Adsorbate phase transitions on nanoclusters from nested sampling

Nested sampling was employed to investigate adsorption equilibria on the truncated-octahedral Lennard-Jones nanocluster LJ$_{38}$ while systematically varying adsorbate-surface well depth and Lennard-Jones size parameters. Evaluation of the canonical partition function over a wide temperature range identifies two successive phase transitions: (i) condensation of the gas phase onto the cluster surface at higher temperatures, and (ii) lateral rearrangement of the adsorbed layer at lower temperatures. For identical interactions, the condensate first populates both three- and four-fold hollow sites; when adsorbate-adsorbate interactions are weakened, preference shifts to the four-coordinated (100) sites. Size mismatch governs low-temperature behavior: smaller adsorbates aggregate to increase mutual contacts, whereas larger ones distribute more evenly to maximize coordination with the cluster. These findings highlight key trends in facet competition and lattice mismatch, and showcase nested sampling as an automated, unbiased tool for exploring surface configurational space and guiding investigations of more complex, realistic interfaces.