Intrinsic Size Effect in Scaffolded Porous Calcium Silicate Particles and Mechanical Behavior of Their Self-Assembled Ensembles

Scaffolded porous submicron particles with well-defined diameter, shape, and pore size have profound impacts on drug delivery, bone-tissue replacement, catalysis, sensors, photonic crystals, and self-healing materials. However, understanding the interplay between pore size, particle size, and mechanical properties of such ultrafine particles, especially at the level of individual particles and their ensemble states, is a challenge. Herein, we focus on porous calcium-silicate submicron particles with various diameters-as a model system-and perform extensive 900+ nanoindentations to completely map out their mechanical properties at three distinct structural forms from individual submicron particles to self-assembled ensembles to pressure-induced assembled arrays. Our results demonstrate a notable "intrinsic size effect" for individual porous submicron particles around ∼200-500 nm, induced by the ratio of particle characteristic diameter to pore characteristic size distribution. Increasing this ratio results in a brittle-to-ductile transition where the toughness of the submicron particles increases by 120%. This size effect becomes negligible as the porous particles form superstructures. Nevertheless, the self-assembled arrays collectively exhibit increasing elastic modulus as a function of applied forces, while pressure-induced compacted arrays exhibit no size effect. This study will impact tuning properties of individual scaffolded porous particles and can have implications on self-assembled superstructures exploiting porosity and particle size to impart new functionalities.