Colloids self-similar

Weitz D A and Huang J S 1984 Self-similar structures and the kinetics of aggregation of gold colloids Kinetics of Aggregation and Geiationed F Family and D P Landau (Amsterdam North-Holland) pp 19-28... 

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. 

This section was published originally in a chapter entitled Similarities in self-assembly of proteins and surfactants An attempt to bridge the gap, by Erik van der Linden and Paul Venema, in Food Colloids, Self-Assembly and Material Science, Eds. E. Dickinson, and M.E. Leser, published by Royal Society of Chemistry, Cambridge, UK ISBN 9780854042715. Reproduced here with permission. 

Figure 19.2 Self-similarity analysis for nanotextured silver surfaces prepared in different ways. The root mean square roughness inferred from atomic force microscopy is plotted versus measurement area. The various surfaces are 100 nm thick evaporated silver films (solid squares, red line)-, 5.2 nm thick evaporated silver films (open circles, green line) nanoparticle films assembled from colloid attachment to self-assembled monolayers (solid circles, blue line) films from deliberate precipitation of silver colloid (solid up-triangles, black line) Tollens reaction films (open down-triangles, orange line). Lines with slopes H = 1.0 and H = l.S representing two-dimensional and 1.5 dimensional surfaces respectively are...

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 ... 

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. 

Rogak, S.N. and Flagan, R.C. (1990). Stokes drag on self-similar clusters of spheres. J. Colloid Interface Sci., 134, 206-218. 

Processes in nature often result in fractal-like forms that differ from the mathematical fractals such as the Koch curve in two ways (a) the self-similarity is not exact but is a congruence in a statistical sense and (b) the number of repeated splittings is finite and random fractals have an upper and a lower cutoff length. A spatial example of a random fractal is the colloidal gold particle agglomerate shown earlier in Figure 7.4. 

Self-similar behavior has also been observed in computer simulation of aggregation processes. Thus aggregates of colloidal particles in diffusion-limited aggregation processes have been found to display self-similar behavior (Meakin, 1983). 

The preemulsified carriers contain water. These products usually require homogenization through colloidal mills or similar equipment to reduce the particle size and ultimately stabilize the product. The preemulsified as well as the clear self-emulsifying products require the use of a solvent when the carrier-active material is a soHd. 

The UV-visible spectrum (Fig. 6) of the aggregates described earlier shows a 0.25-eV shift toward lower energy of the plasmon peak with a slight decrease in the bandwidth (0.8 eV) compared to that observed in solution (0.9 eV). As observed earlier with monolayers, by washing the support, the particles are redispersed in hexane and the absorption spectrum remains similar to that of the colloidal solution used to make the self-assemblies. 

Experiments on interactions of polysaccharides with casein micelles show similar trends to those with casein-coated droplets. For example, Maroziene and de Kruif (2000) demonstrated the pH-reversible adsorption of pectin molecules onto casein micelles at pH = 5.3, with bridging flocculation of casein micelles observed at low polysaccharide concentrations. In turn, Tromp et al. (2004) have found that complexes of casein micelles with adsorbed high-methoxy pectin (DE = 72.2%) form a self-supporting network which can provide colloidal stability in acidified milk drinks. It was inferred that non-adsorbed pectin in the serum was linked to this network owing to the absence of mobility of all the pectin in the micellar casein dispersion. Hence it seems that the presence of non-adsorbed pectin is not needed to maintain stability of an acid milk drink system. It was stated by Tromp et al. (2004) that the adsorption of pectin was irreversible in practical terms, i.e., the polysaccharide did not desorb under the influence of thermal motion. 

The fact that positive ions migrate toward the cathode and negative ions migrate toward the anode is so well known as to be virtually self-evident. It seems equally evident, therefore, that positively and negatively charged colloidal particles should display similar migrations. Indeed, this is the case. Because we are relatively familiar with the conductivity of simple electrolytes, we start our discussion of electrokinetic phenomena with a comparison of the mobilities of the particles in the small ion and macroion size domains. 

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