Diffusion-controlled reactions, activation definition

Figure 10 shows that Tj is a unique function of the Thiele modulus. When the modulus ( ) is small (- SdSl), the effectiveness factor is unity, which means that there is no effect of mass transport on the rate of the catalytic reaction. When ( ) is greater than about 1, the effectiveness factor is less than unity and the reaction rate is influenced by mass transport in the pores. When the modulus is large (- 10), the effectiveness factor is inversely proportional to the modulus, and the reaction rate (eq. 19) is proportional to k ( ), which, from the definition of ( ), implies that the rate and the observed reaction rate constant are proportional to (1 /R)(f9This result shows that both the rate constant, ie, a measure of the intrinsic activity of the catalyst, and the effective diffusion coefficient, ie, a measure of the resistance to transport of the reactant offered by the pore stmcture, influence the rate. It is not appropriate to say that the reaction is diffusion controlled it depends on both the diffusion and the chemical kinetics. In contrast, as shown by equation 3, a reaction in solution can be diffusion controlled, depending on D but not on k. 

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 final result is again a dimensionless number that compares the rate of reaction to the rate of mass transfer to the active sites in the pores. This is a conservative estimate because the concentration gradient depicted by curve 1 is likely to be steeper than the linear plot shown if the rate is very high. Furthermore, for a value of t s 0.95, the inequalities required in equation 4.88 for l -order and zero-order reactions are 0.6 and 6, respectively therefore, if a Weisz-Prater criterion (equation 4.93) of 0.3 or less is used, rates for all reactions with an order of 2 or less should have negligible mass transfer limitations. In addition, if the Weisz-Prater number is greater than 6, pore diffusion limitations definitely exist [20]. This transition region from kinetic to diffusion control occurs frequently around a TOF 1 s for many supported metal catalysts [22]. 

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