Correlation of Secondary Particle Number with the Debye–Hückel Parameter for Thickening Mesoporous Silica Shells Formed on Spherical Cores

Mesoporous silica shells were formed on nonporous spherical silica cores during the sol–gel reaction to elucidate the mechanism for the generation of secondary particles that disturb the efficient growth of mesoporous shells on the cores. Sodium bromide (NaBr) was used as a typical electrolyte for the sol–gel reaction to increase the ionic strength of the reactant solution, which effectively suppressed the generation of secondary particles during the reaction wherein a uniform mesoporous shell was formed on the spherical core. The number of secondary particles (N2nd) generated at an ethanol/water weight ratio of 0.53 was plotted against the Debye–Hückel parameter κ to quantitatively understand the Debye screening effect on secondary particle generation. Parameter κa, where a is the average radius of the secondary particles finally obtained in the silica coating, expresses the trend in N2nd at different concentrations of ammonia and NaBr. N2nd was much lower than that expected theoretically from the variation of secondary particle sizes at a constant Debye–Hückel parameter. A similar correlation with κa was observed at the high and low ethanol/water weight ratios of 0.63 and 0.53, respectively, with different hydrolysis rate constants. The good correlation between N2nd and κa revealed that controlling the ionic strength of the silica coating is an effective approach to suppress the generation of secondary particles for designing mesoporous shells with thicknesses appropriate for their application as high-performance liquid chromatography column packing materials.