Power-law correlations and finite-size effects in silica particle aggregates studied by small-angle neutron scattering

Small-angle neutron scattering from normal, compressed, and water-suspended powders of aggregates of fine silica particles has been studied. The samples possessed average densities ranging from 0.008 to 0.45 g/${\mathrm{cm}}^3$. Assuming power-law correlations between particles and a finite correlation length ξ, we derive the scattering function S(q) from specific models for particle-particle correlation in these systems. S(q) was found to provide a satisfactory fit to the data for all samples studied. The fractal dimension $d_f$ corresponding to the power-law correlation was 2.61±0.1 for all dry samples, and 2.34±0.1 for the water-suspended samples. The intensity of scattering was found to scale with the correlation length in the manner expected for a fractal system.