Effect of temperature on the permeability coefficient

Transport through dense films may be considered as an activated process which can usually be represented by an Arrhenius type of equation. This implies that the temperature may have a large effect on the transpon rate. The following equation expresses the temperature dependence of the penneability coefhcienL 

It can be seen that the energy of activation is more or less the same for the various gases in polyethylene and is about between 35 and 45 kJ/mol. Since the permeability coefficient depends both solubility and diffusivity both parameters must be involved to understand the temperature effect. For the solubility of non interactive gases in polymers a similar Arrhenius equation expresses the temperature effect. 

A similar temperature effect can be observed for the diffusion of gases in a polymer. The process can be considered as a thermally activated process and also the difhision coefficient follows an Arrhenius behaviour 

For small noninteracdve gases the temperature effect of the permeability coefficient is more determined by diffilsion since the solubility does change so much with temperature. In this case permeability anddiffusivity dependence are about the same. For the larger molecoles the situation is more complex since two effects diffusion and solubility are opposing. Furthermore, both parameters are concentradon dependent and should be considered from component to component. 

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The effect of temperature on the permeability coefficients and permselectivity of air separation for all the polyphenylene oxides studied is the same. Qualitatively it agrees with the numerous similar dependencies reported in the literature, i.e. permeabilities of oxygen and nitrogen increase as the temperature rises, while the permselectivity decreases (Fig. 2). It is worth noting that even at 348K the permselectivity for the polyphenylene oxide copolymer is still above 4. At this temperature the permeability coefficients are twice those at 273K. 

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