Highly porous layers of silica nano-spheres sintered by drying: Scaling up of the elastic properties from the beads to the macroscopic mechanical properties

TL;DR

This study compares homogenization and Kendall's models to predict the elastic properties of silica nano-sphere layers, finding homogenization accurate below 35% porosity and Kendall's model effective across all porosities, revealing covalent bonding during drying.

Contribution

It demonstrates the effectiveness of homogenization schemes for elastic predictions in nano-porous silica layers and links Kendall's adhesion parameter to particle fracture energy.

Findings

Homogenization accurately predicts bulk and shear moduli below 35% porosity.

Kendall's approach fits the entire porosity range for Young's modulus.

Adhesion energy aligns with particle fracture energy, indicating covalent bonding.

Abstract

Layers obtained by drying a colloidal dispersion of silica spheres are found to be a good benchmark to test the elastic behaviour of porous media, in the challenging case of high porosities and nano-sized microstructures. Classically used for these systems, Kendall's approach explicitely considers the effect of surface adhesive forces onto the contact area between the particles. This approach provides the Young's modulus using a single adjustable parameter (the adhesion energy) but provides no further information on the tensorial nature and possible anisotropy of elasticity. On the other hand, homogenization approaches (e.g. rule of mixtures, Eshelby, Mori-Tanaka and self-consistent schemes), based on continuum mechanics and asymptotic analysis, provide the stiffness tensor from the knowledge of the porosity and the elastic constants of the beads. Herein, the self-consistent scheme accurately predicts both bulk and shear moduli, with no adjustable parameter, provided the porosity is less than 35%, for layers composed of particles as small as 15 nm in diameter. Conversely, Kendall's approach is found to predict the Young's modulus over the full porosity range. Moreover, the adhesion energy in Kendall's model has to be adjusted to a value of the order of the fracture energy of the particle material. This suggests that sintering during drying leads to the formation of covalent siloxane bonds between the particles.