Brush-mediated angular constraints reshape structure, rigidity, and percolation in colloidal depletion gels

Abstract

Colloidal gels, like many other soft and disordered solids derive their mechanical properties not only from the strength of interparticle attraction but also from the symmetry of the forces that constrain particle motion. Although noncentral interactions are known to profoundly alter rigidity and elasticity, they are typically introduced through particle anisotropy, surface roughness, or patchy interactions, obscuring their independent role. Here, we demonstrate a minimal and geometry-preserving route to emergent noncentral forces in colloidal gels by reducing the density of surface-grafted polymer brushes. At low brush density, partial brush interpenetration introduces an effective angular bending rigidity at particle contacts, despite fully isotropic particle geometry. This emergent constraint suppresses local densification, stabilizes low-coordination networks, and produces highly ramified gel structures with enhanced elasticity. Combining experiments, simulations, and mean-field theory, we show that these noncentral constraints reorganize structure and mechanics across length scales, shifting gelation boundaries and increasing the elastic modulus by nearly a factor of 3. Our results establish surface brush density as a generic control parameter for programming interaction symmetry in soft particulate matter, with implications for rigidity, percolation, and mechanical design in disordered systems.