Ergodicity breaking and aging dynamics in Laponite–Montmorillonite mixed clay dispersions†
Abstract
Ergodicity breaking and aging dynamics in a mixture of colloidal clays, Laponite (L) and Montmorillonite (MMT), were investigated. The intensity of the light scattered off L-MMT dispersions scaled with solid volume fraction (ϕ) as, I ∼ ϕα, with α = 1.49, for Laponite α = 0.95, for 2 × 10−4 < ϕ < 8 × 10−3, and it remained invariant above ϕ = 8 × 10−3. For MMT, α = 1.38 and no such invariance was noticed. Ergodic to non-ergodic transitions were observed in aged samples with a characteristic ergodicity breaking time, τEB ≈ 102 − 105 s. Dynamic structure factor, g1(q,t) exhibited two-mode relaxation, g1(q,t) = a exp(−t/τ1) + (1 − a) exp−(t/τ2)β. The stretching parameter, β was found to decrease linearly with aging time, tw whereas slow mode relaxation time increased as τ2 ∼ exp (btw) and τ1 remained invariant of tw. Spatial dependence of τ1 and τ2 showed, τ1,τ2 ∼ q−2 in the ergodic phase, considered arising from the diffusive motion. After the ergodicity breaking time (t > τEB), the slow mode relaxation was no more diffusive and revealed τ2 ∼ q−1, indicating dynamic arrest of the platelets in the glass phase. The temporal evolution of the slow mode relaxation time τ2 in full aging regime i.e. above τEB, followed a power law growth. The τEB was found to decrease with concentration as τEB ∼ exp(−ϕ/ϕ0). A sharp rise in anisotropy, Dp in the L-MMT glass system occurring precisely at the ergodicity breaking time was observed with the overall aging dependence given by Dp ∼ t0.46w. Heterogeneity in these samples was probed from the Cole–Cole plot of