Diffusion Arrhenius equation

Table 10.1 Self diffusion coefficients of some liquid metals expressed by an Arrhenius equation...

When oxidation is a diffusion process the oxidation rate should be related to the temperature by the Arrhenius equation... 

We can also show that the diffusion coefficient, D, used in these Laws is temperature dependent, and can fit it to an Arrhenius equation ... 

As has been described in Ref. 70, this approach can reasonably account for membrane electroporation, reversible and irreversible. On the other hand, a theory of the processes leading to formation of the initial (hydrophobic) pores has not yet been developed. Existing approaches to the description of the probability of pore formation, in addition to the barrier parameters F, y, and some others (accounting, e.g., for the possible dependence of r on r), also involve parameters such as the diffusion constant in r-space, Dp, or the attempt rate density, Vq. These parameters are hard to establish from first principles. For instance, the rate of critical pore appearance, v, is described in Ref. 75 through an Arrhenius equation ... 

The mobility or diffusion of the atoms over the surface of the substrate, and over the film during its formation, will occur more rapidly as the temperature increases since epitaxy can be achieved, under condition of crystallographic similarity between the film and the substrate, when the substrate temperature is increased. It was found experimentally that surface diffusion has a closer relationship to an activation-dependent process than to the movement of atoms in gases, and the temperature dependence of the diffusion of gases. For surface diffusion the variation of the diffusion coefficient with temperature is expressed by the Arrhenius equation... 

It follows from this discussion that all of the transport properties can be derived in principle from the simple kinetic theory of gases, and their interrelationship through A, and c leads one to expect that they are all characterized by a relatively small temperature coefficient. The simple theory suggests that this should be a dependence on T1/2, but because of intermolecular forces, the experimental results usually indicate a larger temperature dependence even up to r3/2 for the case of molecular inter-diffusion. The Arrhenius equation which would involve an enthalpy of activation does not apply because no activated state is involved in the transport processes. If, however, the temperature dependence of these processes is fitted to such an expression as an algebraic approximation, then an activation enthalpy of a few kilojoules is observed. It will thus be found that when the kinetics of a gas-solid or liquid reaction depends upon the transport properties of the gas phase, the apparent activation enthalpy will be a few kilojoules only (less than 50 kJ). 

At high temperatures there is experimental evidence that the Arrhenius plot for some metals is curved, indicating an increased rate of diffusion over that obtained by linear extrapolation of the lower temperature data. This effect is interpreted to indicate enhanced diffusion via divacancies, rather than single vacancy-atom exchange. The diffusion coefficient must now be represented by an Arrhenius equation in the form... 

The specific conductivities of molten salts are frequently represented, as a function of temperature by an Arrhenius equation, but it is unlikely that the unit step in diffusion has a constant magnitude, as in the corresponding solids and the results for NaCl may be expressed, within experimental error, by the alternative equations... 

Diffusion coefficients vary considerably with temperature. This variation is generally expressed in terms of the Arrhenius equation ... 

The activation energy can be determined from the gradient of a plot of In D versus 1 IT (Fig. 5.19). Such graphs are known as Arrhenius plots. Diffusion coefficients found in the literature are usually expressed in terms of the Arrhenius equation D0 and Ea values. Some representative values for self-diffusion coefficients are given in Table 5.2. 

The critical value c of the diffusion coefficient is the value of which makes this relationship an equality and is related to the closure temperature Tc through the Arrhenius equation (8.4.4). Therefore... 

The rate of diffusion, D, and the rate of permeability, P, increase exponentially as shown by the Arrhenius equation for diffusion... 

Because D increases with increasing temperature (the Arrhenius equation 1-73), time-dependent D is often encountered in geology because an igneous rock may have cooled down from a high temperature, or metamorphic rock may have experienced a complicated thermal history. If the initial and boundary conditions are simple and if D depends only on time, the diffusion problem is easy to deal with. Because D is independent of x. Equation 3-9 can be written as... 

The problem of calculating reaction rate is as yet unsolved for almost all chemical reactions. The problem is harder for heterogeneous reactions, where so little is known of the structures and energies of intermediates. Advances in this area will come slowly, but at least the partial knowledge that exists is of value. Rates, if free from diffusion or adsorption effects, are governed by the Arrhenius equation. Rates for a particular catalyst composition are proportional to surface area. Empirical kinetic equations often describe effects of concentrations, pressure, and conversion level in a manner which is valuable for technical applications. 

The diffusion coefficients, as expected, increase with increasing temperature. Variation of the diffusion coefficient as a function of temperature can be expressed in terms of the Arrhenius equation, which, in logarithmic form, is... 

It is generally found that the constant , in contrast to co, depends on temperature. If the temperature dependence of (T) is represented by the standard Arrhenius equation, then the apparent activation energy appears to be on the order of 10 kJ/mol, which is close to the activation energy of most fluid diffusion processes. 

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