Transition from semiorder to disorder in the aggregation of dense colloidal solutions

Carpineti, Marina; Giglio, M.

doi:10.1103/physrevlett.70.3828

Cited by 101 publications

(53 citation statements)

References 15 publications

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“…We initiate aggregation by adding MgCl 2 to a concentration of 6 mM; with initial volume fractions 4.6 3 10 23 # w # 1.58 3 10 22 , gels form within several hours, leading to macroscopically homogeneous structures. Static light scattering [4,10,12] from these gels at lower w confirms d f ϳ 1.9, slightly above the value expected for DLCA, and consistent with the initial aggregation being in the intermediate regime between 1064 0031-9007͞99͞82 (5)͞1064 (4) diffusion-and reaction-limited cluster aggregation; we note, however, that diffusion still dominates at longer times, leading to a well-defined average cluster size.…”

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confidence: 82%

“…In the latter case the distribution of cluster sizes is fairly narrow and the characteristic cluster size grows linearly with time. Aggregation of clusters eventually leads to a spacefilling structure which is no longer fractal on all length scales but which can instead show long-range correlations as revealed by a scattering peak corresponding to a characteristic cluster size R c aw 1͑͞d f 23͒ , where w is the initial volume fraction of monomer particles [3,4]. The clusters themselves are close packed, forming a ramified, tenuous gel structure.…”

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confidence: 99%

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Strain Hardening of Fractal Colloidal Gels

1999

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We report on experiments on the rheology of gels formed by diffusion-limited aggregation of neutrally buoyant colloidal particles. These gels form very weak solids, with the elastic modulus, G 0 ͑v͒, larger than the loss modulus, G 00 ͑v͒, and with both G 0 ͑v͒ and G 00 ͑v͒ exhibiting only a very weak frequency dependence. Upon small but finite strains g , 0.45 the elastic modulus increases roughly exponentially with g 2 . We explain the observed strain hardening with the highly nonlinear elastic response of the rigid backbone of the gel to elongational deformation. [S0031-9007 (98) Colloidal particles aggregating by attractive interactions form highly disordered clusters; these structures are, on average, self-similar, and the mass of a cluster, M, scales with its radius, R, aswhere a is the size of the colloidal monomer and M 0 is its mass [1]. The fractal mass exponent d f characterizes the ramification of the cluster and varies between d f 2.1 for reactionlimited cluster aggregation and d f 1.8 for diffusionlimited cluster aggregation (DLCA) [2]. In the latter case the distribution of cluster sizes is fairly narrow and the characteristic cluster size grows linearly with time. Aggregation of clusters eventually leads to a spacefilling structure which is no longer fractal on all length scales but which can instead show long-range correlations as revealed by a scattering peak corresponding to a characteristic cluster size R c aw 1͑͞d f 23͒ , where w is the initial volume fraction of monomer particles [3,4]. The clusters themselves are close packed, forming a ramified, tenuous gel structure. This structure should be an elastic material with unique properties, which are determined not only by d f , but also by the connectivity or chemical dimension, d b , which characterizes the scaling of the contour length within the cluster.

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confidence: 82%

mentioning

confidence: 99%

Strain Hardening of Fractal Colloidal Gels

1999

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“…This is consistent with the onset of gelation, which occurs when the colloidal aggregates grow large enough to form a space-filling network. For DLCA gels, the average cluster size at gelation is R c a 1=d f ÿ3 0 [16]. We calculate R c 2:3 10 ÿ3 cm for our sample; this corresponds to a wave vector q 1360 cm ÿ1 , and is in good agreement with the final position of the peak of Iq.…”

