Smoluchowski aggregation kinetics, gelation, ergodicity breaking and aging dynamics of (1:1) Laponite-Montmorillonite mixed clay dispersions

Abstract

Abstract Herein, we report clay concentration dependent hierarchical self-assembly, ergodicity breaking with the aging dynamics for (1:1) Laponite-Montmorillonite mixed dispersions which turned into colloidal gels after a characteristic gelation time tg. Growth dynamics could be universally described by, η r ∼ ( 1 − t t g v i s c ) − ∝ ; t ≪ t g v i s c and G 0 ∼ ( t t g r h e o − 1 ) γ ; t ≫ t g r h e o where η r is relative viscosity of gelling dispersion, and G0 is low frequency storage modulus of the gel. Growth exponents decreased from α = 1.0 to 0.3 and γ = 1.5 to 1.2, when clay concentration was increased to 1.25% (w/v). Above this concentration, there was increase in value of exponent α from 0.3 to 0.8 while γ remained invariant (≈1.3). For [Clay] ≤ 1.25% (w/v), t g v i s c ≫ t g r h e o implying early network formation, when [Clay] > 1.25% (w/v), t g v i s c ≈ t g r h e o . Dynamic structure factor data revealed presence of two relaxation modes: the fast mode relaxation time t1 was independent of aging time tw while the slow mode relaxation time showed τ 2 ∼ t w k s . Nucleation time tn determined from slow mode relaxation, scattered intensity and ergodicity parameter were consistent. At low clay concentration nucleation and growth occurred over a time scale tn ∼ 103 s, while at higher concentration (>1.25%), this was instantaneous leading to faster gelation and dynamic arrest. Difference between the gelation time tg and tn was large at low clay concentration which converged with increase in clay concentration. The transition from ergodic to non-ergodic phase occurred at τEB ∼ 105 s (ergodicity breaking time) and τEB decreased with clay concentration. Smoluchowski aggregation model was used to describe the diffusion limited nucleation and growth of aggregates that eventually self-assembled to form entropic gels.