Surface diffusion distance

The motion of the growth steps is consistent with the hypothesis that vapour molecules are adsorbed in equilibrium concentration upon the flat basal surface and that those within some characteristic surface diffusion distance /g can migrate to the step and become incorporated in the crystal. If the step height is h -4 Ig then the rate of step motion should be... 

It is known that even condensed films must have surface diffusional mobility Rideal and Tadayon [64] found that stearic acid films transferred from one surface to another by a process that seemed to involve surface diffusion to the occasional points of contact between the solids. Such transfer, of course, is observed in actual friction experiments in that an uncoated rider quickly acquires a layer of boundary lubricant from the surface over which it is passed [46]. However, there is little quantitative information available about actual surface diffusion coefficients. One value that may be relevant is that of Ross and Good [65] for butane on Spheron 6, which, for a monolayer, was about 5 x 10 cm /sec. If the average junction is about 10 cm in size, this would also be about the average distance that a film molecule would have to migrate, and the time required would be about 10 sec. This rate of Junctions passing each other corresponds to a sliding speed of 100 cm/sec so that the usual speeds of 0.01 cm/sec should not be too fast for pressurized film formation. See Ref. 62 for a study of another mechanism for surface mobility, that of evaporative hopping. 

Slime is a network of secreted strands (extracellular polymers) intermixed with bacteria, water, gases, and extraneous matter. Slime layers occlude surfaces—the biological mat tends to form on and stick to surfaces. Surface shielding is further accelerated by the gathering of dirt, silt, sand, and other materials into the layer. Slime layers produce a stagnant zone next to surfaces that retards convective oxygen transport and increases diffusion distances. These properties naturally promote oxygen concentration cell formation. 

The charge injection from the sensitizer, S, dissolved in the electrolyte solution, might formally be considered as a photogalvanic process. The S molecules must be able to diffuse to the semiconductor surface during their lifetime, t0. Assuming the usual lifetime, r0—10 6 to 10 4s and the diffusion coefficient, D of 10 5cm2/s, the effective diffusion distance of S, <5d (see Eq. 2.5.9) is very small ... 

By mixing an absorbing granulate or powder with the product to be dried, the distances the diffusion can become very small, or the water molecules may move by surface diffusion. In both cases, the problem is the same First to find an acceptable drying agent (absorber) and then to separate it quantitatively from the dried product. 

The Einstein equation for surface diffusion gives Ds = X2A /2 St, where XA is the average distance between vacant adsorption sites and Si. is the residence time on a site. 

The first component h2/Z) is the period of time required to traverse a distance b in any direction, whereas the second term/ (alb) strongly depends on the dimension-ahty. Adam and Delbrtlck define appropriate boundary conditions and equations describing the concentration of molecules in the diffusion space in terms of space coordinates and time. They treated four cases (1) onedimensional diffusion in the linear interval a < jc < h (2) two-dimensional diffusion on the circular ring a < r < b (3) three-dimensional diffusion in a spherical shell a < r < b, and (4) combined three-dimensional and surface diffusion. They provide a useful account of how reduced dimensionahty of diffusion can (a) lower the time required for a metabolite or particle originating at point P to reach point Q, and (b) improve the likelihood for capture (or catch) of regulatory molecules by other molecules localized in the immediate vicinity of some target point Q. 

If compared to the neuro muscular junction at skeletal muscle the diffusion distance for the transmitter in the synaptic cleft is much longer. Furthermore, the membrane of the target cell is not specialized at the site of the junction but has receptors at the whole surface. In contrast to the all or nothing response of the skeletal muscle cell, the response of the sympathetic target cell to the transmitter is concentration-proportional, or graduated. 

Because an "infinite" or a "semi-infinite" reservoir merely means that the medium at the two ends or at one end is not affected by diffusion, whether a medium may be treated as infinite or semi-infinite depends on the timescale of our consideration. For example, at room temperature, if water diffuses into an obsidian glass from one surface and the diffusion distance is about 5 /im in 1000 years, an obsidian glass of 50 / m thick can be viewed as a semi-infinite medium on a thousand-year timescale because 5 fim is much smaller than 50 /im. However, if we want to treat diffusion into obsidian on a million-year time-scale, then an obsidian glass of 50 fim thick cannot be viewed as a semi-infinite medium. 

Diffusion from the surface of a three-dimensional sample, such as a sphere, as long as the diffusion distance is much smaller than the radius of the sample, e.g., 4(Df)i 2 < 1% of the radius. For larger diffusion distances, approximation using Equation 3-40 does not work well. For example, in three-dimensional diffusion, the center is more easily affected by diffusion than in one-dimensional... 

If one is interested in the diffusion time instead of the diffusion distance, for a given X, the time (fmid) required for the concentration at this x to reach midconcentration (Coo + Co)/2 is proportional to the square of its distance from the surface (derived from Equation 3-42b) ... 

If the plane source is on the surface of a semi-infinite medium, the problem is said to be a thin-film problem. The diffusion distance stays the same, but the same mass is distributed in half of the volume. Hence, the concentration must be twice that of Equation 3-45a ... 

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