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confidence: 64%

Time-Dependent Strength of Colloidal Gels

et al. 2005

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Colloidal silica gels are shown to stiffen with time, as demonstrated by both dynamic light scattering and bulk rheological measurements. Their elastic moduli increase as a power law with time, independent of particle volume fraction; however, static light scattering indicates that there are no large-scale structural changes. We propose that increases in local elasticity arising from bonding between neighboring colloidal particles can account for the strengthening of the network, while preserving network structure. DOI: 10.1103/PhysRevLett.95.048302 PACS numbers: 82.70.Gg, 61.43.Hv, 62.20.Dc, 82.70.Dd Gels are dilute connected networks which are capable of supporting applied stresses; they are commonly used to control the rheological properties of complex materials. Such networks can be formed by the aggregation of colloidal particles, which occurs when an attractive interaction is induced between them. Network elasticity is highly sensitive to the connectivity and arrangement of particles in the constituent aggregates. Colloidal gels are out-ofequilibrium systems; as a result, these networks frequently display time-dependent properties, due to network restructuring. This kind of aging is modeled for generic nonequilibrium systems as an evolution toward lower energy states, as the system explores a complex energy landscape [1,2]. However, network elasticity is also dependent on the interactions between particles; therefore, time-dependent interactions may also lead to changes in network properties. For colloidal gels, it is generally assumed that interparticle attractions, such as those described by Derujaguin-LandauVerwey-Overbeek [3,4] or Asakura-Oosawa potentials [5], determine local bond elasticity, thus, in principle, limiting their strength [6,7]. In the absence of a steric stabilization layer, particle interactions can also arise from physical bonds, as a result of covalent bonding or polymer entanglements. Within this framework, time evolution of network properties can be linked to the interparticle potential, for example, through the transport of particles from secondary to primary minima [8]. Aging can also be a consequence of time-dependent physical bonding; for example, the sintering of aggregated polystyrene particles is thought to drive local shrinkage that deforms the network [9]. The strength of the local interparticle bonds will have a direct impact on the network elasticity; however, these critical effects have never been explored.In this Letter, we present measurements of the elasticity of colloidal silica gels. Surprisingly, we find that, upon gelation, their storage moduli G 0 increase as a power law in time, G 0 t 0:4 , independent of initial volume fraction . Moreover, the time evolution of the network persists long after gelation occurs, for the duration of the measurement. As a consequence, their elasticity maintains the same volume fraction dependence, G 0 3:6 , independent of time. We postulate that the stiffening of the network is a result of chemical reactions at the junctions be...

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“…A decrease of the structure factor of the simulated aggregates towards scattering angle zero has been observed for w = 0.05, i.e., D----1.78, indicating a semi-ordered state with respect to the agglomeration of clusters. Recently, this has been experimentally observed for diffusion limited aggregates (D ~ 1.75), whereas this feature for reaction limited growth is missing [37]. Scaling is also observed for the fraction of interconnected mass ot with density ~b, however, the observed scaling exponent cannot be easily related to either dn~n nor D. More helpful is the representation of the product otg versus the cluster size ~ (Fig.…”

Section: Resultsmentioning

confidence: 85%

Scaling properties and structure of aerogels

Emmerling

Fricke

1997

J Sol-Gel Sci Technol

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Abstract. Young's modulus as well as solid thermal and electrical conductivitiy of aerogels have been observed to scale with density. No quantitative explanations were available up to now for these experimental findings. To establish a quantitive relationship between morphological and topological features of fractal gel networks, a simulation procedure is introduced that allows to produce three-dimensional gel structures, from which two important parameters can be extracted: i) the fraction o~ of interconnected mass of the gel network and ii) the ratio y of Pythagorean distance to minimum path length on the gel backbone. Surprisingly the product o~),, which enters important macroscopic parameters such as elasticity or solid thermal (and electrical) conductivity, was found to scale with an exponent that is only a function of the mass fractal dimension D. Also, an analytical relation between modulus and conductivity can be derived.

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Transition from semiorder to disorder in the aggregation of dense colloidal solutions

Cited by 101 publications

References 15 publications

Strain Hardening of Fractal Colloidal Gels

Strain Hardening of Fractal Colloidal Gels

Time-Dependent Strength of Colloidal Gels

Scaling properties and structure of aerogels

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