Unexpected maximum in the concentration dependency of the relaxation frequency of Brownian stress in a colloidal suspension

Abstract

Concentrated and semidiluted sheared suspensions of silica nanoparticles in Diglycidyl Ether of Bisphenol A have recently been shown to exhibit a low-frequency relaxation process of the shear moduli measured by oscillatory rheology. This process, which is slower than the structural α-process of the matrix, was interpreted as Brownian stress relaxation resulting from strain-induced perturbations of the isotropic filler distribution. In this paper, we extend the rheological investigation of the low-frequency anomaly to ultra-diluted DGEBA/silica suspensions. We illustrate that the Brownian relaxation process depends in a complex manner on the filler volume concentration: For very dilute systems, the relaxation frequency increases with the concentration, whereas for semidilute or concentrated systems, the opposite behavior can be observed. This nonmonotonic dependency of the relaxation frequency leads to a maximum of the relaxation frequency at a volume concentration around 0.133. It can no longer be modeled by Peclet frequencies, since the classical Peclet frequencies depend only on a single concentration dependent physical quantity, viz., the suspension viscosity. A modified Peclet frequency depending on the suspension viscosity and the average surface-to-surface distance between the fillers as a structural, concentration dependent length scale allows for an accurate description of the Brownian relaxation for all concentrations.