Nonergodicity transitions in colloidal suspensions with attractive interactions

Bergenholtz, Johan; Fuchs, Matthias

doi:10.1103/physreve.59.5706

Cited by 342 publications

(466 citation statements)

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“…At high densities they show two distinct glass transitions (repulsion-driven and attraction-driven), with a re-entrant dependence on attraction strength [1]. This scenario was first predicted by mode coupling theory (MCT) [2,3,4], and depends on both the attraction range δ (in units of particle diameter) and well-depth ε (in units of k B T ). MCT is remarkably successful, at least for large volume fractions φ 0.4.…”

Section: Pacs Numbersmentioning

confidence: 99%

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Cluster Mode-Coupling Approach to Weak Gelation in Attractive Colloids

2004

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Mode-coupling theory (MCT) predicts arrest of colloids in terms of their volume fraction, and the range and depth of the interparticle attraction. We discuss how effective values of these parameters evolve under cluster aggregation. We argue that weak gelation in colloids can be idealized as a two-stage ergodicity breaking: first at short scales (approximated by the bare MCT) and then at larger scales (governed by MCT applied to clusters). The competition between arrest and phase separation is considered in relation to recent experiments. We predict a long-lived 'semi-ergodic' phase of mobile clusters, showing logarithmic relaxation close to the gel line. PACS numbers:Hard-sphere colloids with short-range attractions can undergo several types of arrest. At high densities they show two distinct glass transitions (repulsion-driven and attraction-driven), with a re-entrant dependence on attraction strength [1]. This scenario was first predicted by mode coupling theory (MCT) [2,3,4], and depends on both the attraction range δ (in units of particle diameter) and well-depth ε (in units of k B T ). MCT is remarkably successful, at least for large volume fractions φ 0.4.At lower volume fractions, however, there is no comparable theoretical framework. Yet 'weak gelation', in which bonding is strong but not so strong as to be irreversible, can lead to nonergodic soft solids, of nonzero static elastic modulus, at volume fractions of just a few percent [5]. It might be argued that a finite modulus requires a percolating network of bonds whose lifetime exceeds that of the experiment. However this is simplistic: as shown by the case of repulsive glasses, a finite modulus can arise with no bonding at all. We argue here that the rigidity of weak gels arises not from bond percolation but from kinetic ergodicity breaking [6], just as it does in glass formation. This suggests that an MCT-like approach to weak gelation could be fruitful.MCT takes its structural input from equilibrium liquid state theory; it cannot address states of arrest where this structure is strongly perturbed [7]. This matters relatively little at φ 0.4, where each particle interacts with many others, and not much room is left for structural development upon a quench. But more severe consequences must be expected at low volume fractions where strongly nonuniform, ramified gels arise. Here the pathway to complete nonergodicity (starting from a homogenized fluid sample, say) must involve a nontrivial episode of structure formation, akin to irreversible cluster aggregation (ICA). Such kinetics certainly dominates for irreversible ("strong") gelation (ε −1 = 0), where particles aggregate on contact into clusters, with various kinetic universality classes [8]. Relative simplicity is restored at low φ thanks to the invariance of this aggregation process under coarse graining in the (ordered) limit δ, ε −1 → 0 and φ → 0. This scaling limit is controlled by an ICA 'fixed point', where details of the short-ranged attraction are irrelevant. The resulting fractal cluster...

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Section: Pacs Numbersmentioning

confidence: 99%

“…The flow is bounded by the MCT transition surface in this space, which divides ergodic (upper left) from nonergodic regions. This surface [2,3,4] comprises a dome joined to a sheet. Below the dome lie attractive glasses and to the right of the sheet, repulsive ones.…”

Section: Pacs Numbersmentioning

confidence: 99%

Cluster Mode-Coupling Approach to Weak Gelation in Attractive Colloids

2004

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“…In addition to liquid-glass transitions, for certain interactions MCT also predicts glass-glass transitions: In this case an existing first glass state with f 1 q transforms into a second distinct glass state with f 2 q > f 1 q discontinuously. Such glass-glass transitions were predicted for the square-well system (SWS) where the hard-core repulsion is supplemented by a short-ranged attraction [4,5,6]. In the SWS, the first glass state is driven by repulsion like in the HSS and the second glass state is driven by attraction.…”

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confidence: 99%

Disconnected Glass-Glass Transitions and Diffusion Anomalies in a Model with Two Repulsive Length Scales

Sperl

Zaccarelli²,

Sciortino³

et al. 2010

Phys. Rev. Lett.

