A microscopic model of adsorption in cluster forming systems with competing
interaction is considered. The adsorption process is described by the master
equation and modelled by a kinetic Monte Carlo method. The evolution of the
particle concentration and interaction energy during the adsorption of
particles on a plane triangular lattice is investigated. The simulation results
show a diverse behavior of the system time evolution depending on the
temperature and chemical potential and finally on the formation of clusters in
the system. The characteristic relaxation times of adsorption vary in several
orders of magnitude depending on the thermodynamic parameters of the final
equilibrium state of the adsorbate. A very fast adsorption of particles is
observed for highly ordered adsorbate equilibrium states
