Quantifying Growth Kinetics of Single Nanoparticles in Sub-Femtoliter Reactors
Matthew W. Glasscott, Caleb M. Hill, Jeffrey E. Dick
Abstract
The progression of nanoscience necessitates quantitative tools to understand reactivity at the nanoscale. Here, we report a quantitative model that describes both the electrokinetic and diffusion-limited growth of a single nanoparticle (NP) within sub-femtoliter reactors and apply the model to quantify growth kinetics of platinum NPs within single aqueous nanodroplets (rdrop ≈ 500 nm). The time-resolved growth mechanism of the platinum NPs can be observed by studying the collisions of chloroplatinate-filled aqueous nanodroplets with ultramicroelectrodes (UMEs). If the potential of the UME is biased sufficiently negative to drive the reduction of chloroplatinate to platinum metal, transients in the amperometric trace can be observed for individual nanodroplet collision events. At low overpotentials, a parabolic increase in current following t2, indicative of electrokinetic growth, is observed, and at high overpotentials, an instantaneous rise in current following t1/2, indicative of diffusion-controlled growth, is observed. Each transient is followed by a rounded peak and a slow decay to baseline, which can be explained by the competition between the rate of NP growth and the rate of metal precursor consumption (electrolysis). We demonstrate that the model couples electrocrystallization and nanodroplet electrolysis to quantitatively predict the collision transient shape, amplitude, and duration. Importantly, the only adjustable parameter in the developed model for electrokinetic growth is the heterogeneous rate constant, k, allowing the growth kinetics of single NPs to be directly evaluated. We measured k for 100 single platinum NPs and found k = 0.003 ± 0.001 cm·s–1 for the growth of platinum NPs on a platinum UME. This platform permits rapid data acquisition for the high-throughput study of the growth kinetics of single NPs, and the model can be generalized to elucidate kinetic and mass-transfer rates under nanoscale conditions of high spatial confinement.