Coagulation kinetics and aggregate morphology in the intermediate regimes between diffusion-limited and reaction-limited cluster aggregation

Asnaghi, D.; Carpineti, Marina; Giglio, M.; Sozzi, M.

doi:10.1103/physreva.45.1018

Cited by 142 publications

(81 citation statements)

References 24 publications

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“…Numerous previous studies have shown an inverse relation between dr and coagulation rate (Lin et al 1989;Hackley and Anderson 1989;Areal et al 1990;Asnaghi et al 1992;Zhang and Buffle 1996) and this pattern is observed in the present study for aggregates formed by counterion screening in the presence of KC1 (Figure 8a). However, the coagulation rate for phosphate-induced destabilization (Figure 8b) shows a completely different trend.…”

Section: Discussionsupporting

confidence: 71%

Comparison of Hematite Coagulation by Charge Screening and Phosphate Adsorption: Differences in Aggregate Structure

Chorover

Zhang

Amistadi

et al. 1997

Clays and clay miner.

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Abstract--The formation and structure of hematite aggregates were examined by dynamic and static light scattering techniques. A large range in coagulation kinetics was studied by varying either indifferent electrolyte (KC1) concentration or surface complexing anion (H2PO4) concentration, PT, at pH 6.0 ~ 0.1. Diffusion limited aggregation (DLA) was induced by counterion screening at [KC1] > 80 mM or by surface charge neutralization at Pr = 31 IxM (and ionic strength = 1.0 raM). In DLA, the fractal dimension, de, of aggregates formed by either surface charge neutralization or counterion screening was 1.7 2 0.1. A reduction in the rate of coagulation in KC1 for [KC1] < critical coagulation concentration (CCC) produced an increase in df to 2.1 _+ 0.1. For aggregation induced by phosphate adsorption at constant ionic strength, there was no apparent trend in df with coagulation rate. The value of df was consistently less than 1.8 when reaction limited aggregation (RLA) resulted from surface charge neutralization rather than counterion screening. TEM observations of aggregates formed in the presence or absence of phosphate confirm that, when RLA is induced by phosphate adsorption, resulting aggregates are much looser in structure than those formed by counterion screening. The results suggest that the high-affinity binding of phosphate to hematite may result in a nonrandom distribution of surface charge that facilitates the coalescence of positive and negative charge crystal faces.

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Section: Discussionsupporting

confidence: 71%

Comparison of Hematite Coagulation by Charge Screening and Phosphate Adsorption: Differences in Aggregate Structure

Chorover

Zhang

Amistadi

et al. 1997

Clays and clay miner.

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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.…”

supporting

confidence: 81%

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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“…A new nonuniversal scaling relationship was proposed that collapses the size distribution at the small end of the size spectrum. Apart from the effect of initial conditions on the small end of the size spectrum, the van Dongen and Ernst predictions are consistent with reported experimental observations (12,13,15,(22)(23)(24)(25), Monte Carlo simulations of the coagulation process (26)(27)(28)(29), and analytical studies of the von Smoluchowski equation (30)(31)(32)(33). The λ and µ values for several physical coagulation kernels are listed in Table 1.…”

Section: Predictions For a Generalized Kernelsupporting

confidence: 83%