Substrate-Mediated Evaporation and Stochastic Evolution of Supported Au Nanoparticles

We use in situ transmission electron microscopy with automated tracking to study supported gold nanoparticles (NPs) during high-temperature vacuum annealing. \rev{The average mass loss per NP is governed by a flat, nearly size-independent substrate-mediated evaporation profile.} On top of \rev{this mean shrinkage}, individual NPs show significant fluctuations in apparent growth or shrinkage, and NP volume follows a \rev{random-walk-like trajectory. To rationalize both the ensemble-mean behavior and the particle-resolved variability, we develop a self-consistent theory that couples substrate-mediated evaporation to collective 2D Ostwald-type mass exchange through a shared adatom field, described in terms of a renormalized screening length and background concentration. In the experimentally relevant regime, the theory predicts an approximately size-independent mean shrinkage rate and clarifies how net mass loss suppresses classical coarsening.} \rev{Superimposed on this deterministic drift, we quantify stochastic volume trajectories and capture their fluctuation spectrum with a minimal Langevin description consistent with intermittent adatom attachment and detachment events.} In addition, we characterize the lateral diffusive motion of NPs, which is responsible for their coalescence. Altogether, our results highlight that stochasticity is intrinsic at the nanoscale \rev{and that predicting the evolution of supported NPs at early and intermediate times requires a unified framework combining substrate-mediated evaporation, collective mass exchange, and stochastic fluctuations.