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I know that heat affects material permeation (increasing it); but I have not been able to find much in the way of data other than biologically, on how it effects materials such as plastics.

Does heat increase permeation exponentially, linearly, etc..?

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Because diffusion processes go like e^kT, the apparent permeabililty will rise exponentially. The picture is a bit more complex than this for plastics, because they expand significantly with temperature, thereby lowering their bulk density and enhancing their permeability.

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