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

Abstract

SynopsisConcentrated 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 a-process of the matrix, was interpreted as Brownian stress relaxation resulting from straininduced 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. V C 2015 The Society of Rheology.

Influence of suspension viscosity on Brownian relaxation of filler particles

“…In line with the interpretation suggested in Shikata and Pearson (1994), van der Werff et al (1989) and Watanabe et al (1997), this low-frequency event was described as a Brownian relaxation. In contrast to the works cited above, it has been shown (Dannert et al 2015) that the Peclet time is not able to predict Brownian relaxation times in dilute suspensions. To adequately describe the evolution of the relaxation time as a function of x V , a modified Peclet time has been introduced by substituting the particle radius by the average interparticle distance.…”

“…In addition to Δδ(r BPA ), Fig. 8 also shows the x V dependence of the loss angle change (Δδ) as calculated from data published in Dannert et al (2015). Clearly, Δδ increases with the filler content.…”

“…8, it turns out that Δδ(r BPA ) does not substantially change with an increasing amount of the curing agent in the DGEBA/BPA/SiO 2 suspensions (with a constant filler content, x V = 0.05). In the study of Dannert et al (2015), the authors have investigated the lowfrequency process in DGEBA/SiO 2 suspensions (r BPA = 0) as a function of the volume concentration (x V ) of silica nanoparticles. In addition to Δδ(r BPA ), Fig.…”

“…5). A method to overcome this difficulty is described in detail in Dannert et al (2015). The obtained relaxation times are listed in Table 5 and represented in Fig.…”

“…Wideband dielectric spectroscopy (Capaccioli et al 1998;Corezzi et al 2002) also does not give a hint to slow relaxation processes in pure DGEBA. The situation changes when adding nanoscaled filler particles to the DGEBA matrix: In previous works, Dannert et al (2015Dannert et al ( , 2014 have published data on a low-frequency relaxation process observed in colloidal suspensions formed by DGEBA and spherical silica nanoparticles. In contrast to other matrix relaxation processes found in DGEBA such as α-relaxation, β-relaxation and the strong γ-relaxation, the newly reported low-frequency process does not show an independent temperature dependency.…”