1

Molecular Dynamics Simulation and Its Applications in Engineering Thermophysics

Bing-Yang Cao

Department of Engineering Mechanics

Tsinghua University, Beijing, China

5 June, 2009

University of Brighton, 5 June 2009

Workshop at Centre of Automotive Engineering Research

2

Outlines

1. Why need molecular dynamics (MD) simulation?

2. How to do MD simulations?

3. Applications in engineering thermophysics3.1 Interface & Phase transition3.2 Fluid flow in nanochannels3.3 Thermal properties of carbon nanotubes

4. Concluding remarks

3

1. Why need MD Simulation?

Gas Liquid Solid

Q: How to know the thermophysical properties and transport laws of these molecular systems?

4

Theoretical & Experimental methods?

Kinetic theory (Boltzmann)Statistical mechanics (Hamilton)Solid physics (Phonons/Lattice dynamics)

Experimental (Measurement)

Approximation & Simplification often neededComplex problems are insolvable

Difficulty for extreme conditionsUnknown physical mechanisms

5

Theoretical & Experimental methods?

Kinetic theory (Boltzmann)Statistical mechanics (Hamilton)Solid physics (Phonons/Lattice dynamics)Approximation & Simplification often neededComplex problems insolubleDetails

Coordinates & Velocities of all molecules

Computer

6

MD simulation method

( )ir t

( ) ii

rv tt

∂=∂

Q: Temperature?A:21

2 23

imv

k NT =

∑

7

MD simulation method

( )ir t

( ) ii

rv tt

∂=∂

Q: Thermal conductivity?

Molecular Dynamics Simulation

A:(Green-Kubo formula)

8

Advantage of MD simulation

Exp. MD Theo.More Details &

ApplicabilityNo Approximation & Simplification

“Computer Experiment”

Interface/Phase transitionNanoscale (1~100nm)Supertransient (fs-ns)Other extreme conditions

Do what exp. & theo. can not do:

9

2. How to do MD simulations

Newton’s equation of motion

2.1 Equation of motion & potential

2

2

( )ii id r tm F

dtφ= = −∇

( )i iji j i

rφ φ≠

=∑∑Pair potential

MD technique: calculate potential & force

10

2.2 Examples of potential

(1) LJ potential for simple molecules

Lennard-Jones (LJ) potential

11

2.2 Examples of potential

(1) LJ potential

12

2.2 Examples of potential

(1) LJ potential

T-ρ phase diagram p-v phase diagram

Phase equilibrium (liquid-vapor or liquid-solid ) can be simulated!

13

2.2 Examples of potential

(2) TB potential for covalent system (C, Si)

Tersoff-Brenner (TB) potential

14

2.2 Examples of potential

(2) TB potential

15

2.2 Examples of potential

(2) TB potential

Graphene

Carbon nanotube

C60

Silicon Crystali-

zation

Silicon Crystal

16

2.2 Examples of potential

(3) OPLS potential for n-alkanes

Optimized Potential for Liquid Simulation (OPLS)

(Applicable for Diesel fuel: C12H26)

Nonbonded interaction:

Bond bending potential:

Bond torsion potential:

CH3 & CH2 are regarded as separate units

17

2.2 Examples of potential

(3) OPLS potential for n-alkanes

Parameters:

2 59.4CH Kε = 3 88.1CH Kε =

2 3 72.3CH CH Kε − = 0.39nmσ =262500 /k K radθ = 0 112degθ =

0 1116c K= 1 1462c K=

2 1578c K= − 3 368c K= −

4 3156c K= 5 3788c K= −

18

2.2 Examples of potential

(3) OPLS potential

Phase diagram

Critical pressureCritical temperature

B. Smit et al., J. Chem. Phys. 1995, 102: 2116

The OPLS potential is successful to simulate the phase equilibrium of n-alkanes.

19

2.3 Algorithms

Integration of equation of motion

Numerous equations

Numerous potential pairs

Small time steps

Heavy computation burden

20

2.4 Equilibrium & Nonequilibrium MD

EMDUniform

NEMDNonuniform

in temperature, pressure, density etc.

NEMD is applied more widely than EMD.

21

3 Applications in engineering thermophysics

1. Interface & Phase transition2. Fluid flow in nanochannels3. Thermal properties of carbon nanotubes

22

3.1 Interface & Phase transition

To obtain liquid-vapor phase equilibrium and its interface.Statistics on molecule number evaporated and condensed.

