Analytical approach for the collective diffusion: Multicomponent mixture of particles coadsorbed on a multisite square lattice

Diffusion in a multicomponent mixture of particles coadsorbed on a multisite lattice is investigated by a theoretical approach. The investigated multiparticle system is a mixture of the m types of particles (atoms and/or molecules) adsorbed on a square lattice composed of the three types of different sites. The lattice can be subdivided onto three square homogeneous sublattices composed of sites of the same type. As the binding energies for the particles of different types are different, there are 3m average occupancies (coverages) describing the particle distribution over the sites. The particles perform stochastic jumps between the nearest neighbor and the next nearest neighbor sites. The system of balance equations, which control on the atomistic level the exchange of particles between sublattices and migration of particles over the surface, is reduced to the system of diffusion equations describing the evolution of the hydrodynamic fluctuations of coverages. The diffusion equations are derived in the Onsager-like representation and in the Fickian representation. The approach gives also the analytical expressions for the transport coefficients and Fickian diffusivities. These expressions are derived with the account of the pair lateral interactions between particles adsorbed in the nearest and the next nearest neighbor sites. The transport coefficients and diffusivities are expressed via the thermodynamic quantities - the chemical potentials, correlation functions and the isothermal susceptibilities. The diffusion equations and similar analytical expressions for the diffusivities and transport coefficients are derived also for the hard square multisite lattice gas model.