Elucidating the effects of surface roughness-induced geometric frustration on the linear viscoelastic moduli in dense colloidal suspensions*

Elastic (G') and viscous (G'') moduli in dense colloidal suspensions, interacting solely via hard sphere potential, are determined by the entropic effects and the hydrodynamic interactions between the constituent particles. In suspensions with rough colloids, these interactions are modified by the additional restriction in rotational diffusion. In this study, we probe the near-equilibrium structure of suspensions with smooth and rough colloids to decouple the effects of surface roughness on the linear viscoelastic moduli. We use smooth and rough poly(hydroxystearic acid)-grafted-poly(methylmethacrylate) (PHSA-g-PMMA) colloids of similar particle diameters (2a ≈ 1.5 μm) dispersed in the index-matched solvent squalene, at volume fractions 0.45 ≤ φ < φ_max, to study the effects of surface roughness on linear viscoelastic properties of these suspensions. Frequency sweep experiments in the linear rheological regime revealed that beyond a crossover concentration (φ > φ_c), the linear viscoelastic moduli of rough suspensions are 1000 times larger than the smooth counterparts. Furthermore, the scaling of the high-frequency elastic modulus (G'_∞) with respect to the applied frequency (ω) is system dependent: suspensions with smooth colloids show G'_∞ ∼ ω^1/2 while rough particle suspensions exhibit a plateau with G'_∞ ~ ω⁰. Combining mode-coupling formulation, dynamic localization theory, and the high-frequency moduli analysis we conclude that the higher magnitude of the linear viscoelastic moduli in rough colloidal suspensions is a consequence of the modification in the length scales and time scales associated with the “caging phenomena” in the dense suspensions, and the enhanced hydrodynamic lubrication interactions introduced by the surface roughness-induced geometric frustration.