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 . (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 . Funding C. S. G. is grateful for funding from NASA’s Office of Graduate Research through the Space Technology Research Fellowship. References  C. Yue et al., Micro. Tech., 16(633), 2010.  R. C. Yu et al., PRL, 68(2050), 1992.  R. J. Bell and D. C. Hibbins-Butler, JPC, 8, 787 1975.  P. B. Allen and J. L. Feldman, PRB, 48(581), 1993.  J. D. Gale and A. L. Rohl, Mol. Sim., 29(291), 2003.