The kinetics of irreversible aggregation processes

Odriozola, Gerardo; Moncho-Jordá, A.; Schmitt, Artur; Callejas-Fernández, J.; Martínez-Garcı́a, R.; Hidalgo‐Álvarez, R.

doi:10.1007/3-540-45725-9_19

Cited by 4 publications

(7 citation statements)

References 10 publications

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“…To interpret the experimental and simulation results within the framework of nonequilibrium statistical mechanics, we study a kinetic master equation for partially reversible aggregation used before in colloidal and protein aggregation [3,40,41] (see Methods). The equation describes changes in the cluster sizes c k for all clusters k = 1..N due to dissociation into clusters of i and j particles occurring with rate constant K − ij , and merging of clusters with i and j particles occurring with rate constant K + ij .…”

Section: A Cluster Growth and Critical Scalingmentioning

confidence: 99%

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

et al. 2020

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The arrest of attractive particles into out-of-equilibrium structures known as gelation is central to biophysics, material science and food and cosmetic applications, but a complete understanding is lacking. In particular for intermediate particle density and attraction, the structure formation process remains unclear. Here, we show that the gelation of short-range attractive particles is governed by a nonequilibrium percolation process. We combine experiments on critical Casimir colloidal suspensions, simulations, and analytic modelling with a master kinetic equation to show that cluster sizes and correlation lengths diverge with exponents ∼ 1.6 and 0.8, respectively, consistent with percolation theory, while detailed balance in the particle attachment and detachment processes is broken. Cluster masses exhibit power-law distributions with exponents −3/2 and −5/2 before and after percolation, as predicted by solutions to the master kinetic equation. These results revealing a nonequilibrium continuous phase transition unify the structural arrest and yielding into related frameworks.

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Section: A Cluster Growth and Critical Scalingmentioning

confidence: 99%

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

et al. 2020

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“…Here, we assume density matching so that we can neglect sedimentation. In this work, a recently proposed aggregation kernel 25 is used to model aggregation under both the DLCA and the RLCA regimes, including conditions where crossover from RLCA to DLCA occurs. The kernel is given by where K B is the Brownian aggregation rate constant, which describes the collision frequency of the clusters due to their random movement in the solvent.…”

Section: Population Balance Equationmentioning

confidence: 99%

“…The analysis was performed by simulating various combinations of the independent variables. Five values of d 0 (25,50,100,200, and 500 nm), nine values of φ 0 (10 -4 , 5 × 10 -4 , 0.001, 0.003, 0.005, 0.007, 0.01, 0.05, and 0.1), and 10 values of W (1, 10, 100, 500, 10 3 , 10 4 , 10 5 , 10 6 , 10 7 , and 10 8 ) gave 450 possible combinations. For each combination, the population balance equation model was numerically solved for times up to the arrest time, where φ ) φ* and the time evolution behaviors of the distribution properties d h, m c , and N* were computed.…”

Section: Process Analysis and Optimizationmentioning

confidence: 99%

Precursor Aggregate Distributions for Particulate Gels

Bonanomi¹,

Sandkühler²,

Šefčı́k³

et al. 2004

Ind. Eng. Chem. Res.

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We analyze the aggregation process leading to gel formation in colloidal dispersions under quiescent conditions in order to identify possible precursor aggregate distributions for particulate gels. The aggregation process is described with an experimentally validated population balance model, which allows us to calculate how the aggregate mass distribution evolves in time. When the cumulative occupied volume fraction of fractal aggregates reaches a certain limit, the random cluster-cluster aggregation regime crosses over to an interconnection regime, and a gel network forms. The aggregate distribution at the end of the aggregation regime is the precursor for the subsequently formed particulate gel. We demonstrate that, when aggregation proceeds fully in the reaction-limited regime, the precursor aggregate distribution depends only on the solid volume fraction while being insensitive to both the primary particle size and the stability ratio. However, the stability ratio is an important operating parameter controlling the overall aggregation and gelation time. The situation can be significantly changed by entering the diffusion-limited aggregation regime. The interplay among these various factors is illustrated through an example of the optimal design of the precursor aggregate distribution. Primary particle size, solid volume fraction, and stability ratio are used as design parameters, and the objective function is formulated in terms of specific requirements on the precursor cluster mass distribution. These requirements were determined on the basis of qualitative arguments about the relation between the precursor structure and the gel mechanical properties.

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“…, as discussed extensively in ref. [17]. The corresponding fragment distribution becomes p ij = f ij /(j − 1).…”

mentioning

confidence: 99%

“…We also compare the numerical distributions to an expression proposed by Odriozola et al [17], who analysed the fragment distribution of DLCA clusters generated by a slightly different algorithm. They fitted the fragment size distribution, specifically, f ij which is the number of bonds that upon breaking would divide a cluster into fragments of sizes i and j − i, to a four-parameter function,…”

mentioning

confidence: 99%

Morphology-dependent random binary fragmentation of in silico fractal-like agglomerates

Drossinos

Melas

Kostoglou

et al. 2019

EPL

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Linear binary fragmentation of synthetic fractal-like agglomerates composed of spherical, equal-size, touching monomers is numerically investigated. Agglomerates of different morphologies are fragmented via random bond removal. The fragmentation algorithm relies on mapping each agglomerate onto an adjacency matrix. The numerically-determined fragment size distributions are U-shaped, clusters break predominantly into two largely dissimilar fragments, becoming more uniform as the fractal dimension decreases. A symmetric beta distribution reproduces the fragment distribution rather accurately. Its exponent depends on the structure (fractal dimension) and number of monomers of the initial agglomerate. A universal fragment distribution, a function only of the initial fractal dimension, is derived by requiring that it satisfy the fragmentation conversation laws and the straight-chain limit. We argue that the fragmentation rate is proportional to the initial agglomerate size.

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The kinetics of irreversible aggregation processes

Cited by 4 publications

References 10 publications

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

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

Precursor Aggregate Distributions for Particulate Gels

Morphology-dependent random binary fragmentation of in silico fractal-like agglomerates

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