Surface nonuniform, kinetics

Although the role of surface nonuniformity in catalytic kinetics has been acknowledged by many researchers, a limited number of investigations has sought to quantify its impact on observable kinetics. Quantitative analysis of catalytic processes has advanced significantly by consolidating experimental, theoretical and semiempirical information via microkinetic analysis... 

In conclusion, it appears that a non-uniform surface behaves catal3dically much more like a uniform surface than suspected from a knowledge of its thermodynamic behavior. Rate equations are similar for a given mechanism on a uniform or non-uniform surface. This result justifies the common practice of neglecting nonuniformity of catalytic surfaces in kinetic studies. 

The first treatment of the influence of surface nonuniformity on kinetic behavior was that of Constable [1]. He considered the surface to be composed of different sites of the i-th type, with ni representing the number of sites of type i with an activation energy of E,. The overall rate constant is then, if the preexponential factor is assumed invariant ... 

In real adsorbed layers, the kinetics is more complicated, as the active sites could have different activity associated with various defects. Similarly to the treatment of adsorption, we will present here a special model of surface nonuniformity, which was developed by M. Temkin. The rate of sorption on an ideal surface is given by ... 

In some particular cases when the reaction occurs either at low or at high surface coverage, the kinetics is insensitive to surface nonuniformity. Thus, the description has to be exacdy the same when applying either concept of uniform or nonuniform surfaces generally speaking, the uniform surface can be treated just as a special case of the more general model of nonuniform surfaces. 

The distribution of current (local rate of reaction) on an electrode surface is important in many appHcations. When surface overpotentials can also be neglected, the resulting current distribution is called primary. Primary current distributions depend on geometry only and are often highly nonuniform. If electrode kinetics is also considered, Laplace s equation stiU appHes but is subject to different boundary conditions. The resulting current distribution is called a secondary current distribution. Here, for linear kinetics the current distribution is characterized by the Wagner number, Wa, a dimensionless ratio of kinetic to ohmic resistance. 

Accdg to his theory, combustion initiated at open end of the pipe first takes place in the circumferential region of one spiral, and then the flame is propagated in the gas stream, forming a sort of an elongated cone between the reference surfaces AA and BB, as shown in Fig B. The process of combustion here is essentially nonuniform. The depth of the reaction zone is detd directly from kinetics (as in the case of one-dimensional propagation... 

The diversity of possibilities of the general picture of a nonuniform surface makes it indefinite and hence scarcely suitable for concrete applications. On the basis of experimental data on heat of adsorption, adsorption equilibria, adsorption and desorption kinetics, the kinetics of reactions and electrode processes, a special model of a nonuniform surface has been formulated (41) that describes the experiments satisfactorily and without excessive mathematical complexity. 

X. Adsorption Equilibrium and the Kinetics of Reaching it on Nonuniform Surfaces... 

Thus the kinetic equation of a simple two-stage reaction on a nonuniform surface, if both its stages are irreversible, is of the form... 

The comparison of (63) and (217) that answer the same simple mechanism reveals graphically the difference in the features of kinetics on uniform and nonuniform surfaces. 

It was later demonstrated that if the reaction mechanism corresponds to scheme (295) and the linear relation between standard Gibbs energy of adsorption and Gibbs activation energy of adsorption is obeyed [see (91)], then the kinetic (305) corresponds in general to the exponential nonuniformity of the surface with even nonuniformity included as a particular case (44). In the general case the exponent m is not equal to transfer coefficient a, but is connected with it according to (143).5... 

The results of kinetic studies conform with the notion of a reaction proceeding on a evenly or exponentially nonuniform surface in the region of medium coverages as described by the following mechanism ... 

Experimental data on the reaction kinetics agree with the kinetic equation for a reaction on a nonuniform surface in the region of medium coverages if the mechanism is as follows ... 

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