Predicting kinetic nanocrystal shapes through multi-scale theory and simulation: Polyvinylpyrrolidone-mediated growth of Ag nanocrystals

In the shape-controlled synthesis of colloidal Ag nanocrystals, structure-directing agents, particularly polyvinylpyrrolidone (PVP), are known to be a key additive in making nanostructures with well-defined shapes. Although many Ag nanocrystals have been successfully synthesized using PVP, the mechanism by which PVP actuates shape control remains elusive. Here, we present a multi-scale theoretical framework for kinetic Wulff shape predictions that accounts for the chemical environment, which we used to probe the kinetic influence of the adsorbed PVP film. Within this framework, we use umbrella-sampling molecular dynamics simulations to calculate the potential of mean force and diffusion coefficient profiles of Ag atom deposition onto Ag(100) and Ag(111) in ethylene glycol solution with surface-adsorbed PVP. We use these profiles to calculate the mean-first passage times and implement extensive Brownian dynamics simulations, which allows the kinetic effects to be quantitatively evaluated. Our results show that PVP films can regulate the flux of Ag atoms to be greater towards Ag(111) than Ag(100). PVP's preferential binding towards Ag(100) over Ag(111) gives PVP its flux-regulating capabilities through the lower free-energy barrier of Ag atoms to cross the lower-density PVP film on Ag(111) and enhanced Ag trapping by the extended PVP film on Ag(111). Under kinetic control, {100}-faceted nanocrystals will be formed when the Ag flux is greater towards Ag(111). The predicted kinetic Wulff shapes are in agreement with the analogous experimental system.