Understanding the role of Reynolds number on self-assembly formation of nanoparticles

Abstract Self-assembly formation of nanoparticles (NPs) is a central theme in nanotechnology that has garnered significant attention in both academia and industry. The size of self-assembled NPs plays crucial role in their physicochemical properties. It has long been known that when macromolecules in a solvent being exposed to an anti-solvent, they can spontaneously form NPs of varying sizes through static diffusion (mixing rate = 0) and dynamic convection (mixing rate > 0). However, the impact of solvent mixing rate on the size of self-assembled NPs remains a mystery. Here, for the first time, we mathematically and experimentally prove that Reynolds number (Re), which quantifies fluid turbulence, is decisive on the self-assembly formation of NPs, by exponentially influencing the way kinetic energy of precursor molecules converting into surface energy of subsequent NPs. We surprisingly find that various self-assembly systems share a very similar critical value of Re about 1,000 ~ 1,200, which predetermines whether self-assembly occurs following a low or high energy dissipation pathway. This new framework further enables us to quantitatively determine energy conversion efficiency of a self-assembly process, measure surface tension of NP in a complex system, and predict NP size at arbitrary Re (including 0), which cannot be achieved in the past due to the limits of technology.