Modelling the synthesis of nanoparticles in continuous microreactors: The role of diffusion and residence time distribution on nanoparticle characteristics

Abstract

A mathematical model for the liquid-phase synthesis of spherical nanoparticles in continuous flow microand milli-reactors was developed, accounting for residence time distributions (RTD). These distributions were derived for the reactants and the particles involved in the synthesis. The kinetic parameters needed to describe the reactions were calculated from experimental data available in the literature from batch reactors, with the aid of population balance modelling. They were subsequently used, without further modification, to simulate the synthesis in flow reactors via population balance modelling, averaging the results at the reactor outlet using the reactor RTDs. The model was employed to describe the synthesis of silica nanoparticles as a case study, and validated against flow reactor results from the literature. The results demonstrate direct RTD effects and indirect diffusion-induced effects on the evolution of the particle size distribution during the flow synthesis. The former are created by the inherent widening of the RTDs, due to the different residence time experienced by each fluid element, leading to a broadening of the particle size distribution. The latter are induced by the difference in diffusivity between nanoparticles and liquid reactants, which leads to different dispersion processes in the reactor for the different components of the reaction mixture. These effects appear as the major cause of particle size distribution difference between (single phase) flow and batch syntheses. Highlights • A model for the design of microreactors synthesising nanoparticles is proposed; • The model utilises only kinetics and diffusion parameters from the literature; • Residence time distribution effects on nanoparticle size distribution is quantified; • Effects of transport phenomena on reaction kinetics in the flow synthesis are shown.

Highly reproducible, high-yield flow synthesis of gold nanoparticles based on a rational reactor design exploiting the reduction of passivated Au(iii)

“…This process is generally slow and poses some doubts on scalability of these reactors, as well as complicating the optimization of these systems. We have recently shown 37 that, for syntheses where the characteristic reaction time is much larger than the mixing time, it is possible to directly use batch kinetic data to predict the outcome of flow reactors. In this study we apply this concept to design a reactor with the constraint of complete conversion of the gold precursor, since the presence of unreacted gold precursor would affect the economic competitiveness of the process.…”

“…In order to minimize the standard deviation of the obtained particle size distribution, one needs to minimize the width of the reactor residence time distribution. 22,37,50 This is possible by adopting a reactor configuration where the reactive stream is segmented in liquid droplets by an inert secondary phase. This class of reactor is referred to as segmented flow reactors (SFR).…”

“…Further improvement deriving by the use of droplet reactors is the narrowing of the residence time distribution (RTD) of the reactor, leading to a narrower particle size distribution. 37 Du Toit et al synthesized citratecapped AuNPs via a Turkevich protocol, using heptane to segment the aqueous reactive stream. 17 The reaction was initiated by UV-vis irradiation, used to enhance the nucleation rate, and the irradiation took place in a 0.8 mm I. D. glass capillary followed by an FEP coil (1 mm I.D.)…”

A Modular Millifluidic Platform for the Synthesis of Iron Oxide Nanoparticles with Control over Dissolved Gas and Flow Configuration

“…for the small-and large-scale system respectively). These values together with the reactor aspect ratio ( / ~3000 and ~8000 respectively for the large and small-scale system) indicate that both smalland large-scale reactors behave in good approximation accordingly to the Taylor-Aris model [60,61]. Since both reactors are characterised by very large values of , one can approximate = /192 [61], resulting to values of the axial dispersion number / from ~0.05 to ~0.2 as the reactor scale increases.…”

“…After calculating this quantity, we can conclude that both reactors (small and large scale) exhibit laminar flow; Re increased with the increase of the reactor scale from 42 to 88. For a detailed description of the reactor behaviour, it is necessary to know the properties of the reactants and those of the particles during the synthesis [60], as their diffusivity is size-dependent. We can assume that all the precursor reacts upon mixing with the base [31] causing the precipitation of a mixture of phases, and then the particles grow via an aggregative process, evolving towards the final stable magnetite/maghemite phase [19].…”