23

3.1 Interface & Phase transition

Evaporation and condensation coefficients can be calculated.Theoretical models can be corrected or developed.

24

3.1 Interface & Phase transition

A droplet on a surface

25

3.1 Interface & Phase transition

The contact angle can be measured for various materials and structures.The wettability is very important for micro/nano-scale fluid flow and heat transfer.

26

3.1 Interface & Phase transition

References:

• B.Y. Cao, M. Chen, Z.Y. Guo. Liquid flow in surface-nanostructured channels studied by molecular dynamics simulation. Physical Review E, 2006, 74: 066311 (SCI:121OC, IF: 2.438)

• B.Y. Cao, M. Chen, Z.Y. Guo. Wettability of surface with nano-structures studied by using molecular dynamics simulation. Chemical Journal of Chinese Universities, 2005, 26(2): 277-280 (SCI: 896XH, IF: 0.724)

27

3.2 Fluid flow in nanochannels

Couette flow in nanochannels

28

3.2 Fluid flow in nanochannels

The velocity profile can be obtained for various conditions (temperature or pressure) to measure the velocity slip.Molecular collision behaviors is also obtained to know how much momentum is transported during a collision.

Velocity profilesMolecular collision behaviors

at 100K (a) & 300K (b)

29

50 100 150 200 250 300 350 4000.0

0.1

0.2

0.3

0.4

Present simulations Fit of present results Our three-dimensional simulations Yamamoto's MDS result

TMA

C

T (K)

Tangential momentum accommodation coefficient (TMAC), that is to measure the velocity slip, can be extracted, and studied of its parameter dependence.Complex boundary conditions (e.g. different surface roughness) can also be considered.

3.2 Fluid flow in nanochannels

f=f0+f1exp(-βT)

2 ( )slip wallf vv

f xλ− ∂

=∂

30

References:

• B.Y. Cao, M. Chen, Z.Y. Guo. Temperature dependence of the tangential momentum accommodation coefficient for gases. Applied Physics Letters, 2005, 86: 091905 (SCI:924PT, IF: 4.127)

• B.Y. Cao, M. Chen, Z.Y. Guo. Effect of surface roughness on gas flow in microchannels by molecular dynamics simulation. International Journal of Engineering Science, 2006, 44(13-14): 927-937 (SCI: 090RI, IF: 1.060)

3.2 Fluid flow in nanochannels

31

3.3 Thermal properties of carbon nanotubes

Carbon nanotubes with a temperature difference are simulated.The thermal conductivity can be obtained by measuring the temperature profile.

Heat conduction in carbon nanotubes

32

3.3 Thermal properties of carbon nanotubes

The thermal conductivity increases with the increasing nanotube length.The exponential power for its length dependence decreases with the increasing nanotube length . It shows the ballistic transport behaviors of phonons, different from the traditional diffusion mode.

33

3.3 Thermal properties of carbon nanotubes

A thermally driven nanomachinebased on carbon nanotubes

34

(5, 5)@ (10, 10)MET: translation

(8, 0)@ (13, 0)MET: rotation

(8, 2)@ (17, 2)MET: helix

3.3 Thermal properties of carbon nanotubes

Behaviors of the outer tube

35

3.3 Thermal properties of carbon nanotubes

According to the MD results, a new theory has been developed to characterize the behaviors of the thermally driven nanomachines based on phonon dynamics!

36

References:

• B.Y. Cao, Q.W. Hou, Z.Y. Guo. Nanomotors actuated by phonon current. Chapter In: MEMS: Technology, Fabrication Processes and Applications. New York: Nova Science Publishers, 2009

• Q.W. Hou, B.Y. Cao*, Z.Y. Guo. Thermal conductivity of carbon nanotube: From ballistic to diffusive transport. ActaPhysica Sinica, 2009 (In press)

3.3 Thermal properties of carbon nanotubes

37

4 Concluding remarks

Difficulty:

System size: ~nanometerTime scale: ~picosecondEngineering situations: complex

38

4 Concluding remarks

Hotspots in thermophysics:

Phase transition/InterfacesMicro/nano-fluidicsThermophysical properties of nanostructuresPhenomena under extreme conditions

39

Thanks for your attention!

Acknowledgements:

The visit at the University of Brighton is funded by awards from Royal Academy of Engineering (UK) and Tsinghua University (China).