Several notes on the elastic properties of mesoporous materials

Abstract

In this paper, the dependence of the Young’s elastic modulus of a mesoporous material on the geometric characteristics (volume and shape) of pores has been analyzed. The geometric characteristics of pores have been determined in the framework of the fractal-geometry approach by the values of their effective diameter and fractal dimension. The presented estimates demonstrate that the effect (being characteristic of nanoscale particles), which consists a significant dependence of elastic moduli on the size and shape of a particle, can also be realized in mesoporous materials (the pore size being form 5 up to 50 nm) while the mesoporous samples themselves can be of macroscopic dimensions. Using the example of mesoporous silver, it has been shown that reducing the pore size and «complicating» the pore shape lead to a significant decrease in the Young’s elastic modulus. The results have been obtained in the framework of the cohesive energy-based model.

Keywords

• elastic modulus
• mesoporous materials
• fractal dimension
• cohesion
• size distributions
• hardy-ramanujan-rademacher formula