Asymmetric diffusion

Most electrochemical studies at the micro-ITIES were focused on ion transfer processes. Simple ion transfer reactions at the micropipette are characterized by an asymmetrical diffusion field. The transfer of ions out of the pipette (ejection) is controlled by essentially linear diffusion inside its narrow shaft, whereas the transfer into the pipette (injection) produces a spherical diffusion field in the external solution. In contrast, the diffusion field at a microhole-supported ITIES is approximately symmetrical. Thus, the theoretical descriptions for these two types of micro-ITIES are somewhat different. 

Iqdari and Velde (unpub. data, 1992, see Table 8.2) described experiments of Ce diffusion in apatite soaked in CeCl2 with asymmetric diffusion profiles. For one of their runs carried out at 1100°C for 15 days, and described as an example of a non-linear least-square fit in Section 5.2, it has been found that the relationship between the Ce concentration CCt and the distance X to the mineral surface is described by... 

Cabodi, M., Chen, Y.F., Turner, S., Craighead, H., Laterally asymmetric diffusion array with out-of-plane sample injection for continuous sorting of DNA molecules. 

Regourd (R34) reviewed structural and other aspects of slags. XRD patterns show an asymmetric, diffuse band from the glass peaking at about 31 20 (CuK d = 0.29 nm) and extending from about 20 to about 37 and a weaker band at about 48 20 (0.19 nm). Crystalline phases, if present in sufficient quantity, give superimposed, sharper peaks melilite and merwinite are the most usual. Neither periclase nor lime is found and, since it is present either in the glass or in these inert, crystalline phases, MgO is not a potential cause of expansion, as it may be in a clinker (S89). 

A major improvement in fractionation of biomolecules based on rectification of Brownian motion was developed by Oudenaarden. With this technique, originally applied for the analysis of lipid biolayers, a laterally asymmetric diffusion array was fabricated. The separation was done in a direction that was not parallel to the direction of main flow, and lead to the components of the sample to physically discrete positions in the device. This approach brings with it the distinct possibility of inject sample continuously with separation accomplished in a DC electric held. 

Fig. 13. The cross section optic images of the diffusers based on sample 2. (a) symmetric diffuser, (b) asymmetric diffuser.

A strongly asymmetric diffusion profile has been observed after a certain diffusion time by means of electron probe microanalysis. This profile is shown in Fig, 6-1 [11]. 

Thus, according to this theory, polarity of transport is produced by an asymmetry in cellular permeability to the auxin anions (see also Sect. 3.2.3.3), but polar transport is basically an asymmetric diffusion (Goldsmith 1977, p 457). Therefore, the theory requires that profiles of the distribution of radioactivity in plant parts which had been supplied with a constant concentration of labeled auxin should fit to a solution of Pick s second law of diffusion, which relates the concentration to both the time of transport and the distance from the source, namely to error function curves. Such curves are constructed from... 

Figure 17.3.10 The asymmetric diffusion field (see the inset) and its corresponding asymmetric cyclic voltammogram at a p-L/L interface supported at a micropipet. 1 corresponds to linear diffusion and 2 shows the steady-state voltammogram corresponding to hemispherical diffusion.

The specific geometry of the micropipet produces an asymmetric diffusion field, i.e., ion transfer from inside the pipet to ontside is confined to a linear diffusion field which can produce a peak-shaped wave in cyclic voltammetry. In the reverse process, the diffusion field is hemispherical, which produces a steady-state wave in cyclic voltammetry (see the inset in Figure 17.3.10). This unique characteristic of micropipets has been used to identify species responsible for limiting the potential window as well as in the development of mechanisms for FIT reactions (47, 65). Dual-pipets have been used in the generation/ collection mode for ionic processes, and these have employed to study complicated ET-IT and IT-IT coupling reactions (96). 

Fig. 8. Skew scattering (a) and side-jump scattering processes (b) for asymmetric diffusion.

In the case of the asymmetric diffusion, cross-correlations between different Wigner matrices have to be accounted for. ... 

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