Restricted Mobility of the Reactants

One will characterize the average concentration of particles (6la, a — 3, y) and the average fraction of their pairs (0lBl(r)) that take into account the ordered distribution c(2 x 2) of the particles on a surface. 

In the formula (51) the functions SlaX(r ot) and S bXX(a) have the form of Eqs. (34a) and (36a) in which the site numbers have been replaced with the indices of the site types. As previously, the type of a pair of sites is unambiguously related to the distance between them. 

The number of equations for two-body probabilities is also sharply reduced. For the first neighbors, four equations relative to 6fy( 1) are needed, ij — AA, AB, BA, and BB, while for the second neighbors three equations relative to O lfl) are needed, ij — AA, AB, and BB. The normalizing relations have the form 

The addends of equations of type (54) are expressed in terms of the rates of elementary processes (51) by formulas similar to (39) and (40). The system of equations is solved with the given initial conditions for 0 Jr — 0), 0ly(l,t = 0) and 0 (2,t = 0). 

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