1. Microscale Heat Transfer

(1)

1 Shigeo Maruyama

Eng. Res. Inst. & Dept. Mech. Eng.

The University of Tokyo

e-mail: [email protected] http://www.photon.t.u-tokyo.ac.jp/~maruyama

August 2000, National Tsing Hua University

MD Simulation

for Microscale Heat Transfer MD Simulation

for Microscale Heat Transfer

1.1 Why do we deal with Molecular Dynamics?

1.2 Molecular Dynamics Method and Monte Carlo Method 1.3 Quantum Dynamics, ab initioCalculations

1. Microscale Heat Transfer 1. Microscale Heat Transfer

Heat and Mass Transfer through Interphase (Phase Change, Ablation) Stress at Composite Materials

Seeking for a New Materials(Especially Thermal Properties) Manufacturing Process of Thin Film (CVD, etc)

Physical Properties of Thin Film Faulingof Solid Materials

Numerical Prediction of Physical Properties High Speed and High Flux Energy Transfer Control ofCluster

Thermal Phenomena including Chemical Reactions Manufacturing and Control with Laser,

Electron Beam and Molecular Beam

Quantum Effectn &

State of Electron Fields of Applications of

Molecular Heat Transfer

1. Microscale Heat Transfer and MD Simulation?

Solid

Liquid Gas

Absorption CVD Fouling Condensation Absorption Nucleation

Wetting Nucleation Thin Film

3 Phase Boundary

Supercritical Cluster

Laser Mixing,

Physical Property

Contact Resistance Point Contact Phase Change

Reaction

Inter-phase Phenomena Inter-phase Phenomena

Microscopic Problems

• Clustering

• Ultra-super cooling/heating

• Uniform phase change

• Ultra-fast phase change Macroscopic Problems

• Nucleation (homogeneous & heterogeneous)

• Maximum heat flux

• Condensation coefficient

30

20

10

0 10 20 30 40

Phase change phenomena Phase change phenomena

A Classification of Quantum Molecular Dynamics Methods

MD Car-

Parrinello

Tight- Binding

Classical MD

Non- Adiabatic QMD

Shibahara- Kotake QMD DFT

Hückel

Function Electron Nuclear

MD

td-DFT MD

HF MD

Steady Schrödinger Eq.

Simple

WF MD

MD Wave Packet Selected Degree of Freedom Born-Oppenheimer Approximation

Time-Dependent Schrödinger Eq.

DFT HF

MP

CI Beck3

LYP MO

Nuclear Motion (Vib, Rot) Electron Electron

Quantum Chemistry Light-Matter

Molecule-Surface Reaction

Dynamics

Electronic Excitation

(2)

2 Schrödinger Equation

Electron

∂ ψ

∂ψ H i t =

H M m

Z Z e Z e e

k k k

i i

k l

k l

k

k i

k i i j i j

0= − ∇ − ∇ +

− −

− +

¦₂² ² ¦₂² ² ¦_R _R² ¦_R ²_r ¦_r−²_r

, , ,

E R

r ⋅

¿¾

½

¯®

− +

+

≈^H ¦_i^eⁱ ¦_k^Z^k^e ^k

H ₀

it E

e r t

r,) ()

( ψ₀

ψ =

0

0 ψ

ψ H

E =

hν

electrons rrrri

nuclei RRRRk

The Born-Oppenheimer Approximation

Born-Oppenheimer Approximation

Electron Ψ

= Ψ E H

¦

¦ ^∇ ⁻ ^∇ ⁺ ₋ ⁻ ₋ ⁺ ₋

−

=

j

i i j

i

k k l

k l

k k l

l k i

i k

k k

e e Z e Z Z m

M _,

2

, 2

, 2 2 2 2 2

2 H 2

r r r R R R

e AB e e j i ij i

k ki

k i

i e

e E R

r e r

e Z

Hψ m ψ ( )ψ

2 ,

2

, 2 2

2 =

¿¾

½

¯®

∇ − +

=

¦

¦ ¦

) ( )

; (rR NR

e

mol=ψ χ

Ψ

N N AB

B A AB e B

A k

k k N

N R

e Z R Z M E

H χ χ Totalχ

2

, 2 2

E )

2 ( =

¿¾

½

¯®

− ∇ − +

=

¦

₌

Electrons moves much slowly than nuclei

Molecular Orbital Calculations - Quantum Chemistry Steady Schrödinger Eq.

Molecular Orbital Method

Electron

cf. Gaussian94 HF: Hartree-Fock Theory

LCMO(linear combination of atomic orbitals)

Basis Sets

MP: Moller-Plesset Perturbation Theory, MP2, MP3, MP4 CI: Configuration Interaction

Electron Correlations

Polarized, Diffuse: 6-31G(d), 6-311+G(d,p), 6-311++G(3df, 3pd)

Density Functional Theory - Quantum Chemistry Steady Schrödinger Eq.

Electron

cf. Gaussian94 DFT: Density Functional Theory

B3LYP: Beck’s 3 parameter Exchange Functional with Lee-Yang-Parr Correlation

) ( ) ( ) 2 ( 1 2

r r

r _i _i _i

i V ψ =εψ

»¼º

«¬ª− ∇ +

) ( ' ' ) ' ) (

( xc

1

r r r r

r r

r rZ d V

V

N

a a

a +

+ −

− −

=

¦

₌

³

^ρ

Exchange-Correlation

Car-Parrinello Method

Electron

DFT for Electronic Wave Function Molecular Dynamics for Nuclei

Fictitious mass of electronic degree Hellmann-Feynman

Force

Time Time

Position of Nuclei