Scaling behaviour of the rheology of aggregate networks formed from colloidal particles

Abstract

The instantaneous shear modulus G and compactive strength Py of aggregate networks formed from silica particles with a mean diameter of 26 nm have been determined as a function of particle concentration. The data are compared with similar data obtained earlier for a range of polystyrene spheres with diameters between 60 and 960 nm and with compactive strength data obtained for polystyrene spheres at higher volume fractions by Sutherland. It is shown that clusters of submicron spheres formed by rapid aggregation become spacefilling and form a network at a critical volume fraction Φg of ca. 0.05. Above this concentration the data for Py and G suggest that aggregate networks show universal behaviour which is consistent with the scalings G∼ϕµ, dPy(ϕ)//d ln ϕ∼G(ϕ), with µ= 4 ± 0.5. This latter value for the exponent agrees well with that predicted by Ball and Brown by assuming the clusters comprising the network are fractal. For diffusion-limited cluster–cluster aggregation (DCA) they obtained a value of µ= 3.6. The data for Py imply a particle size dependence of the type Py∼am with m between –2 and –3, where a is the particle radius. More data are required to establish the precise dependence; the observed trend is, however, not inconsistent with what might be expected from a consideration of interparticle forces which implies a scaling of a–2.3. The scaling behaviour of the yield stress in shear flow and the dependence of the shear modulus on strain for non-negligible strains is also discussed.