Anomalous heat conduction in polyethylene chains: Theory and molecular dynamics simulations

Asegun Henry and Gang Chen

Phys. Rev. B 79, 144305 – Published 24 April 2009

Abstract

In 1955 Fermi, Pasta, and Ulam showed that a simple model for a nonlinear one-dimensional chain of particles can be nonergodic, which implied infinite thermal conductivity. A more recent investigation of a realistic model for an individual polyethylene chain suggests that this phenomenon can even persist in real polymer chains. The reason for the divergent behavior and its associated mechanism, however, remains unclear. This paper presents a general formulation for normal-mode vibrational contributions to thermal conductivity, which is then used to analyze molecular dynamics simulations of individual polyethylene chains. Our analysis shows that cross correlations for midfrequency longitudinal-acoustic phonons are responsible for the divergent thermal conductivity in our model.

Received 7 January 2009

DOI:https://doi.org/10.1103/PhysRevB.79.144305

Authors & Affiliations

Asegun Henry and Gang Chen

Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA

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Vol. 79, Iss. 14 — 1 April 2009

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Images

Figure 1
(Color online) Green-Kubo thermal-conductivity integrals. The results of five independent simulations are shown, which exhibited contrasting behavior. Cases 1–4 use identical simulation parameters and procedures but were initialized with different random velocities. Case 5 uses the same initial velocities as case 4; however the masses of three carbon atoms and five hydrogen atoms were increased to heavier isotopes.Reuse & Permissions
Figure 2
(Color online) Normal mode correlation functions (fluctuating lines) and thermal-conductivity contributions (gray-dashed lines) for the longest wavelength modes $(λ = 40 ucs)$ of the four acoustic polarizations in case 3. In each panel the correlation corresponds to the two modes indicated by wave-vector index $n$ and polarization $p$ . The raw data (left-vertical axis) is shown with light solid thin lines. Smoothed local average values (left-vertical axis) are shown with dark solid thick lines. (a)–(d) show mode autocorrelations while (e) and (f) show cross correlations. In each panel the cumulative contribution to thermal conductivity (right-vertical axis), based on Eq. (12), is shown with gray-dashed lines.Reuse & Permissions
Figure 3
(Color online) Normal mode cross-correlational functions (fluctuating lines) and thermal-conductivity contributions (gray-dashed lines) for $TA x$ and Tors polarizations in case 3. In each panel the correlation corresponds to the two modes given by wave-vector index $n$ and polarization $p$ . The raw data (left-vertical axis) is shown with light solid thin lines. Smoothed local average values (left-vertical axis) are shown with dark solid thick lines. The cumulative contribution to thermal conductivity (right-vertical axis), based on Eq. (12), is shown with gray-dashed lines.Reuse & Permissions
Figure 4
(Color online) Normal mode correlation functions (fluctuating lines) and thermal-conductivity contributions (gray-dashed lines) for LA modes in case 3. In each panel the correlation corresponds to the two modes indicated by wave-vector index $n$ and polarization $p$ . The raw data (left-vertical axis) is shown with light solid thin lines. Smoothed local average values (left-vertical axis) are shown with dark solid thick lines. The cumulative contribution to thermal conductivity (right-vertical axis), based on Eq. (12), is shown with gray-dashed lines. (b) illustrates the short-time behavior of the correlation in (a).Reuse & Permissions
Figure 5
(Color online) Normal mode correlation functions (fluctuating lines) and thermal-conductivity contributions (gray-dashed lines) for LA modes in cases 1 and 2. (a), (c), and (e) correspond to case 1 while (b), (d), and (f) correspond to case 2. In each panel the correlation corresponds to the two modes indicated by wave-vector index $n$ and polarization $p$ . The raw data (left-vertical axis) is shown with light solid thin lines. Smoothed local average values (left-vertical axis) are shown with dark solid thick lines. The cumulative contribution to thermal conductivity (right-vertical axis), based on Eq. (12), is shown with gray-dashed lines.Reuse & Permissions
Figure 6
(Color online) Normal mode correlation functions (fluctuating lines) and thermal-conductivity contributions (gray-dashed lines) for LA modes in cases 4 and 5. (a), (c), and (e) correspond to data from divergent case 4 while (b), (d), and (f) correspond to case 5, which is equivalent to case 4 with the addition of isotopes. In each panel the correlation corresponds to the two modes indicated by wave-vector index $n$ and polarization $p$ . The raw data (left-vertical axis) is shown with light solid thin lines. Smoothed local average values (left-vertical axis) are shown with dark solid thick lines. The cumulative contribution to thermal conductivity (right-vertical axis), based on Eq. (12), is shown with gray-dashed lines.Reuse & Permissions

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