Tortuosity model films

The value of permeability obtained by the series model is zero, indicating that a perfectly aligned planar arrangement of GO nanosheets in direction obstructing the fluid path will practically make the thin nanocomposite film impermeable. The values obtained for the tortuosity model for the range of orientation angles from 0° to 90° lie in the permeability boundary values predicted by the series and the parallel models. 

Consider an electrode covered with a film that has continuous pores or channels from the solution to the electrode (Figure 14.4.1, process 6). We can ask how the electrolysis of a species in solution at such an electrode differs from that at the bare (unfilmed) electrode. The answer depends upon the extent of coverage of the electrode by the film, the size and distribution of the pores, and the time scale of the experiment. The situation is complicated, because the pores can have different dimensions and degrees of tortuosity, and their distribution within the film may not be uniform. Thus, theoretical treatments of such films often use idealized models. The theory for electrodes of this type is closely related to that for ultramicroelectrode arrays (Section 5.9.3), which, however, often involve a better-defined geometry and uniform distribution of active sites (81, 82). 

The permeation of gases in such a complex structure is very difficult to model due to the lack of information on the phase structures and properties, as well as the complexity of such modelling. Qualitatively, the reduced mobility and the chain orientation in semi-ordered interphases due to the stiff and ordered crystallites would make the permeability smaller. For the Pebax grades with shorter polyether blocks and longer polyamide blocks, the tortuosity of the diffusion path will increase sharply when the polyether and amorphous PA phases become finely divided by the crystalhne phase. Nevertheless, we tried to use the PA phase crystallinity to simulate the CO2 and nitrogen permeabilities in Pebax films with the simple resistance model [35] to estimate the influence of the Pebax structure on the permeability. 

One of the principal assumptions of the Nielsen model is that the plates are oriented parallel to the polymer surface. In literature some results where the plates are randomly oriented along the film thickness are reported. In order to overcome this problem, Bharadwaj proposed an extension of the Nielsen model able to describe the effects of the sheet orientation on the relative permeability. The new study addressed both of these issues by modifying a simple model developed to describe permeability in filled polymers on the basis of tortuosity arguments. The tortuosity factor is modified to include the orientational order, and the relative permeability is given by Equation (11.5) ... 

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