Mechanism glassy polymer diffusion

Water molecules combine the tendency to cluster, craze and plasticize the epoxy matrices with the characteristic of easily diffusion in the polymer1 10). The morphology of the thermoset may be adversaly influenced by the presence of the sorbed moisture. The diffusion of the water in glassy polymers able to link the penetrant molecules is, therefore, characterized by various mechanisms of sorption which may be isolated giving useful information on the polymer fine structure. 

In this contribution we present results obtained with tetra-ethyleneglycol diacrylate (TEGDA). This compound was chosen since its polymer shows an easily discernible maximum in the mechanical losses as represented by tan 5 or loss modulus E" versus temperature when it is prepared as a thin film on a metallic substrate. When photopolymerized at room temperature it forms a densely crosslinked, glassy polymer, just as required in several applications. Isothermal vitrification implies that the ultimate conversion of the reactive double bonds is restricted by the diffusion-limited character of the polymerization in the final stage of the reaction. Therefore, the ultimate conversion depends strongly on the temperature of the reaction and so does the glass transition. 

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.)... 

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... 

Section IIA summarizes the physical assumptions and the resulting mathematical descriptions of the "concentration-dependent (5) and "dual-mode" ( 13) sorption and transport models which describe the behavior of "non-ideal" penetrant-polymer systems, systems which exhibit nonlinear, pressure-dependent sorption and transport. In Section IIB we elucidate the mechanism of the "non-ideal" diffusion in glassy polymers by correlating the phenomenological diffusion coefficient of CO2 in PVC with the cooperative main-chain motions of the polymer in the presence of the penetrant. We report carbon-13 relaxation measurements which demonstrate that CO2 alters the cooperative main-chain motions of PVC. These changes correlate with changes in the diffusion coefficient of CO2 in the polymer, thus providing experimental evidence that the diffusion coefficient is concentration dependent. 

B. Diffusion Mechanism in Glassy Polymers - Experimental Evidence... 

Because of the assumed dual sorption mechanism present in glassy polymers, the explicit form of the time dependent diffusion equation in these polymers is much more complex than that for rubbery polymers (82-86). As a result exact analytical solutions for this equation can be found only in limiting cases (84,85,87). In all other cases numerical methods must be used to correlate the experimental results with theoretical estimates. Often the numerical procedures require a set of starting values for the parameters of the model. Usually these values are shroud guessed in a range where they are expected to lie for the particular penetrant polymer system. Starting from this set of arbitrary parameters, the numerical procedure adjusts the values until the best fit with the experimental data is obtained. The problem which may arise in such a procedure (88), is that the numerical procedures may lead to excellent fits with the experimental data for quite different starting sets of parameters. Of course the physical interpretation of such a result is difficult. 

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... 

The basic transport mechanism through a polymeric membrane is the solution diffusion as explained in Section 4.2.1. As noted, there is a fundamental difference in the sorption process of a rubbery polymer and a glassy polymer. Whereas sorption in a mbbery polymer follows Henry s law and is similar to penetrant sorption in low molecular weight liquids, the sorption in glassy polymers may be described by complex sorption isotherms related to unrelaxed volume locked into these materials when they are quenched below the glass transition temperature, Tg. The various sorption isotherms are illustrated in Figure 4.6 [47]. 

Chapter 4(71) focuses on the characterization of sorption kinetics in several glassy polymers for a broad spectrum of penetrants ranging from the fixed gases to organic vapors. The sorption kinetics and equilibria of these diverse penetrants are rationalized in terms of the polymer-penetrant interaction parameter and the effective glass transition of the polymer relative to the temperature of measurement. The kinetic response is shown to transition systematically from concentration independent diffusion, to concentration dependent diffusion, and finally to complex nonFickian responses. The nonFickian behavior involves so-called "Case II" and other anomalous situations in which a coupling exists between the diffusion process and mechanical property relaxations in the polymer that are induced by the invasion of the penetrant (72-78). ... 

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. 

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. 

The mechanisms of gas diffusion are very different at temperatures above and below the glass-transition temperature, T, of the polymers, i.e., when the polymers are in their "rubbery" or "glassy" state, respectively (1,3-8). The difference in these mechanisms is reflected in the significant differences observed in the dependence of the diffusion coefficient, as well as of the permeability and solubility coefficients, on the penetrant gas pressure or concentration in polymers and on the temperature. 

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