Diffusion coefficient Arrhenius form

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 temperature dependence of the diffusion coefficients can be described by the conventional form of the Arrhenius expression,... 

The diffusion coefficients for 131I, 133Xe, and 132Te are given as a function of the temperature in Figures 1, 2, and 3, respectively. These data are summarized in Table I according to an Arrhenius form of the temperature dependence of the diffusion coefficients where... 

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... 

This expression has the Arrhenius form and E is the maximum value of the potential energy, an activation energy for deposition. This is expected because the potential profile of fig. 2 resembles the plot of the energy against reaction coordinate used in the theory of rate processes. The factor /(//m) accounts for the dependence of the diffusion coefficient on the distance and evaluations show that it can decrease the frequency factor in eqn (16) by two orders of magnitude. 

Diffusion data arc generally reported in terms of a diffusion coefficient D (cm /s), and its temperature dependence is best described by an Arrhenius equation of the form ... 

The diffusion coefficient for gases in mbbers has an Arrhenius form ... 

Thermal effects constitute a significant portion of the study devoted to catalysis. This is true of electrochemical reactions as well. In general the reaction rate constants, diffusion coefficients, and conductivities all exhibit Arrhenius-type dependence on temperature, and as a rule of the thumb, for every 10°C rise in temperature, most reaction rates are doubled. Hence, temperature effects must be incorporated into the parameter values. Fourier s law governs the distribution of temperature. For the example with the cylindrical catalyst pellet described in the previous section, the equation corresponding to the energy balance can be written in the dimensionless form as follows ... 

A form of Fick s law describes the diffusion of gases through the amorphous polymer matrix. The diffusion coefficient has been observed to follow an Arrhenius relationship, characteristic of an activated process. 

Also consider what happens if we vary the temperature and tr> to determine the reaction s activation energy. Let the temperature dependence of the diffusMty, Pa, be represented also in Arrhenius form, with faiff the activation energy of the diffusion coefficient. Let rxn be the intrinsic activation energy of the reaction. The observed activation energy from Equation 7.69 is... 

Figure 7.8 A form of Arrhenius plot found for almost-pure crystals with low impurity concentrations. Note D, diffusion coefficient T, temeprature (in kelvin) Dq, preexponential, or frequency, factor...

The measured diffusion coefficient can be expressed as a function of temperature in the form of an Arrhenius equation. 

Gas molecnles that enconnter geometric constrictions experience an energy barrier such that sufficient kinetic energy of the diffusing molecule, or the groups that form this barrier, in the membrane is required in order to overcome the barrier and make a successful diffusive jump. The common form of the Arrhenius dependence for the diffusion coefficient can be expressed as... 

As in the case of any diffusion process, one should expect an Arrhenius-like behavior for the repetition diffusion coefficient T j in the following form ... 

Borgwardt and Bruce (1986) used the unreacted core model with product layer diftusion control and showed good aggrement with the experimental data obtained with 1 /im particles. Combining Eq.2.11 with Eq.2.10, and expressing the diffusion coefficient (DJ in the product layer in Arrhenius form (see Section 2.3) and writing the grain radius in terms of surface area as... 

Calcium sulfate product layer is essentially nonporous and the difhision process through this layer is generally considered as a solid state migration of ions. The effective diffusivity values reported in the literature for the diffusion coefficient of SOi in the calcium sulfate layer ranged between lO m /s - 10 mVs and it is defined in Arrhenius form as follows ... 

The temperature dependence of rate constants for both gaseous and liquid-state reactions is usually well described by the Arrhenius formula, Eq. (12.3-2). For activation-limited reactions, the activation energies are roughly equal to those for gas-phase reactions. This is as expected, since the collisional activation is very similar to that of gaseous reactions. In the case of diffusion-limited reactions, the temperature dependence of the rate constant is governed by the diffusion coefficients. Diffusion coefficients in liquids commonly have a temperature dependence given by Eq. (10.4-5), which is also of the same form as the Arrhenius formula ... 

It is known that a priori a diffusion coefficient obeys the Arrhenius law. We thus expect a law of the form ... 

For a known grating period A of the diffraction grating, the diffusion coefficient D can be calculated and if the relaxing species has diffiisive character, the difiiision coefficient will show an Arrhenius behavior of the form (equation 6)... 

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