Kinetics of Ag₃₀₀ nanoclusters formation: The catalytically effective nucleus via a steady‐state approach

Abstract

The kinetics of formation of silver nanoparticles consisting of nearly 300 metal atoms is investigated, which were prepared by reduction of silver nitrate with hydrazine in ethylene glycol at 25 • C without any stabilizer other than the glycol solvent. The resulting sigmoidal kinetic curves are analyzed by using the 1997 Finke-Watzky two-step mechanism of slow continuous nucleation with subsequent fast autocatalytic surface growth. The kinetics of homogeneous nucleation of metal nanoparticles was analyzed using the assumption about the stepwise adjunction of precursor and the quasi steadystate approximation. The equations were proposed to calculate the concentration of the formed metal nanoparticles and their mean size from the experimentally determined values of the Finke-Watzky rate constants. It is shown that a stepwise nucleation process can be described in the terms of the catalytically effective nucleus concept and that the number of atoms in the catalytically effective nucleus can be estimated. K E Y W O R D Scatalytically effective nucleus concept, homogeneous nucleation, kinetics, silver nanoparticles 266

Nanoparticle Formation Kinetics, Mechanisms, and Accurate Rate Constants: Examination of a Second-Generation Ir(0)n Particle Formation System by Five Monitoring Methods Plus Initial Mechanism-Enabled Population Balance Modeling

“…The simplest, discovered first, two-step mechanism contained within Scheme and explicitly given back in Scheme , namely that of A → B (rate constant k 1 ) and A + B → 2B (rate constant k 2 ), is especially well-tested in a number of other particle formation and growth systems across nature, including homogeneous catalyst formation, − heterogeneous catalyst formation, − protein aggregation, − solid-state kinetics, , dye aggregation, and other areas of nature showing “cooperative”, autocatalytic phenomena . The use to date of pretty much any and all applicable physical methods in those >560 citations of the 1997 paper documents that the two-step mechanism is the best-tested, best-supported, and currently most accepted kinetic model for the initial treatment of particle formation kinetic data at the PEStep level for a broad variety of nucleation and growth systems across nature. − ,− However, it is not yet clear which physical methods are both necessary and sufficient to yield a reliable particle formation mechanism? Additionally, not yet addressed are which physical methods in what combinations are needed to yield what level of precision and, notably, what accuracy in the resultant rate constants?…”

The kinetics of homogeneous and two‐step nucleation during protein crystal growth from solution

“…Many examples of this kinetic behavior for cluster formation are found in the experimental literature. [10][11][12][13][14] Nanev and Tonchev find this kinetic behavior specifically for nucleation within supersaturated insulin solutions for seven different initial supersaturations. 7 Morris et al used the Finke-Watzky two-step kinetic model to study over 10 cases of protein aggregation from the literature.…”

“…The solution for Equation is the sigmoid function for . Many examples of this kinetic behavior for cluster formation are found in the experimental literature . Nanev and Tonchev find this kinetic behavior specifically for nucleation within supersaturated insulin solutions for seven different initial supersaturations .…”

How to Manage a Crystallization Process Aimed at Obtaining a Desired Combination of Number of Crystals and Their Distribution by Size: Learn Here

“…[ 8 ] Without seeing the nuclei themselves, this nucleation rule has been deduced from measurements of crystal number densities N (which is the number of nuclei arising in unit volume/on unit surface) as a function of the nucleation time t . Being phenomenologically substantiated, [ 9–24 ] the logistic dependence of N on t is a sound basis for considering some basic rules that govern crystal nucleation (and somewhat indirectly, also the crystal growth).…”