Colloidal fractal nature

There are some very special characteristics that must be considered as regards colloidal particle behavior size and shape, surface area, and surface charge density. The Brownian motion of particles is a much-studied field. The fractal nature of surface roughness has recently been shown to be of importance (Birdi, 1993). Recent applications have been reported where nanocolloids have been employed. Therefore, some terms are needed to be defined at this stage. The definitions generally employed are as follows. Surface is a term used when one considers the dividing phase between... 

Walstra, P., van Vliet, T., Bremer, L.G.B. (1991). On the fractal nature of particle gels. In Dickinson, E. (Ed.). Food Polymers, Gels and Colloids, Cambridge, UK Royal Society of Chemistry, pp. 369-382. 

Vreeker, R., L.L. Hoekstra, D.C. den Boer, and W.G.M. Agterof, The Fractal Nature of Fat Crystal Networks, in Food Colloids and Polymers Stability and Mechanical Properties, edited by E. Dickinson and P. Walstra, The Royal Society of Chemistry, Cambrige, 1993, pp. 16-30. 

P. Walstra, T. van Vliet, L. G. B. Bremer. On the fractal nature of particle gels. In E. Dickinson, ed. Food Polymers, Gels, and Colloids. Royal Soc. Chem., Cambridge, 1991, p. 369. 

Grout et al. (1998) question the description of natural samples by simple power laws. According to these authors natural systems are often multifractal which means the fractal dimension varies for different size scales. Veerapaneni and Wiesner (1997) studied the effect of filtration velocity on the fractal dimension of deposits formed by 69 nm colloids. Fractal dimensions increased with increased velocities where a lower head loss was measured, this was attributed to columnar structures formed. 

Farin, D. and Avnir, D. (1989). The fractal nature of molecule-surface interactions and reactions. In The Fractal Approach to Heterogeneous Chemistry Surfaces, Colloids, Polymers, Avnir, D. (ed.). John Wiley Sons, Ltd, New York, p. 271. 

Tang, S., Mar, Y. and Sebastine, I.M. (2001). The fractal nature of Escherichia coli biological floes. Colloids Surf. B Biointerfaces, 20, 211-218. 

Bremer, LGB, BH Bijsterbosch, R Schrijvers, T van VUet, P Walsira. (1990). On the fractal nature of the structure of casein gels. Colloids Surf 51 159—170. 

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. 

Kerker, M. et ah. Determination of particle size by the minima and maxima in the angular dependence of the scattered light. Range of validity of the method, J. Colloid Set, 19, 193-200, 1964. Mandelbrot, B., The Fractal Geometry of Nature, Freeman, San Franciso, CA, 1983. 

Aggregating Particles. Repulsive colloidal interaction forces between particles hardly affect sedimentation, but the effect of attractive forces can be very strong. Aggregates naturally sediment faster than single particles. Fractal aggregates containing N particles tend to move faster than... 

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. 

In nature, ordered colloidal systems are unusual for two reasons. First, large scale lattices require monodispersity of the individual particle units within the lattice. Second, both diffusion limited aggregation and reaction limited aggregation in solution produce fractal structures rather... 

Shamurina, M. V. Roldugin, V. I. Pryamova, T. D. Visotskii, V. V. Aggregation of colloidal particles in curing systems. Colloidal Journal, 1994,56(3), 451-454. Naphadzokova, L. Kh. Kozlov, G. V. Fractal Analysis and Synergetics of Catalysis in Nanosystems. Moscow, Publishers of Academy of Natural Sciences, 2009,230. Rammal, R. Toulouse, G. Random walks on fiactal structures and percolation clusters. J. Phys. Lett. (Paris), 1983,44(1), L13-L22. 

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