Truncated fractal modeling of H2O-vapor adsorption isotherms

Adsorbent-adsorbate interaction in fractal surfaces is complicated but important in soil science. The main objectives of the present work were (i) to test a truncated version of the Frankel-Halsey-Hill (FHH) model with experimental H2O-vapor adsorption data, (ii) to describe, analytically, the space filling of H2O-vapor as a function of the fractal dimension and (iii) to search for potential relationships between fractal parameters and different available soil physical and chemical attributes. We used 48 H2O-vapor adsorption isotherm data sets corresponding to light, medium and heavy alluvial soils. The truncated model fitted experimental data quite well (R2 > 0.98 in most cases) within the entire data range. Surface fractal dimensions (Ds) ranged from 2.18 to 2.97. This allowed us to estimate a lower bound for water adsorption while a new estimate of monolayer capacity was also considered. The surface filling was larger for higher Ds values. Model parameters correlated positively with CEC, specific surface area, clay and sand fractions. All the Ds values estimated from the truncated model were larger than those computed from its classical fractal FHH counterpart. This could mean that, while the classical FHH model is sensitive to the multilayer geometry, our truncated FHH version could be related to the monolayer geometry and the adsorbent fractal surface.