Effect of Division Methods of the Adsorption Isotherm on the Fractal Dimension of Clay Minerals Calculated Based on the Frenkel–Halsey–Hill Model

Division of adsorption isotherms is a key step in calculating the fractal dimension of clay minerals based on the Frenkel–Halsey–Hill (FHH) model, which has a great effect on the accuracy of the results. In this study, three pure clay minerals (montmorillonite, illite, and kaolinite) and clay mixtures prepared according to different mass ratios of pure clay minerals were taken as systems. Pore structures of these clay mineral samples were investigated by low-temperature N2 adsorption and CO2 adsorption, and the relationships between the pore structure parameters and the mass ratio of the clay minerals were studied. Three division methods were applied, that is, adsorption isotherms divided by the starting point of the hysteresis loop (method I), by the extreme point of the first derivative of adsorption isotherms (method II), and by linearity regions according to FHH linear fitting data (method III), to divide the N2 and CO2 adsorption isotherms into one or two regions. Fractal dimension values were calculated from different isotherm regions using the FHH model. The linear degree of fractal dimension values and the specific surface area were taken as criteria to judge the rationality of fractal dimensions. The results show that the specific surface area and the micropore volume of clay mixtures with less illite can be predicted based on the mass ratio and pore parameters of pure clay minerals. Fractal dimension values calculated from the low relative pressure stage of N2 adsorption isotherms using method III could give accurate fractal dimension values. As for the CO2 adsorption isotherm, although fractal dimension values obtained from its high relative pressure stage using method III show a good linear relationship with the specific surface area, the fractal dimension values are not between 2 and 3.