Fractal aggregates kinetics

Other possible methods of obtaining fractal dimensions are light- and small-an-gle-X-ray-scattering (SAXS). The first method gives information about mass fractality of aggregates and aggregation kinetics (Fleischmann et al., 1990), whereas the latter allows mass and surface fractals to be differentiated (Schmidt, 1990). 

To additionally account for the effect of the aggregate structure on the aggregation kinetics, a colhsion diameter xc is introduced which can be calculated based on the fractal dimension Z)F of the aggregate (Eq. (5)). 

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 ... 

A three-dimensional lattice model (section 3.1.1) was used to simulate aggregation kinetics, in which single particles and intermediate clusters move on Brownian or linear trajectories. Initially, = 50,000 particles are placed randomly in a cubic lattice of size L = 215x 215x 215. A combined cluster is formed whenever a particle or a cluster moves to a lattice point adjacent to another particle or intermediate cluster. This model produces DLCA clusters [77] with fractal dimension around 1.8 (Brownian trajectories) and 2 (linear trajectories). A sequence of two integers is used to describe the... 

Let us consider the reasons of the distinctions mentioned, involving the representations of models of the irreversible aggregation and of the fractal analysis. In terms of the fractal analysis, kinetics of polymerisation is described by a general relationship [18] ... 

Chapters 4 and 5 [34, 35], A number of computer simulations and statistical models have been proposed to explain growth, polymerization and aggregation processes that lead to the formation of fractal structures that closely resemble those found in nature. Attempts have been made to relate the fractal dimensions of aggregates to their formation mechanisms and aggregation kinetics. 

E. Blanco, M. Ramirez-del-Solar, N. De la Rosa-Fox, and A. F. Craievich, SAXS Study of Growth Kinetics of Fractal Aggregates in TEOS-Water-Alcohol Solutions with Formamide, J. Non-Cryst. Solids., 147 148, pp. 238-44, 1992. 

Highly stable water colloid solution of Cgo fnUerene (maximum concentration 2 mg/mL) was prepared by transfer of Cgo (purity >99.5%) from toluene to water using ultrasound sonication. Analysis of the UV/vis, Raman, FTIR, and SANS spectroscopic data showed that the water colloid solution of Cgo fullerenes contains single Cgo molecules in the hydrated state. However, their clusters and solids (nanocrystallites) have different sizes (1-36 nm in dependence of Qo concentration in water). The aggregation kinetics indicated that the structure of Cgo aggregates could be described as a fractal with a dimension of 1.8-2.0 nm. 

Fractal Structures and Aggregation Kinetics of Protein-Functionalized Colloidal Particles... 

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