On the Mechanisms of Coalescence of Nanodroplets and Sintering of Solid Particles
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he Mechanisms of Coalescence of Nanodroplets and Sintering of Solid Particles V. M. Samsonova, *, I. V. Talyzina, S. A. Vasilyeva, b, and M. I. Alymovb aTver
bMerzhanov
State University, Tver, 170100 Russia Institute of Structural Macrokinetics and Problems of Materials Science, Russian Academy of Sciences, Chernogolovka, Moscow oblast, 142432 Russia *e-mail: [email protected] Received April 20, 2020; revised April 24, 2020; accepted April 28, 2020
Abstract—The droplet coalescence theory, which implies the refinement and further development of the Frenkel approach, has, for the first time, been used for predicting the characteristic time of coalescence of nanodroplets. The coalescence times obtained for gold nanodroplets agree, in the order of magnitude, with the results of our molecular-dynamics experiments. In addition, the characteristic times of coalescence have been evaluated theoretically for macroscopic droplets of epoxy resin. The results obtained are in good agreement with Geguzin’s experimental data. It has been concluded that the viscous flows arising in coalescing droplets and the corresponding dissipation of the surface free energy underlie the coalescence mechanism of not only macroscopic, but also nanosized droplets. At the same time, the results of our molecular-dynamics calculations and available experimental data indicate that the sintering of crystalline nanoparticles cannot be explained by the Frenkel mechanism of solid body viscous flow. DOI: 10.1134/S1061933X20050154
1. INTRODUCTION The term “coalescence” refers to the process of aggregation of particles or bubbles with the formation of a larger daughter particle (bubble). This term is commonly used as applied to the confluence of droplets, while the formation of a unified stable structure (agglomerate) from two or more solid particles is referred to as sintering or coagulation. Initially, the term “sintering” had exclusively the technical meaning and corresponded to the final stage of the powder metallurgy process, which is preceded by the preparation, mixing, and pressing of powders. There is no distinct differentiation between coalescence and sintering, although it is obvious that, in powder metallurgy, the sintering is realized at some temperature T that is ∞ lower than melting temperature Tm( ) of a bulk phase. In 1940s, it was recognized that the coalescence and sintering processes are of interest from not only the applied, but also the fundamental point of view, and Sauerwald initiated the scientific study of sintering [1]. Before long, Frenkel developed the first physical theory of sintering [2], and the activity of researchers, who studied this process [3–5], was governed by his ideas for, at least, 25 years. The Frenkel theory was often referred to in later articles and monographs [6–8]. It is of interest that Geguzin’s monograph [4] contains, in addition to the highest appreciation of Frenkel as the theoretical physicist, some crit-
ical considerations concerning his theory [2]. In particular, Frenkel saw much more similarities
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