Generalized Langevin Equation Theory of Thermal Conduction across Material Interfaces

The thermal conduction across material interfaces is studied using a generalized Langevin equation (gLE) theory. A general statistical formula of thermal interfacial conductance (TIC) is derived at the slow fluctuation limit in terms of the time auto-correlation functions of interfacial heat current (QACF) < q(t) q(0)> and the heat capacity C-V. At the bulk limit of C-V -> 8, this general TIC formula reduces to the previously proposed Green-Kubo type of TIC formula. Beyond the bulk limit, the TIC of a material with finite CV can be calculated using the first and second moments of the interfacial QACF. These statistical TIC formulas provide the basis to adopt equilibrium molecular dynamics simulations to calculate the TIC of real material interfaces beyond the bulk limit, including the interfaces at the nanoscale. The TIC of two types of non-Markov model interfaces with analytic forms of QACF is predicted by the reported gLE theory, and the results of these non-Markov interfaces are compared with those of a Markov interface.

Automated summary

The study uses a generalized Langevin equation theory to investigate thermal conduction across material interfaces, deriving a statistical formula for thermal interfacial conductance at the slow fluctuation limit. This formula provides a basis for calculating TIC of real material interfaces beyond the bulk limit, including interfaces at the nanoscale, by using equilibrium molecular dynamics simulations. The TIC of non-Markov model interfaces with analytic forms of QACF is also predicted and compared with those of a Markov interface.