NMR determination of the fractal dimension in silica aerogels

${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$ 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 ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$ magnetization follows a power law in a very large time range (up to 5 orders of magnitude). This nonexponential relaxation m(t)∼${\mathit{t}}^{\mathrm{\alpha }}$ reflects the mass distribution in the sample: M(r)∼${\mathit{r}}^{\mathit{D}}$ 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.