Simple Fickian diffusion expression

In equation IV. 6, Dik represents the ordinary diffusion coefficient for binary interactions, and a, is the thermal diffusion ratio. The reactants are often present in small amounts (<1%) relative to the carrier gas thus, the multicomponent diffusion expression (equation IV. 6) may be replaced by a simple Fickian diffusion expression that includes thermodiffusion... 

The expressions derived above, in particular Eqs. 17 and 21, allow one to derive self- or transport diffusivities in a straightforward manner, since the width has a simple DQ law. This Fickian diffusion is only observed at large distances, corresponding to small Q values. Typically, in a molecular Uquid, Fickian diffusion is observed for distances larger than 10 A. For a molecule diffusing in a zeolite, one has to probe translation over a few unit cells (pa 60 A). At smaller distances (larger Q values), there is usually a deviation from the linear relation between Aa> and Q. This sort of deviation is quite general and is due to the details of the elementary diffusive steps. 

If the polymer is above its glass transition tempetature, Tg, it responds rapidly to changes in its physical condition and we have Fickian or Case I diffusion. This is the simplest case, and for T>T, Henry s law is valid for sorption and the diff ion coefficient is a constant (ideal Fickian diffusion). Its temperature dependence is well approximated by a simple Arrhenius expression with a constant activation energy. 

Simple gases interact weakly with polymers with a consequence that their diffusion behavior is Fickian. This means that the diffusion coefficient G does not depend on concentration and time but only on temperature. The dependence on temperature is expressed by an Arrhenius type equation as... 

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