Internal Dynamics and Elasticity of Fractal Colloidal Gels

Abstract

The dynamic structure factor of fractal colloidal gels is shown to exhibit a stretched exponential decay to a finite plateau with an exponent of about 0.7. The value of the plateau depends on both initial particle volume fraction f 0 and scattering wave vector. We show that this behavior results from the contribution of internal elastic modes of many length scales, and present a model which accounts for the data. From the observed plateau we determine that the very small elastic modulus scales as G ϳ f 3.9 0 , in agreement with predictions, and with direct mechanical measurements. [S0031-9007(97)05169-7] PACS numbers: 82.70.Dd, 61.43.Hv, 63.50. + x, 82.70.Gg Colloidal aggregates form fascinating structures; despite the apparent disorder of their shape, they possess a remarkable degree of symmetry, and can be well described as fractals [1]. This scale invariance has facilitated the description of their structure and its relationship to the kinetics of their formation [2]. One of the unique features of a fractal structure is that its density decreases as its size grows; as a result, colloidal aggregates ultimately gel to form a very weak solid, comprised of a connected, disordered network that fills all space [3][4][5]. If the aggregation is predominantly diffusion limited, the average clusters that form the gel are surprisingly uniform in size, resulting in a strong peak in the static light scattering intensity at low angles [3,5]. By contrast, if the aggregation is reaction limited, the large polydispersity in the cluster size precludes the low angle scattering peak [4]. Suspensions with exceedingly low initial particle volume fraction f 0 can gel, provided buoyancy matched particles are used to avoid sedimentation. The resultant solid is a very interesting material; although it is a highly disordered network, the scale invariant structure is nevertheless well determined. This makes colloidal gels ideal models for the study of the internal dynamics and related mechanical properties of disordered networks in general. Unfortunately, however, such gels are so weak that it is very difficult to measure their properties with mechanical techniques.In this Letter, we overcome this experimental limitation by using dynamic light scattering (DLS) to measure the internal dynamics of fractal colloidal gels, and develop a model that allows us to determine their mechanical properties. We show that colloidal gels exhibit unusual behavior. At early times the dynamics appear as anomalous or "stretched" diffusion with an exponent independent of scattering wave vector q or initial particle volume fraction f 0 ; this is in sharp contrast with polymer gels, where stretched diffusive behavior is observed only after an initial regime of simple exponential decay [6,7]. For colloidal gels, it is still possible to define an effective diffusion coefficient, which scales as q 22 ; this is in sharp contrast with DLS from internal motions of polymers, where a q 23 behavior is expected [8]. For colloidal gels formed from higher f 0 , the dyn...

Slow dynamics, aging, and glassy rheology in soft and living matter

“…4a illustrates, laponite suspensions following rejuvenation unexpectedly display a very similar increase in the plateau value despite the fact that the interparticle interactions are likely unaffected by the rejuvenation. One possibility for this increase in the rejuvenated laponite suspensions is a slow strengthening of force networks in the suspensions weakened by the shear flow and a concomitant decrease in thermal fluctuations of these networks that create a fast partial decay in g 2 (q, t) in analogy with the picture developed in [65]. Thus, the increase in the plateau value during formation and after rejuvenation could have different origins.…”

“…In some cases, the characteristic relaxation time τ f measured for the faster, initial decay scales with q as τ f ∼ q −2 , indicating caged diffusive dynamics [2]. In the case of a fractal colloidal gel, the DSF f (q, t) characterising the initial decay exhibits a stretched exponential form with an exponent of 0.7 [65] and is understood in terms of the contribution of thermally excited, overdamped modes of the gel strands. The second, slower relaxation in these soft glassy materials is more counter-intuitive and is characterised by a DSF with a compressed exponential form (f (q, t) ∼ exp[−(t/τ s ) p ], where p ≈ 1.5), with τ s varying with q according to the relation τ s ∼ q −1 .…”

Cluster Mode-Coupling Approach to Weak Gelation in Attractive Colloids

“…It has inspired successful phenomenological gel models, e.g. [19,20,21], for which CMCT could provide a more rational (albeit still speculative) basis. Experiments [22] demonstrate that even for moderate attractions the assumed closeness to the ICA limit is well justified at low volume fractions in some cases, while in others the measured fractal dimension lies higher than for the appropriate ICA model [23].…”

Nonergodicity transitions in colloidal suspensions with attractive interactions

“…Also Poon et al [11] have made such observations in the so-called transient gelation region of the colloid-polymer phase diagram for short polymers. Krall and Weitz [35] have shown that, in the limit of strong particle aggregation, suspensions become nonergodic even at low colloid densities. To date, however, only a speculative connection has been made between the gel and liquid-glass transitions [15].…”