Diffusion-Limited Growth of a Spherical Nanocrystal in a Finite Space

Reason for the work: The potential applications of nanoscale materials in nanophotonics, nanoelectronics, bioimaging, and biosensing have stimulated the research in the synthesis of nanocrystals, nanowires, and so forth. There is a great need to understand the spatiotemporal evolution of nanocrystals in the solution-route synthesis in order to better design advanced synthesis techniques for the manufacturing of monodisperse nanocrystals of high quality. Most significant results: We analyze the size effect on the diffusion-limited growth of a spherical nanoparticle in a finite space (spherical cavity) on the basis of the Gibbs-Thomson relation and obtain an analytical formulation of the monomer concentration in the finite space in an implicit form and an integro-differential equation for the growth rate of the spherical nanoparticle. The monomer concentration in the finite space decreases slower than that with a stationary nanoparticle. The growth of the spherical nanoparticle consists of two stages-an initially linear growth stage and a later power-law stage. The result from the infinite space with a stationary nanoparticle is inapplicable to the analysis of the growth of spherical nanoparticles in a finite space. Conclusions: There exists a size effect on the growth of nanocrystals in a finite space. The dependence of the growth behavior of nanocrystals on the growth time and temperature needs to be investigated in order to experimentally determine the fundamental mechanisms controlling the growth of nanocrystals in the solution-route synthesis.