The diffusion of oxygen in polymers

The diffusion of oxygen in polymers is unaffected by any complication due to the concentration dependence of the diffusion constant [583]. The effect of temperature on the diffusion is given by the relationship 

The fundamental differential equation for the diffusion of oxygen into the polymer takes the form 

Frequently the diffusion occurs effectively in only one direction. If there is a gradient of concentration along the x-axis only, where x is the distance from the film surface, eqn. (106) reduces to 

It can be seen from eqn. (109) that the rate of oxidation in films depends on the relatively low rate of oxygen supply by diffusion, and is directly proportional to the concentration of oxygen. In the case of very thin samples the oxidation rate appears to be independent of thickness. The dependence of the induction period on the pressure of oxygen in such cases indicates that oxidation is also limited by oxygen diffusion, and the observed deviation of the behaviour of very thin samples may be explained by the fact that volatile oxidation products promote further oxidation processes. 

Wilson [666, 667] and Bauman and Maron [47] show that it is possible to express the reaction rate as a function of film thickness, diffusion constant and solubility of oxygen in the film. When the thickness of the film is reduced to less than a certain value, the chemical reaction and not the diffusion becomes the controlling factor. The activation energy of the oxidation reaction amounts to 16—35 kcal mole-1, or even more, whereas the activation energy of the diffusion of gases in polymer films [39] is of the order of only 10 kcal mole-1. Control by diffusion is facilitated at higher temperatures by the decrease of oxygen solubility in the films. 

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