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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. 

Herein, this work aims to demonstrate the topological effect on the mechanicalx characteristics of selfassembled block copolymers (BCPs). The lamellae-forming polystyrene- block -polydimethylsiloxane (PSb -PDMS) can be self-assembled into various nanostructured monoliths with the use of PS-selective solvent for solvent annealing, giving diamond, gyroid, and cylinder structures with increasing the swelling degree of PS domain (the effective volume fraction of the PS segment after solvent annealing followed by evaporation). The stiffness of the self-assembled monoliths is scrutinized by nanoindentation test. For intrinsic PS- b -PDMS monolith with lamellar structure, the reduced elastic modulus as calculated from the measured stiffness is 0.91 GPa. By contrast, the PS- b -PDMS monolith with cylinder structure gives a significant reduction in reduced elastic modulus with the value of 0.52 GPa due to the introduced microporosity to the PS domain from solvent annealing using PS-selective solvent, resulting in the lower confrontation for continuous layer-by-layer deformation of hard PS and soft PDMS domains. In the case of gyroid-structured PS- b -PDMS monolith, it is unexpected to exhibit a significant increase in the reduced elastic modulus with a value of 1.6 GPa: note that the effect of microporosity is still significant. Accordingly, the enhancement of the reduced elastic modulus is attributed to the effect of deliberate structuring with network topology ( i.e., three-dimensional co-continuous hard PS and soft PDMS domains) that is able to hold the occurrence of large-scale deformation. In contrast to the gyroid with a three-strut texture, the diamond-structured PS- b -PDMS monolith with a four-strut texture is superior to the gyroid with a reduced elastic modulus of 2.2 GPa, further confirming the suggested topology effect.