On Fracton Model of Thermal Properties of Nanostructures

A model of heat capacity of self-similar structures is considered on the basis of fracton representation of local movements of atom groups. The governing temperature dependences of Helmholtz free energy, thermal energy and heat capacity of the system are obtained which are analogous to those of Debye theory of crystal heat capacity. Limiting cases of the obtained dependences are analyzed as well as conditions of the heat balance of homogenous nanostructures of fractal dimension (with zero connectivity). A single stable structure is found for the homogenous fractal with zero connectivity.