Size dependency for the thermal physical properties of nano-sized objects in representation of Hill's nanothermodynamics

TL;DR

This paper develops a method to determine how the thermal physical properties, like specific heat, of nano-sized objects depend on their size using Hill's nanothermodynamics, avoiding the traditional additivity assumption.

Contribution

It introduces a statistical approximation for the volume-dependent factor in Hill's partition sum to model size effects in nanothermodynamics.

Findings

Derived a size-dependent expression for specific heat of nanoparticles.

Established a statistical approach for non-additive thermodynamic properties.

Demonstrated the applicability to Gibbs' free energy in nanoscale systems.

Abstract

We consider the problem of constructing the size dependence for the thermal physical properties of nano-sized objects, taking specific heat as an example. The base methodology is Hill's nanothermodynamics. Having to abstain from use of the additivity concept leads to the problem of building the generalised (Hill's) partition sum on base of the combinatorial statistics averaging. The generalised (Hill's) partition sum includes a volume-dependent factor, for which we construct a statistical approximation. Thence the expression for the size dependence of thermodynamical potential is constructed, taking Gibbs' free energy as an example. Combining the author-introduced size factor and expressions for specific heat allows us to construct size dependence for the specific heat of nano-scaled object (nanoparticle). Keywords: nanoparticles, nanothermodynamics, size dependence, thermal physics, specific heat