Migration path

Figure 3 A perspective of the atomic postions around the migration path, running from the moving atom to the vacancy. In some calculations an impurity is located at positions 1 or 2.

Figure 4 The wind valence in A1 along the migration path. The initial and saddle point positions are at the origin and at 0.5 respectively. The lower curve is for Cu, the upper curves are for self-electromigration. The dashed and the dotted curve show the influence of a Cu atom at positions 1 and 2 of Fig. 3 respectively, on the wind force in pure A1 (thick curve).

From the experimental results, the ER effect in polymer gels is explained as follows (Fig. 8). When an electric field is applied, the particles electrically bind together and cannot slip past each other. Larger shear forces are needed in the presence of an electric field. Thus, the electric field apparently enhances the elastic modulus of the composite gel. The difference in ER effects between an oil and a gel is that the polarized particles necessarily cannot move between the electrodes to produce the ER effect in a gel. In order for the ER effect to occur, it is important to form migration paths before application of an electric field. 

Concerning the effect of dispersion of the particles, straight migration paths as shown in Fig. 9 are effective to show a large ER effect. 

The formation of migration paths of dispersed particles as shown in Fig. 9 suggests a new approach for the modulation of polymer blends and morphology. It is expected that ER or MR effects show not only smartness but also unique anisotropy therefore, many workers are studying these effects from the point of view of polymer processing. 

Much of the quantitative information in this paper is derived from first-principles calculations based on density functional theory (DFT). Experimentally it is difficult to determine ion migration paths and energy barriers along migration paths in structural transformations such as from i-LiJV[n02 to 5-LiMn204. Examining the atomic-scale ionic movements that could occur in such a transformation using first-principles calculations can therefore be informative. 

Cowan, G. A., "Migration Paths for Oklo Reactor Products and Application to the Problem of Geological Storage of Nuclear Wastes", IAEA Symp., Paris, Dec. 19-21, 1977... 

The shorter migration distance on paper than in free solution has been explained on the basis of a longer migration path along the tortuous capillaries of the paper (A8, D15, K22), with a field actually smaller than that calculated from the potential measured at the ends of the strip. It seems impossible to make absolute mobility measurements on paper, although relative mobilities may be obtained for clinical use (M22). 

The sample of 0.01-0.02 ml is applied as a spot either by means of a micropipette or, more easily, by means of a small thin paper disk impregnated with the protein solution. The application zone is slightly dried beforehand to avoid diffusion and to favor rapid uptake of the sample. To obtain each fraction as an isolated spot and with little trailing along the migration path, the immediate uptake of the entire microspot by the application zone of the substrate is important. If the application... 

It is the main advantage of this rapid two-dimensional technique that it applies the important principle of a two-dimensional method to microsamples there is no mixing of fractions running simultaneously on the same migration path as in zone electrophoresis, but on the contrary, uncontaminated fractions are separated within very short time. For clinical research the method has a bright future because of the theoretical purity of the spot, which is not obtainable with zone electrophoresis. Good results have already been gained in work on animal serum (Dl). 

Fig. 95. (Top left) Ditopic ligand for the self-assembly of discrete M-Ln edifices. (Top right) Structure of [CrYb(115)3]6+, redrawn from (Imbert et al., 2003). (Bottom) Schematic representation of the energy migration paths occurring in the RuYb and CrYb edifices, with associated rate constants in s 1 (Torelli et al., 2005).

Fig. 4. Selected molecular configurations involved in (a) n-hexane and (b) n-butane and n-octane hopping on Pt(lll) along easy migration paths. The molecular motion follows the sequence 1-2-3 in (b). Filled (open) circles indicate the carbon backbone position of the molecule at the binding site (transition state), diamonds correspond to Pt surface atoms [66].

The molecular migration pathway in chromatography is a statistical pathway in which each molecule randomly executes the steps that constitute its particular migration path. If it were possible to outline the choices faced by a molecule (such as whether or not to adsorb in a given time interval or which streampath to follow around a particle), and the probability of each option, we would in theory be able to calculate the probability that the molecule would follow a particular path. Since all identical molecules are identically inclined, the probability of a certain path for a single molecule is equal to the fraction of all molecules taking that path. If, for instance, the probability is known for two paths, one displacing the molecule 20 mm and... 

One cannot expect a molecule that follows a random migration path, full of frivolous excursion, to arrive after a fixed time at exactly the same point as its equally frivolous companions. There will be a mean distance of migration X, but the individual molecules will exhibit fluctuations about this mean due to the peculiarities of their own migration. These statistical fluctuations will lead to zone broadening. The statistical (stochastic) theory of zone broadening was first developed by Giddings and Eyring [4] and has been expanded subsequently by a number of authors [5-8]. 

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