Phonon Transport Theories and Simulation Gang Chen Mechanical Engineering Department Massachusetts Institute of Technology Cambridge, MA 02139 http://web.mit.edu/nanoengineering
Annual Review of Heat Transfer, v. 17, 2013 Phonon Mean Free in Bulk Materials DFT MD equilibrium Interfaces Green's function Equilibrium MD Transport Nonequilibrium MD Monte Carlo Simulation Boltzmann equation Dissipative Particle Dynamics Effective Media, maybe in composite application Electron-Phonon Interactions First principle on electron phonon scattering Electron Monte Carlo Applications Phonon control Nanowires and nanoporous materials CNT/graphene Thermoelectric materials Polymers Keivan Esfarjani and Jivtesh Garg Alan McGaughey Tim Fisher Yann and Volz Shiomi Nicolas Hajicontantinou Jayathi Murthy Jennifer Lukes Nan CeWen Natalie Mingo Eric Pop Baowen Li Julia Galli Maruyama Ronggui Yang Asegun Henry
DFT: Multiscale Simulation Continuum Band Structure Interatomic Potentials Effective Medium Properties Boltzmann Transport Equation, Monte Carlo DFT: 1 nm 10 nm 100 nm 1 m 10 m 100 Band m Ab-Initio Molecular Dynamics? Green s Function Classical Nonequilibrium Or Equilibrium Molecular Dynamics: Transport Properties Structure Interatomic Potentials Equilibrium Molecular Dynamics: Bulk material properties
Phonon Mean Free Paths from Molecular Dynamics 1. Equilibrium MD Simulations Provide Atomic Velocities. 2. Project Velocities onto Phonon Modes from Lattice Dynamics Calculations. 3. Auto-correlation and Fourier Transform of Phonon Kinetic Energy. 4. Extract Phonon Lifetime. 1 5. Mean Free Path = Lifetime x Group Velocity v g Alan McGaughey, Carnegie Mellon University
First Principle (DFT)calculations First Principle Calculation i t H e-band, e-dos ph-band, ph-dos Anharmonic Interatomic force constants 1 1 V V0 iui ijuiu j 2! 3! i ij ijk ijk u u i j u k 1 4! ijkl ijkl u u i j u k u l Scattering calculation k W i f k k k k 2 2 f V i k Molecular dynamics simulations m i d 2 ri 2 dt V Alloy effects Thermal conductivity + mean free path (mode-dependent) D. Brodio et al., PRB, 80 (2009) Esfarjani et al., Phys. Rev. B 84, 085204, 2011.
1000K 300K 300K 1000K
Interface Transmission Green s Function Thermal conductance from Equilibrium Molecular Dynamics Z. Huang, T.S. Fisher, J.Y. Murthy, J. Appl. Phys. 109, 074305, 2011. Chalopin et al., unpublished
Transport Process Phonon Boltzmann Transport Equation f t v f f t scat Equilibrium Monte Carlo McGauhey, APL, 2012 Effective Medium Theory Percolation regime Size and interface effects Thermoelectric effects 27 years becomes 1 day 1 day becomes 9 sec. Peraud and Hadjiconstantinou, Physical Review B, 84, 205331, 2011
Internal vs. External Size Effects
Heat Conduction Mechanisms Inside Nanostructures Segment Length [nm] Si / Ge Regime Map 10 5 10 4 10 3 10 2 Nanowire 25 45 65 Bulk Avg. 10 1 SLNW k=5 [W/m-K] Super- (300 K) lattice 10 0 10 0 10 1 10 2 10 3 10 4 10 5 Diameter [nm] Classical Size Effect Casimir winner D CNTs High Wave Effects 3D to 1D transition Coherence? Localization? Divergence?
Scattering and Correlation Paradigms Henry and Chen, PRB, 79, 144305, 2009. Correlation p p dt E E E t E C C V k k 0 2 2 2 1 0 v v 1
Conduction vs. Radiation Contact conductance ~10 8 W/m 2.K 12
Fluids and Convection Gas: Knudsen regime, well-established Microchannel convection: Single phase (Poiseuille went down to ~15 m) Multiphase flow and heat transfer Superhydrophilic/superhydrophobic surfaces Electrokinetic flow, heat, and mass transfer Nanofluids: thermal conductivity, radiative coupling We have limited understanding of thermal transport in fluids. Heat, mass, and charge transport in soft materials, complex fluids, and phase change.
Acknowledgements Inputs from Y. Chalopin: molecular dynamics T. Fisher: Green s function G. Galli: thermoelectrics N. Hajiconstantinou: Monte Carlo J. Lukes: dissipative particle dynamics A. McGauhey: molecular dynamics Sponsors: DOE (BES, ARPA-E, EERE, EFRC), AFOSR, NSF, Industry