Thermal Transport in 2D Nanostructures
Seyed Mehdi Vaez AllaeiUniversity of TehranTehran, Iran
Workshop on “Quantum transport in graphene”(In memory of late Prof. Malek Zareyan, 1971-2014)
24th April 2014(4 Ordibehesht 1393)School of Physics, IPM
Outline
Introduction Motivation Thermal Transport MD Simulation
Molecular Dynamics Simulation of Thermal Transport
Thermal transport in nanoscale devices and Results
Interface Thermal resistance Tunning Thermal Conductivity Thermal Rectification
Direct Conversion of Heat into Electricity
The thermoelectric effect is the direct conversion of temperature differences to electric voltage and vice versa.
Thermal Rectification
C H
H C
%100×−= −
−+
J
JJTR
● Thermal counterpart of the electrical diod● Heat Transfer that is dependent on the sign of temperature gradient
Thermal Rectification inLow Dimensional Systems
Theory Models of Thermal Rectifier Morse on-site potential
Thermal Rectification:Experimental Realization
Experimental observation of thermal rectification in nanostructures, 2006
C.W. Chang, D. Okawa, A. Majumdar, A. Zettl, Science 314, (2006).
Outline
Introduction Motivation Thermal Transport MD Simulation
Molecular Dynamics Simulation of Thermal Transport
Thermal transport in nanoscale devices and Results
Interface Thermal resistance Tunning Thermal Conductivity Thermal Rectification
From Fourier ...macroscopic theory
Joseph Fourier 1768-1830 “Analytic theory of Heat” continuum theory, partial differential equations Steady-state condition: J = κ T∇
K is known as Thermal conductivity coefficient
T
x
Interface Thermal Resistance(continued)
ΔT
1 2
R=ΔT/q
R~ 10-9 -10-7 m2-K /W
Important at NanoscaleSystem Size
R~ 10-5 -10-4 m2-K /W
Contact resistance
Perfectly matched interface Mismatched interface
Outline
Introduction Motivation Thermal Transport MD Simulation
Molecular Dynamics Simulation of Thermal Transport
Thermal transport in nanoscale devices and Results
Interface Thermal resistance Tunning Thermal Conductivity Thermal Rectification
Outline
Introduction Motivation Thermal Transport MD Simulation
Molecular Dynamics Simulation of Thermal Transport
Thermal transport in nanoscale devices and Results
Interface Thermal resistance Tunning Thermal Conductivity Thermal Rectification
Nanoscale Thermal Rectifiers (overview)
TR ~ 20 % Length dependence
TR
G. Wu and B. Li, Phys. Rev. B 76, 085424 (2007).
Nanoscale Thermal Rectifiers (overview)
N. Roberts, D. Walker, 2008
N. Yang, G. Zhang, B. Li, APL (2009)J. Hu, X. Ruan, Y. Chen, Nano Lett. (2009).
Nanoscale Thermal Rectifiers (overview)
carbon nanohorn1
G. Wu, B. Li, J. Phys.: Cond. Matt. (2008)N. Yang, G. Zhang, B. Li, APL (2008)
▪ Carbon nanotube and nanoribbon junction
X. Ni, G. Zhang, and B. Li, J. Phys.: Condensed Matter 23, 215301 (2011).
Nanoscale Thermal Rectifiers (overview)
Interface Thermal Resistance andThermal Rectification
Hybrid graphene / graphane (hydrogenated graphene)
Hybrid CNT/ hydrogenated CNT Multi-walled CNT (MWCNT)
Graphene/Graphane Hybrid
20nm 20nm 20nm
Graphene Hydroenated graphene
Graphene/Hydrogenated graphene
R=5.91 m2K/W R=12.95 m2K/W< < R=32.8 m2K/W
Pristine/Hydrogenated CNTDifferent hydrogen
coverage is implemented.
K. Gordiz, SMVA, (to be appeared in J. Appl. Phys.)
Radial thermal rectification in MWCNTs
Effect of: number of layers Length Averag
temperature
K. Gordiz, SMVA, F. Kowsary, APL 99, 251901 (2012)
Graphene Thermal Conductivity: MD estimations
K ~ 3000 ± 100 W/m-K.
B. Mortazavi, A. Rajabpour, S. Ahzi , Y. Rémond , SMVA, Solid State Comm. 152, 261 (2012)
L. Lindsay, D.A. Broido, Phys. Rev. B 82, 205441 (2010)
Thermal Transport inBilayer Graphene
K ~ 3000 - 4000 W/mK
Weak van der Waals inter-layerLennard-Jones interactions
Nature Mat. 9 (2010)
Thermal Transport inBilayer Graphene (continued)
The concentration of just 1% of sp3 bonds can reduce the in-plane thermal conductivity by a factor of about 50%.
