An extreme-condition model for quantifying growth kinetics of colloidal metal nanoparticles

A strategy has been developed for analyzing growth kinetics of colloidal metal nanoparticle quantitatively by focusing both the very early and the very late growth stages, at which the size of growing nanoparticles and the reaction time follow linear functions. Applying this extreme-condition model to a microwave-assistant synthesis of colloidal silver nanoparticles, for the first time, results in the determination of intrinsic kinetics parameters involving in the growth of the silver nanoparticles. The diffusion coefficient (D) of the precursor species containing Ag⁺ is 4.9 × 10^–14 m²/s and the surface reaction rate constant (k) of the precursor species on the surface of the growing silver nanoparticles is 8.7 × 10^–8 m/s in an ethylene glycol solution containing 0.15 M polyvinylpyrrolidone at 140 ℃. The extreme-condition model is ready to deconvolute the intrinsic kinetics parameters of growing colloidal nanoparticles once the enlargement rate of the nanoparticles can be experimentally measured in real time and with high temporal resolution. Availability of the high-fidelity values of k and D will provide the crucial information to guide the design and synthesis of colloidal metal nanoparticles with the desirable properties.