Aggregate surface fractal dimension

The estimations according to the equation (1) have shown that value for Al(OH)j aggregates varies within the limits of 0.83-2.62 mcm. Using the calibrating plots, adduced in work [4], Al(OH)j aggregates surface fractal dimension value can be estimated as equal to 2.20 and their stracture fractal dimension revalue as... 

A three-dimensional mass fractal dimension. Dm, describes the packing of particles forming an aggregate. Its value varies from 1 to 3. Unlike the Ds, which ascribes a low value to a smooth surface, the higher the value of Dm, the more densely packed is the aggregate. Mass fractal dimension of 3 corresponds to a solid structure. A lower Dm shows a loose and commonly branchier structure of the fractal aggregate (Fig. 3). 

Laser diffraction technique is able to generate the envelope diameter distribution of the aggregates in the aerosol cloud, as well as the surface and mass fractal dimensions as explained in Light Scattering under both Boundary and Surface Fractal Dimensions and Mass Fractal Dimension. However, validation of Eq. (25) by comparison studies between the impaction and laser diffraction techniques is required. 

Although there are fractal systems in the environment which are not aggregates, such as the fractal surface roughness of fractures and wear particles, the texture of clouds and the distribution of stars in the night sky, these are less often of interest in the study of environmental systems. Surface fractal dimensions are also considered important in environmental systems and, although they are subject to many of the same principles discussed later, are not treated explicitly here. 

Filgueira, R.R., Sarli, GO., Piro, A.I. and Fournier, L.L. (1998). Surface-fractal dimension of soil aggregates and rock particles. In Fractals and Beyond. Complexities in the Science, Novak, M.M. (ed.). World Scientific, Singapore, pp. 223-229. 

Effects on Idpe/pp blends with components of similar initial viscosities. Advances in Polymer Technology, Vol.lO, No.3, (October 1990), pp. 163-172, ISNN1098-2329 Yu, J. Xu, T. Tian, Y. Chen, X. Luo, Z. (2002). The effects of the aggregation structure parameters on impact-fractured surface fractal dimension and strain-energy release rate for polypropylene. Materials Design, Vol.23, No.l, (February 2002), pp. 89-95, ISSN 0261-3069... 

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). 

One way of measuring the fractal dimension of aggregates is discussed in Chapter 5 (See Section 5.6a and Example 5.4). In the example below, we illustrate the relation between the fractal structure of aggregates and the surface area of the aggregates. 

In principle, however, the effective surface area for heat transfer from the single monomer is decreased by the contact area between the particles. The fractal dimension of the aggregates varies in different systems and depends on the evolution process. For dense aggregates, heat transfer rates are decreased due to the reduced heat exchange area compared to primary particles only connected by point contact in a chain like structure (Liu et al., 2006a-c). This leads to an overestimation of... 

The rate of aggregation of fully renneted micelles is very sensitive to temperature. At room temperature it is appreciably less than the diffusional collision rate, which led Payens (1977) to consider the possibility that only a fraction of the surface is reactive (so-called hot spots). The idea of hot spots is consistent with the low fractal dimension of micelle clusters formed during renneting and leads to only a proportion of all encounters between fully renneted micelles being successful. In effect, a statistical prefactor is included in the reaction kernel to reduce the diffusion rate to a level comparable with experiment. However, Payens developed the idea of hot spots only within his theory of the aggregation of fully renneted micelles. 

The surface area per unit mass. A, of a fractal particle depends on the radius of the individual particles, r, the radius of the aggregate, R, and the fractal dimension ... 

Porosity within a particle is a manifestation of the shape of a particle. Fractal particles will have internal porosity as a result of their shapes. Fractal particles with low fractal dimensions (i.e., <2.0) will have a broad pore size distribution, where the largest pore approaches the size of the aggregate. Fractal particles with large fractal dimensions (i.e., >2.0) will have narrower pore size distributions with most of the porosity occurring at a size much smaller than that of the aggregate. Calcination of metal salt particles or metal hydroxides to produce oxides is another common method to produce internal porosity. In the gas evolution that takes place in transformation to the oxide, pores are opened up in the particle structure. The opening of pores in a hydrous alumina powder can increase its surface area from 0.5 m /gm (its external area) to 450 mVgm (its internal pore area). 

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