Fractal dimension from Nitrogen

Fig. 11 Surface fractal dimensions ds on atomic length scales of furnace blacks and graphitized blacks in dependence of specific surface. The data are obtained from nitrogen adsorption isotherms in the multilayer regime...

Fractal geometry has been used to describe the structure of porous solid and adsorption on heterogeneous solid surface [6-8]. The surface fractal dimension D was calculated from their nitrogen isotherms using both the fractal isotherm equations derived from the FHH theory. The Frenkel-Halsey-Hill (FHH) adsorption isotherm applies the Polanyi adsorption potential theory and is expressed as ... 

The problem of transfer across a fractal surface has been considered in the electrochemical behavior of rough and porous carbon electrodes [36]. The fractal dimension can be determined from nitrogen gas adsorption data, from transmission electron microscopy (TEM), and nanoscopy image analysis. 

Figure 3. Concentration of nitrogen in the different size classes as a function of time. The maximum particle mass in each size interval is twice that of the smallest particle in the interval. Because of the fractal dimension used to relate mass and length, the maximum radius within a particle size class is 1.38 times the minimum radius. There are 22 size classes in all. Dividing algae compose the smallest size class, with minimum and maximum particle radii of 10 and 13.8 xm. The largest size class has particles with radii ranging from 0.8 to 1.11 cm. The rapidity with which coagulation changes the concentration of the largest particles is evident.

Celts, R., Cornejo, J. and Hermosin, M.C. (1996). Surface fractal dimension of synthetic clay-hydrous iron oxides associations from nitrogen adsorption and mercury porosimetry. Clay Miner., 31, 355-356. 

Sokolowska, Z., Hajnos, M., Hoffmann, Ch., Renger, M. and Sokolowski, S. (2000). Surface fractal dimension of thermally treated peat soils from adsorption isotherms of nitrogen. J. Plant Nutr. Soil ScL, 163, 441 146. 

Notes The specific surface area (in mVg) and the pore volumes (in cmVg) of nanopores (Sna o and at radius for the model of cylindrical pores for LiChrolut EN (or half-width for carbon adsorbents) R<1 nm, mesopores (S eso and V eso) at 1 < / < 25 nm and macropores (5 acro and V acro) at / > 25 nm were determined by integration of the fs(R) and/v(/ ) functions, respectively. The fractal dimension Djj2 and D 2o values were determined from the nitrogen and water adsorption isotherms. The Aw value determines the average error of the model of pores due to roughness of the pore walls. 

Our results show that the scaling behavior reported in Ref. 11 originates in the roughness of the underlying quartz substrate and is not intrinsic to the room temperature silver deposition process. Among the systems which we have studied, The films deposited onto optically polished substrates held at low temperature appear to provide the closest experimental realizations of theoretical deposition models. This is reasonable, since restricted growth can be expected at low temperature. Based on comparisons with x-ray reflectivity measurements, we conclude that the fractal dimension deduced from OUT liquid nitrogen isotherms is accurate to 0.1. 

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