NMR determination of the fractal dimension in silica aerogels

²⁹Si nuclear relaxation experiments were performed in different forms of silica (alcogel, aerogel, amorphous, and crystallized) doped with paramagnetic impurities. Magic-angle spinning is used to quench the nuclear-spin diffusion. Under this condition, the saturation recovery of the ²⁹Si magnetization follows a power law in a very large time range (up to 5 orders of magnitude). This nonexponential relaxation m(t){~}t^α reflects the mass distribution in the sample: M(r){~}rD with {α}=D/6. In aerogels, the measured fractal dimension D{}2.2 is in agreement with that determined by small-angle x-ray scattering. In densified materials, a dimension D{}3 is actually observed.