Thermodynamical Description of Adsorbed Layer Dynamics

The equations of isothermal kinetics (8.3.7)-(8.3.9) for the one-particle distribution function CcUi include lateral interactions both via the dependence of the transition probabilities on the coverage (the mean-field approximation) and via direct correlations between elementary processes in different cells. The strict consideration of the problem of lateral interaction may be given by methods of statistical thermodynamics. 

Let us consider the main ideas of these methods on an example of a structureless lattice gas of monolayer adsorbate. The distribution of adatoms over discrete cells can be described by a many-particle distribution function F n,t) (n = (ni,Ti2. .. n, ), k = Nc), where rij is the occupation number of a cell number j uj = 0,1 for single-place cells), Nc - the total number of ceils that is considered to be a constant (we neglect here the processes of surface reconstruction). The distribution function F(n, t) is normalized by the condition 

Here Ho n) is the thertnodynamical Hamiltonian of the adsorbate, j is the the adsorption potential of the j-th cell, uj2jk is the energy of the p air interaction between the j th and k-th particles, is the chemical potential of the adsorbate, and Zp is the adsorbate partition function. Introducing the thermodynamical expression for adatom energy in adsorption cell 

The following quantities can be defined in terms of the many-pai-ticle distribution function F n,t) the mean occupancy of the j-th cell 

The main question in this approach is the evaluation of the transition probabilities W (n, n). For this purpose let us assume, that at the same time only single-particle acts of adsorption, desorption and diffusion can occur. Under this assumption the transition probabilities can be expanded following the ideas by Asada (Asada 1990). The elementsiry act of adsorption into the j-th cell with an eye to lateral interactions contributes to W n, n) as follows 

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