Small-angle neutron-scattering studies of the fractal-like network formed during desorption and adsorption of water in porous materials

Small-angle neutron scattering (SANS) has been used to study the adsorption and desorption behavior of a ${\mathrm{D}}_2$O/${\mathrm{H}}_2$O water mixture in porous materials. When the porous solid is partially saturated, a feature appears in the scattering having a fractal-like power-law form ${\mathit{Q}}^{\mathrm{-}\mathit{D}}$ (where Q is the scattering wave vector) in the very-low-Q region, extending to below the limit of the instruments used and which covers a maximum range of about one and one-half orders of magnitude in Q. The gradient measured during desorption D, being 1.75±0.1 for porous Vycor glass, 1.85±0.1 for Ludox, and 2.0±0.1 for a silica sol-gel, indicates that the percolation network forms a fractal-like geometry under these conditions. The gradient for adsorption is less than 1.0 for both Vycor and Ludox, and no power-law form of SANS is seen at all for the silica sol-gel. This implies that fractal-like percolation networks are not formed during the adsorption process.