Substrate-Mediated Evaporation and Stochastic Evolution of Supported Au Nanoparticles

TL;DR

This study combines in situ microscopy and theory to understand how supported gold nanoparticles evaporate, fluctuate, and coalesce at high temperatures, revealing the importance of stochastic processes and substrate effects.

Contribution

It introduces a self-consistent theoretical model coupling substrate-mediated evaporation with collective mass exchange, explaining size-independent shrinkage and stochastic volume fluctuations.

Findings

Average mass loss is size-independent due to substrate effects.

Nanoparticle volume exhibits stochastic fluctuations modeled by Langevin dynamics.

Net mass loss suppresses classical coarsening, affecting nanoparticle evolution.

Abstract

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.