Why do magnetic nanoparticles form messy clumps? Taking into account the bridging or sticking of ligands in simulations

Experiments on magnetic nanoparticles in a viscous medium have shown that agglomerates form that display complex shapes. However, most theoretical results predict more simple, ordered shapes, such as single-particle width chains. To account for this discrepancy we have created a theoretical model that phenomenologically includes the bridging or "stickiness" between ligands on nearby nanoparticles. This interaction is accounted for through a unitless stickiness parameter c that can be varied between 0 (no bridging between ligands) and 1 (irreversible bridging or sticking together on impact). An analytic estimate for the value of c is provided based on a comparison between the time for a particle to diffuse to an agglomerate compared to the time for it to reorient into the local magnetic field direction. Numerical Langevin simulations are performed using ferromagnetic, 50 nm and 25 nm diameter magnetite nanoparticles with various ligand coating lengths in hexane in order to support the analytic estimate. The simulations produce agglomerates that are qualitatively and quantitatively similar to experimental results.