Cluster Growth Through Monomer Adsorption Processes

We propose a monomer adsorption model, in which only the monomersare allowed to diffuse and adsorb onto other clusters. By means of the generalized rate equation we investigate the kinetic behavior of the system with a special rate kernel. For the system without monomer input, the concentration a_j(t) of the A_j clusters (j>1) asymptotically retains a nonzero quantity, while for the system with monomer input, it decays with time and vanishes finally. We also investigate the kinetics of an interesting modelwith fixed-rate monomer adsorption. For the case without monomersource, the evolution of the system will halt at a finite time; while the system evolves infinitely in time in the case with monomer source. Finally, we also suggest a connection between the fixed-rate monomer adsorption systems and growing networks.