Abstract

The thermal conductivity of nanometric objects or nanostructured materials can be determined using nonequilibrium molecular dynamics (NEMD) simulations. The technique is simple in its principle, and resembles a numerical guarded hot plate experiment. The “sample” is placed between a hot source and a cold source consisting of thermostatted sets of atoms. The thermal conductivity is obtained from the heat flux crossing the sample and the temperature profile in the system. Simulation results, however, exhibit a strong dependence of the thermal conductivity on the sample size. In this paper, we discuss the physical origin of this size dependence, by comparing MD results with those obtained from simple models of thermal conductivity based on harmonic theory of solids. A model is proposed to explain the variation of the thermal conductivity with system size.

References

1.
Cahill
,
D. G.
,
Goodson
,
K.
, and
Majumdar
,
A.
,
2002
, “
Thermometry and Thermal Transport in Micro/Nanoscale Solid State Devices
,”
ASME J. Heat Transfer
,
124
(
2
), pp.
223
241
.
2.
Chen
,
G.
, and
Shakouri
,
A.
,
2002
, “
Heat Transfer in Nanostructures for Solid State Energy Conversion
,”
ASME J. Heat Transfer
,
124
(
2
), pp.
242
252
.
3.
Kulish
,
V. V.
,
Lage
,
J. L.
,
Komorov
,
P. L.
, and
Raad
,
P. E.
,
2001
, “
A Fractional-Diffusion Theory for Calculating Thermal Properties of Thin Films From Surface Transient Thermoreflectance Measurements
,”
ASME J. Heat Transfer
,
123
(
6
), pp.
1133
1138
.
4.
Mazumber
,
S.
, and
Majumdar
,
A.
,
2001
, “
Monte Carlo Study of Phonon Transport in Solid Thin Films Including Dispersion and Polarization
,”
ASME J. Heat Transfer
,
123
(
4
), pp.
749
759
.
5.
Zeng
,
T.
, and
Chen
,
G.
,
2001
, “
Phonon Heat Conduction in Thin Films: Impact of Thermal Boundary Resistance and Internal Heat Generation
,”
ASME J. Heat Transfer
,
123
(
2
), pp.
340
347
.
6.
Wang
,
X.
,
Hu
,
H.
, and
Xu
,
X.
,
2001
, “
Photo-Acoustic Measurement of Thermal Conductivity of Thin Films and Bulk Materials
,”
ASME J. Heat Transfer
,
123
(
1
), pp.
138
144
.
7.
Li
,
B.
,
Pottier
,
L.
,
Roger
,
J. P.
,
Fournier
,
D.
,
Watari
,
K.
, and
Hirao
,
K.
,
1999
, “
Measuring the Anisotropic Thermal Diffusivity of Silicon Nitride Grains by Thermoreflectance Microscopy
,”
J. Eur. Ceram. Soc.
,
19
, p.
1631
1631
.
8.
Gomes
,
S.
,
Trannoy
,
N.
,
Grossel
,
Ph.
,
Depasse
,
F.
,
Bainier
,
C.
, and
Charraut
,
D.
,
2001
, “
Scanning Thermal Microscopy: Characterization and Interpretation of the Measurement
,”
Int. J. Thermophys.
,
40
, pp.
949
958
.
9.
Hmina
,
N.
, and
Scudeller
,
Y.
,
1998
, “
Thermal Interface Resistance and Subsurface Effusivity of Submicron Metallic Films on Dielectric Substrates: An Experimental Method for Simultaneous Determination
,”
Int. J. Heat Mass Transfer
,
41
(
18
), pp.
2781
2798
.
10.
Bincheng
,
L.
,
Potier
,
L.
,
Roger
,
J. P.
, and
Fournier
,
D.
,
1999
, “
Thermal Characterization of Thin Superconducting Films by Modulated Thermoreflectance Microscopy
,”
Thin Solid Films
,
352
(
1–2
), pp.
91
96
.
11.
Maruyama
,
S.
,
2002
, “
A Molecular Dynamics Simulation of the Heat Conduction in Finite Length SWNTs
,”
Physica B
,
323
, pp.
193
195
.
12.
Berbert
,
S.
,
Kwon
,
Y. K.
, and
Tomanek
,
D.
,
2000
, “
Unusually High Thermal Conductivity of Carbon Nanotubes
,”
Phys. Rev. Lett.
,
84
(
25
), pp.
4613
4616
.
13.
Jund
,
P.
, and
Jullien
,
R.
,
1999
, “
Molecular-Dynamics Calculation of the Thermal Conductivity of Vitreous Silica
,”
Phys. Rev. B
,
59
(
21
), pp.
13707
13711
.
14.
Daly
,
B. C.
, and
Maris
,
H. J.
,
2002
, “
Calculation of the Thermal Conductivity of Superlattices by Molecular Dynamics Simulations
,”
Physica B
,
316–317
, pp.
247
249
.
15.
Allen, M. P., and Tildesley, D. J., 1987, Computer Simulation of Liquid, Oxford University Press Inc., New York.
16.
Frenkel, D., and Smit, B., 1996, Understanding Molecular Simulation, Academic Press, San Diego.
17.
