Thermal Transport in 2D Nanostructures - School of Physicsphysics.ipm.ir/conferences/qtg/note/S.M.Vaez.pdf · Thermal Transport in 2D Nanostructures ... Theory Models of Thermal Rectifier

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

World Energy Use in 2005 (15TW)

Direct Conversion of Heat into Electricity

The thermoelectric effect is the direct conversion of temperature differences to electric voltage and vice versa.

Power Dissipation Challenges

Thermal Properties: Graphene

Thermal Properties: Silicene

~ 15 – 40 W/mK

Graphene

ACS Nano, 2513 (2008)

Thermal Properties: Graphene

A. Rajabpour, SMVA, APL (2012)

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

A Chain Model for Heat Conduction

Jian-Sheng Wang's presentation

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





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

Size Effect and Thermal Transport

Thin film

Superlattice

w

Bulk

Λbulk

Phonon mean free path

Interface Thermal Resistance

NEMD simulation

Kapitza Resistance

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

Heat Carriers: Phonons!-Kapitza resisrtance (in low dimensional systems)


Approaches to Heat Transport

Jian-Sheng Wang's presentation

Outline





Molecular Dynamics Simulation

Equilibrium Methods

Non-equilibrium Methods

Non-equilibrium Methods (continued)

MD Simulation of Thermal Transport

Equilibrium MD Non-equilibrium MD Package: LAMMPS

Non-equilibrium Simulation of Thermal Transport

Lz

PB

C

PBC

Fixed atoms

Non-equilibrium Thermal Transport (continued)

Outline





Nanoscale Thermal Rectifiers (overview)

TR ~ 20 % Length dependence

TR

G. Wu and B. Li, Phys. Rev. B 76, 085424 (2007).

Heat-pulse rectification in carbon nanotube Y junctions

PRB 79, 115432 (2009)

Nano-trousers !!


N. Roberts, D. Walker, 2008

N. Yang, G. Zhang, B. Li, APL (2009)J. Hu, X. Ruan, Y. Chen, Nano Lett. (2009).


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).


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

Graphene/Graphane Hybrid (continued)

Thermal Rectificatin

H

TR= 22.3%

Graphene/Graphane Phonone Power Spectra

Graphene/Graphane Interface (continued)

A. Rajabpour, SMVA, F. Kowsary, APL (2011)

Pristine/Hydrogenated CNTDifferent hydrogen

coverage is implemented.

K. Gordiz, SMVA, (to be appeared in J. Appl. Phys.)

Pristine/Hydrogenated CNT (continued)

Radial thermal rectification in MWCNTs

Heat flow

K. Gordiz, SMVA, F. Kowsary, APL 99, 251901 (2012)


Effect of: number of layers Length Averag

temperature

K. Gordiz, SMVA, F. Kowsary, APL 99, 251901 (2012)

Tuning Thermal Conductivity

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)

Graphene Dispersion Curve

LAMMPS: USER-PHONONT=300K

FHI-AIMS: DFT

Linearized BoltzmannTransport Equation

Relaxation timeapproximation

Ab initio Calculation for Graphene

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)



Graphyne

Silicene

Thermal Transport in Silicene

Thermal Transport in Silicene (continued)

Bilayer Silicene: MD Simulations

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

Thanks for your attentions!

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

Graphyne (continued)

Dispersion Relation of Graphene

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

Thank you so much for your attention!

Thin Film Thermal Characterization

World Energy Use in 2005 (15TW)

J. Christofferson, et al, J. Electronic Packaging,130 (4) 041101, 2008

Publication in the subject of Thermal Transport

EMD for measuring Kapitza resistance

A Rajabpour, S Volz, JAP 108, 094324 (2010)

World Marketed Energy Use1990-2035

Nitrogen doped Graphene

Phonone Power Spectra

Molecular Dynamics (MD) Simulations

mi ai=Fi=- U� 2-body

3-body


E. Pereira,

”Sufficient conditions for thermal rectification in general graded materials”,

PRE 83, 031106 (2011)

Nitrogen doped Graphene (continued)

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


# of publications

N.A. Roberts, D.G. Walker, Int. J. Thermal Sci., 2011

DNA sequencing by Graphene

Engineering science paradigm: Multi-scale view of materials

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

Continuum vs. Atomistic Model

Solving the Equations

Interacting Potential

Film

Curvature Effect

(b) Circumferential (c) Longitudinal

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"

http://en.wikipedia.org/wiki/Andre_Geim

http://en.wikipedia.org/wiki/Konstantin_Novoselov

http://en.wikipedia.org/wiki/University_of_Manchester

http://en.wikipedia.org/wiki/Nobel_Prize_in_Physics

http://en.wikipedia.org/wiki/Two-dimensional_space

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, …)

Typical MD simulation procedure


Temperature Gradient


The temprature profiles of layers.

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.

Outline (continued)

Thermal Transport LJ Superlattices: in-plane thermal conductivity Nitrogen doping and Curvature effectson TC of

graphene Tunning TC of bilayer graphene

Documents

Thermal Transport in 2D Nanostructures - School of Physicsphysics.ipm.ir/conferences/qtg/note/S.M.Vaez.pdf · Thermal Transport in 2D Nanostructures ... Theory Models of Thermal Rectifier