Mercury intrusion porosimetry as a quantitative tool for the shape estimation of supraparticles generated via spray-drying

Abstract

Supraparticles are hierarchically structured assemblies of nanoparticles whose size and structural features such as shape, surface roughness, and porosity critically govern their functionality in applications such as energy storage and catalysis. While size and porosity can be measured reliably using established techniques, there is a lack of robust and statistically meaningful methods for assessing supraparticle shape. In this work, we present a novel methodology for estimating supraparticle shape based on mercury intrusion porosimetry (MIP). First, we were able to unravel that the characteristic two-stage intrusion profile of supraparticles corresponds to inter- and intra-supraparticle pores. Then, deconvolution of the MIP pore size distributions enabled separation of these contributions, while assignment of their physical origin was realized by comparison of the extracted intra-supraparticle peaks with the pore size distributions of constituent nanoparticles. By employing a design of experiment that enabled varying supraparticle size and shape independently, we established that the extent of bimodality in MIP pore size distributions is strongly correlated with supraparticle shape. Quantitative shape descriptors obtained from scanning electron microscope-based circularity measurements were compared with statistical metrics of bimodality (Ashman’s D and peak separation) derived from deconvoluted distributions. A clear relationship emerged: supraparticles with higher circularity exhibited more pronounced bimodality, whereas irregular particles showed diminished or poorly resolved bimodal features. This work therefore introduces a statistically reliable approach for simultaneous evaluation of supraparticle porosity and shape, with direct implications for scale up, process optimization and quality control in industrial spray-drying processes.