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Building on mode-coupling-theory calculations, we report a novel scenario for multiple glass transitions in a purely repulsive spherical potential: the square-shoulder. The liquid-glass transition lines exhibit both melting by cooling and melting by compression as well as associated diffusion anomalies, similar to the ones observed in water. Differently from all previously investigated models, here for small shoulder widths a glass-glass line is found that is disconnected from the liquid phase. Upon increasing the shoulder width such a glass-glass line merges with the liquid-glass transition lines, featuring two distinct endpoint singularities that give rise to logarithmic decays in the dynamics. These findings can be explained analytically by the interplay of different repulsive length scales. 66.30.jj, 64.70.ph, 64.70.pe In the field of glassy slow dynamics, many experiments and simulations have been inspired in recent years by the modecoupling theory of the glass transition (MCT) [1]. The theory deals with density autocorrelation functions φ q (t) with wave vectors q, and predicts their long-time limits f q . While in the liquid state f q = 0, the glass state is defined by f q > 0. MCT was first applied to the hard-sphere system (HSS) where a liquid-glass transition was identified [2], and confirmed by experiments [3]. In addition to liquid-glass transitions, for certain interactions MCT also predicts glass-glass transitions: In this case an existing first glass state with f 1 q transforms into a second distinct glass state with f 2 q > f 1 q discontinuously. Such glass-glass transitions were predicted for the square-well system (SWS) where the hard-core repulsion is supplemented by a short-ranged attraction [4,5,6]. In the SWS, the first glass state is driven by repulsion like in the HSS and the second glass state is driven by attraction. The competition between these two mechanisms is responsible for the emergence of glass-glass transitions. Such a line of glass-glass transitions extends smoothly a line of liquid-glass transitions into the glass state and terminates in an endpoint singularity. Close to the endpoint singularity the dynamics is ruled by logarithmic relaxation [7]. The predicted logarithmic decays were identified in computer simulations and establish the relevance of endpoint singularities for the description of glassy dynamics [8,9]. A second dynamical anomaly predicted for the SWS concerns a reentrant liquid-glass line that causes melting by cooling [4,5,6]. This prediction of MCT was confirmed by computer simulation [10] and by experiments in colloidal suspensions [11,12].In this work we replace the attractive length scale in the SWS by a second repulsive length scale δ of the squareshoulder system (SSS) as shown in Fig. 1. The SSS can be considered the simplest potential with two competing interparticle distances; it is applied to describe properties of metallic glasses like cerium or cesium [13] In the following, the glass-transition diagrams are calculated from the singularities of ...

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“…The connection between repulsion and attraction driven glass transitions at high densities has been understood within a microscopic theoretical framework, namely mode coupling theory (MCT) [11,12,13,14,15]. Yet, the mechanisms of solidification at intermediate attraction strengths and low to intermediate densities are still not completely understood [16,17].…”

Section: Introductionmentioning

confidence: 99%

Bond formation and slow heterogeneous dynamics in adhesive spheres with long-ranged repulsion: Quantitative test of mode coupling theory

et al. 2007

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A colloidal system of spheres interacting with both a deep and narrow attractive potential and a shallow long-ranged barrier exhibits a prepeak in the static structure factor. This peak can be related to an additional mesoscopic length scale of clusters and/or voids in the system. Simulation studies of this system have revealed that it vitrifies upon increasing the attraction into a gel-like solid at intermediate densities. The dynamics at the mesoscopic length scale corresponding to the prepeak represents the slowest mode in the system. Using mode coupling theory with all input directly taken from simulations, we reveal the mechanism for glassy arrest in the system at 40% packing fraction. The effects of the low-q peak and of polydispersity are considered in detail. We demonstrate that the local formation of physical bonds is the process whose slowing down causes arrest. It remains largely unaffected by the large-scale heterogeneities, and sets the clock for the slow cluster mode. Results from mode-coupling theory without adjustable parameters agree semi-quantitatively with the local density correlators but overestimate the lifetime of the mesoscopic structure (voids).

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Nonergodicity transitions in colloidal suspensions with attractive interactions

Cited by 342 publications

References 73 publications

Cluster Mode-Coupling Approach to Weak Gelation in Attractive Colloids

Cluster Mode-Coupling Approach to Weak Gelation in Attractive Colloids

Disconnected Glass-Glass Transitions and Diffusion Anomalies in a Model with Two Repulsive Length Scales

Bond formation and slow heterogeneous dynamics in adhesive spheres with long-ranged repulsion: Quantitative test of mode coupling theory

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