THERMAL EXPANSION INVESTIGATIONS OF SINGLE WALLED CARBON NA - PowerPoint Presentation

Slide1

THERMAL EXPANSION INVESTIGATIONS OF SINGLE WALLED CARBON NANOTUBES BY RAMAN SPECTROSCOPY AND MOLECULAR DYNAMICS SIMULATIONS

*Daniel Casimir, Prabhakar Misra, Raul Garcia-SanchezInternational Symposium on Molecular Spectroscopy (ISMS)University of Illinois at Urbana-ChampaignJune 18, 2014Slide2

Outline

History / Overview of Carbon NanotubesCarbon Nanotube StructureProblem DescriptionMolecular Dynamics SimulationRaman Spectra of Carbon NanotubesConclusions/Future WorkSlide3

History

Soviet scientists Radushkevic, and Lukyanovic report the first TEM images of multi-walled carbon nanotubes. (Radushkevic et. al. Russ. J. Phys. Chem., 26, pp. 88-95)

1952

Morinobu

Endo, accidentally rediscovered single and multi walled

nanotubes

, while trying to grow carbon fibers on a substrate. (A. Oberlin, E.

Endo,

J

.

Cryst

. Growth ,32 pp. 335-49

)

1976

1991 - 1993

Sumio

Iijima

again rediscovers multi-walled carbon

nanotubes

while trying to understand the growth mechanism of buckyballs, another carbon allotrope.

(S.

Iijima

,

Nature, 354, pp.56-8)Slide4

Applications

Gas sensors

Field Emission Sources

“New

Coating Turns Nanotubes Into Dense, Strong

Batteries”

Developed at MIT

How It Works:

1. Heat the Tube

One end of a microscopic carbon nanotube, coated with reactive fuel,

is

ignited by a laser.

2. Herd the Particles

A wave of heat races through the inside of the tube,

pushing

electrons toward the other end.

3. Harvest the Energy

The movement of the electrons forms an electric current.

A. Hutchinson, Popular Mechanics, May, 2010

Sergei Skarupo, Nanomix,

Evaluation Engineering,

June

2007

Li-Ion

batteries

Applied Physics Letters, March 26, 2007, Vol. 90, 133108.Slide5

Carbon Nanotube Lattice

Nanotubes can be separated into two major classifications, namely chiral and achiralFortunately, using a folding construction on a flat graphene lattice, the primitive lattice of any single wall nanotube based on these two classifications can be constructed.

Chiral

Armchair

Zigzag

P. Wong; D. Akinwande, (2011).

Carbon Nanotube and Graphene Device Physics.

Cambridge University PressSlide6

Chirality

Chiral vector

n, an m are integers with m ≤ n.

Nanotube circumference is given the magnitude of Ch

Tube diameter:

P. Wong; D. Akinwande, (2011).

Carbon Nanotube and Graphene Device Physics.

Cambridge University PressSlide7

The Goal

Measurements and calculations of the axial coefficient of thermal expansion of carbon nanotubes exhibit an unusual and debated temperature dependence where it is negative at low temperatures exhibiting contraction then gradually becomes positive, transitioning to thermal expansion. There are some studies that contradict this behavior.There is also a large variation in the reported values for the temperatures where the transition from contraction to expansion take place, and also the temperature where maximum contraction occurs.

Kwon, et.al PRL 92, no. 1, (2004)

H. Jiang, et. al. J. Eng. Mat. & Tech., (2004)Slide8

Molecular Dynamics

The theoretical basis of this computer based technique involves little more than Newton’s laws of motion

Relation to Statistical Mechanics

Ergodic Hypothesis

Relation to thermodynamics

Equipartition Theorem

Temperature

Pressure, (Virial Theorem)Slide9

Large-Scale Atomic Molecular Massively Parallel Simulator(LAMMPS)

Open source Molecular dynamics distribution provided by Sandia National LabsSome of its capabilities are the capability to model many particle types, e.g. structure-less atoms, finite sized spherical particles

Manybody / Bond-Order Interaction potentials such as the Tersoff potential, Reactive Empirical Bond Order (REBO) Potential, Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) Potential, Reactive Force Field (ReaxxFF)

Multiple Ensemble Choices, NVT, NPT, NPHMany other tools for post-processing , plotting, and visualization of simulations results

http://lammps.sandia.gov/Slide10

AIREBO Many Body Potential

Adaptive Intermolecular Reactive Empirical Bond Order Potential (AIREBO)Stuart, Tutein, Harrison, Journal Chemical Physics, vol. 112, pp. 6472-6486 (2000).

