Rheological and mechanical properties of silica colloids: from Newtonian liquid to brittle behaviour

Abstract

Rheological and mechanical properties of aqueous mono-disperse silica suspensions (Ludox® HS40) are investigated as a function of particle volume fraction (ϕ _p ranging from 0.22 to 0.51) and water content, using shear rate tests, oscillatory methods, indentation and an ultrasonic technique. As the samples are progressively dried, four regimes are identified; they are related to the increasing particle content and the existence and behaviour of the electrical double layer (EDL) around each particle. For 0.22 ≤ ϕ _p ≤ 0.30), the suspensions are stable due to the strong electrostatic repulsion between particles and show Newtonian behaviour (I). As water is removed, the solution pH decreases and the ionic strength increases. The EDL thickness therefore slowly decreases, and screening of the electrostatic repulsion increases. For 0.31 ≤ ϕ _p ≤ 0.35, the suspensions become turbid and exhibit viscoelastic (VE) shear thinning behaviour (II), as they progressively flocculate. For 0.35 ≤ ϕ _p ≤ 0.47, the suspensions turn transparent again and paste-like, with VE shear thinning behaviour and high elastic modulus (III). At higher particle concentration, the suspensions undergo a glass transition and behave as an elastic brittle solid (IV, ϕ _p = 0.51).

Appendices

Appendix 1: DLVO calculations

In the DLVO theory of colloidal interactions, the potential U between two identical spherical particles of diameter a and surface separation x is the sum of the attractive van der Waals potential, U _vdW, and the electrostatic repulsion potential, U _rep, which are written when κa/2 > > 1:

$$ U=U_{\rm vdW} + U_{\rm rep} $$

(9)

$$ U_{\rm vdW}(x)= - \frac {A.a/2}{12.x^2} $$

(10)

$$ U_{\rm rep}(x)= 2 \pi \epsilon (a/2) \psi_{\rm D}^2 ln(1+{\rm exp}(-\kappa x)) $$

(11)

where A = 0.8 × 10^− 20 J is the Hamaker constant for silica in water (e.g. Larson 2002), ϵ is the permittivity of the liquid dispersant, e is the charge of an electron and T = 293 K is the temperature. Figure 9a presents the different contributions and the potential as κ ^− 1 decreases for our samples. U is characterized by one stable attractive minimum (“p” on Fig. 9a), a metastable secondary minimum (“s”) and a barrier potential in between. Aggregation will occur when the particles fall into “p”.

One important parameter entering Eq. 10 is the surface potential, ψ _D. Unfortunately, we were unable to measure it for the different samples. For the Newtonian samples, U has been calculated taking the value ψ _D = −30 mV measured at ϕ _p = 0.22 by Trompette and Clifton (2004). However, we expect ψ _D to vary with the ionic strength; it usually increases with increasing I (e.g. Schneider et al. 2011). For the non-Newtonian samples, the DLVO model allows an estimate of ψ _D from the shear modulus (Buscall et al. 1982):

$$ G_{\rm o}^{\rm th} = \frac{\alpha}{R} \frac{\partial^2 U}{\partial x^2} $$

(12)

where α = 0.833 and $R = a(0.74 / \phi_{\rm p})^{1/3}$ for particles arranged in a face-centered cubic lattice. Figure 12 shows the measured shear modulus as a function of the calculated $G_{\rm o}^{\rm th} / \psi_{\rm D}^2$. Despite the uncertainty on the G _o measurements (cf. “Rheological measurements” section), the data points are aligned for 0.32 ≤ ϕ _p ≤ 0.38 and the slope gives a value ψ _D = −22 mV. This is the value that we took to estimate the interaction potential for the non-Newtonian samples in Fig. 9a.

Fig. 12

Experimental limiting shear modulus G _o as a function of the theoretical $G_{\rm o}^{\rm th}/\psi_{\rm D}^2$ (Buscall et al. 1982). The data points are aligned for 0.32 ≤ ϕ _p ≤ 0.38, with a slope giving ψ _D = −22 mV (labelled 0.0005) and quite different from the 0.0009 slope expected if ψ _D = −30 mV. On the other hand, the two very pasty samples (ϕ _p > 0.38) do not follow either trends

Appendix 2: Thixotropy

We investigated thixotropy in samples with ϕ _p = 0.31 and ϕ _p = 0.36, i.e. a sample with fluid VE behaviour and another with solid VE behaviour, respectively. We performed the test under a constant shear load in each single test interval. The sample with ϕ _p = 0.31 still displays a very low degree of structural decomposition during the shear phase, and a complete structural regeneration occurs quickly during the rest phase (Fig. 13a). On the contrary, the sample with ϕ _p = 0.36 exhibits an irreversible structural change; the initial structural strength is not recovered during the rest phase (Fig. 13b). This may originate from the increasing presence of aggregates in the samples as ϕ _p increases and their destruction during the application of shear. The process is irreversible as the samples undergo failure. The difference between the two samples is coherent with the fact that the ϕ _p = 0.31 sample is the first one presenting non-Newtonian behaviour (Fig. 3), while the ϕ _p = 0.36 is already paste-like.

Fig. 13

Thixotropic behaviour determined for a ϕ _p = 0.31 and b ϕ _p = 0.36. Three intervals are preset for the measurements: the rest phase, Δt ₁, under low shear-rate, $\dot{\gamma}=$ 0.1 s^− 1; the load phase, Δt ₂, under high shear-rate, $\dot{\gamma}=$ 1,000 s^− 1 and the removing load phase, Δt ₃, in which the same conditions of the first phase are applied