A Variational Approach to Extracting the Phonon Mean Free Path Distribution from the Spectral Boltzmann Transport Equation

Abstract

The phonon Boltzmann transport equation (BTE) is a powerful tool for studying non-diffusive thermal transport. Here, we develop a new universal variational approach to solving the BTE that enables extraction of phonon mean free path (MFP) distributions from experiments exploring non-diffusive transport. By utilizing the known Fourier solution as a trial function, we present a direct approach to calculating the effective thermal conductivity from the BTE. We demonstrate this technique on the transient thermal grating (TTG) experiment, which is a useful tool for studying non-diffusive thermal transport and probing the mean free path (MFP) distribution of materials. We obtain a closed form expression for a suppression function that is materials dependent, successfully addressing the non-universality of the suppression function used in the past, while providing a general approach to studying thermal properties in the non-diffusive regime.

17 pages, 2 figures

References in corpus (3)

• Direct Measurement of Room Temperature Non-diffusive Thermal Transport Over Micron Distances in a Silicon Membrane
• A new regime of nanoscale thermal transport: collective diffusion counteracts dissipation inefficiency
• Multidimensional quasiballistic thermal transport in transient grating spectroscopy

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• Variational Approach to Solving the Spectral Boltzmann Transport Equation in Transient Thermal Grating for Thin Films
• Molecular dynamics simulations of the lattice thermal conductivity of CuInTe2
• Reconstruction of the phonon relaxation times using solutions of the Boltzmann transport equation
• Impact of the regularization parameter in the Mean Free Path reconstruction method: Nanoscale heat transport and beyond
• Monte Carlo Simulation of Single-Crystalline PbSe Nanowire Thermal Conductivity Using First-Principle Phonon Properties