Kinetic growth of field-oriented chains in dipolar colloidal solutions

Miguel, M. Carmen; Pastor-Satorras, Romualdo

doi:10.1103/physreve.59.826

Cited by 50 publications

(29 citation statements)

References 24 publications

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“…28 It should be stressed that the dynamical scaling property of anisotropic two-dimensional systems during coarsening processes has been reported by several authors and demonstrated by computer simulations performed under confined conditions, i.e., in very thin layers or in slab geometries with thicknesses similar to the values of the characteristic correlation distance ͓R͑t͒ =2 / q 1 ͔ in the plane. [31][32][33][34][35] Geometrical confinement effects were not expected in the samples studied here because the film thicknesses ͑Ϸ200 nm͒ are about ten times the largest R͑t͒ values derived from our SAXS curves. Therefore, the present study reveals the validity of the dynamic scaling hypothesis in intrinsic bidimensional coarsening processes.…”

Section: Resultsmentioning

confidence: 84%

Dynamical scaling properties of nanoporous undoped and Sb-dopedSnO2supported thin films during tri- and bidimensional structure coarsening

et al. 2007

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The coarsening of the nanoporous structure developed in undoped and 3% Sb-doped SnO 2 sol-gel dip-coated films deposited on a mica substrate was studied by time-resolved small-angle x-ray scattering ͑SAXS͒ during in situ isothermal treatments at 450 and 650°C. The time dependence of the structure function derived from the experimental SAXS data is in reasonable agreement with the predictions of the statistical theory of dynamical scaling, thus suggesting that the coarsening process in the studied nanoporous structures exhibits dynamical self-similar properties. The kinetic exponents of the power time dependence of the characteristic scaling length of undoped SnO 2 and 3% Sb-doped SnO 2 films are similar ͑␣ Ϸ 0.09͒, this value being invariant with respect to the firing temperature. In the case of undoped SnO 2 films, another kinetic exponent, ␣Ј, corresponding to the maximum of the structure function was determined to be approximately equal to three times the value of the exponent ␣, as expected for the random tridimensional coarsening process in the dynamical scaling regime. Instead, for 3% Sb-doped SnO 2 films fired at 650°C, we have determined that ␣Ј Ϸ 2␣, thus suggesting a bidimensional coarsening of the porous structure. The analyses of the dynamical scaling functions and their asymptotic behavior at high q ͑q being the modulus of the scattering vector͒ provided additional evidence for the two-dimensional features of the pore structure of 3% Sb-doped SnO 2 films. The presented experimental results support the hypotheses of the validity of the dynamic scaling concept to describe the coarsening process in anisotropic nanoporous systems.

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Section: Resultsmentioning

confidence: 84%

Dynamical scaling properties of nanoporous undoped and Sb-dopedSnO2supported thin films during tri- and bidimensional structure coarsening

et al. 2007

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“…The cluster diffusion coefficients do not depend on the direction in which the clusters move, i.e., hydrodynamic corrections are not important as they are in case of constant magnetic fields (author?) [9].…”

Section: Discussionmentioning

confidence: 99%

Aggregation of magnetic holes in a rotating magnetic field

Černák

Helgesen

2008

Phys. Rev. E

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We have experimentally investigated field induced aggregation of nonmagnetic particles confined in a magnetic fluid layer when rotating magnetic fields were applied. After application of a magnetic field rotating in the plane of the fluid layer, the single particles start to form two-dimensional (2D) clusters, like doublets, triangels, and more complex structures. These clusters aggregated again and again to form bigger clusters. During this nonequilibrium process, a broad range of cluster sizes was formed, and the scaling exponents, z and z ′ , of the number of clusters N (t) ∼ t z ′ and average cluster size S(t) ∼ t z were calculated. The process could be characterized as diffusion limited clustercluster aggregation. We have found that all sizes of clusters that occured during an experiment, fall on a single curve as the dynamic scaling theory predicts. Hovewer, the characteristic scaling exponents z ′ , z and crossover exponents ∆ were not universal. A particle tracking method was used to find the dependence of the diffusion coefficients D s on cluster size s. The cluster motions show features of Brownian motion. The average diffusion coefficients < D s > depend on the cluster sizes s as a power law < D s >∝ s γ where values of γ as different as γ = −0.62 ± 0.19 and γ = −2.08 ± 0.51 were found in two of the experiments.

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“…Nevertheless this model takes into account that the force between two aggregates depends on their respective size and also that the average distance between aggregates increases during the aggregation process. Several numerical simulations have focused on the exponent of the growth of the chain average size l with time: l(t) ∝ t α and have found α between 0.5 and 0.7; the last limit corresponds to the case where dipolar forces dominate Brownian forces [3,4]. A detailed analysis of the power law exponents was carried out both by Brownian dynamics simulation and experimentally, for large box sizes with energy of the dipole-dipole interaction of the particles being between two and three order of magnitude larger than the thermal energy kT [5].…”

Section: Introductionmentioning

confidence: 99%

Kinetics of internal structures growth in magnetic suspensions

Bossis

Lançon

Meunier

et al. 2013

Physica A: Statistical Mechanics and its Applications

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a b s t r a c tThe kinetics of aggregation of non Brownian magnetizable particles in the presence of a magnetic field is studied both theoretically and by means of computer simulations. A theoretical approach is based on a system of Smoluchowski equations for the distribution function of the number of particles in linear chain-like aggregates. Results obtained in the two dimensional (2D) and three dimensional (3D) models are analyzed in relation with the size of the cell, containing the particles, and the particle volume fraction ϕ. The theoretical model reproduces the change of the aggregation kinetics with the size of the cell and with the particle volume fraction as long as the lateral aggregation of chains is negligible.The simulations show that lateral aggregation takes place when, roughly, ϕ 2D > 5% and ϕ 3D > 1.5%.Dependence of the average size of the chains with time can be described by a power law; the corresponding exponent decreases with the particle volume fraction in relation with the lateral aggregation.In the 3D simulations, dense labyrinthine-like structures, aligned along the applied field, are observed when the particle concentration is high enough (ϕ 3D > 5%).

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Kinetic growth of field-oriented chains in dipolar colloidal solutions

Cited by 50 publications

References 24 publications

Dynamical scaling properties of nanoporous undoped and Sb-dopedSnO2supported thin films during tri- and bidimensional structure coarsening

Dynamical scaling properties of nanoporous undoped and Sb-dopedSnO2supported thin films during tri- and bidimensional structure coarsening

Aggregation of magnetic holes in a rotating magnetic field

Kinetics of internal structures growth in magnetic suspensions

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