Diffusional surface-bulk exchange

The key to obtaining pore size information from the NMR response is to have the response dominated by the surface relaxation rate [19-26]. Two steps are involved in surface relaxation. The first is the relaxation of the spin while in the proximity of the pore wall and the other is the diffusional exchange of molecules between the pore wall and the interior of the pore. These two processes are in series and when the latter dominates, the kinetics of the relaxation process is analogous to that of a stirred-tank reactor with first-order surface and bulk reactions. This condition is called the fast-diffusion limit [19] and the kinetics of relaxation are described by Eq. (3.6.3) ... 

Diffusional mass transfer processes can be essential in complex catalytic reactions. The role of diffusion inside a porous catalyst pellet, its effect on the observed reaction rate, activation energy, etc. (see, for example, ref. 123 and the fundamental work of Aris [124]) have been studied in detail, but so far several studies report only on models accounting for the diffusion of material on the catalyst surface and the surface-to-bulk material exchange. We will describe only some macroscopic models accounting for diffusion (without claiming a thorough analysis of every such model described in the available literature). 

Numerous data on dynamic surface tension [77-93] and dynamic surface elasticity [94-103] of aqueous micellar solutions have been published until now. These data evidence the influence of micelles on the adsorption kinetics, although they are present only in the bulk phase. This effect can surprise on a first glance because it is well-known that the surface activity of micelles is negligible and hence their adsorption is almost zero. However, the influence of micelles can be easily explained if one takes into account that the adsorption kinetics of surfactants at fluid -fluid interface is determined by the diffusional exchange between the subsurface and the bulk phase [104, 105]. It is exactly the diffusion of monomers that changes in the presence of micelles. This point of view is widely accepted and difficulties arise only if one tries to obtain quantitative estimates of the observed effects. 

The adsorption kinetics of oxygen and nitrogen on CMS were studied using different experimental methods volumetric, gravimetric, chromatographic, thermal desorption, and isotope exchange [11]. From the analysis of the literature it follows that the transport process controlling the uptake rate seem to obey to two different mechanisms, either a surface barrier at the micropore entrances, or a diffusional molecular transport within the bulk of the micropores. 

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