Einstein’s mobility

If we postulate diat die chemical potentials of all species are equal in two phases in contact at any interface, dieii Einstein s mobility equation may be simply applied, in Pick s modified form, to describe die rate of a reaction occun ing dirough a solid product which separates die two... 

A number of metals, such as copper, cobalt and h on, form a number of oxide layers during oxidation in air. Providing that interfacial thermodynamic equilibrium exists at the boundaries between the various oxide layers, the relative thicknesses of the oxides will depend on die relative diffusion coefficients of the mobile species as well as the oxygen potential gradients across each oxide layer. The flux of ions and electrons is given by Einstein s mobility equation for each diffusing species in each layer... 

According to (1.3b), the nonconvectional electro-diffusion flux component j. is a superposition of the following two terms. The first is the diffusional Fick s component proportional to the concentration gradient VC. The second is the migrational component, proportional to the product of the ionic concentration Cj and the electric force —ZiFV

proportionality factor. Einstein s equality (1.3c) relates ionic mobility to diffusivity >. ... 

The values of the exponents quoted in Table XII have been estimated numericcilly by renormalization group techniques. Intuitively, there should be a close relationship between conductivity and percolation probability, and one would guess that their critical exponents should be identical. This is not true. Dead ends contribute to the mass of the infinite network described by the percolation probability, but not to the electric current it carries. Figure 39 shows the different growth of the percolation probability and the conductivity. It is convenient to set the conductivity equal to unity at = 1, as in Fig. 39. We note, in passing, that diffusivity is proportional to conductivity, in agreement with Einstein s result in statistical physics that diffusivity is proportional to mobility. 

It is possible, however, to speak of relative consistencies of the polymers of Fig. 5-10 or, in another sense, of the relative mobilities of diffusing species in them. If such a distinction is made, the materials could be arranged (in order of increasing consistency or decreasing diffusing species mobility) as polyethylene, polypropylene, polyisobutylene, and polystyrene. This fact checks with Einstein s original relation, which showed diffusivity to be related directly to the mobility of the diffusing species. 

However, Einstein s relation [18] relates the mobility to the diffusion coefficient of the charge carriers. Therefore, we must expect... 

As is well known, the mobility of charge carriers and, in particular, the ionic mobility /x is related to the diffusion coefficient D by Einstein s relationship... 

In electrochemistry several equations are used that bear Einstein s name [viii-Lx]. The relationship between electric mobility and diffusion coefficient is called Einstein relation. The relation between conductivity and diffusion coefficient is called - Nernst-Einstein equation. The expression concerns the relation between the diffusion coefficient and the viscosity and is known as the Stokes-Einstein equation. The expression that shows the proportionality of the mean square distance of the random movements of a species to the diffusion coefficient and the duration of time is called Einstein-Smoluchowski equation. A relationship between the relative viscosity of suspension and the volume fraction occupied by the suspended particles - which was derived by Einstein - is also called Einstein equation [ix]. 

The photomicrographic measurements refer directly to polymer motion under the influence of an external force. However, measurements of migration velocity v as a function of applied electrical field E show that some of these electrophoretic measurements were made in a low-field linear regime, in which the electrophoretic mobility jx is independent of E. Linear response theory and the fluctuation-dissipation theorem are then applicable they provide that the modes of motion used by a polymer undergoing electrophoresis in the linear regime, and the modes of motion used by the same polymer as it diffuses, must be the same. This requirement on the equality of drag coefficients for driven and diffusive motion was first seen in Einstein s derivation of the Stokes-Einstein equation(16), namely thermal equilibrium requires that the drag coefficients / that determine the sedimentation rate v = mg/f and the diffusion coefficient D = kBT/f must be the same. 

The dynamic,s underlying EINSTein is patterned after mobile CA rules, and are somewhat reminiscent of Braitenberg s Vehicles [brait84]. Specifically, EINSTein takes a artificial-life-like bottom-up, synthesist approach to the modeling of combat, rather than the more traditional top-down, or reductionist approach,... 

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