Determination of fractal dimensions of solid carbons from gas and liquid phase adsorption isotherms

The total surface area, micropore volume, and fractal dimensions of five different carbons (Sorbonorite 4, GAC 1240, and three amorphous carbons) were evaluated from analysis of gas (N2) and liquid (phenanthrene) adsorption isotherm data. The modified BET and fractal Frenkel–Halsey–Hill (FHH) models were used to estimate surface fractal dimensions. Micropore volumes were estimated from Dubinin–Radushkevich (DR) plots and were compared to those calculated from standard N2 adsorption isotherm data using de Boer’s t-method. The estimated surface fractal dimensions using the modified BET and FHH models (DS=3+3h, and P/P0 from 0.0 to 0.4) were (2.7, 2.6, 2.1, 2.4, and 2.1) and (2.5, 2.6, 1.9, 2.4, and 1.9), respectively. The FHH fractal analysis suggested that van der Waals forces are the dominant interaction forces between nitrogen and carbon surfaces. Depending on the method of analysis, the fractal dimensions of the carbons with suggested micropore structure, Sorbonorite 4 and GAC 1240, were 2.5–2.9 and 2.6–2.9, respectively. Analysis of the adsorption–desorption data suggested that amorphous carbons with fractal dimensions of 2.1 (from the modified BET model) have smooth surfaces, with respect to their micropore structure. Further analysis of the adsorption data showed that the slopes of the linear segment of the plots of adsorption potential versus relative amount adsorbed are dependent on the pore size range and surface structure (fractal dimension) of the carbons.