Diffusivity real activation energy

Let the real activation energy be Qo and Q be the activation energy calculated on the basis of equation (31) then Q/Qo may range anywhere from unity to essentially zero, depending on the degree of the diffusion effect whose magnitude is calculable on the basis of the formulas given. 

Fig. 13. Universal relation of apparent activation energy Q, real activation energy Qo, and the diffusion parameter -q.

It should be noted that a diffusion step occurs with a null enthalpy. The sign of the apparent activation energy, if it exists, unlike the sign of a real activation energy, is not necessarily positive due to possible negative enthalpic terms, i.e. due to the presence of highly exothermic steps that precede the determining step. 

In order to obtain a definite breakthrough of current across an electrode, a potential in excess of its equilibrium potential must be applied any such excess potential is called an overpotential. If it concerns an ideal polarizable electrode, i.e., an electrode whose surface acts as an ideal catalyst in the electrolytic process, then the overpotential can be considered merely as a diffusion overpotential (nD) and yields (cf., Section 3.1) a real diffusion current. Often, however, the electrode surface is not ideal, which means that the purely chemical reaction concerned has a free enthalpy barrier especially at low current density, where the ion diffusion control of the electrolytic conversion becomes less pronounced, the thermal activation energy (AG°) plays an appreciable role, so that, once the activated complex is reached at the maximum of the enthalpy barrier, only a fraction a (the transfer coefficient) of the electrical energy difference nF(E ml - E ) = nFtjt is used for conversion. 

The Mallard-Le Chatelier development for the laminar flame speed permits one to determine the general trends with pressure and temperature. When an overall rate expression is used to approximate real hydrocarbon oxidation kinetics experimental results, the activation energy of the overall process is found to be quite high—of the order of 160kJ/mol. Thus, the exponential in the flame speed equation is quite sensitive to variations in the flame temperature. This sensitivity is the dominant temperature effect on flame speed. There is also, of course, an effect of temperature on the diffusivity generally, the dif-fusivity is considered to vary with the temperature to the 1.75 power. 

Activation Energy, Real/Mole Diffusing System Mt/Mo,-Initial Mt/Mo, = 0.60... 

In Eq. (3). is the flux when intracrystalline transport is rate controlling, Af, is the real flux. 8 AE is the difference between the activation energy for escape from within the crystal to the externally adsorbed layer and the activation energy for diffusion. It is generally a positive quantity [35]. K and K represent the Langmuir parameters for adsorption on the external and internal surfaces, respectively. When internal and external adsorption isotherms are taken to be identical or are within Henry s law range, Eq. (3) becomes... 

The method for adjustment of active coefficients is a simplified treatment for real complex kinetic reactions and of a very simple form. However, it cannot reveal the nature of the process. The decrease of apparent activation energy due to diffusion effect cannot be reflected by the equation that intrinsic kinetic equation is produced by active coefficients including various factors. 

The value of the activation energy calculated for a reversible decomposition of a solid may thus be just a procedural value of no real physical meaning other than a number characterizing the individual thermoanalytical experiment. Many sophisticated kinetic methods neglect the distinction between micro-kinetics (molecular level, true chemical kinetics) and macro-kinetics (overall processes in the whole sample bulk). The conventional process of the type, Asoiid Bsoiid + Cgas, as applied to the entire solid sample, consists of many elementary processes, some of them of purely physical in nature (e.g. heat transfer, diffusion). The experimentally obtained kinetic data may then refer to only one of these processes, which is the slowest one, often difficult to link up with a particular reaction mechanism. 

However, real solids are more complex. In the common case where the concentration of the diffusant is much higher than that of vacant sites, one must consider vacancies as the diffusing entities, in a similar fashion to the hole formalism used in semiconductors. More generally, the concentration to be used is that of the diffusing lattice defects, e.g. vacancies, interstitial ions, etc. The result is still of the Arrhenius form, however, and plots of In(crr) vs. l/T are linear with a slope of — EJkT. Consequently, the requirement for high mobility is simply a low activation energy, as expected for an open structure. 

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