Diffusion microscopic view

The microscopic view of diffusion starts with the movements of individual ions. Ions dart about haphazardly, executing a random walk. By an analysis of one-dimensional random walk, a simple law can be derived (see Section 4.2.6) for the mean square distance-cc traversedby an ionin atimef. This is theEinstein-Smoluchowski equation... 

In choosing between these two models, one needs to consider the specific process. The use of mass transfer coefficients represents a lumped, more global view of the many process parameters that contribute to the rate of transfer of a species from one phase to another, while diffusion coefficients are part of a more detailed model. The first gives a macroscopic view, while the latter gives a more microscopic view of a specific part of a process. For this reason, the second flux equation is a more engineering representation of a system. In addition, most separation processes involve complicated flow patterns, limiting the use of Pick s Law. A description of correlations to estimate values of k for various systems is contained in Appendix B. 

Fig. 2.1.18. Microscopic view of a case of relatively mild asbestosis. Note the pattern ofpaucicellular diffuse interstitial fibrosis. Asbestos bodies cannot be seen at this low magnification...

In PEFC porous media, the pore size distribution and surface properties are tailored to achieve the desired two-phase flow characteristics. Typically, highly hydrophobic PTFE is added to the naturally hydrophilic diffusion media structure. The result is a mixed hydrophobic-hydrophilic surface and internal structure. Figure 5.30 shows a microscopic view of a wet diffusion media material. 

Figure 530 Microscopic view of wet diffusion media paper surface. Some of the surfaces coated in PTFE in the DM are hydrophobic, while the base carbon fiber is hydrophilic. As a result, the fundamental description of the flow through this medium is extremely difficult [39]. Image courtesy of Prof. Massoud Kaviani.

The resolution of infra-red densitometry (IR-D) is on the other hand more in the region of some micrometers even with the use of IR-microscopes. The interface is also viewed from the side (Fig. 4d) and the density profile is obtained mostly between deuterated and protonated polymers. The strength of specific IR-bands is monitored during a scan across the interface to yield a concentration profile of species. While in the initial experiments on polyethylene diffusion the resolution was of the order of 60 pm [69] it has been improved e.g. in polystyrene diffusion experiments [70] to 10 pm by the application of a Fourier transform-IR-microscope. This technique is nicely suited to measure profiles on a micrometer scale as well as interdiffusion coefficients of polymers but it is far from reaching molecular resolution. 

The success of the Potts-Guy equation led many authors to advocate a single mechanism as the rate determining step for permeation through the skin barrier for all or at least a wide range of solutes diffusion was assumed to occur primarily via the interkeratinocyte lipids of the stratum corneum, a mixture of ceramides, fatty acids, and sterols. While from a macroscopic point of view these lipids may be modeled as a bulk solvent, on a microscopic scale they... 

Historically most of the microscopic diffusion models were formulated for amorphous polymer structures and are based on concepts derived from diffusion in simple liquids. The amorphous polymers can often be regarded with good approximation as homogeneous and isotropic structures. The crystalline regions of the polymers are considered as impenetrable obstacles in the path of the diffusion process and sources of heterogeneous properties for the penetrant polymer system. The effect of crystallites on the mechanism of substance transport and diffusion in a semicrystalline polymer has often been analysed from the point of view of barrier property enhancement in polymer films (35,36). 

In order to develop a consistent free-volume diffusion model, there are some issues which must be addressed, namely i) how the currently available free-volume for the diffusion process is defined, ii) how this free-volume is distributed among the polymer segments and the penetrant molecules and iii) how much energy is required for the redistribution of the free-volume. Any valid free-volume diffusion model addresses these issues both from the phenomenologic and quantitative points of view such that the diffusion process is described adequately down to the microscopic level. Vrentas and Duda stated that their free-volume model addresses these three issues in a more detailed form than previous diffusion models of the same type. Moreover, it was stated that the model allows the calculation of the absolute value of the diffusion coefficient and the activation energy of diffusion mainly from parameters which have physical significance, i.e. so-called first principles . In the framework of this model the derivation of the relation for the calculation of the self-diffusion coefficient of the sol-... 

---