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Carnegie Mellon University THERMAL TRANSPORT IN C

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Carnegie Mellon University THERMAL TRANSPORT IN C
THERMAL TRANSPORT IN C60 MOLECULAR
CRYSTALS AT AND ABOVE ROOM TEMPERATURE Carnegie
Mellon
University
Caroline S. Gorham, and Alan J. H. McGaughey
Department of Mechanical Engineering
Carnegie Institute of Technology, Carnegie Mellon University
The thermal conductivity of solid fullerene molecular systems has garnered significant interest as an example of materials whose thermal
transport is dominated by Einstein-type oscillators. Using classical molecular dynamics (MD) simulations and quantum mechanical
harmonic lattice dynamics (HLD) calculations, this study isolates the roles of inter- and intra- molecular vibrational degrees of freedom on
the bulk thermal conductivity (κ) of the face-centered cubic C60 molecular crystal. The resistance to thermal transport due to the nearestneighbor molecular interface is isolated using non-equilibrium MD methods; the predicted thermal conductivity, calculated within a
nearest-neighbor resistor network, is negligible. Thermal diffusivity of non-propagating vibrations is dominant.
Harmonic Lattice Dynamics (HLD)
Methods
Motivation
Interface Driven Fullerene/Polymer Photovoltaics
hν
Fig. 1. Charge
transfer at the donor/
acceptor interface in a
bulk heterojunction
photovoltaic device.
e-
Removal of heat is vital to device performance and efficiency.
Frequencies at k=0 are found by
solving the eigenvalue equation,
2
ω (0,ν)e(0,ν)= D(0)e(0,ν).
Fig. 5. Orientationally
disordered FCC-phase.
Low κ Driven by Internal Contacts
Results
(c)
We aim to thermally characterize the interface and the highenergy vibrations isolated to individual molecules.
Classical Molecular Dynamics (MD)
Methods
We solve for the time evolution of a system of
2
2
atomic components, i, as Fi = mid ri /dt .
Fig. 3. (a) Thermal current is applied between a molecular source and
sinks to determine the thermal interface resistance, Rnn. (b) A resistance
network describes effective nearest-neighbor thermal conductivity, κnn [1].
(a)
(b)
1 source
36 sinks
Rnn
node
Thermal Conductivity (W/m-K)
Results
0
10
Ref. 2
κbulk
κnn
10-2
-Temperature independence
of κbulk indicates a lack of
changes in the anharmonic
thermal environment.
-Rnn is large enough that κnn
is < 5% of κbulk at hightemperatures.
200
400
600
800
Temperature (K)
Fig. 4. Temperature-dependent κbulk and κnn, simulated with classical MD.
Cutoff to Propagating Thermal Transport
A phase quotient, PQ(ω),
ωcut
indicates the parallel or antiparallel motions of nearestneighbor bonds.
+1
PQ(ω) =
0
100
101
Frequency (THz)
102
.
i)
Σ e(0, e(0, j) .
Bonds i, j Σ | e(0, i) . e(0, j) |
Bonds i, j
-A random phase is found
for ω larger than ωcut.
Fig. 6. Frequency-dependent phase quotient.
Thermal Conductivity of Non-Propagating States
Thermal Conductivity (W/m-K)
(b)
(a)
Phase Quotient, PQ(ω)
Fig. 2. Weak interface bonding is modified with (a) polymer intercalation,
(b) surface functionalization, or (c) distribution of thermal connections.
100
-Above ωcut, we anticipate that
vibrational states have
sufficiently small mean free
paths, Λ < λ, and are hence
non-propagating.
ωcut
10-5
10-10
0
10
1
10
Frequency (THz)
-Calculated as a summation
over discrete non-propagating
states, [4, 5] the total harmonic
thermal
conductivity,
κ
,
harmonic
2
10 is 0.53 W/m-K.
Fig. 7. Frequency-dependent κharmonic.
Summary of Results
~ κnn is a marginal contribution to the bulk κ.
~ κbulk is dominated by non-propagating
vibrations [4].
Funding
C. S. G. is grateful for funding
from NASA’s Office of
Graduate Research through the
Space Technology Research
Fellowship.
References
[1] C. Yue et al., Micro. Tech.,
16(633), 2010.
[2] R. C. Yu et al., PRL,
68(2050), 1992.
[3] R. J. Bell and D. C.
Hibbins-Butler, JPC, 8, 787
1975.
[4] P. B. Allen and J. L.
Feldman, PRB, 48(581), 1993.
[5] J. D. Gale and A. L. Rohl,
Mol. Sim., 29(291), 2003.
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