The Young’s Modulus of Nanomaterials: Size Effect

Abstract

Purposes The Young’s moduli of nanomaterials are completely different from these of their bulk counterparts, and the size effect on Young’s modulus is greatly obvious. Moreover, the change trend of Young’s modulus with size is complicate. With size dropping, the Young’s moduli of some metallic nanomaterials increase, while they decrease for some semiconductor nanomaterials. However, the reason why size effect on the Young’s modulus of nanomaterials varies, is still unclear. Methods In this study, on the basis of the thermodynamic theory and cohesive energy of nanomaterials, a theoretical model for the size-dependent Young’s modulus of nanomaterials is deduced. In this model, the inherent relationship between atomic potential and the Young’s modulus is taken into account, and material coefficient that directly reflects the bond nature in a material is introduced. The established model can well explain the change trend of Young’s modulus with size for metallic and nonmetallic materials, and also discover the contributions of surface modulus and interior modulus for the Young’s modulus in a nanomaterial. Simultaneously, the physical mechanism of relationship of Young’s modulus with size or atomic bond is explained. Conclusions The predictions for the Young’s moduli of zero-dimensional nanoparticles, one-dimensional nanowires, and two-dimensional nanofilms are obtained by analyzing the established theoretical model in this study.

Keywords

• nanomaterials
• young’s modulus
• size effect
• thermodynamic
• cohesive energy