Effects of Size and Shape on the Tolerances for Misalignment and Probabilities for Successful Oriented Attachment of Nanoparticles
Oriented attachment (OA) of nanoparticles is an important pathway of crystal growth, but tools for quantitatively modeling OA are lacking. Here we present several simple models that relate the probability of achieving OA to basic geometric parameters such as particle size, shape, and lattice periodicity. A Moiré-domain model is applied to understand twist-misorientations between parallel surfaces, and it predicts that the range of twist angles yielding perfect OA is inversely related to the width of the contact area. This is confirmed and further developed using a surface functional model, which predicts how crystallographic registration forces drive the emergence of complex orientational energy landscapes. The energy landscapes are predicted to possess local minima that can trap particles in imperfect alignments, and these local minima become deeper and more numerous as the contact area increases, making OA more challenging for large particles. Further, a second set of models is presented to understand the sequence of events by which two crystallographic faces become co-planer after collision. We use a ‘central force approximation’ to quantitatively predict the odds of attaining coalignment between various faces when particles collide with random misalignments, and we show that in the absence of biasing forces, the probability of attaining alignment on a given face is roughly proportional to its solid angle as viewed from the center of the particle. The model predicts that OA is most favorable between well-faceted particles and becomes exceedingly unlikely for large spherical particles that express many microfacets.