Theoretical study on the tendency of heat capacity of nanostructures using modified Debye's method

As one of the most important basic properties of thermal physics, the theoretical study of specific heat capacities impacts numerous fields. With the recent rapid discovery of nanomaterials, the specific heat capacity of nanostructures has attracted more and more attention. In recent years, relevant theoretical explanations continue to grow, but it is undeniable that theoretical models have to keep up with the new discoveries. This paper provides new theoretical approaches to properly scrutinise some of these phenomena. Two modified Debye's models are constructed and investigated, based on the assumptions of simple cubic lattice structures and the lattice vibration of structures under low temperatures (1.5-15 K). While the first model focuses on the limited degree of freedom for nanostructures, the second model retains the trend of Debye's model taking into account the sound velocity under the influence of boundary conditions. We further notify that the first model fits well with the experimental data qualitatively and the second one successfully explains the proportional relationship between the heat capacity of nanostructures of various shapes and sizes, respectively. Hence, these two models can form a basis to stimulate further theoretical developments to come.