One-Site Reactions

The difference E (ri) — Ej(ri) determines the change in the magnitude of the activation barrier of desorption (i — A) or adsorption (i — V, one will take the real properties of the vacant sites into consideration in the final expressions) because of interaction of the nearest neighbors in comparison with an ideal system. For two-body interaction one has 

Expression (13) can be considered as a modified expression for rate of a reaction within the framework of the law of mass action (5), where the place of the rate constant has been taken by the product K (n) = K Qxp fi[E (n) — Ei(n)], while the place of the concentration of the particles has been taken by the concentration of the quasi-particles, which are the following configurations of the real particles at the center of a cluster there is particle i, and around it there are n particles of A and (z-n) particles Y (the quantity K (n) can be interpreted as the rate constant for a quasi-particle). 

Consequently, by going over to larger quasi-particles, one can formally retain the structure of the expressions of the law of mass action, i.e., the product of the rate constant of a reaction and the reactant concentration. But one must have in view that the number of such quasi-particles sharply grows with increasing s and z (and the radius of interaction). 

The rate of a reaction relating to a surface as a whole is obtained by the averaging expression (13) over all the local configurations differing in the number of particles of A in the c.s. around particle i  

Here 5gy — s j — e(y C is the statistical weight of the configuration with n particles of A around the central particle / having the z neighboring sites. The ways of an approximate calculation of the functions 0, n) were discussed in Appendix B. In the quasi-chemical approximation, they are expressed in terms of the function 6, and 0y, where 6, — Nt/N, N, is the number of particles of species / on N total sites, and Oy — (1 + A y)NyjzN (Ny is the number of pairs of particles if). 

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