Lattice Gas LG Model

In a vicinity of each cell a the potential will be assumed to be of a simplified form 

For Vf z) they use one of the empirical potentials with one well, while for Vr R) the approximation of harmonic or anharmonic multidimensional oscillator is generally applied. 

Let us introduce the following normalizing condition for the distribution function 

In the expressions (6.1.3), (6.1.4) symbol means the sum over discrete and the integraJ over continuous variables. The overage 0 P,R,t) has the meaning of the 

In this case the local layer coverage can be calculated as follows 

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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. 

One of the first KMC simulations of Li-ion diffusion was reported in 1994 by Deppe et al. who used both a KMC and a lattice gas (LG) model. Their system consisted of a two-dimensional InSe cathode and a Li-doped borated glass separator. The diffusion behavior from both approaches (KMC and LG) led to the same conclusion that the charge interactions at the interface play a crucial role in the ionic diffusion across the interface. However, similar to other applications of KMC, the quantitative results were found to be sensitive to the reaction energy barriers used in the model. Unfortunately, no direct comparisons were made with experimental systems, so it was challenging to identify... 

Makeev, A.G., D. Maroudas, A.Z. Panagiotopoulos, and LG. Kevrekidis. 2002b. Coarse bifurcation analysis of kinetic Monte Carlo simulations a lattice gas model with lateral interactions. Journal of Chemical Physics 117(18) 8229-8240. 

The first model of this type was a cellular automaton, called the Lattice-Gas-Automaton (LG). The algorithm consists of particles which jump between nodes of... 

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