On the Two-Step Mechanism for Synthesis of Transition-Metal Nanoparticles

Abstract

The two-step particle synthesis mechanism, also known as the Finke-Watzky (1997) mechanism, has emerged as a significant development in the field of nanoparticle synthesis. It explains a characteristic feature of the synthesis of transition metal nanoparticles, an induction period in precursor concentration followed by its rapid sigmoidal decrease. The classical LaMer theory (1950) of particle formation fails to capture this behavior. The two-step mechanism considers slow continuous nucleation and autocatalytic growth of particles directly from precursor as its two kinetic steps. In the present work, we test the two-step mechanism rigorously using population balance models. We find that it explains precursor consumption very well, but fails to explain particle synthesis. The effect of continued nucleation on particle synthesis is not suppressed sufficiently by the rapid autocatalytic growth of particles. The nucleation continues to increase breadth of size distributions to unexpectedly large values as compared to those observed experimentally. A number of variations of the original mechanism with additional reaction steps are investigated next. The simulations show that continued nucleation from the beginning of the synthesis leads to formation of highly polydisperse particles in all of the tested cases. A short nucleation window, realized with delayed onset of nucleation and its suppression soon after in one of the variations, appears as one way to explain all of the known experimental observations. The present investigations clearly establish the need to revisit the two-step particle synthesis mechanism.

The role of nanoparticle size and ligand coverage in size focusing of colloidal metal nanoparticles

“…Despite observing continuous nucleation in many colloidal synthesis studies, the nal polydispersity can be as low as 10-20%. 7,22,44,59,67 As shown in Fig. 2, there is a continuous formation of Pd nanoparticles (increase in the concentration of nanoparticles) that overlaps with the nanoparticles growth (increase in the average diameter) from t ¼ 0 to 0.2 h, which is consistent with our previous work.…”

“…PBM explicitly identies the nanoparticles of different sizes during synthesis and therefore allows for predicting the particle size distribution (concentration of nanoparticles, average diameter, and polydispersity). 22,47,59 As the nanoparticle surface area and surface coverage of ligands evolve with time, we can identify the nanoparticles using a bivariate number density n(v,a l ,t), where n(v,a l ,t)dvda l signies the number of nanoparticles in size (volume) range v to v + dv with ligand covered surface area in the range a l to a l + da l per reaction volume at time t. The developed PBM framework is based on Perala and Kumar modeling approach, 54 but we take into account the reversible binding of ligand with the metal precursor as well as with the nanoparticle surface. In addition, the rates of nanoparticle growth and surface binding of ligands are considered to be proportional to the number of available surface sites and not the volume of the nanoparticles as used in our previous work and other literature reports.…”

Nanoparticle shape, thermodynamics and kinetics

“…We should note that for many solvent syntheses of nanoparticles the typical size of 3D nuclei in the initial stage of the reaction is 1-2 nm (e.g. results from in situ scattering experiments and kinetic modelling [23,[198][199][200][201][202][203][204][205][206][207][208][209][210][211][212][213][214]); it is straightforward to show that this has to be about the same size as that of the critical radius for a terrace. For completeness, as the reaction proceeds the concentration of the metal in solution drops so the chemical potential driving force will become even smaller, a point we will return to in section 4.3.…”

Combined Experimental and Theoretical Investigation of Heating Rate on Growth of Iron Oxide Nanoparticles

“…To gain insight on NPs' nucleation and growth process at the molecular level, we set up a numerical model based on classical nucleation theory. [31][32][33]28 The model relies on a rate equation that accounts for population balance, 31,[43][44][45][46][47]28,29,48 which describes the dynamics of the precursor-to-monomer conversion:…”