Colloids fractal

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. 

For compact, homogeneous objects in tliree dimensions, p= 3. Colloidal aggregates, however, tend to be ratlier open, fractal stmctures, witli 3. For a general introduction to fractals, see section C3.6 and [61]. 

Schaefer D W, Martin J E, Wiltzius P and Cannell D S 1984 Fractal geometry of colloidal aggregates Phys. Rev. Lett 52 2371-4... 

Rouw P W and de Kruif C G 1989 Adhesive hard-sphere colloidal dispersions fractal structures and fractal growth in silica dispersions Phys. Rev. A 39 5399-408... 

Avnir D (ed) 1989 The Fractal Approach to Heterogeneous Chemistry Surfaces, Colloids, Polymers (New York Wiley)... 

Perikinetic motion of small particles (known as colloids ) in a liquid is easily observed under the optical microscope or in a shaft of sunlight through a dusty room - the particles moving in a somewhat jerky and chaotic manner known as the random walk caused by particle bombardment by the fluid molecules reflecting their thermal energy. Einstein propounded the essential physics of perikinetic or Brownian motion (Furth, 1956). Brownian motion is stochastic in the sense that any earlier movements do not affect each successive displacement. This is thus a type of Markov process and the trajectory is an archetypal fractal object of dimension 2 (Mandlebroot, 1982). 

Fig. 31. Fractal structures obtained experimentally at different stages of aggregation of a colloidal monolayer of 1 /im sulfonated polystyrene particles on the surface of an aqueous calcium chloride solution, initially uniformly distributed (Robinson and Earnshaw, 1992).

Figure 6.16 shows a clear transition between the low volume fraction response and that at higher volume fractions. Perhaps the major problem with a fractal model is that it underestimates the complexity of colloidal... 

M. Carpineti and M. Giglio Spinodal-Type Dynamics in Fractal Aggregation of Colloidal Clusters. Phys. Rev. Lett 68, 3327 (1992). 

Schmidt, P. W. in The Fractal Approach to Heterogeneous Chemisty Surfaces, Colloids, Polymers Avnir, D. Ed. John Wiley Chichester 1989. 

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... 

Amal, R. Raper, J.A. Waite, T.D. (1990) Fractal structure of hematite aggregates. J. Colloid Interface Sd. 140 158-168 Amal, R. Raper, J.A. Waite, T.D. (1992) Effect of fijlvic add adsorption on the aggregation... 

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... 

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. 

Fig. 36 Self-assembly of DNA-coated colloids observed in optical microscopy, (a) Fractal-like aggregates of microspheres with 14,000 DNA molecules per each sphere, (b, c) Similar colloids with 3,700 DNA/sphere form small crystals, (d) Upon heating by only 2°C, the crystallites and the aggregates both melt into monomers. Adapted with permission from [153]...

P(r) can be transformed into a distribution of the particle size as defined by the hydrodynamic radius Rh. But only for TDFRS, and not for PCS, a particle size distribution in terms of weight fractions can be obtained without any prior knowledge of the fractal dimension of the polymer molecule or colloid, which is expressed by the scaling relation of Eq. (39). This can be seen from the following simple arguments ... 

The behaviour and magnitude of the storage and loss moduli and yield stress as a function of applied stress or oscillatory frequency and concentration can be modelled mathematically and leads to conclusions about the structure of the material.3 For supramolecular gels, for example, their structure is not simple and may be described as cellular solids, fractal/colloidal systems or soft glassy materials. In order to be considered as gels (which are solid-like) the elastic modulus (O ) should be invariant with frequency up to a particular yield point, and should exceed G" by at least an order of magnitude (Figure 14.2). 

In spite of this, the structure of colloidal particles of FWS remains yet hypothesized only. Current model, which is not at variance with known experimental data, intends that FWS contains both single fullerene molecules and their fractal clusters in hydrated state [5],... 

---