Size effects in energy transport between thermal contacts mediated by nanoparticles

We investigate size effects in phononic energy transport in a system of two nanoparticles interconnected by a molecule and attached to thermal contacts also by molecules. In the considered closed system, the nanoparticles and contacts are described by ensembles of finite numbers of harmonic oscillators within the Drude-Ullersma model. The macroscopic character of the contacts is simulated by a large value of the ratio Δ/Δ_{B}=n (n>100) of mode spacings Δ and Δ_{B} corresponding to the nanoparticles and contacts, respectively. Quasistatic energy transport on the timescale Δ^{-1} is investigated. Equations describing the dynamics of the averaged eigenmode energies that belong to the nanoparticles and contacts are derived and solved. The resulting expressions for the energy current exiting (entering) the contacts as well as the energy current between the nanoparticles are obtained and investigated. The latter current accounts for energy accumulation by (depletion from) the nanoparticles. The finite size effects result in reversibility features and peculiarities at time moments t=2πℓΔ^{-1} for non-negative integers ℓ. They are qualitatively the same as in a previously studied system of two equal nanoparticles mediated by a molecule, despite the presence of the macroscopic contacts. The thermal conductance of the whole nanojunction is derived and explored. The energy currents and thermal conductance of the nanojunction in a case when its parameters are known from the experiment are computed using the developed model.