(232n) Shape-Controlled Synthesis of Ag Nanocrystals Mediated By Polyvinylpyrrolidone: Thermodynamics Vs. Kinetics 

Functional nanomaterials, especially metallic materials, are highly shape sensitive, which drives the devel- opment of shape-controlled nanomaterial synthesizing techniques. Structure-directing agent (SDA)-mediated solution-phase metal nanocrystal synthesis has shown its ability to produce a large variety of nanostructures, but to further increase the product homogeneity and quantity, fundamental understanding of the workings of SDAs is a priority. Computational means can serve as an excellent tool to investigate such phenomena in low length and time scales. We use molecular dynamic (MD) simulations to study the role of polyvinylpyrrolidone (PVP) in PVP-mediated formation of {100}-faceted Ag nanocrystals in ethylene glycol (EG) solution. Though not fully understood in previous studies, the consensus is that PVP promotes the expression of Ag(100) facets via stronger binding to Ag(100) than Ag(111). In investigating the role of PVP, we consider both thermodynamic and kinetic control. We compute the solid-liquid interfacial free energy γ_sl of Ag(100) and Ag(111) in contact with the PVP- EG solution using the multi-scheme thermodynamic integration (TI) method we have developed based on the previous â??cleaving wallâ? method [1, 2]. We find that although PVP lowers γ_Ag(100) more than γ_Ag(111) comparing to the bare surfaces (i.e. in contact with vacuum), Ag(111) still has the lower γ_sl, thus more thermodynamically stable. For the kinetic control, we compare the facet growth rates of Ag(100) and Ag(111) by looking at the deposition flux to these surfaces and predict the kinetic Wulff shapes [3]. We calculate the mean first-passage time of a free Ag atom going from the solution phase to the Ag surface using the Smoluchowski equation, and find that the difference in growth rates is a combined effect of both the probability a PVP segment attracts a solution-phase Ag atom and the diffusion of the Ag atom inside the PVP layer adsorbed on the surface. Due to stronger binding affinity to Ag(100) facets, PVP chains pack more loosely on Ag(111) and extend longer into the solution phase; thus, PVP layer on Ag(111) can have larger probability to attract a solution-phase Ag and the diffusion is faster for the Ag atom inside such PVP layer. Our findings in the kinetic study are consistent with experimental observations. Combining the interfacial free energy study and kinetic Wulff shape study, we resolve the role of PVP in Ag nanocube formation and demonstrate the dominance of kinetic control in such formation. Our findings can be indicative for other similar SDA/metal combinations and the methods used in this work can be applied to a broader range of systems.