Array diffusional cases

The work of T.J. Davies et al. [. Solid State Electrochem. 9 (2005) 797] identified four diffusional cases which arise at micro electrode arrays. As time passes and diffusion layers grow, the behaviour changes from one to the next. The cases are ... 

Many nanoparticle arrays exhibit diffusional Case 4 behaviour because the nanoparticles are deposited in sufficient density on the substrate that their diffusion layers overlap extensively. If the nanoparticles are being exploited for their catalytic properties, this is highly economical by comparison to the use of a macroelectrode of a catalytic metal, since only a very small quantity of the catalyst is required to achieve an equivalent current. 

Fig. 10.4. The four limiting cases of diffusional behaviour to an array of microdisc electrodes.

In other electrode configurations, the electrodes, either a microdisc or an array of electrodes, can be recessed, that is, the electrode is not planar to the insulating material and consequently the diffusional profiles will quantitatively change [10] recessed electrodes are typically produced unintentionally when photolithography is used. In the case of an array of recessed microdiscs. 

Fig. 9.17 Diffusion at a nanoparticle array. Case 1 almost planar diffusion at an isolated nanoparticle where the diffusion layer thickness is small compared to the nanoparticle radius. Case 2 convergent diffusion to diffusionally independent nanoparticles. Case 3 partially overlapping diffusion layers between adjacent nanoparticles. Case 4 heavily overlapping diffusion layers leading to effectively linear diffusion to the array as a whole. Reproduced from Y.G. Zhou etal, Chem. Phys. Lett. 497 (2010) 200, with permission from Elsevier.

Permeability. Nonwoven fibrous media are also being extensively used in filtration and barrier applications. Several analytical approaches have been proposed for describing the dependence of their permeability on the shape and volume fraction of fibers (53-56). For simplicity, all these studies assumed that the fibrous media is made of a regular array of equidimensional cells, each consisting of a fiber segment surrounded by air. This is certainly not the case experimentally as fibrous media are made from a deposition process in which fibers are laid into a dense and compact mat. In one approach (57), the permeability of the sheet to diffusional flow is studied by a Monte-Carlo process. Here, the sheet is put in contact with a large external bath of small particles which diffuse through the... 

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