Shape Selection in Diffusive Growth of Colloids and Nanoparticles

Abstract

We report numerical investigations of a three-dimensional model of diffusive growth of fine particles, the internal structure of which corresponds to different crystal lattices. A growing cluster (particle) is immersed in, and exchanges monomer building blocks with a surrounding medium of diffusing (off-lattice) monomers. On-surface dynamics of the latter is accounted for by allowing, in addition to detachment, monomer motion to the neighboring vacant crystal sites, according to probabilistic rules mimicking local thermalization. The key new feature of our model is the focus on the growth of a single cluster, emerging as a crystalline core, without development of defects that can control large-scale growth modes. This single, defect-free core growth is imposed by the specific dynamical rules assumed. Our results offer a possible explanation of the experimentally observed shape uniformity, i.e., fixed, approximately even-sized proportions, in synthesis of uniform colloids and nanoparticles. We demonstrate the basic principles of well-defined particle shape emergence in such growth. Specifically, several shapes are possible for a given crystal structure. Formation of shapes that follow the crystal symmetry and are uniform, can be a result of the nonequilibrium nature of the growth process. The shape of a growing particle can be controlled by varying the relative rates of kinetic processes, as well as by adjusting the concentration of monomers in the surrounding medium. ______________________________________________________________________________ Posted as e-print 0902.3243 at www.arxiv.org

Kinetics modeling of nanoparticle growth on and evaporation off nanotubes

“…Each attached crystal-lattice atom that is not fully blocked, can hop to vacant nearest neighbors (in our case; generally also to next nearest neighbors, etc., depending on the model choices 33 ). The probabilities for such moves are proportional to temperature-dependent Boltzmann factors.…”

Nonequilibrium kinetic modeling of sintering of a layer of dispersed nanocrystals

“…23,[36][37][38]42 Here we outline the model with emphasis on those implementation details which are specific to the present work. We assume that atoms (or ions, or molecules) are initially all in nanocrystals.…”

“…Here such processes are modelled within the kinetic MC approach suitable for describing the dynamics of the surface and shape morphology in sintering starting with nanocrystals of linear sizes of order 20 atomic layers. The model was recently developed 36 for growth of nanoparticles of well-defined shapes. It was also applied to formation of on-surface structures of interest for catalysis.…”

“…Presently, typical models of sintering [10][11][12][13][14][15][16][17][18][19][20][21][22][23][32][33][34][35][38][39][40][41] consider only specific scales of the process. Our kinetic MC model was originally developed 23,36 for the regime in which well-defined nanoparticle -4 -shapes are known to emerge 36,42 in situations when particles are grown by plentiful external supply of diffusing solute matter atoms. The model is therefore mesoscopic, with the microscopic parameters introduced via temperature-dependent Boltzmann weights, as described in the next section, which describes the theoretical model.…”

“…In the present work, we consider a more realistic (for the experimentally relevant case of noble metals) FCC lattice structure and invest a significantly larger computation effort than in the earlier study that introduced this kinetic model for sintering, 36 surveyed in Sec. 2.…”