UGAL Model

This model, as wets discussed in Chap.6, gives one an opportunity to describe the kinetics of non-ideal gas media in static and fluctuating surface field. Therefore, when approximating the kinetic operators (6.2.4), (6.2.5) one can use the results of quasiparticle method for non-ideal media kinetics (Dubrovskiy and Bogdanov 1979b), theory of liquids (Croxton 1974), theory of Brownian motion (Akhiezer and Peletminskiy 1977), theory of phase transitions, models of equilibrium properties of such systems (Jaycock and Parfitt 1981) with further application of methods of statistical thermodynamics of irreversible processes (Kreuzer and Payne 1988b) and experimental data on pair correlation function (Flood 1967). 

the UGAL model gives additional possibilities for studying the adsorption kinetics of gaseous and liquid film formation. 

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To formulate the UGAL model let us introduce the distribution function of gEiseous particles gdb, r, t) normalized by (6.1.12). The description of the adsorbate kinetics is reduced then to solving a Cauchy problem... 

Operator F( c), responsible for the weak interactions, has the Fokker-Planck form, while strong interactions operator N(yc) is approximated in different ways, depending on the type and mechanism of the transition. The latter operator is responsible for large momentum transfers and significant changes of physical and chemical characteristics of the molecule. For example, in case of inelastic interactions and chemical reactions one can use representation (6.1.18) with the only difference, that in the UGAL model there stands a unified distribution function c(6, r,t). For large momentum tremsfer the model of hard spheres is used. 

FVom the above said it follows that the UGAL model is convenient for the description of meclianisms of film growth from gaseous and liquid phase in isothermal conditions, when the temperatures and molecular free paths are small, trajectories of molecules have stochaistic character, and the adiabatic mechanisms of elementary processes take place. 

One can evaluate the kinetic boundary operators in (6.3.2) on the base of the UGAL model as well. Such results for some simple interaction and kinetics models have been published elsewhere (Cercignani 1975 Balakhonov and Zak 1988). 

To describe the detailed kinetics at interphase boundary within the LG or UGAL models one has to know a large niunber of the probabilities and rate constants of elementary and kinetic processes. Depending on the information available they can be taken from classical and quantum dynamical models, thermodynamics and phenomenology, and from experiment. We are going to consider here some models of elementary processes in adsorbed layer and corresponding approximations for the probabilities and kinetic coefficients. 

We shall deal here with a Lattice Gas (LG) model and a model of Unified Gas-Adsorbate Layer (UGAL). These two models correspond to two alternative approaches in the statistical theory of equilibrium adsorbates (Flood 1967) and can be considered as mutually complementary ones. Which of them should be used depends on the adsorbate properties (ideal, weakly non-ideal, liquid, polycrystalline, localized, partially localized, delocalized), external conditions (isothermaJ, non-isothermal), meclianisms of elementai y processes (adiabatic, non-adiabatic), etc. 

Having at one s disposal kinetic equations for adsorbate and gas phase one has an opportimity to consider different regimes and derive for these regimes appropriate macroscopic transport equations by the kinetic theory methods. The investigations of transport processes at interphase boundary in the framework of UGAL - type models have been presented elsewhere (Borisov et al. 1988 Borman et al. 1988). 

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