Tunable heat conduction through coupled Fermi-Pasta-Ulam chains

We conduct a study on heat conduction through coupled Fermi-Pasta-Ulam (FPU) chains by using classical molecular dynamics simulations. Our attention is dedicated to showing how the phonon transport is affected by the interchain coupling. It has been well accepted that the heat conduction could be impeded by the interchain interaction due to the interface phonon scattering. However, recent theoretical and experimental studies suggest that the thermal conductivity of nanoscale materials can be counterintuitively enhanced by the interaction with the substrate. In the present paper, by consecutively varying the interchain coupling intensity, we observed both enhancement and suppression of thermal transport through the coupled FPU chains. For weak interchain couplings, it is found that the heat flux increases with the coupling intensity, whereas in the case of strong interchain couplings, the energy transport is found to be suppressed by the interchain interaction. Based on the phonon spectral energy density method, we attribute the enhancement of the energy transport to the excited phonon modes (in addition to the intrinsic phonon modes), while the upward shift of the high-frequency phonon branch and the interface phonon-phonon scattering account for the suppressed heat conduction.

Figure 1

Schematics of the coupled FPU chains.

Figure 2

Dependence of the heat flux of coupled FPU chains on the interchain coupling strength $k_c$ for (a) $k_1=k_2=1.0$, (b) $k_1=1.0$ and $k_2=5.0$, and (c) different system sizes $N=50$, 100, 500 at $k_1=1.0$ and $k_2=5.0$. (d) Dependence of $NJ$ (the product of the chain's length and heat flux) on $N$ (the chain's length) at $k_1=1.0,k_2=5.0$, and $k_c=0.0$. $J_1$ and $J_2$ denote the heat flux of chain 1 and chain 2, respectively. $J_t$ is the total heat flux of the coupled system.

Figure 3

Contour plot of phonon SED of chain 1 with $k_1=k_2=1.0$: (a) $k_c=0.0$, (b) $k_c=0.3$, (c) $k_c=1.0$, and (d) $k_c=2.0$; ${\omega }_1$ is the frequency of chain 1.

Figure 4

Contour plot of phonon SED of two coupled FPU chains with $k_1=1.0,k_2=5.0$: dispersion relation of chain 1 for $\left({\text{a}}_1\right) k_c=0.0,\left({\text{b}}_1\right) k_c=0.3,\left({\text{c}}_1\right) k_c=0.5,\left({\text{d}}_1\right) k_c=2.0$, and $\left({\text{e}}_1\right) k_c=4.0$ and dispersion relation of chain 2 for $\left({\text{a}}_2\right) k_c=0.0,\left({\text{b}}_2\right) k_c=0.3,\left({\text{c}}_2\right) k_c=0.5,\left({\text{d}}_2\right) k_c=2.0$, and $\left({\text{e}}_2\right) k_c=4.0$.

Figure 5

Phonon SED peaks for the coupled FPU chain with $k_1=k_2=1.0$.

Figure 6

Plot of ${\kappa }^{\prime }$ versus $k_c$ for the coupled FPU chains with $k_1=k_2=1.0$.

Figure 7

Phonon SED peaks for the coupled FPU chains with $k_1=1.0,k_2=5.0$.

Figure 8

Plot of ${\kappa }^{\prime }$ versus $k_c$ for the coupled FPU chains with $k_1=1.0,k_2=5.0$ for (a) chain 1 and (b) chain 2.

Figure 9

Dependence of the energy density on the frequency while $k_1=1.0,k_2=5.0$, wave vector $q=3$. Energy density distributions of (a) chain 1 and (b) chain 2 when $k_c=0.0$, of (c) chain 1 and (d) chain 2 when $k_c=0.3$, and (e) chain 1 and (f) chain 2 when $k_c=4.0$. Here ${\omega }_{1-},{\omega }_{2+}$ are the intrinsic phonon frequencies of chain 1 and chain 2, respectively; ${\omega }_{1+},{\omega }_{2-}$ are their excited phonon frequencies.

Figure 10

Dependence of the heat flux on the interchain coupling strength $k_c$ for (a) coupled harmonic chains and (b) coupled FK chains (external potential $V_1=V_2=1.0$) while $k_1=1.0,k_2=5.0$; $J_1$ and $J_2$ denote the heat flux of chain 1 and chain 2, respectively, and $J_t$ is the total heat flux of the coupled system.