Capture numbers in the presence of repulsive adsorbate interactions

Capture numbers are used in models of nucleation and growth on surfaces, and have been widely applied to predict nucleation densities and other quantities via rate equations. In conventional nucleation theory, much effort has historically been expended on obtaining good expressions for capture numbers in the diffusion-limited case. However, recent experiments and calculations have shown that weak repulsive interactions between adsorbate atoms on relatively smooth (e.g., close-packed metal) surfaces may shift nucleation kinetics towards the attachment-limited case. This paper clarifies the distinctions between diffusion- and attachment-limited kinetics, and emphasizes the increased importance of the transient nucleation regime in the latter case, which is due to a combination of delayed nucleation and reduced capture. The consequences of long-range repulsive adsorbate interactions for the form and values of the capture numbers are explored, and the effects of attachment-limited kinetics in relation to low-temperature deposition and annealing experiments are demonstrated. An approximate interpolation scheme between attachment- and diffusion-limited kinetics is proposed, and tested against kinetic Monte Carlo simulations. Using this scheme to interpret recent scanning-tunneling microscopy results on Cu/Cu(111), lower and upper bounds on the maximum adatom-adatom potential repulsive energy of 10 and 14 meV are deduced.