Porous fractals

The selectivity and deactivation processes in pore fractals such as the Sier-pinski gasket were simulated by Gavrilov and Sheintuch (1997) and Sheintuch (1999). Their studies investigated, e.g., the effect of the fractal pore structure on the selectivity of a system that incorporates two parallel reactions. Geometrical factors, which influence dynamic processes in a porous fractal solid media, were also investigated by Garza-Lopez and Kozak (1999). 

STM has also been applied to the characterization of porous fractals. Thus, an investigation of a series of activated carbons prepared from olive stones STM and other techniques allowed Pfeifer et al. [16] to document the first case of a jfflre fractal (i.a, such carbons hosted an extended fractal network of pores). As expected from stich a structure where most channels are deep inside the solid and invisible ft-om the outside, only sparse entrances about 1.3 nm wide were observed by STM on the surface of such materials (white arrow in Fig, 5) the STM image also shows little external roughness, as could be expected. 

Melnichenko, Y. B., H. Mayama, G. Cheng, and T. Blach. 2010. Monitoring phase behavior of sub- and supercritical COj confined in porous fractal silica with 85% porosity. Langmuir 26 6374-6379. 

In the non-densified xerogels, the Raman spectra show a relatively sharp band centered at about 16 cm , for the xerogel with % = 800°C, and at about 18 cm, for the xerogel with % = 860°C. In the samples treated below 800°C, it is not possible to observe the low frequency bump. The strong quasi-elastic scattering is due to vibrational dynamics of the porous fractal-like system, but probably also to residual water inside the pores. The low frequency bumps are attributed to surface vibrations of the particle-pore structure. The peak frequency increases with the annealing temperature, as the mean pore size, measured by SAXS experiments, decreases (see Raman Spectroscopy ofNanocrystals ). The Raman... 

Size Exclusion Chromatography and Surface Effects in Porous Fractals 137... 

SIZE EXCLUSION CHROMATOGRAPHY AND SURFACE EFFECTS IN POROUS FRACTALS... 

Depletion and size exclusion chromatography Here we take the walls of the porous fractal to be repulsive the macromolecules are repelled from the solid surface. A "depletion layer of size = / surrounds the fractal depletion can detect fractality. 

Adsorbed polymer chains (Dp = 5/3) (Fig. 4) The porous fractal is exposed to a dilute polymer solution. This case is studied in detail in ref. (19). For polymer adsorbed by a planar surface, de Gennes pointed out that the profile is selfsimilar and given by the simple law... 

We estimate Kd for a column packed with a porous fractal material. In our notation, Vi PL and from Eq. (23)... 

De Gennes has studied the capillary condensation for the two strictly seifsimilar porous fractals iterative pits and iterative floes shown in Fig. 2 A,B. 

IV.3 Conclusions One could test the above prediction by using large aggregates made of colloidal particles of size a - 1000 A to 10 pm or surface porous fractals. However, the situation is complicated by two effects ... 

For charged porous fractals, we have shown that depletion of counterions and capacitance measurements may lead to a simple derivation of D.. For dilute aggregates, the electrophoretic mobility should be sensitive to the fractal dimension only if the charge per grain (or per monomer) is maintained during aggretation. 

Fig. 1.2 The porous (fractal) surface of TiN electrode enlarges the surfece area the fractal structure is visible at the bottom. The picture is from Multi Channel Systems GmbH, with permission...

We have considered briefly the important macroscopic description of a solid adsorbent, namely, its speciflc surface area, its possible fractal nature, and if porous, its pore size distribution. In addition, it is important to know as much as possible about the microscopic structure of the surface, and contemporary surface spectroscopic and diffraction techniques, discussed in Chapter VIII, provide a good deal of such information (see also Refs. 55 and 56 for short general reviews, and the monograph by Somoijai [57]). Scanning tunneling microscopy (STM) and atomic force microscopy (AFT) are now widely used to obtain the structure of surfaces and of adsorbed layers on a molecular scale (see Chapter VIII, Section XVIII-2B, and Ref. 58). On a less informative and more statistical basis are site energy distributions (Section XVII-14) there is also the somewhat laige-scale type of structure due to surface imperfections and dislocations (Section VII-4D and Fig. XVIII-14). 

Obviously, the diffusion coefficient of molecules in a porous medium depends on the density of obstacles that restrict the molecular motion. For self-similar structures, the fractal dimension df is a measure for the fraction of sites that belong... 

Nevertheless, fractal structure is an issue in porous materials. 

Su-Il Pyun provide a comprehensive review of the physical and electrochemical methods used for the determination of surface fractal dimensions and of the implications of fractal geometry in the description of several important electrochemical systems, including corroding surfaces as well as porous and composite electrodes. 

Since Avnir and Pfeifer s pioneer works83"86 regarding the characterization of the surface irregularity at the molecular level by applying the fractal theory of surface science, the molecular probe method using gas adsorption has played an important role in the determination of surface fractal dimension of the porous and particulate materials. 

In practical application, it was reported that the platinum particles dispersed in highly porous carbonized polyacrylonitrile (PAN) microcellular foam used as fuel-cell electrocatalyst160 have the partially active property. The fractal dimension of the platinum particles was determined to be smaller than 2.0 by using the potentiostatic current transient technique in oxygen-saturated solutions, and it was considered to be a reaction dimension, indicating that not all of the platinum particle surface sites are accessible to the incoming oxygen molecules. 

Porous materials have attracted considerable attention in their application in electrochemistry due to their large surface area. As indicated in Section I, there are two conventional definitions concerning with the fractality of the porous material, i.e., surface fractal and pore fractal.9"11 The pore fractal dimension represents the pore size distribution irregularity the larger the value of the pore fractal dimension is, the narrower is the pore size distribution which exhibits a power law behavior. The pore fractal dimensions of 2 and 3 indicate the porous electrode with homogeneous pore size distribution and that electrode composed of the almost samesized pores, respectively. 

Besides the molecular probe method using gas adsorption,107 162 recently, the TEM image analysis method163"167 has been applied to evaluate the surface fractal dimension of porous materials. The most attractive fact in this method is that the pores in different size ranges can be extracted from the TEM images which include contributions from many different pore sizes by the inverse fast Fourier transform (FFT) operation by selecting the specific frequency range.165 167... 

Restricted media and fractals. Morphology of porous solids. Determination of dimensionality. 

Lee et al. s study also investigates the hydrophilicity of the heterocatalyst. They mention that the highly acidic surface of the material is more hydrophobic than the pure titanium oxide surface. They theorize that this is because the acidic surface results in fewer adsorbed OH ions and thus a weaker interaction with water. As expected, this increased hydrophobicity leads to an increase in the stability of dispersions of nanoscale powders of this material. Saltiel et al. showed that WOs-coated titanium oxide powders were much more stable than their uncoated counterparts. Even after agglomeration, the agglomerates of the coated powders were more porous than those of pure titanium oxide (the coated powders had a fractal dimension of 1.55 while the pure titanium oxide powders had a fractal dimension of 1.60). 

While chemically modified electrodes are excellent for stopping side reactions, they tend not to possess smooth continuous layers but, rather, they are often porous or so rough as to be virtually three-dimensional (Figure 5.5). The electrode surface is often said to be fractal for this reason. 

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