Quantifying the dispersion quality of partially aggregated colloidal dispersions by high frequency rheology

Abstract

An important parameter for the performance of nanomaterials is the degree by which the nanoparticles are dispersed in a matrix. Optical microscopy or scattering methods are useful to characterise the state of dispersion, but are not generally applicable to all materials. Electron microscopy methods are laborious in preparation and typically offer only quantitative information on a very local scale. In the present work we investigate how high frequency rheological measurements can be used for partially dispersed suspensions at intermediate to higher particle loadings, even for high viscous matrices. Although the contribution of the particles is particularly visible in the low frequency linear viscoelastic behaviour, a more direct relationship between rheological properties and degree of dispersion can be derived from the loss modulus in the high frequency limit. To this end, a home-built piezo shear rheometer is constructed to extend the frequency range typically accessible by commercial rotational rheometers. Measurements on spherical silica particles, with a varying degree of dispersion in low molecular weight PDMS, are used to demonstrate how high frequency rheometry can be used to quantify dispersion quality. The linear viscoelastic properties are compared to analytical scaling theories to demonstrate that a hydrodynamically dominated regime is reached. The dependence of the relative high frequency loss modulus on volume fraction is then compared to predictions of a hydrodynamic viscosity model for the derivation of a dispersion quality index. It is used to follow the evolution of the dispersion quality as a function of mixing time and consumed power.

Bulk rheometry at high frequencies: a review of experimental approaches

“…The resolution of these piezo shear rheometers (PSR-1) is largely determined by the accurate detection and analysis of the response signal. The most accurate results were obtained with linear shear rheometers using piezoelectric stacks and applying an extensive calibration step, with measurable complex viscosities as small as 0.05 Pa•s and a phase accuracy within 2 • (Schroyen et al 2017). A discussion on different sources of error can be found in Athanasiou et al (2019).…”

“…In case of a dilute Brownian suspension, the characteristic relaxation time can be predicted through the diffusional motion of a particle inside the medium. Relaxation frequencies typically decrease with volume fraction due to a reduced selfdiffusion coefficient (Brady 1993;Bergenholtz et al 1998a) and are influenced by colloidal interactions, particle shape, and structural effects, necessitating experimental characterisation (Bergenholtz et al 1998b;Kirkwood and Auer 1951;Schroyen et al 2017). At volume fractions above the glass transition, colloidal dispersions display multiple relaxation mechanisms: high-frequency measurements are highly useful to directly determine the fast 'beta' relaxation processes related to local in-cage rearrangements (Hecksher et al 2017;Athanasiou et al 2019).…”

“…At frequencies that are very high compared with the characteristic relaxation frequency, the viscous response is dominated by bulk hydrodynamic stresses depending only on the effective volume fraction taken up by the fillers (Sierou and Brady 2001). The limiting hydrodynamic high-frequency response can therefore be used to quantify the local microstructure and dispersion state in attractive, partially dispersed suspensions (Bossis et al 1991;Vermant et al 2007;Schroyen et al 2017). This is of large practical interest, Fig.…”

“…The lines present the theoretical limits for hydrodynamic lubrication (dashed) and repulsive hard-sphere (dotted) interactions and delineate the HF scaling regimes e.g. for product evaluation or for scanning the efficiency of dispersion methods (Potanin 1993;Schroyen et al 2017). Furthermore, the ability of separating microstructural contributions would be of large interest for studying nonequilibrium structures and thixotropy in attractive systems, but requires an integrated high-frequency and large-shear instrument.…”

“…Furthermore, the high-frequency response directly mimics the time scales of several practical applications and is relevant for instance for the characterisation of printing inks in light of their performance (Vadillo et al 2010), or for studying biological materials (Kudryashov et al 2001;Singh et al 2006;Nassar et al 2010;Johannsmann et al 2013). Another practical application for colloidal dispersions, which can often be unstable, lies in the use of the high-frequency limiting hydrodynamic scalings to directly evaluate the dispersion quality (Schroyen et al 2017). Conventional rotational rheometers typically operate at maximal frequencies below f = 10 − 50 Hz, the limit being set by inertial effects of both instrument and sample.…”