Kinetic conditions for secondary-layer sodium population during adsorption on two-dimensional VS2

The possibility of sodium occupying a second adsorption layer on monolayer VS2 has been suggested by earlier first-principles calculations. The present work addresses the complementary kinetic question of when this proposed second layer becomes populated during adsorption and how its onset is controlled by competing atomic interactions. We employ a two-layer lattice kinetic Monte Carlo model informed by first-principles energetics to investigate the evolution of sodium adsorption beyond monolayer coverage. Effective first-layer lateral interactions, interlayer stacking interactions, and intrinsic second-layer site energies are systematically varied to determine their influence on the first-layer coverage at which sustained second-layer population occurs. Increasing first-layer repulsion promotes earlier second-layer population, whereas stronger interlayer stacking interactions delay its onset by stabilizing continued occupation of the first layer. The intrinsic stability of second-layer sites further shifts the onset by controlling the energetic preference for upper-layer occupation. The robustness of these trends is examined through threshold, deposition-attempt frequency, lattice size, and ensemble-sampling sensitivity analyses, demonstrating that the principal mechanistic conclusions remain unchanged across the ranges examined. For representative parameters, the total coverage approaches an apparent plateau of approximately 1.07–1.09 monolayers over the simulated interval. These results develop the static first-principles prediction of secondary-layer occupation into a dynamical adsorption scenario, identifying the kinetic conditions under which a sustained second-layer population can emerge and persist in Na/VS2.