Energy Landscapes of Clusters Bound by Short‐Ranged Potentials

Abstract

The study of atomic and molecular clusters has long been an active research field for both experimentalists and theoreticians. For atomic clusters bound by simple isotropic potentials detailed predictions of the structure, dynamics and thermodynamics are often available from calculations. [1–4] Many of these properties are unique to the finite size regime, including systems with melting points above the bulk value, [5] and negative microcanonical heat capacities. [6] Making detailed connections between theory and experiment can be problematic, but often leads to important new insights. For example, ingenious experiments to probe the thermodynamics of gas phase sodium clusters [7–10] have provided new benchmarks for comparison with calculations. [11, 12] Recent work by Meng et al. provides new data for the properties of clusters in the mesoscopic regime. [13, 14] Using colloidal particles of polystyrene microspheres as “pseudoatoms”, these authors have obtained direct structural information from optical microscopy. The ability to distinguish different geometries provides details for comparison with calculations based on model potentials. In particular, the probability distribution for alternative structures can be obtained from the occurrence frequencies based on thousands of isolated clusters contained in “microwells” that minimise the cluster–surface interaction. The prospect of comparisons with structural “phase diagrams” predicted from theory [15] is particularly exciting. The colloids studied by Meng et al. are bound by attractive forces that result from a depletion interaction with a range of about 1.05 times the particle diameter and a pair well depth of around 4kBT, [13] where T is the temperature and kB is Boltzmann’s constant. The effective range of the potential, compared to the pair equilibrium separation, is therefore very short. A similar effect occurs for clusters of C60 molecules due to the excluded volume of the fullerene cage. The properties of both clusters and bulk phase C60 can be understood by analysing how the strain energy caused by nearest-neighbour contacts that deviate from the optimal pair separation varies with the range of the potential. [16, 17] Unstrained, close-packed geometries are favoured for C60 clusters, rather than icosahedra and polytetrahedral arrangements. [18–22] Bulk liquid C60 is desta