Theoretical Analysis of Non-Catalytic Growth of Nanorods on a Substrate

Abstract

A theoretical analysis explaining the whole process of the growth of nanorods on a substrate without a catalyst is presented. Prior to the growth of the nanorods, the reaction precursors form nuclei on the substrate. The nuclei undergo cluster migration caused by the surface diffusion of adatoms on the substrate, and this migration continues until the mean free time of the adatoms is larger than surface diffusion time. The most probable mechanism by which cluster migration takes place is the one that leads to the minimization of the cluster free-energy, namely the migration of six adatoms into one fixed adatom. This cluster migration continues during several (typically smaller than 6) consecutive nuclei growth steps. After the process of cluster migration comes to an end, the nuclei grow in an isotropic manner by collection of the adatoms, until the nucleus reaches the thermodynamic size limit. The one-dimensional growth of nanorods on the nuclei, which is associated with the critical radius, begins when the reactant dose is smaller than a certain value, which is determined by the thermodynamic size limit and the mass transport parameter. The mass transport of the reaction precursors leads to the expansion of the radius and elongation of the height of the nanorods, and the growth rate of the height is greater than that of the radius. This difference in the growth rate causes the aspect ratio to increase with increasing growth time. By comparing the experimental data in the literature (ZnO nanorods), the presented analysis explains well the noncatalytic growth of nanorods on a substrate.

Uninterrupted and reusable source for the controlled growth of nanowires

“…We believe that ZnO particles nucleates first on the substrate24252635. After reaching the thermodynamic size limit, nanowire growth proceeds in the [0001] direction (supplementary fig.…”

“…Therefore, the requirement demands to synthesize catalyst free nanowires. Non-catalytic growth of several nanowires (Si, Ge, GaN, ZnO, Ga 2 O 3 , CdSe, B) and their heterostructures have been possible1617181920212223242526. Nanowires produced by non-catalytic growth mechanism seem to best suit the nanowire technology development as there is no involvement of catalytic nanoparticles.…”

“…Nanowires produced by non-catalytic growth mechanism seem to best suit the nanowire technology development as there is no involvement of catalytic nanoparticles. It is believed that non-catalytic growth proceeds in two steps26: (1) nucleation of seed nanoparticles controlled by thermodynamic size limit and (2) subsequent one-dimensional anisotropic growth without catalyst.…”

“…Theoretical descriptions on the catalytic as well as non-catalytic growth of nanowires are available in the literature26272829. The diameter of nanowires is mainly controlled by the size of the catalyst272829, while the diameter of nanowires obtained by non-catalytic growth is governed by thermodynamic limit26. However, the length and hence, the aspect ratio of the nanowires, is expected to increase with growth duration.…”

Biomolecule-Assisted Synthesis of Nanocrystalline CdS and Bi<sub>2</sub>S<sub>3</sub> for Photocatalytic Hydrogen Evolution

“…isotropic growth and anisotropic growth. Generally, a reaction is more likely to lead to an anisotropic growth with a relatively slow supply of reaction precursors than that with fast one [15]. As it has been known, the solubility of CdS in aqueous solution is much higher than Bi 2 S 3 with their Ksp values at   1.4 × 10 -29 and 1.82 × 10 -99 , respectively.…”