Kubo, R., Toda, M., and Hashitsume, N., 1985, Statistical Physics II, Springer, Berlin.
18.
Barrat
,
J. L.
, and
Chiaruttini
,
F.
,
2003
, “
Kapitza Resistance at the Liquid Solid Interface
,”
Mol. Phys.
,
101
, p.
1605
1605
.
19.
Evans, D. J., and Morris, G. P., 1990, Statistical Mechanics of Nonequilibrium Liquids, Academic Press, New York.
20.
Baranyai
,
A.
,
1996
, “
Heat Flow Studies for Large Temperature Gradients by Molecular Dynamics Simulations
,”
Phys. Rev. E
,
54
(
6
), pp.
6911
6917
.
21.
Hansen
,
D. P.
, and
Evans
,
D. J.
,
1994
, “
A Generalized Heat Flow Algorithm
,”
Mol. Phys.
,
81
(
4
), pp.
767
779
.
22.
Maiti
,
A.
,
Mahan
,
G. D.
, and
Pantelides
,
S. T.
,
1997
, “
Dynamical Simulations of Nonequilibrium Processes—Heat Flow and the Kapitza Resistance Across Grain Boundaries
,”
Solid State Commun.
,
102
(
7
), pp.
517
521
.
23.
Zheng
,
Q.
,
Su
,
G.
,
Wang
,
J.
, and
Guo
,
H.
,
2002
, “
Thermal Conductance for Single Wall Carbon Nanotubes
,”
Eur. Phys. J. B
,
25
, pp.
233
238
.
24.
Plimpton
,
S. J.
,
1995
, J. Comput. Phys., 117(1) code available at http://www.cs.sandia.gov/tech8reports/ssjplimp.
25.
Lukes
,
J. R.
,
Li
,
D. Y.
,
Liang
,
X. G.
, and
Tien
,
C. L.
,
2000
, “
Molecular Dynamics Study of Solid Thin Film Thermal Conductivity
,”
ASME J. Heat Transfer
,
122
, p.
536
536
.
26.
Mu¨ller-Plathe
,
F.
,
1997
, “
A Simple Non-Equilibrium Molecular Dynamics Method for Calculating the Thermal Conductivity
,”
J. Chem. Phys.
,
106
(
14
), p.
6082
6082
.
27.
Ikeshoji
,
T.
, and
Hafskjold
,
B.
,
1994
, “
Non-Equilibrium Molecular Dynamics Calculation of Heat Conduction in Liquid and Through Liquid Gas Interface
,”
Mol. Phys.
,
81
, pp.
251
261
.
28.
Kotake
,
S.
, and
Wakuri
,
S.
,
1994
, “
Molecular Dynamics Study of Heat Conduction in Solid Materials
,”
JSME Int. J., Ser. B
,
37
(
1
), pp.
103
108
.
29.
Olischlger
,
C.
, and
Scho¨n
,
J. C.
,
1999
, “
Simulation of Thermal Conductivity and Heat Transport in Solids
,”
Phys. Rev. B
,
59
(
6
), pp.
4125
4133
.
30.
Chantrenne, P., and Barrat, J. L., 2004, “Analytical Model for the Determination of Thermal Conductivity in Nanostructures,” Superlattices Microstruct., to be published.
31.
Chapman, S., and Cowling, T. G., 1970, The Mathematical Theory of Non-Uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases, third ed., Cambridge University Press.
32.
Fujita, S., 1996, Statistical and Thermal Physics, Part I, R. E. Krieger Publishing Company, Malabar, FL.
33.
Rosenblum
,
I.
,
Adler
,
J.
, and
Brandon
,
S.
,
1998
, “
Calculation of Thermal Properties of Diamond From Simulated Phonon Spectra
,”
Comput. Mater. Sci.
,
12
, pp.
9
25
.
34.
Che
,
J.
,
C¸agin
,
T.
, and
Goddard
,
W. A.
,
2000
, “
Thermal Conductivity of Carbon Nanotubes, Nanotechnology
,”
Nanotechnology
,
11
, pp.
65
69
.
35.
Volz
,
S.
, and
Chen
,
G.
,
1999
, “
Lattice Dynamic Simulation of Silicon Thermal Conductivity
,”
Physica B
,
263–264
, pp.
709
712
.
36.
Motoyama
,
S.
,
Ichikawa
,
Y.
,
Hiwatari
,
Y.
, and
Oe
,
A.
,
1999
, “
Thermal Conductivity of Uranium Dioxide by Nonequilibrium Molecular Dynamics Simulation
,”
Phys. Rev. B
,
60
(
1
), pp.
292
298
.
37.
Kittel, C., 1996, Introduction to Solid State Physics, Wiley, New York.
38.
Ashcroft, N. W., and Mermin, N. D., 1976, “Solid State Physics,” Harcourt College Publishers, Fort Worth, TX.
39.
Chaikin, P. M., and Lubensky, T. C., 1995, Principle of Condensed Matter Physics, Cambridge Press University.
40.
Zou
,
J.
, and
Balandin
,
A.
,
2001
, “
Phonon Heat Conduction in a Semiconductor Nanowire
,”
J. Appl. Phys.
,
89
(
5
), pp.
2932
2938
.
41.
Quesnel
,
D. J.
,
Rimai
,
D. S.
, and
DeMejo
,
L. P.
,
1993
, “
Elastic Compliances and Stiffnesses of the FCC Lennard-Jones Solid
,”
Phys. Rev. B
,
48
(
10
), pp.
6795
6807
.
42.
Lepri
,
S.
,
Livi
,
R.
, and
Politi
,
A.
,
2003
, “
Thermal Conduction in Classical Low-Dimensional Lattices
,”
Phys. Rep.
,
377
, pp.
1
80
.
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