Fractal colloidal aggregates

Fig. 2. Putative microstructure of a fractal colloidal aggregate network.

Ball, R.C., Fractal Colloidal Aggregates Consolidation and Elasticity, Physica D 38 13-15 (1989). 

Liu, J., Shih, W.Y., Sarikaya, M. and Aksay, LA. (1990). Fractal colloidal aggregates with finite interparticle interactions Energy dependence of the fractal dimension. Phys. Rev. A., 41, 3206-3213. 

Kim, J and Kramer,T A (2006), Improved orthokinetic coagulation model for fractal colloids Aggregation and breakup . Chemical Engineering Science, 61(1) 43-53. 

For compact, homogeneous objects in tliree dimensions, p= 3. Colloidal aggregates, however, tend to be ratlier open, fractal stmctures, witli 3. For a general introduction to fractals, see section C3.6 and [61]. 

Schaefer D W, Martin J E, Wiltzius P and Cannell D S 1984 Fractal geometry of colloidal aggregates Phys. Rev. Lett 52 2371-4... 

In contrast, the three- or two-dimensional morphologies of colloidal aggregates via Brownian particle trajectories show a fractal-like structure. One of the most prominent features of the surface deposits formed by the diffusion-limited aggregation mechanism is the formation of isolated treelike clusters (9). In our experiments, the surface morphology of the silica-coated polyethylene composite prepared by... 

Fig. 36 Self-assembly of DNA-coated colloids observed in optical microscopy, (a) Fractal-like aggregates of microspheres with 14,000 DNA molecules per each sphere, (b, c) Similar colloids with 3,700 DNA/sphere form small crystals, (d) Upon heating by only 2°C, the crystallites and the aggregates both melt into monomers. Adapted with permission from [153]...

The simplest fractals are mathematical constructs that replicate a given structure at all scales, thus forming a scale-invariant structure which is self-similar. Most natural phenomena, such as colloidal aggregates, however, form a statistical self-similarity over a reduced scale of applicability. For example, a colloidal aggregate would not be expected to contain (statistical) self-similarity at a scale smaller than the primary particle size or larger than the size of the aggregate. 

Although DLS is most often used to size solid colloidal particles, the technique has also been applied to characterize aerosols [78,86,87], emulsion droplets [88,89], amphiphilic systems [90-92], and macromolecular solutions [12,16,93]. Another common application is the study of the fractal structure and kinetics of colloidal aggregation [94-102], More information about dynamic light scattering and its applications can be found in Refs. 23. 103 (104), and 105, in reviews, Refs. 11, 13, 36, 37, 49, 50, and 106, and in collections of papers Refs. 12. 14. 16. 93 (107), 105, and 108-114. 

Figure 17.20. Interfloc and intrafloc links between fractal clusters of colloidal aggregates.

This theory was first developed for colloidal aggregate networks and was later adapted to fat crystal networks (52-54). In colloidal systems (with a disordered distribution of mass and statistical self-similar patterns), the mass of a fractal aggregate (or the distribution of mass within a network), M, is related to the size of the object or region of interest (R) in a power-law fashion ... 

Floes pack in a space-filling, Euclidean fashion hence, at the floe level of structure, the material can be considered as an orthodox amorphous substance. Within the floes, however, particles pack in a non-Euclidean, fractal fashion. For such a structural arrangement, the volume fraction of particles in a floe (O ) is equivalent to the volume fraction of particles in the entire system (O), namely = O. This well-known relation of polymer physics (11) has been experimentally shown to also apply to colloidal aggregates above their gelation threshold (12). 

Fractal structures have been examined, in particular, in diffusion-controlled aggregation process (polymerization) [7-9], in colloids (aggregates of particles) [10-13], and in percolation clusters [1-3],... 

Schaefer, D.W. et al.. Fractal geometry of colloidal aggregates, Phys. Rev. Lett., 52, 2371, 1984. Hurd, A.J. and Flower, W.L., In situ growth and structure of fractal silica aggregates in a flame, J. Colloid Interface Set, 122, 178, 1988. 

Problem 7-24. Sedimentation of a Colloidal Aggregate. Colloidal particles often aggregate because of London-van der Waals or other attractive interparticle forces unless measures are taken to stabilize them. The aggregation kinetics are such that the aggregate formed has a fractal dimension Df, which is often less than the spatial dimension. The fractal dimension measures the amount of mass in a sphere of radius R, i.e., mass R D<. For a fractal aggregate composed of Aprimary particles of radius Op with mass mp, estimate the sedimentation velocity of the aggregate when the Reynolds number for the motion is small. What is the appropriate Reynolds number ... 

Jullien R. The application of fractals to colloidal aggregation. Croatica Chem Acta 1992 65 215-235. 

On the basis of experimental observations of aggregation, including electron microscopy and QELS, Matsushita (15) concluded that at least some colloidal aggregates can be well described in terms of fractal geometry and that the size distribution of aggregates and the kinetics of their aggregation can also be related to their fractal structure. 

Natural fractals such as clouds, polymers, aerogels, porous media, dendrites, colloidal aggregates, cracks, fractured surfaces of solids, etc., possess only statistical self-similarity, which, furthermore, takes place only in a restricted range of sizes in space [1,4,16]. It has heen shown experimentally for solid polymers [22] that this range is from several angstroms to several tens of angstroms. 

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