Growth of Fractally Rough Colloids

Keefer, Keith D.; Schaefer, Dale W.

doi:10.1103/physrevlett.56.2376

Cited by 168 publications

(90 citation statements)

References 8 publications

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“…For CNT, Bauhofer and Kovacs 1 have related experimental t values for threedimensional percolating systems between 1.3 and 4, which would be consistent with the MCFFS value t = 2.21 ± 0.15. Other studies have also shown that the percolation threshold is dependent of conductive fillers morphology (size, shape and the aspect ratio) [24][25][26][27] . The distribution of scattered points is not a real situation of electrically conductive composites; however, this method of particles distribution has been widely adopted for comparison with known percolation threshold values [28][29][30][31] .…”

Section: Verification Of Simulator For Scattered Pointsmentioning

confidence: 99%

Assessment of Percolation Threshold Simulation for Individual and Hybrid Nanocomposites of Carbon Nanotubes and Carbon Black

2017

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Modeling electrical conductivity of polymer composites with conductive fillers has great applicability to predict conductive materials behavior. In this study, the electrical behavior of simple and hybrid systems prepared from Carbon Black (CB) and Carbon Nanotubes (CNT) was studied.There have been few advances reported in the literature regarding the modeling of hybrid systems, which motivated the development of this study. More specifically, a program was developed with the intention to describe the electric percolation threshold and the effect of synergism between the conductive fillers. Simulation was performed using the Monte Carlo method and Fortran programming language, considering concentration and geometry of conductive fillers to the system in two dimensions. Finally, simulation results were compared with the experimental results and this method proved to be effective in predicting the systems percolation threshold, being an important contribution to predict material behavior, which allows reducing the number of samples to be prepared in an experimental study.

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Section: Verification Of Simulator For Scattered Pointsmentioning

confidence: 99%

Assessment of Percolation Threshold Simulation for Individual and Hybrid Nanocomposites of Carbon Nanotubes and Carbon Black

2017

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“…While the NMR technique has been applied to the determination of fractal dimensions of synthetic silicas (Devreux et al 1990), it is not apparent that it should be applicable to natural materials like clays for the following reason. Silica aggregation is usually a fractal process (Schaefer and Martin 1984;Keefer and Schaefer 1986;Schaefer 1989;Bottero et al 1990). Thus, in a synthetic siliceous material it is possible to end up with a fractal distribution of paramagnetic impurities that can be related to D m. However, in clay minerals the distribution of paramagnetic impurities, for example Fe, on exchange sites and/or substituted in the crystal lattice is a function of the clay's crystallography.…”

Section: ~%~ M~~176mentioning

confidence: 99%

Comparison of Techniques for Determining the Fractal Dimensions of Clay Minerals

Malekani

Rice

Lin

1996

Clays and clay miner.

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Abstract---Small-angle X-ray scattering (SAXS), adsorption and nuclear magnetic resonance (NMR) techniques were used to determine the fractal dimensions (D) of 3 natural reference clays: 1) a kaolinite (KGa-2); 2) a hectorite (SHCa-1), and 3) a Ca-montmorillonite (STx-1). The surfaces of these clays were found to be fractal with D values close to 2.0. This is consistent with the common description of clay mineral surfaces as smooth and planar. Some surface irregularities were observed for hectorite and Camontmorillonite as a result of impurities in the materials. The SAXS method generated comparable D values for KGa-2 and STx-1. These results are supported by scanning electron microscopy (SEM). The SAXS and adsorption methods were found to probe the surface irregularities of the clays while the nuclear magnetic resonance (NMR) technique seems to reflect the mass distribution of certain sites in the material. Since the surface nature of clays is responsible for their reactivity in natural systems, SAXS and adsorption techniques would be the methods of choice for their fractal characterization. Due to its wider applicable characterization size-range, the SAXS method appears to be better suited for the determination of the fractal dimensions of clay minerals.

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“…Mass fractal scaling can be associated with the packing efficiency of an aggregate, which in turn depends on the type of aggregation, e.g., diffusion or reaction limited mechanism. [13][14][15][16][17][18][19][20][21] On the other hand, surface fractal scaling only relates to the perimeter of a particle or aggregate of particles and correlates with its specific surface area. [1][2][3][4][5] The core idea behind mass fractals stems from our need to statistically describe aggregation processes involving primary particles.…”

Section: Introductionmentioning

confidence: 99%

“…The fractal nature of colloids can be experimentally quantified using scattering techniques, and based on a combination of theoretical and experimental evidence [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] two distinct scaling laws have been used to describe experimental observations: mass fractals and surface fractals. Mass fractal scaling can be associated with the packing efficiency of an aggregate, which in turn depends on the type of aggregation, e.g., diffusion or reaction limited mechanism.…”

Section: Introductionmentioning

confidence: 99%

Not just fractal surfaces, but surface fractal aggregates: Derivation of the expression for the structure factor and its applications

Besselink

Stawski

Driessche

et al. 2016

The Journal of Chemical Physics

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Densely packed surface fractal aggregates form in systems with high local volume fractions of particles with very short diffusion lengths, which effectively means that particles have little space to move. However, there are no prior mathematical models, which would describe scattering from such surface fractal aggregates and which would allow the subdivision between inter-and intraparticle interferences of such aggregates. Here, we show that by including a form factor function of the primary particles building the aggregate, a finite size of the surface fractal interfacial sub-surfaces can be derived from a structure factor term. This formalism allows us to define both a finite specific surface area for fractal aggregates and the fraction of particle interfacial sub-surfaces at the perimeter of an aggregate. The derived surface fractal model is validated by comparing it with an ab initio approach that involves the generation of a "brick-in-a-wall" von Koch type contour fractals. Moreover, we show that this approach explains observed scattering intensities from in situ experiments that followed gypsum (CaSO 4 ·2H 2 O) precipitation from highly supersaturated solutions. Our model of densely packed "brick-in-a-wall" surface fractal aggregates may well be the key precursor step in the formation of several types of mosaic-and meso-crystals. C

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Growth of Fractally Rough Colloids

Cited by 168 publications

References 8 publications

Assessment of Percolation Threshold Simulation for Individual and Hybrid Nanocomposites of Carbon Nanotubes and Carbon Black

Assessment of Percolation Threshold Simulation for Individual and Hybrid Nanocomposites of Carbon Nanotubes and Carbon Black

Comparison of Techniques for Determining the Fractal Dimensions of Clay Minerals

Not just fractal surfaces, but surface fractal aggregates: Derivation of the expression for the structure factor and its applications

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