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Adding nonadsorbing polymers to hard microsphere dispersions generates osmotic depletion attractions that can be quantitatively predicted and designed to manipulate colloidal phase behavior. Whether depletion described by classical theories is the mechanism for polymer-mediated nanosphere attractions is less evident. Colloidal hard nanospheres and nonadsorbing polymers are challenging to realize given the diverse interactions typically present in nanoparticle dispersions. Here, we use small-angle x-ray scattering to assess whether the depletion mechanism holds at the nanoscale, leveraging a recent finding that uncharged, oleate-capped indium oxide nanocrystals exhibit near–hard-sphere interactions in toluene. Classical modeling of polystyrene depletant as penetrable spheres predicts depletion-induced phase boundaries, nanocrystal second osmotic virial coefficients, and colloidal structuring in agreement with experiments for polymer radii of gyration up to 80% of the nanocrystal radius. Experimentally observed weakening of depletion interactions for larger polymer-to-nanocrystal size ratios qualitatively follows theoretical predictions that account for how polymer physics influences depletant interactions. 

Colloids that attractively bond to only a few neighbors (e.g., patchy particles) can form equilibrium gels with distinctive dynamic properties that are stable in time. Here, we use a coarse-grained model to explore the dynamics of linked networks of patchy colloids whose average valence is macroscopically, rather than microscopically, constrained. Simulation results for the model show dynamic hallmarks of equilibrium gel formation and establish that the colloid–colloid bond persistence time controls the characteristic slow relaxation of the self-intermediate scattering function. The model features re-entrant network formation without phase separation as a function of linker concentration, centered at the stoichiometric ratio of linker ends to nanoparticle surface bonding sites. Departures from stoichiometry result in linker-starved or linker-saturated networks with reduced connectivity and shorter characteristic relaxation times with lower activation energies. Underlying the re-entrant trends, dynamic properties vary monotonically with the number of effective network bonds per colloid, a quantity that can be predicted using Wertheim’s thermodynamic perturbation theory. These behaviors suggest macroscopic in situ strategies for tuning the dynamic response of colloidal networks.