Second virial coefficient measurements of dilute gold nanocrystal dispersions using small-angle X-ray scattering

Small-angle X-ray scattering (SAXS) was used to study the size-dependent two-body solvent-mediated interparticle interactions between dodecanethiol-coated gold nanocrystals (2-6 nm in diameter) in dilute toluene dispersions. Using a modified Zimm analysis of concentration-dependent X-ray scattering data, the second virial coefficient B-2 was measured as a function of nanocrystal diameter and compared to theoretical predictions. The measured values of B-2 are more negative than those expected for hard spheres, indicating that interparticle attractions are significant in this system, even though the particles are dispersed in good solvents for the ligands. The data can be fit using a square well potential to model the pair interactions with nanocrystal size-dependent well depths ranging between 0.1 and 0.4 kT and a range of interaction of 30 A. The interaction potentials between particles in the larger size range (i.e., >5 nm diameter) are close to those expected from a simple steric stabilization model accounting for the core-core van der Waals attraction modified by an osmotic repulsion between adsorbed chains. Smaller particles, however, exhibited significantly stronger attraction than expected from this simple model, which could possibly be due to decreased ligand surface coverage at the smaller nanocrystal sizes.