When does a nanoparticle become a cluster?

Abstract

We identify physical criteria to differentiate the behavior of aggregates having a number of atoms N < 104, classifying them as nanoparticles or clusters. This is achieved by investigating finite Lennard-Jones spherical aggregates using molecular dynamics, under equilibrium and non-equilibrium conditions. Ten aggregates ranging from N = 4235 to N = 73 atoms are analyzed at equilibrium, introducing an energetic criterion based on local potential energy profiles and a structural criterion based on the pair distance distribution. Two distinct size regimes emerge: a scalable regime characterized by linear variations in the microscopic properties and by a homogeneous internal region, and a non-scalable regime presenting abrupt changes in the microscopic observables, such as steep local potential energy gradients and dominance of surface atoms. Non-equilibrium sublimation simulations at elevated temperatures suggest a third criterion, denoted non-equilibrium criterion, where aggregates initially sublimate at a linear rate before sharply accelerating upon reaching a threshold size. This occurs at the transition between scalable and non-scalable regimes and is confirmed by instantaneous local potential energy profiles. To reconcile with existing size-related terminology, we categorize aggregates in the scalable linear regime as nanoparticles and those in the non-scalable nonlinear regime as clusters. Crucially, all three criteria independently identify the same size threshold, underpinning the universal role of the local potential energy environment in controlling the aggregate structure and dynamics. These findings, explicitly obtained with pairwise-additive, short-range, and isotropic interactions, address the ambiguity with the distinction between nanoparticles and clusters, providing new insights that clusters must be explicitly treated as finite systems and are dominated entirely by surface atoms and interactions.