Silica nanocluster binding rate coefficients from molecular dynamics trajectory calculations

Oxide nanoparticle growth from vapor phase precursors occurs in high temperature aerosol reactors first via the formation of nanoclusters, which are nanometer-scale condensed-phase species composed of 10¹-10² atoms. The binding rate for nanoclusters, defined as the rate at which two nanoclusters collide with and stick to one another, is hence of interest in predicting nanoparticle size distribution functions in an aerosol. We have utilized molecular dynamics (MD) trajectory calculations to determine the homogeneous (equal-sized) and heterogeneous (disparate-sized) binding rate coefficients of SiO₂ (silica) nanoclusters composed of 18, 144, and 333 atoms. MD trajectory calculations incorporated all-atom models of nanoclusters using a combined Born–Huggins–Mayer-Lennard-Jones potential model, which accounts for both short range interactions and electrostatic interactions. MD calculations were utilized to determine the binding probability as a function of both initial relative velocity and impact parameter; integration of the binding probability across impact parameter and relative velocity space yields the binding rate coefficient. MD trajectory calculations reveal that the most common type of encounters between nanoclusters leading to binding are grazing collisions, i.e. instances where collision would not occur without induced dipole potential influences. The resulting binding rate coefficients are found to be extremely weakly dependent on system temperature, which is in contrast to the use of rate coefficient models which are the product of a hard-sphere collision rate coefficient and a constant enhancement factor (leading to a rate coefficient proportional to the square root of temperature). Enhancement factors defined from MD trajectory calculations fall in the range of 3–9 as system temperature decreases from 1500 K to 300 K. Such large values suggest that potential interactions need to be considered when modeling oxide nanocluster growth in the gas phase.