Carbon surfaces fractality

The Surface Fractal Investigatioii of Anode Electrode of Molten Carbonate Fuel Cell... 

Van der Waals forces between solid/gas interactions and the liquid/gas surface tension forces represent the limiting cases, but in general both the forces competitively affect the adsorption process. Therefore, in determining the surface fractal dimension of the carbon specimen, it is very important to use appropriate relation between C and dFSF. According to Ismail and Pfeifer,111... 

The Pore Structures and Surface Fractal Characteristics of Meso/Macroporous Carbon Specimens I, n, and III Calculated from the Analyses of the N2 Gas Adsorption Isotherms. Reprinted with permission from G. -J. Lee and S. -I. Pyun, Carbon, 43 (2005) 1804. Copyright 2005, with permission from Elsevier. 

Figure 7 demonstrates on a logarithmic scale the dependence of perimeter P on area A of the pores obtained from the binary TEM image of CAS30 in Figure 6b. The (log P - log A) plots obtained from the carbon specimen displayed two straight lines with different slopes that can be divided into region I and II, indicating multifractal geometiy of the carbon specimen. The individual surface fractal dimensions in regions I and II were determined from Eqs. (26) and (27) to be 2.08 + 0.018 and 2.72 + 0.046, respectively. The transition area Ab from region I to II were determined to be 108 nm2, which corresponds to the pore diameter of 12 nm based upon spherical pore shape.

As a matter of fact, for porous carbon electrode it is still a troublesome issue to relate the determined surface fractal dimension dFss with the CPE exponent a. The effect of the surface inhomogeneity on the ion penetration into the pores during doublelayer charging/discharging will be discussed in detail in the following Section V.3. 

On the other hand, for the microporous carbons with pore size distribution (PSD) with pore fractality, the pore fractal dimensions56,59,62 which represent the size distribution irregularity can be theoretically calculated by non-linear fitting of experimental adsorption isotherm with Dubinin-Astakhov (D-A) equation in consideration of PSD with pore fractality.143"149 The image analysis method54,151"153 has proven to be also effective for the estimation of the surface fractal dimension of the porous materials using perimeter-area method.154"159... 

The observed almost universal value of the surface fractal dimension ds 2.6 of furnace blacks can be traced back to the conditions of disordered surface growth during carbon black processing. It compares very well to the results evaluated within the an-isotropic KPZ-model as well as numerical simulations of surface growth found for random deposition with surface relaxation. This is demonstrated in some detail in [18]. 

For imprinted mesoporous carbons, the overall fractal dimension, determined from gas adsorption data, indicate that these materials are composed of two groups of pores. The surface fractal dimension of the carbonization-induced pores surface and that of the silica-imprinted pores surface has been obtained from TEM image analysis [38]. 

Since the FHH method is relatively simple, it was widely used for determining the surface fractal dimension of several solids, including active carbons [35, 56], aerogels [57], metal films, oxides and related compounds [55]. In particular, Pfeifer and Lui [55] have provided an almost comprehensive review on this topic. Section 6.5 will briefly review applications to soils. 

Xu, W., Zerda, T.W., Yang, H. and Gerspacher, M. (1996). Surface fractal dimension of graphitized carbon black particles. Carbon, 34, 165-171. 

Kano, F., Abe, I., Kamaya, H. and Ueda, I. (2000). Fractal model for adsorption on activated carbon surfaces Langmuir and Freundlich adsorption. Surf. Sci., 467,131-138. 

Tsunoda, R., Ozawa, T. and Ando, J.-I. (1998). Ozone treatment of coal and coffee grounds-based active carbons water adsorption and surface fractal micropores. J. Colloid Interface Sci.,2tt5, 265—270. 

To account for the cathode CL (PEM) transport properties changes induced by carbon corrosion (ionomer degradation) we can use, for example, spatially-averaged fractal representations of the CLs to describe the impact of carbon (ionomer) mass loss on the microstructural properties changes, such as the evolution of the carbon instantaneous surface area or effective diffusion coefficients in the CL. We have used this approach for example ini d68,i79 relate the temporal evolution of the cathode thickness and carbon surface area with the carbon corrosion kinetics, by representing the carbon phase as a two-dimensional Sierpinski carpet projected in the cathode thickness direction (Fig. 11.11). 

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