A nanomaterial equation of state has been combined with Grüneisen approximation in present work to investigate the influence of high pressure on phonon density of state function of C60 through evaluating variations of lattice vibration frequencies and variation of mode density. Furthermore, the effect of high pressure on Debye temperature has been determined by using a formula of volume dependence of Debye temperature. Volume compression ratio in C60 has been computed, using a nanomaterial equation of state. Expressions of pressure dependence of phonon density of state and Debye temperature have been combined with volume compression ratio value. The evaluated result of volume compression ratio and phonon density of state have been compared with the experimental observations and good agreement can be seen.

Surface effect and crystal structure lead to formulating a theoretical model to study the influences of size on thermodynamic parameters, such as melting temperature, Debye temperature, melting entropy and specific heat capacity, of nanoparticles. The cohesive energy as a thermodynamic quantity was used to relate the ratio of surface area to volume of nanomaterial with thermodynamic properties which depend on size of the nanomaterial. In this contribution, Si and Au nanoparticles were considered to study due to their potential applications in science and technology. It was found that melting temperature, Debye temperature, melting entropy of nanoscale size material is decreased with decreasing the size up to their critical sizes. Whereas, the specific heat capacity tends to enhance with reduction in nanoparticle size. The present results for melting temperature, melting entropy and Debye temperature are compared with experimental and theoretical observations and adequate agreements are observed.