Adsorbate phase transitions on nanoclusters from nested sampling

TL;DR

This study addresses adsorption phase behavior on a nanoscale cluster by applying surface-focused nested sampling (NS) to a fixed $LJ_{38}$ nanocluster with freely mobile adsorbates. NS directly constructs the canonical partition function $Z(N,V,\beta)$ and derives thermodynamic observables, revealing two distinct, coverage-dependent transitions: gas-to-adsorbate condensation at higher temperature and a subsequent lateral ordering at lower temperature, with site- and facet-specific motifs determined by interactions and size. The work systematically explores equal interactions, weakened adsorbate–adsorbate coupling, and size mismatch, showing how facet competition and lattice mismatch shift adsorption motifs and thermodynamics; it also benchmarks NS against parallel tempering, finding NS more robust and cost-effective unless a global minimum is supplied. The results demonstrate NS as a powerful, unbiased framework for surface thermodynamics on complex interfaces and point to its applicability to more realistic, multi-component adsorbates and heterogeneous surfaces.

Abstract

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.

Figures (12)

• Figure 1: Cluster of 38 LJ particles in the truncated octahedral global minimum structure, employed as surface in the current work. The four-coordinated (100) facet and the three-coordinated (111) facet are highlighted by red and black polygons, respectively.
• Figure 2: Top panel: Constant volume heat capacity of systems consisting of an LJ$_{38}$ cluster and $n$ free LJ particles, with equal interaction parameters. Results of two independent nested sampling calculations are shown for each system to demonstrate the level of convergence. Bottom panel: average coordination number of free particles, as a function of temperature. Dashed vertical lines mark the position of the heat capacity peaks and corresponding average coordination numbers for one of the $n=5$ and $n=15$ calculations.
• Figure 3: Probability of having a specific number of neighbors at a given temperature, in case of the LJ$_{38}$ cluster and seven free LJ particles ($n=7$), with equal interaction parameters. The top panel shows the coordination taken into account only between free particles and cluster atoms in order to distinguish the occupancy of (111) (threefold-coordinated) and (100) (fourfold-coordinated) sites. The bottom panel shows the coordination number only between free particles to quantify particle aggregation on the surface. The heat capacity is shown by a solid black line in both panels, with vertical dashed lines highlighting its peaks. Snapshots shown above the plots are typical configurations in temperature regions A, B, and C, with the rhombic arrangement of atoms highlighted by red dotted lines.
• Figure 4: Phase-space-volume-averaged radial distribution of $n=14$ free particles around the center of the cluster. Lines are shifted for better visibility and for the baselines to correspond to the appropriate temperature on the heat capacity curve, shown in the left-hand panel. Lines are colored to represent different temperature ranges. Snapshots of typical structures in each temperature range are shown as illustrations, as well as to demonstrate the distance of various adsorbates from the center of the cluster.
• Figure 5: Snapshot of the ground state structures of the LJ$_{38}$ cluster with free particles $n=12-15$. Atoms corresponding to the fixed cluster are colored dark green, while free atoms are yellow. The bottom row shows the same structures from a different angle, with atoms occupying hcp positions highlighted in orange. In the case of $n=15$, the snapshots show two energetically equivalent configurations, with the two four-coordinated surface positions marked by $\alpha$ and $\beta$.