Kinetic Model of Multilayer Film Growth

Let us describe a phenomenological model of the multilayer film growth that is a simplified version of the general kinetic model of multilayer adsorption presented in Chap.6. The latter model allows one to evaluate the distribution function 0(fi,R,t) by solving general equation (6.1.19) and then to calculate main parameters of a multilayer adsorption film (h. A, H). 

Suppose that the covearge of the first layer (l,t) can be expressed through Fi(x) by 

The function Fi(t) describes the kinetics of the first layer formation and can be defined by solving the Kolmogorov model equation (12.1.14). We shall use here more simple approximations for time dependence of Fi(t), namely (Belen kiy 1980, Kashchiev 1977) 

Following the ideas by Wetter (1967), let us postulate a system of kinetic equations on the coverages of succesive layers 

The physical sense of this model is that the coverage of the layer number P + 1 depends only on its own kinetic parameters (w/3+1, Fp+i) and on the coverage of the proceeding layer, Introducing coverage differencies 9 I3, t) = ((, t) — +1, t), 

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