Experimental Determination of Particle Size-Dependent Surface Charge Density for Silica Nanospheres

Surface charge densities of spherical silica nanoparticles of varied size spanning from 4.1 to 495.7 nm in NaCl solution with a concentration from 0.003 to 1.2 mM at a pH value of 8.0 were determined by converting their corresponding measured zeta potential with Poisson-Boltzmann model. The magnitude of the derived surface charge density (negative) at a given NaCl concentration of 0.225 mM decreases monotonically with the increasing particle size and reaches almost a steady value when the size exceeds 30 nm, revealing clearly the effect of the nanoparticle curvature on the surface charge density. The experimental data provide a consensus for the validity of different models describing the relation between the surface charge density and the electric potential, that is, the surface complexation model and the Poisson-Boltzmann model for the charged nanospheres in electrolyte solution. We found that if the former includes the curvature-dependent deprotonation constant of the surface silanol groups, both models would give a consistent result.