Linking Particle Dynamics to Local Connectivity in Colloidal Gels

Abstract

Colloidal gels are a prototypical example of a heterogeneous network solid whose complex properties are governed by thermally-activated dynamics. In this Letter we experimentally establish the connection between the intermittent dynamics of individual particles and their local connectivity. We interpret our experiments with a model that describes single-particle dynamics based on highly cooperative thermal debonding. The model, in quantitative agreement with experiments, provides a microscopic picture for the structural origin of dynamical heterogeneity in colloidal gels and sheds new light on the link between structure and the complex mechanics of these heterogeneous solids.Attractive interactions can drive a dilute colloidal suspension towards a solid state formed by a samplespanning and mechanically-rigid particle network [1,2]. These colloidal gels are non-equilibrium solids, kinetically arrested en route to their equilibrium state of solidliquid coexistence [3]. Such particle gels are characterized by strong heterogeneity in their local connectivity, mesoscopic structure and their dynamics and mechanics [4][5][6][7]. The microstructure and internal dynamics of colloidal gels can be directly observed with microscopy techniques at the single-particle level. As a consequence, it forms an interesting testing ground to explore the complex and length-scale dependent mechanics of heterogeneous solids. Colloidal gels derive their mechanical rigidity from physically bonded gel strands and nodes that form a percolating elastic network. The linear elasticity of gels is governed by the mechanics of the network architecture and its thermal fluctuations [8,9]. By contrast, the gradual aging of gels to a denser state [1,10] and their non-linear response to applied stresses [11,12], is governed by events occuring at the the much smaller length scale of individual particles. Since the bonds between the particles are typically weak, single particles can debond from strands in the gel by thermally-activated bond breaking [13]. On longer time scales, this result in the gradual restructuration of the gel network, causing it to coarsen, age and relax internal stresses that are built up during gelation [14]. Moreover, thermal-activation at the single particle level plays a crucial role in processes of fatigue that preempt stress-induced failure of the gel network [11]. To date, quantitative descriptions of these thermally-activated phenomena have relied on mean-field approximations [13]. Yet, the inhomogeneity in local coordination that is intrinsic to gels, must play a large role in the intermittent debonding dynamics that are at the origin of this complex non-linear behavior. As a result, linking the structure of colloidal gels to their non-linear mechanics has remained challenging, in particular as the relationship between local connectivity and thermallyactivated dynamics of single particles is not clearly established.In this letter we explore the connection between the local connectivity and intermittent bonding-debonding dy...

Nonequilibrium continuous phase transition in colloidal gelation with short-range attraction

“…At effective interparticle attractions of many k B T , the thermal energy, detailed balance in the particle attachment and detachment process is broken, and the system falls out of equilibrium; in this case, a description based on an underlying equilibrium phase diagram may no longer apply. This is demonstrated by a recent experimental study on the intermittent dynamics of colloidal gels [17] revealing a marked asymmetry in the cooperative bonding and de-bonding processes. This regime, which is most relevant for biological network formation, is often modelled by cluster kinetic equations, but there is no theory that describes the formation of these out-of-equilibrium structures and is able to explain or predict, from first-principles, the fractal dimension of the growing clusters, and its relation to the cluster mass distribution.…”

Elastoplastic behavior of yield stress fluids

“…Yet, the solid regime is of wide interest, not only as its complete description might provide keys for understanding or predicting the solid-liquid transition, but also because of the analogy of these systems with amorphous materials such as metals and glasses or plastic materials [7] and the research on the physical origin of plasticity. It was in particular shown, generally by means of simulations, that plastic deformation manifests as local rearrangements exhibiting a broad distribution of sizes and shapes [25][26], non-affine displacements [27], and connectivity changes between particles [28] that lead to a redistribution of elastic stresses in the system [29]. Furthermore, the collective behavior of these reorganizations includes spontaneous strain localization, intermittent dynamics, power-law distributed avalanches [30] and spatial cooperativity [31].…”

Particle Dynamics in Colloid–Polymer Mixtures with Different Polymer Architectures

“…However, ensemble averaging may mask the effect of local structures on the dynamics of individual particles in the mixture. 24 To further investigate this, we examine the relationship between local connectivity, that is, Z and individual particle dynamics for samples with very similar ⟨Δ r 2 ⟩ for these three different polymers; specifically, the samples labeled with closed symbols in Figure 2 . We determine the value of ⟨Δ r 2 ⟩ ( Z , τ) at lag time τ = 200 s for all three samples and show this as a function of Z , measured in the first frame for each time period τ, as seen in Figure 3 .…”

“… 21 , 22 Restructuring these networks due to external or internal stresses is governed by events happening at the individual particle level, as the bonds between the particles are typically weak; a relation between local connectivity and thermally activated dynamics at the individual particle level has been reported recently for a depletion-induced colloidal gel. 23 , 24 …”