Pore fractal dimension

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. 

Soil Fraction % Organic Matter PZC Pore Diameter (nm) % Surface Area in <10-nm Pores Fractal Dimension"6 ... 

There are two conventional definitions in describing the fractality of porous material - the pore fractal dimension which represents the pore distribution irregularity56,59,62 and the surface fractal dimension which characterizes the pore surface irregularity.56,58,65 Since the geometry and structure of the pore surfaces are closely related to the electro-active surface area which plays a key role in the increases of capacity and rate capability in practical viewpoint, the microstructures of the pores have been quantitatively characterized by many researchers based upon the fractal theory. 

On the other hand, it is impossible to apply the SP method to the correct description of gas adsorption in the micropores, since the adsorption in the micropores does not occur by multilayer adsorption but by micropore volume filling process. In this case, the pore fractal dimension gives a physical importance for the description of structural heterogeneity of the microporous solids. Terzyk et al.143"149 have intensively investigated the pore fractal characteristics of the microporous materials using gas adsorption isotherms theoretically simulated. 

Apore.sp Pore fractal dimension determined by using the... 

Sample Bulk density (g cmO Porosity (%) Pore density (tnm ) Average cross-sectional area (pm ) Roundness of pores Fractal dimension... 

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

Pore fractal dimension detemuned by using the single-probe method using gas adsorption Surface fractal dimension... 

Figure 1.1 A fractal structure overlaid by a grid of squares. In three dimensions the squares are replaced by boxes. Surface, mass and pore fractal dimensions can be estimated by counting the number of squares occupied by the object. Two-dimensional images of three-dimensional objects do not contain the full information about the object, so fractal dimensions of three-dimensional objects need to be estimated in three dimensions [11]. Reproduced with permission of John WUey Sons, Ltd.

Fractal analysis cannot be applied indiscriminately. For the values that are obtained to be mechanistically valid, comparisons must be made among similar measurements of fractal dimensions (e.g. mass, surface or pore fractal dimensions) that are made using a single given analytical technique or techniques based upon similar analytical principles. Future research is required to better relate measurements that are performed in different manners and indeed to better understand the limitations of the fractal measurements. Nonetheless, the majority of future research in the field will necessarily be focused upon applying established determinations of fractal dimensions to understanding the physicochemistry of complex (i.e. natural) systems better (e.g. Chapters 4-9 [32-35, 39, 40]). 

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