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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. 

Depletion interactions are thought to significantly contribute to the organization of intracellular structures in the crowded cytosol. The strength of depletion interactions depends on physical parameters such as the depletant number density and the depletant size ratio. Cells are known to dynamically regulate these two parameters by varying the copy number of proteins of a wide distribution of sizes. However, mammalian cells are also known to keep the total protein mass density remarkably constant, to within 0.5% throughout the cell cycle. We thus ask how the strength of depletion interactions varies when the total depletant mass is held fixed, a.k.a. fixed-mass depletion. We answer this question via scaling arguments, as well as by studying depletion effects on networks of reconstituted semiflexible actin in silico and in vitro. We examine the maximum strength of the depletion interaction potential U∗ as a function of q, the size ratio between the depletant and the matter being depleted. We uncover a scaling relation U∗ ∼ qζ for two cases: fixed volume fraction φ and fixed mass density ρ. For fixed volume fraction, we report ζ < 0. For the fixed mass density case, we report ζ > 0, which suggests that the depletion interaction strength increases as the depletant size ratio is increased. To test this prediction, we prepared our filament networks at fixed mass concentrations with varying sizes of the depletant molecule poly(ethylene glycol) (PEG). We characterize the depletion interaction strength in our simulations via the mesh size. In experiments, we observe two distinct actin network morphologies, which we call weakly bundled and strongly bundled. We identify a mass concentration where different PEG depletant sizes lead to weakly bundled or strongly bundled morphologies. For these conditions, we find that the mesh size and intra-bundle spacing between filaments across the different morphologies do not show significant differences, while the dynamic light scattering relaxation time and storage modulus between the two states do show significant differences. Our results demonstrate the ability to tune actin network morphology and mechanics by controlling depletant size and give insights into depletion interaction mechanisms under the fixed-depletant-mass constraint relevant to living cells. 

Colloidal suspensions are an ideal model for studying crystallization, nucleation, and glass transition mechanisms, due to the precise control of interparticle interactions by changing the shape, charge, or volume fraction of particles. However, these tuning parameters offer insufficient active control over interparticle interactions and reconfigurability of assembled structures. Dynamic control over the interparticle interactions can be obtained through the application of external magnetic fields that are contactless and chemically inert. In this work, we demonstrate the dual nature of magnetic nanoparticle dispersions to program interactions between suspended nonmagnetic microspheres using an external magnetic field. The nanoparticle dispersion simultaneously behaves as a continuous magnetic medium at the microscale and a discrete medium composed of individual particles at the nanoscale. This enables control over a depletion attractive potential and the introduction of a magnetic repulsive potential, allowing a reversible transition of colloidal structures within a rich phase diagram by applying an external magnetic field. Active control over competing interactions allows us to create a model system encompassing a range of states, from large fractal clusters to low-density Wigner glass states. Monitoring the dynamics of colloidal particles reveals dynamic heterogeneity and a marked slowdown associated with approaching the Wigner glass state.