Kinetics of Ostwald Ripening: Crossover From Wagner's Mode to the Lifshitz–slezov Mode

Abstract

The kinetics of the Ostwald ripening in a homogeneous supersaturated solution is studied both numerically and analytically. The time evolution of the grain-size distribution function in a new phase is theoretically described, taking into account the finite value of the maximal size of a grain. Two situations are considered: the kinetics of grain growth is controlled either by the grain-monomer reaction process (an early stage) or by the monomer diffusion process (a late stage). A transition to the final distribution is shown to take place through an intermediate-asymptotical mode of the Ostwald ripening kinetics, the crossover of the kinetic indices is demonstrated, and the duration of intermediate stage is evaluated.

Mechanism of Silver Particle Formation during Photoreduction Using In Situ Time-Resolved SAXS Analysis

“…As is expected from the precipitation of Ag particles formed in a couple of weeks, the particle size distribution might gradually become an asymmetric shape skewed with a tail toward the smaller particle sizes without photoirradiation, which is predicted from the Ostwald ripeningbased growth. Moreover, in the later stage (50 and 85 min) of photoreduction in the case of [Ag]=5 mM (Figure 7a), the particle size distribution is similar to that (Figure 3a) obtained from the TEM image and seems to be fitted with the Wagner-type Ostwald ripening model, indicating a transient regime 46,47 from Ostwald ripening-based growth to the coalescence-based growth. As a result, the formation of irregularly shaped larger particles (>40 nm in diameter, as shown in Figure 2a) is enhanced during the photoirradiation.…”

Mechanisms of Nucleation and Growth of Nanoparticles in Solution

“…From 50 to 85 min, distributions are of interest as they could indicate where the silver changes from Ostwald ripening to coalescence. The distributions were fitted to a Wagner-type Ostwald ripening model showing that there is a transient regime from Ostwald ripening growth to coalescence based growth. − Although the distributions show a skew to larger sizes which does not mean that Ostwald ripening can be ruled out due to the modified LSW models. , Figure a. This matches extremely well with the TEM results from this 5 mM experiment where the size distribution.…”