Polydispersity of primary particles in agglomerates made by coagulation and sintering

The polydispersity of primary particles (PP) in agglomerates is important in a number of applications, including nanocomposites, quantum dots and pigments. A two-dimensional sectional agglomerate and primary particle dynamics (APPD) model for coagulation and sintering is developed conserving the PP number and size distribution once agglomerates are formed. By balancing the complete PP population over all agglomerates, physical and numerical narrowing or broadening of the primary particle size distribution (PPSD) is investigated systematically. Physical narrowing of the PPSD in agglomerates arises by the faster sintering of smaller PP compared to larger ones while numerical narrowing occurs when average PP diameters are employed in the calculation of agglomerate coagulation and sintering. Broadening of the PPSD by numerical diffusion is caused when constant PP spacing is employed, similar to aerosol growth by condensation. Agglomerate and PP dynamics are elucidated during TiO2 formation by detailed two-dimensional (primary and agglomerate) size distributions. The PPSD can become much narrower than the self-preserving size distribution of agglomerates by Brownian coagulation, especially when hard-agglomerates are formed.