Coordination number of disordered packings of identical spheres

Effect of nanoparticle size on the mechanical properties of nanoparticle assemblies

Nanoparticle assemblies (NPAs) have attracted tremendous interests of various research communities. The particle-size-effect on mechanical properties of NPAs is systematically studied. With decreasing the particle size d from 300 nm to 10 nm, the SiO2 NPAs become drastically harder (∼39×), stiffer (∼15×), and tougher (>3.5×). The results are consistent with the data scattered in the literature for various nanoparticle (NP) systems, indicating a fundamentally universal d-effect for all NPAs. A model is developed to correlate the hardness and the NP junction (NPJ) strength f. Here, f is mainly due to van der Waals and capillary interactions, roughly a constant (140 nN) for d = 100-300 nm, and then f decreases with decreasing d from ∼100 nm. The deformation mechanism of NPAs (for indentation depth ≫d) is shear plasticity involving shear breaking of NPJs. The fundamental mechanism for the d-effect is that, with decreasing d, the NPJ's planar density increases much faster than the decrease of f. Moreover, three deformation mechanisms of NPAs, (1) nanoparticle dislodging, (2) shear-band formation, and (3) cracking are naturally d-dependent. These new findings can provide important insights into the fundamental understanding of the inter-NP interaction, the mechanical behavior of the NPAs, and the design of robust NP-based devices.