Empirical potential developed specifically to model solid-phase hydrocarbons.

An extension of the original (REBO) potential allowing for covalent bonding interactions

Lennard-Jones Portion, used for long ranged “intra-molecular” interactions,

e.g. van der Waals forces

Torsional / Angular interactions

Short ranged interactions, made up of a repulsive & attractive

term. The

b

ij

(

Bond-order

) term is a hallmark of most many body potentials.

This term modifies the attraction between two atoms based on the environment (Number of neighbors) of the bond . Slide11

Thermostats (Nose-Hoover Thermostat)

The thermal expansion coefficient calculations require MD simulations of the system at multiple well defined temperatures.

Nose-Hoover Lagrangian

Equilibrium quantities derived from this Lagrangian correspond to the NVT ensemble.

Additional terms in this

Extended Lagrangian

,

s = “dynamical variable used to scale the unit of time”

Q = “plays the role of mass for the artificial coordinate, s”

(3N+1) = “degrees of freedom” Slide12

Sampling Geometry

Michael J.

O’Connell,

Carbon

Nanotubes Properties &

Applications

NIR excitation at 785 nm

“

roping

” RBM Raman band at ~264 cm

-1.

Raman

i

ntensity profiles for various nanotube chiralities both bundled & individual tubes in aqueous solution

(10,2) SWNT

Initial

undeformed

radius

r = 4.36 Angstroms

Initial Sampling

Length ( 179.9 Å)

Kwon, Berber, Tomanek, PRL (92) no. 1, 2004

Resonant Chirality, at 780 nm excitation (10,2)Slide13

Initial MD Results

Fixed boundary simulation box, 160 x 160 x 27 x 310 Å

(10, 2) SWCNT, 2232 atoms

0.5 fs time step,Coupled to Nose-Hoover thermostat after 100000

timesteps

AIREBO PotentialSlide14

Raman Spectroscopy of Carbon Nanotubes

J.R. Ferraro; K. Nakamoto; C.W. Brown, (2002). Introductory Raman Spectroscopy. Elsevier

Resonance Raman Intensity

Normal Raman Intensity

A. Jorio, R.Saito, M.Dresselhauss, G.Dresselhauss, (2011)

Raman Spectroscopy in Graphene Related Systems

. Wiley

I = Dissipated Power

=

Driving Frequency

G

q

=

“Damping Energy”

w

q

=

“Eigen-frequency”

E

g

= Energy difference between “real” electronic levels

E

q

= Phonon energy

The A term represents the change in the polarizability tensor,

involving electronic transition moments

g

r

=

Resonance window width

Slide15

DXR Raman System

780 nm Laser source (Frequency-stabilized single mode diode, High Brightness), wavelength stability < 1 cm-1 over 1 hr. periodFull range grating, spectral range of 50 – 3500 cm-1, spectral resolution 5.0 cm-1

Triplet Spectrograph, (No moving parts), Spectral Dispersion, 2cm-1 per CCD pixel (average value)Automated aperture selections

25 – 50 mm aperturesRayleigh filters (Stokes only)Slide16

Raman Features

G-Band

: Strong peak centered at ~ 1580 cm-1. (Tuinstra & Koenig1970). In-plane bond stretching in the Graphene lattice. This Raman feature is present in all graphitic materials, hence the G label stands for “graphite

G’-Band: Usually at ~ 2600 cm-1 was shown by Nemanich and Solin to be due to a second order two phonon scattering process at non-zero wavenumber, q ≠ 0.

