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Generalized Langevin Equation Theory of Thermal Conduction across Material Interfaces
Author(s) -
Zeng Yi,
Avritte Jalaan T.,
Dong Jianjun
Publication year - 2021
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.202000454
Subject(s) - limit (mathematics) , statistical physics , thermal conduction , langevin equation , thermal conductivity , molecular dynamics , langevin dynamics , heat current , physics , heat equation , thermodynamic limit , thermal , thermodynamics , moment (physics) , mathematics , mathematical analysis , classical mechanics , quantum mechanics
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 ofC V → ∞ , 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 C V 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.