Microstructure of polydisperse colloidal gels

We use confocal microscopy to image colloidal gels formed from highly polydisperse particles. We suspend our polydisperse particles in a density matched solvent, and let the particles spontaneously aggregate through the van der Waals force. The particle size distribution $P(R)$ is roughly log-normal, with the largest particles more than 15 times the size of the smallest particles. The pairing of nearest neighbor particles is consistent with a null hypothesis that pairings are made randomly, that is, any two particle sizes have a probability of being neighbors consistent with their proportionality in $P(R)$. That being said, as expected, larger particles have more nearest neighbors than small ones. This leads to an over-representation of large particles in tetrahedral structures where four particles are mutually nearest neighbors, showing that large particles help provide rigidity to the gel structure. The tetrahedral structures also suggest that particles are able to rearrange during the gelation process, until their motion is stabilized by the multiple contacts with their neighbors. We discuss the implications of how other size distributions $P(R)$ would affect the gel structure.