60]. In tliis model, tire concentration of tire penetrant molecules consists of two parts. One obeys Henry s law and tire otlier a Langmuir isotlienn ... 

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

Appendix Comments Concerning The "Matrix" Model For Sorption and Difffusion in Glassy Polymers... 

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. 

One possible solution to this problem is to develop microscopic diffusion models for glassy polymers, similar to those already presented for rubbery polymers. Ref. (90) combines some of the results obtained with the statistical model of penetrant diffusion in rubbery polymers, presented in the first part of Section 5.1.1, with simple statistical mechanical arguments to devise a model for sorption of simple penetrants into glassy polymers. This new statistical model is claimed to be applicable at temperatures both above and below Tg. The model encompasses dual sorption modes for the glassy polymer and it has been assumed that hole"-filling is an important sorption mode above as well as below Tg. The sites of the holes are assumed to be fixed within the matrix... 

Another model for the sorption and transport of gases in glassy polymers at super atmospheric pressures is the gas-polymer-matrix model, proposed by Raucher and Sefcik (1983). The premise of this model is that the penetrant molecules exist in the glassy polymer as a single population and that the observed pressure dependence of the mobility is completely due to gas-polymer interactions. In the mathematical representation of this model the following expression for sorption and transport is used ... 

The aforementioned analyses were essentially elastic in nature. However, Huang and Kinloch (7,8) developed a two-dimensional, plane-strain model to analyze the stress fields around the dispersed rubbery particles in multiphase, rubber-modified epoxy polymers. The epoxy matrix was modeled as either an elastic or elastic-plastic material. Their work revealed that the plane-strain model predicted higher stress concentrations within the glassy polymeric matrix than the axisymmetric model. Furthermore, they successfully applied their... 

It has been shown in a previous section that, in most cases of practical interest, the rate of gas permeation through nonporous polymer membranes is cOTitrolled by the diffusion of the penetrant gas in the polymer matrix. Many theoretical models have been proposed in the literature to describe the mechanisms of gas diffusion in polymers on a molecular level. Such models provide expressions for gas diffusion coefficients, and sometimes also for permeability coefficients, derived from free volume, statistical-mechanical, energetic, structural, or other considerations. The formulation of these coefficients is complicated by the fact that gas transport occurs by markedly different mechanisms in rubbery and glassy polymers. 

Free volume is an intrinsic property of the polymer matrix and is created by the gaps left between entangled polymer chains. Under the free volume model the absorption and diffusion of molecules in polymers depend greatly on the available free volume. For instance, many polymers show a sorption increase as the amount of free volume increases. One of the earliest models describing this behavior was developed by Fujita et al. [32]. Since then many researchers have worked with different models based on the free volume concept to describe sorption and diffusion in the glassy state [33-36]. 

Hence, the cluster model of polymers amorphous state structure allows to identify structural relaxation mechanisms in them. In the case of glassy loosely packed matrix relaxation process is realized by conformational reorganizations in this structural component (mechanism I) and in the case of its devitrification - clusters mutual motions (mechanism II). 

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