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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
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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
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1. Why need MD Simulation?
Gas Liquid Solid
Q: How to know the thermophysical properties and transport laws of these molecular systems?
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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
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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
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MD simulation method
( )ir t
( ) ii
rv tt
∂=∂
Q: Temperature?A:21
2 23
imv
k NT =
∑
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MD simulation method
( )ir t
( ) ii
rv tt
∂=∂
Q: Thermal conductivity?
Molecular Dynamics Simulation
A:(Green-Kubo formula)
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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:
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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
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2.2 Examples of potential
(1) LJ potential for simple molecules
Lennard-Jones (LJ) potential
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2.2 Examples of potential
(1) LJ potential
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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!
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2.2 Examples of potential
(2) TB potential for covalent system (C, Si)
Tersoff-Brenner (TB) potential
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2.2 Examples of potential
(2) TB potential
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2.2 Examples of potential
(2) TB potential
Graphene
Carbon nanotube
C60
Silicon Crystali-
zation
Silicon Crystal
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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
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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= −
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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.
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2.3 Algorithms
Integration of equation of motion
Numerous equations
Numerous potential pairs
Small time steps
Heavy computation burden
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2.4 Equilibrium & Nonequilibrium MD
EMDUniform
NEMDNonuniform
in temperature, pressure, density etc.
NEMD is applied more widely than EMD.
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3 Applications in engineering thermophysics
1. Interface & Phase transition2. Fluid flow in nanochannels3. Thermal properties of carbon nanotubes
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3.1 Interface & Phase transition
To obtain liquid-vapor phase equilibrium and its interface.Statistics on molecule number evaporated and condensed.
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3.1 Interface & Phase transition
Evaporation and condensation coefficients can be calculated.Theoretical models can be corrected or developed.
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3.1 Interface & Phase transition
A droplet on a surface
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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.
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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)
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3.2 Fluid flow in nanochannels
Couette flow in nanochannels
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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)
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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− ∂
=∂
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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
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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
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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.
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3.3 Thermal properties of carbon nanotubes
A thermally driven nanomachinebased on carbon nanotubes
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(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
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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!
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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
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4 Concluding remarks
Difficulty:
System size: ~nanometerTime scale: ~picosecondEngineering situations: complex
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4 Concluding remarks
Hotspots in thermophysics:
Phase transition/InterfacesMicro/nano-fluidicsThermophysical properties of nanostructuresPhenomena under extreme conditions
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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).
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