Fig. 7. Contact mechanics combined with the ZM formula predicts the plateau moduli and viscosity of granular hydrogels.
Random close packings for hard spheres were generated to simulate the microstructure and microgel contacts in granular hydrogels. (A) 3D rendering of a randomly close packed collection of particles (N = 492), generated computationally according to the Lubachevsky-Stillinger algorithm, at volume fraction ϕRCP = 0.64. The axes represent spatial coordinates x, y, and z. (B) Radial distribution function, g(r), of hard sphere particles with random close packing (black) and soft sphere particles with deformations accounted for (red) as a function of radial distance, r, normalized by the particle radius, R0. The ZM formula was used to predict the LVE properties of granular hydrogels. (C) Experimentally measured (dark gray) and estimated Gp of granular hydrogels (Ø = 55 μm) as a function of polymer content of the microgel building blocks. (D) Zero-shear viscosity, η0, measured (dark gray) at the low shear rate limit and estimated as a function of polymer content. Calculations were based on the shear moduli of bulk hydrogel, Ebulk (blue), that was measured via dynamic mechanical testing. Bands indicate the variation of the predicted Gp as the normal force during contact, FN, values vary over the range of 0.26 ± 0.15 μN. Experimental values are represented as means ± SD (n = 3). Lines represent the mean estimated values (n = 5) of Gp and η0.