Size Distribution of Nanoparticles of ZnO and SnS in the Frame of Lifshits–Slezov–Wagner Modified Theory

Abstract

A generalized Lifshits−Slezov−Wagner distribution for nanoclusters or nanocrystals growth according to two parallel mechanisms (Wagner and diffusion) has been used to explain a series of experimental histograms, which cannot be correctly related to the Wagner or the Lifshits− Slezov distribution separately. A process of the nanoclusters growth at the Ostwald ripening stage of the phase transformation in the solid systems can be correctly described using the generalized distribution of Lifshits−Slezov−Wagner. The Ostwald ripening stage is also present in a process of formation of a new semiconducting nanoclusters phase (phase transformation of the first type) during chemical synthesis of nanoclusters in the liquid medium. That is why the Lifshits−Slezov− Wagner theory can be used for analysis of the mechanism and kinetics of the ZnO and SnS nanoclusters formation from supersaturated solutions. The theory should be modified taking into account possible joined influences of both (Wagner and diffusion) mechanisms on the process of the growth of the nanoclusters. As a result, the SnS nanoclusters experimental histograms were found in good correlation with the generalized distribution of Lifshits−Slezov−Wagner at various values of x. The rate of the nanocluster's growth is controlled mostly by formation of new chemical bonds or a surface chemical reaction, which runs on the nanocluster's surface. The growth of the ZnO nanoclusters can be controlled by any of the Wagner's or diffusion mechanisms. The growth rate constants were estimated by means of comparison between experimental and theoretically calculated temporal changes in the average radii or average diameters of nanoclusters. These constants can be used to optimize technological conditions for synthesis of nanoclusters from supersaturated solutions. A method of evaluation of an important energetic parameter, specific surface energy, on the nanocluster/solvent interface is also proposed in this article.

Ostwald Ripening of the Platinum Nanoparticles in the Framework of the Modified LSW Theory

“…As reported in [46][47][48][49], the modified LSW theory [9,10] proves that the growing of NC in the nanosystems in many cases involves both mechanisms (diffusion and Wagner's) [46]. This paper is devoted to the investigation of the governing role of OR in the process of Pt NC sintering that occurs in a nanocomposite material and involves both mechanisms of growing.…”

Statistical model for nanoparticles formation: Self-consistent field approximation

“…In order to describe precipitation, solidification or massive transformation, the effect of interfaces, the so-called Gibbs-Thomson effect [7][8][9] is taken into account. As a result, different forms of equations (Gibbs-Thomson equations) for the Gibbs free energy of spherical nanoparticles of radius r were obtained [10][11][12][13][14][15]. Kinetic properties in nanoparticle self-formation process have been investigated based on the Boltzmann equation and on the density functional theory [16][17][18][19][20].…”