Permeation of Neutral Hydrogen Species

To express the diffusion of hydrogen as neutral species, we can use the same starting point as for charged species From Eq. (1.15) and by substitution with Eq. (1.14), flux densities of hydrogen atoms and hydrogen molecules expressed in terms of diffiisivities become  

Assuming that the diffusivities are independent of concentration, and that the concentrations are given by the equilibria with hydrogen partial pressure treated earlier, we obtain  

We note that the molecular flux is proportional to the difference in hydrogen pressure (as in gas phase transport through a piorous membrane), whereas atomic transport has a square root dependence, and as such would behave similarly to ambipolar transport of protons and electrons limited by the conductivity of a minority concentration of protons. 

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