Fractal surface structures

Ramadan, M.A. Tawashi, R. Effects of surface geometry and morphic features on the flow characteristics of microspheres suspensions. J. Pharm. Sci. 1990, 79 (10), 929-932. Suzuki, T. Yano, T. Fractal surface structure of food materials recognized by different molecules. Agric. Biol. Chem. 1991, 55 (4), 967-971. 

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... 

The original substrate structure used for our early photosensitization experiments was a fractal surface derived by hydrolysis of an organo-titanium compound, but this has since been replaced with a nanostructured layer deposited from a colloidal suspension of TiOi. This evidently provides for a much more reproducible and controlled high-surface-area nanotexture. Further, because it... 

The behaviour of surface reaction is strongly influenced by structural variations of the surface on which the reaction takes place [23], Normally theoretical models and computer simulations for the study of surface reaction systems deal with perfect lattices such as the square or the triangular lattice. However, it has been shown that fractal-like structures give much better description of a real surface [24], In this Section we want to study the system (9.1.39) to (9.1.42). 

In the context of particle aggregation, the particular fractal structures called mass fractals are usually considered. Mass fractals correlate the location of mass with radius, as opposed to other types of fractal constructs such as boundary fractals, surface fractals, and pore fractals (see Ref. 17). The power law which correlates the size of an aggregate with the number of primary particles in the aggregate is given by... 

In order to complete the study of the structural differences in xerogels with various additive concentrations, fractal analysis has been performed on nitrogen adsorption-desorption data. The generalisation of the classical Frenkel-Halsey-Hill (FHH) equation [6,7] to fractal surfaces has been used. In this approach a film thickness of more than 1.5 layers, is used to probe the geometry of the surface. It describes the multilayer coverage of a fractal structure by the equation [7] ... 

Ozeki, S. 1985. Estimation of pore and surface structures of sohds by dye adsorption The preadsorption method and fractal analysis. Langmuir 5, 186-191. 

Many industrial adsorbents and catalysts exhibit fractal properties in their surface structure over a given range of lengthscales [1]. The surface roughness influences both thermodynamic, kinetic and transport properties. 

Fractal analysis allows consideration of the surface structure of the filler particles, which are characterised by its fractal dimension (d ) and by the self-similarity interval. Because the polymer structure is also described in the framework of the fractal analysis, it becomes possible to consider the interaction between the filler surface and polymer matrix, including the interfacial layers, based on the analysis of their fractal dimensions. Application of the model of irreversible aggregation allows description of the processes of aggregation of the filler particles in a particulate filled composites. This aggregation causes changes... 

Pemyeszi, T Dekany, I. Surface fractal and structural properties of layered clay minerals monitored by small-angle X-ray scatterin and low-temperature nitrogen adsorption experiments. Colloid Polymer Sci. 2003, 281 (1), p. 73-78. 

Wool [57,78] suggests that these principles could be used to develop pretreatments which give a highly ramified, fractal surface to which high adhesion by mechanical interlocking would be expected. Consider a blend of polyethylene with a second phase, perhaps starch, amenable to removal by selective attack or dissolution. Above a critical concentration some of the second phase particles will be connected, forming a fractal structure. Treatment of the polyethylene surface, then, will leave fractal voids, receptive to an adhesive, such as a liquid epoxy resin. 

It can be knovm from Fig. 3 that, in a certain coal particle size, the number of holes inside coal particles increase with the decrease of coal particle size. Besides, with the decrease of coal particle size, the pore structure become more and more complex, and the heterogeneity of pore distribution of coal particles is stronger, moreover, the surface structure of coal particles also tends to become complex, indicating that the surface of coal particles become more rough. As a result, the fractal dimension of coal particles increases to be more and more close to 3, which conclusion is similar to literature (Jiang Xiumin et al. 2003). There is a simple linear relationship between the two ... 

The fate of nuclei is partiele eoagulation, a process in which small particles (assumed to be spherical) collide with each other and coalesce completely to form larger spherical particles. Small particles are indeed spheroidal and the assumption of spherical particles seems to be reasonable (Mitchell and Frenklach 2003, Balthasar et al. 2005). After a certain size, however, the partieles cannot coalesce completely and start to form long chains, which eventually grow into three-dimensional fractal-like structures. Fig. 4.15 shows the new partiele formation and growth pathways. A great role is played by the surface coating of primary hydrophilic soot... 

At present it is known [1] that the majority of catalytic systems are nanosystems. At the heterogeneons catalysis active substance one tries to deposit on the bearers in a nanoparticles form in order to increase their specific surface. At homogeneous catalysis active substance molecules by themselves have often nanometer sizes. It is known too [2] that the operating properties of heterogeneous catalyst systems depend on their geometry and structure of the surface, which can influence strongly on catalytic properties, particularly, on catalysis selectivity. It has been shown experimentally [3] that the montmoril-lonite surface is a fractal object. Proceeding from this, the authors [4] studied the montmorillonite fractal surface effect on its catalytic properties in isomerization reaction. 

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