  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. We discuss the implications of how other size distributions $P(R)$
would affect the gel structure.