A. Rajabpour, SMVA, APL 101, 053115 (2012)
Outlook of Thermal Transport
Silicene Graphyne Self-assembly on Fluid-Solid Interface Comparison to ab initio calculations Contribution of Electrons Thermoelectric Effect ...
Acknowledgement
Ali RajabpourMechanical Engineering Department
IKIU
Kiarash GordizMechanical Engineering Department
Georgia Tec U
Farshad KowsaryMechanical Engineering Department
University of Tehran
Morteza Jalalvand Majid Zeraati Davide DonadioMPI for Polymer
Research, Mainz, Germany
Ismaeil Abdolhosseini Sarsari,
Isfahan University of Technology
Aknowledgement
Sebastian Volz, CNRS, France Davide Donadio, MPI for Polymer Research,
Mainz, Germany Luiz Felipe Pereira, University of Rio Grande
del Norte, Brazil Ismaeil Abdolhosseini Sarsari, Isfahan
University of Technology, Iran
Other Projects
Wave Propagation in Porous Media Encapsulation of Anticancer Drugs and
Antimicrobial proteins into CNTs DNA Translocation through Graphene-based
solid state nanopore GigaHertz MWCNT Oscillators Statics and Dynamics of Granular Media Roughenning Interfaces
Nanoscale Thermal Rectifiers (overview)
E. Pereira,
”Sufficient conditions for thermal rectification in general graded materials”,
PRE 83, 031106 (2011)
Thermal Rectification: The Idea
First report: 1935 C. Starr, “The copper oxide rectifier”,
J. Appl. Phys. 7, 15 (1935)
N.A. Roberts, D.G. Walker, Int. J. Thermal Sci. (2011)
Thermal Rectification in low dimensional systems (continued)
Frenkel-Kontorova (FK) Model, Thermal Diode: Rectification of Heat Flux, B. Li,
L. Wang, and G. Casati, Phys. Rev. Lett. 93, 184301 (2004)
FK + Fermi-Pasta- Ulam (FPU) Model, Interface Thermal Resistance between
Dissimilar Anharmonic Lattices, B. Li, J. Lan, and L. Wang, Phys. Rev. Lett. 95, 104302 (2005).
FK Model Asymmetric Heat Conduction in Nonlinear
Lattices, B. Hu, L. Yang, and Y. Zhang, Phys. Rev. Lett., 97, 124302 (2006).
Thermal Diode: Rectification of Heat Flux
Can be explained by match/ mismatch of PSD of phonons.
B. Li, L. Wang, and G. Casati,Phys. Rev. Lett. 93, 184301 (2004)
Goals
From thermoelectric point of view High electrical conductivity Low thermal conductivity
Tuning thermal conductivity
From Thermal Management point of view Controling heat transport
Thermal RectificationThermal Rectification
Multi-scale Simulation Paradigm
Ηψ = Εψ
F = MA
exp(- ∆E/kT)
domain
quantumchemistry
moleculardynamics
Monte Carlo
mesoscale continuum
Length Scale
Tim
e S
cale
10-10 M 10-8 M 10-6 M 10-4 M
10-12 S
10-8 S
10-6 S
Taken from Grant D. Smith
Department of Materials Science and Engineering
Department of Chemical and Fuels Engineering
University of Utah
http://www.che.utah.edu/~gdsmith/tutorials/tutorial1.ppt
Curvature Effect (continued)
B. Mortazavi , A. Rajabpour, S. Ahzi , Y. Rémond, SMVA, Solid State Comm. 152, 261 (2012)
Tunable superlattice in-plane thermal conductivity
A. Rajabpour, SMVA, Y. Chalopin, F. Kowsary, S. Volz, J. Appl. Phys. 110, 113529 (2011)
Graphene
Andre Geim and Konstantin Novoselov at the
University of Manchester won the Nobel Prize in Physics in 2010
"for groundbreaking experiments regarding the two-dimensional material graphene"
Simulation vs Experiment
Experiment Simulation
Preparing initial materials and conditions
Doing experiment
Data analysis and conclusion
Suitable device
Initial condition
Running the simulation
Data analysis
Suitable method (Quantum Monte Carlo, Density Functional Theory, Molecular Dynamics, …)
Nitrogen doped Graphene
Typical temperature gradient obtained from NEMD simulation of 2% concentration of nitrogen atoms doped in graphene with length of 30 nm, the average temperature is 300 K.