Optimization and validation of a DLS method for nanometric colloidal silica sizing using factorial design

Particle size analysis by dynamic light scattering (DLS) is a fundamental technique for characterizing colloidal systems and nanodispersions. This study presents the development, optimization, and validation of a DLS method for measuring the hydrodynamic diameter ( Z -average) and polydispersity index (PDI) of nanometric colloidal silica. A 2 4−1 fractional factorial design was employed to evaluate the influence of four critical factors: nanosilica suspension concentration, ultrasonication time, rest time after sonication, and equipment equilibration time. Statistical results demonstrated that only the nanosilica concentration had a significant effect on the particle size ( Z -average), indicating that the method is robust regarding the other evaluated parameters. Further optimization of the concentration (ranging from 0.01 to 3.0% v / v ) revealed that excessive dilutions (< 0.1% v / v ) led to an unexpected increase in particle size, likely due to electrostatic destabilization of the suspension. Stable Z -average (~ 19 nm) and PDI values were observed between 0.5 and 3.0% v / v . The difference between the measured hydrodynamic diameter and the nominal particle size of 11 nm can be attributed to the characteristic hydrodynamic shell and minor stable clusters measured by DLS, without compromising method precision. The 1.0% v / v concentration was established as the optimal condition to balance analytical response and sample conservation. The use of factorial design as a tool for robustness and repeatability assessment enabled full method validation, meeting technical requirements in a context where traditional validation parameters—such as linearity, range, and detection limits—are often not applicable to DLS.