Microscale and nanoscale heat transfer

Preface......Page 6
Contents......Page 10
List of Contributors......Page 16
Macroscopic Approach......Page 18
Characteristic Length and Time Scales......Page 19
Macroscopic Approach......Page 22
Macroscopic Approach......Page 24
Characteristic Length and Time Scales......Page 26
Index......Page 29
Distribution Function......Page 32
Averages......Page 33
Definition......Page 34
Equilibrium Distribution Function......Page 35
Dynamical Equation for the Distribution Function......Page 36
The Relaxation Time Model......Page 37
Mean Free Path. Collision Time. Knudsen Number......Page 38
Local Thermodynamic Equilibrium......Page 40
Fourier Law and Thermal Conductivity......Page 41
Example of a Non-LTE System. Short-Scale Conduction in a Gas......Page 42
Can One Speak of Temperature on Short Scales?......Page 43
Calculating the Conductive Flux in the Ballistic Regime......Page 44
Transitions Between Regimes......Page 45
Conclusion......Page 47
Equilibrium Distribution Function......Page 48
Dynamical Evolution of the Distribution Functionfor Free Particles......Page 49
Calculating the Constants A and B for the Fluxin the Ballistic Regime......Page 50
References......Page 51
Index......Page 52
Electrons and Phonons......Page 54
Free Electrons......Page 55
Electrical Conduction......Page 58
Semi-Classical Approach......Page 60
Electrical Conductivity in the Collisional Regime......Page 62
Electrical Conduction in the Ballistic Regime......Page 63
Vibrational Modes in a Lattice......Page 64
Phonon Energy......Page 66
Density of States. Optical and Acoustic Modes......Page 67
Calculating the Heat Flux......Page 68
Calculating the Thermal Conductivity......Page 69
Index......Page 70
Specific Intensity, Flux, Energy Density......Page 72
Absorption, Scattering and Thermal Emission......Page 73
Establishing the RTE. Radiative Energy Balance......Page 76
From the RTE to the Diffusion Approximation......Page 77
From the P1 Approximation to the Diffusion Equation......Page 78
Discussion......Page 81
Transport Regimes......Page 82
Static Transmission.Ohmic Conductance and Short-Scale Deviations......Page 83
Transitions Between Regimes in the Dynamic Case......Page 84
Ballistic and Multiple Scattering Components in the RTE......Page 85
Principle Underlying the Calculation of Thermal Emission. Fluctuation--Dissipation Theorem......Page 87
References......Page 91
Index......Page 92
Introduction......Page 94
Intensity. Internal Energy. Flux......Page 95
Transfer Equation......Page 97
Diffusive Regime......Page 99
General Idea......Page 100
Numerical Solution......Page 104
Discrete Ordinate Method......Page 105
General Idea......Page 106
Choice of Quadratures......Page 107
Integrating the RTE over a Control Volume......Page 111
Integrating over a Control Volume......Page 114
Advantages and Disadvantages......Page 117
References......Page 122
Index......Page 123
Maxwell\'s Equations and Constitutive Relations......Page 124
Plane Wave Expansion......Page 126
Energy Conservation, Poynting Vector, and Energy Density......Page 127
Potentials......Page 128
Dipole Radiation......Page 129
Calculating Radiative Transfer on Short Length Scales......Page 131
Thermal Emission from a Nanoparticle......Page 132
Radiative Power ExchangedBetween Two Spherical Nanoparticles......Page 133
Thermal Near-Field Emission from a Plane Surface......Page 135
Near-Field Radiative Transfer Between Two Planes......Page 143
References......Page 146
Index......Page 147
Monte Carlo Method......Page 150
Heat Flux and Energy Carriers......Page 151
Sampling Random Walks......Page 154
Ballistic and Quasi-Ballistic Transport in Gases......Page 157
Molecules and Heat Flux......Page 158
Random Walk Distributions......Page 160
Collision Distributions......Page 161
Transfer Between a Hot Tip and a Surface......Page 162
Ballistic and Quasi-Ballistic Transport in Insulating Crystals......Page 164
Modelling Random Walks......Page 165
Conduction in a Thin Film......Page 168
References......Page 169
Index......Page 170
Definitions and Notation......Page 172
Integrating Newton\'s Equation......Page 175
Interaction Potentials......Page 177
Implementing the Simulation......Page 179
Energy Distribution......Page 182
Thermal Conductivity Calculation......Page 183
Equilibrium Molecular Dynamics......Page 185
Non-Homogeneous Non-Equilibrium Molecular Dynamics......Page 186
Homogeneous Non-Equilibrium Molecular Dynamics......Page 189
Heat Transfer by Phonons......Page 190
Determining Vibrational Properties......Page 192
References......Page 194
Index......Page 196
Basic Principles of Near-Field Microscopy......Page 198
Historical Perspective: From Conventional Microscopyto Near-Field Microscopy......Page 201
Scanning Probe Microscopes......Page 204
Near-Field Microscopy and Heat Transfer......Page 212
Thermal Probes......Page 219
SThM with the Micrometric Thermoresistive Wire Probe......Page 224
Method......Page 225
Thermal Image Contrast......Page 228
Analysing Measurements in Constant Temperature Mode......Page 237
Analysing Measurements in Constant Current Mode......Page 245
References......Page 247
Index......Page 253
Generating Thermal and Thermoelastic Waves......Page 256
Generating Waves by Thermoelectric Effects......Page 257
Optical Generation......Page 261
Detecting Thermal and Thermoelastic Waves......Page 266
Reflectometry......Page 267
Interferometric Probes......Page 275
Temperature and Displacement Fields.Orders of Magnitude......Page 288
Locating Hot Spots and Mapping Temperature......Page 291
Measuring Thermophysical Properties......Page 295
References......Page 298
Index......Page 301
Physics of MicroscopesCombining Thermal and Thermoelastic Effects......Page 304
Microscopes and Their Resolutions......Page 307
3D Model with Cylindrical Symmetry......Page 308
Microscopes Based on a Thermoelectric Probe......Page 312
Microscopes Based on Detection of Expansion......Page 316
Prospects......Page 318
References......Page 320
Index......Page 323
Introduction......Page 326
Electronic Structure of Noble Metals......Page 327
Lattice Vibrations......Page 330
Optical Response at Equilibrium......Page 331
Femtosecond Pump--Probe Method......Page 333
Kinetic Model. Boltzmann Equation......Page 336
Electron--Phonon Interaction. Bulk Metals......Page 337
Energy Exchange in the Thermal Regime.Two-Temperature Model......Page 339
Electron--Lattice Interactions in Metallic Nanoparticles......Page 342
Vibrational Modes......Page 343
Time-Resolved Studies......Page 345
References......Page 347
Index......Page 348
Investigation of Short-Time Heat Transfer Effects by an Optical Pump–Probe Method......Page 350
Acoustic Generation in the Absence of Heat Diffusion......Page 351
Taking Heat Diffusion into Account......Page 354
Optical Detection of Thermal and Acoustic Transients......Page 362
Experimental Setups......Page 366
Interferometric Detection......Page 368
Cumulative Effects Due to the Pump Pulse Train......Page 369
References......Page 373
Index......Page 375
Index......Page 378