Growth of Nanosize and Colloid Particles by Controlled Addition of Singlets
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Growth of Nanosize and Colloid Particles by Controlled Addition of Singlets Vladimir Privman Center for Advanced Materials Processing, Clarkson University, Potsdam, NY 13699-5820, U.S.A.
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ABSTRACT We outline a theoretical framework for estimating the evolution of the particle size distribution in colloid and nanoparticle synthesis, when the primary growth mode is by externally controlled addition of singlet building blocks. The master equations, analyzed in the leading “non-diffusive” expansion approximation, are reduced to a set of easily numerically programmable relations that yield information on the time evolution of the particle size distribution. INTRODUCTION Recently, we have developed a theoretical model [1,2] that can describe semiquantitatively, without adjustable parameters, growth of monodispersed colloids by precipitation from homogeneous solutions [3-8]. It has been established [1-8] that most monodispersed colloids, i.e., particles of narrow size distribution, with sizes ranging from submicron to few microns, consist of crystalline subunits. The latter are formed as primary particles in a supersaturated solution by the burst-nucleation mechanism [1,9,10]. They then further grow and aggregate, primarily by the mechanism of singlet capture by growing aggregates. At the same time, the resulting aggregates rapidly restructure to form compact, frequently spherical, polycrystalline secondary particles, of density close to that of the bulk material and of narrow size distribution. This two-stage growth mechanism is illustrated in Figure 1. Many important theoretical issues have remained unsolved or only partially addressed in the literature. These include, in particular, shape selection [11-13] and particle morphology properties. Another important open topic involves extensions to nanosize particles. Such particles of sizes less than colloid, from few tens to single nanometers, involve several new interesting challenges and paradigms related to nanotechnology. Firstly, what do we mean by “monodispersed” on the nanoscale? It is quite likely that for most truly large-molecule-dimension nanotechnology applications, uniform size (and shape) really means “atomically identical.” This is particularly true for future electronic devices that involve quantum effects or quantum control. For many other applications, requirements for uniformity will be also quite strict. Therefore, methods of controlling size and shape distribution, which found numerous applications for colloids, will be even more important for nanotechnology. In this work, we outline an evaluation method of particle growth controlled by addition of singlet building blocks. We hope that these ideas will initiate the application of some of the techniques developed in colloid science to nanoparticle synthesis. Our results will be also of interest in interpreting growth, specifically after seeding, in colloidal synthesis.
T3.3.1
Supersaturated Solution
Nucleation and Growth
Primary Particles (Singlets) Size distribution peaked but not very narrow
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