The Stonehart Theory of Crystallite Separation

Subsequently, an equation was provided7 to describe the unidimensional intercrystallite distance on the carbon support surface viz. 

Previously, Stonehart11 had described the mechanism for diffusion of oxygen to an individual platinum crystallite on the carbon support surface. In this instance, at low current-densities, it was anticipated that hemispherical diffusion conditions operate, since the base of the platinum crystallite is shielded by the carbon support and thereby is inactive. 

The number of moles, dNr diffusing across a boundary to a spherical surface of4jtr2 in the time dt, is given by Fick s First Law  

The area at the exterior of the diffusion annulus surrounding the crystallite at (r + dr) is 4w(r + dr)2 and in time, t, the number of moles diffusing across this surface in time dt is  

Owing to the interference of the neighboring crystallites which limits the availability of oxygen, then C =/= CM but is modified by the intercrystallite distance, as well as the electrode potential. Thence the maximum diffusion radius (r + dr)IIBK= X/2 where X is defined above. In this case 

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