A. Jorio, R.Saito, M.Dresselhauss, G.Dresselhauss, (2011)

Raman Spectroscopy in Graphene Related Systems

. Wiley

D – “Defect” Band

: Located at ~ 1300 – 1350 cm-1, this peak is associated with defects, disorders, boundaries and edge effects. (Tuinstra & Koenig 1970)

Graphene

532nm excitation

Graphite

780 nm excitationSlide17

Radial Breathing Mode-Band (

RBM

Raman

Features (Carbon Nanotubes)

Multi-walled carbon nanotube

780 nm excitation, 9 mW Power

4

.00 sec Exposure time, (2 Exposures)

400 lines/mm Grating

25 um

slit

entrance aperture

1.9285 cm-1 ResolutionSlide18

Temperature Effects on Raman Spectra of Purified SWNTs

 Slide19

Temperature Effects on Raman Spectra of SWNTs

Raman BandTrendline EquationR2 coefficient

G+y = -0.0187x + 1594.9

0.9817G-

y = -0.0204x + 1566.2

0.9554

G`

y = -0.0264x + 2579.2

0.6267

D

y = -0.0182x + 1295.6

0.7829

RBM

y = -0.0093x + 267.78

0.8244

While most of the Raman bands show a linear red-shift with increasing temperature, the G’ and D peak red-shift are not obviously linear.

The underlying physical mechanisms behind the D-band are also still debatable.Slide20

Laser Heated Raman Spectra

Terekhov, S.V., et al., AIP Conference Proceedings, (685), 2003

Purified SWCNT: y = 0.0669 x – 1.1624 cm-1

Un-purified SWCNT: y = 0.1306 x + 0.9942

cm-1

Residual Fe Catalyst: 8% (

Purified Sample on the left

)Slide21

Conclusions

Carbon nanotubes serve a variety of important uses and insight into the effects of temperature can lead to a better understanding of the Coefficient of Thermal Expansion.Reproduced the thermal induced linear red-shift in the Raman bands of single-walled carbon nanotubes.Reproduced shifted G+ Raman band in SWCNT samples of different purities, which is useful in estimating the thermal conductivity of a sample.Initial NVT MD results on (10,2) carbon nanotubes

show that the AIREBO potential produces a stable nanotube structure up to 800 KSlide22

References

N.R. Raravikar et.al. (2002). “Temperature dependence of radial breathing mode Raman frequency of single-walled carbon nanotubes”, Physical Review B, 66, pp. 235424-1 – 235424-9.J. Tersoff, (1988). “New empirical approach for the structure and energy of covalent systems”, Physical Review B, 37, no. 12, pp. 6991-7000.H.S.P. Wong; D. Akinwande, (2011). Carbon Nanotube and Graphene Device Physics. Cambridge University Press, New York.Ning Hu

Alamusi; Bi Jia; Masahiro Arai; Cheng Yan; Jinhua Li; Yaolu Liu; Satoshi Atobe;

Hisao Fukunaga, (2012). “Prediction of thermal expansion properties of carbon nanotubes using molecular dynamics simulations”, Computational Materials Science, 54, pp. 249-254.

A

. Jorio; M.S. Dresselhaus; R. Saito, (2011).

Raman Spectroscopy in Graphene Related Systems

. Wiley-VCH Verlag GmbH & Co.,

Weinheim

, Germany.

M.S. Dresselhauss, P.C. Eklund, ADVANCES IN PHYSICS, 2000, VOL. 49, NO. 6

S

. Plimpton,

“Fast

Parallel Algorithms for Short-Range Molecular Dynamics”, J Comp Phys, 117, 1-19 (1995

)Humphrey, W., Dalke, A. and Schulten, K., ``VMD - Visual Molecular Dynamics''

J. Molec. Graphics 1996, 14.1,

33-38Misra P., Casimir D., Garcia-Sanchez R. "Thermal Expansion Properties of Single-Walled Carbon Nanotubes by Raman Spectroscopy at 780 nm wavelength," Optoelectronics

, Photonics & Applied Physics (OPAP) Meeting held February 4-5, 2013 in

Singapore

Misra P., Casimir D., Garcia-Sanchez R.

"

Raman Spectroscopy and Molecular Dynamics Simulation Studies of Carbon

Nanotubes," ICCES'13

Conference held May 24-28, 2013 in Seattle, Washington.