A self-excitation point process model for quantifying nanoparticle agglomeration

Nanoparticle agglomeration refers to the spontaneous clustering of nanoparticles caused by the attractive forces. Agglomeration impacts the physical and mechanical properties of nanoparticles and their composites. Understanding and controlling nanoparticle agglomeration is crucial for optimizing various applications, from nanomedicine to nanoelectronics. In this work, we formulated a self-exciting point process model to analyse nanoparticle agglomeration based on microstructural input. The model is utilised to categorise a specific set of points within the microstructure as either independent (dispersed) or dependent (agglomerated), along with their respective probabilities. We employed this approach to study two distinct scenarios: (a) Agglomeration in experimentally generated microstructures of titanium nanoparticles, and (b) Analysing agglomeration patterns in simulated microstructures of carbon nanotube networks, generated using a stochastic microstructure model. We obtain a quantitative understanding of the connection between the sonication duration and the level of agglomeration in titanium nanoparticles. As the sonication period increases, both the agglomeration percentage and the size of the agglomerates decrease. Furthermore, our analysis of simulated carbon nanotube microstructures, including equiaxed and rope-like agglomeration, shows a close alignment between results obtained from the point process model and those generated by the stochastic microstructure model.