Experimental study of multilayer adsorption on fractal surfaces in porous media

We report a nitrogen adsorption isotherm study on three shale samples that have been previously characterized by small-angle neutron scattering (SANS). The scattering data establish that the pore surfaces in these porous materials are self-similar fractals over a range of length scales between 5 and 500 Å, and the fractal dimension D varies between 2.59 and 2.83. For isothermal adsorption of multilayer liquid film on fractal surfaces, the theoretical predictions are (i) the number of adsorbed molecules N increases with the vapor pressure P as N∼[ln(P₀/P)]^D-3 and (ii) the area of the liquid-vapor interface S_I decreases as S_I∼[ln(P₀/P)]^D-2. We find that fitting our data to these predictions results in D values that are significantly lower than the SANS results. More careful examination of the data reveals systematic deviations from the predicted power-law behaviors. We discuss the assumptions and approximations made in the theories that could have caused this discrepancy.