Normal thermal conduction in lattice models with asymmetric harmonic interparticle interactions

Abstract

We study the heat conduct behavior of a lattice model with asymmetry harmonic inter-particle interactions in this paper. Normal heat conductivity independent of the system size is observed when the lattice chain is long enough. Because only the harmonic interactions are involved, the result confirms without ambiguous interpretation that the asymmetry plays the key role in resulting in the normal heat conduct of one dimensional momentum conserving lattices. Both equilibrium and non-equilibrium simulations are performed to support the conclusion.The heat transport properties of low-dimensional systems have evoked intensive studies for decades [1][2][3][4][5][6][7][8][9][10][11][12][13], aiming at to verify whether the Fourier's law of heat conduction J = −κ∇T (1)

Effective phonon treatment of asymmetric interparticle interaction potentials

“…Especially, it is clearly seen that the results of L-J model are vary similar to the result of a fluid (compare with Fig. 2(d), normal heat conduction is observed in both of them [17,23] ).…”

“…Therefore, here we emphasize that an asymmetric piecewise linear system can be well described by a pure harmonic lattice, only indicate that the centre positions of phonons peaks are same as an equivalent harmonic lattice, but there is essential difference comes from asymmetry between them, e.g., the phonon peak will broaden in true asymmetric piecewise linear lattice, which means that there exist stronger interactions between phonons. Besides, normal heat conduction is also observed in asymmetric harmonic model [17], but these are absent in the equivalent pure harmonic chain.…”

Fourier heat conduction as a strong kinetic effect in one-dimensional hard-core gases

“…However, counterexamples, i.e., momentum conserving systems but yet having a size-independent thermal conductivity, have been found [10][11][12][13]. These counterexamples usually have asymmetric interparticle interactions, including the Toda-like models [12], Lennard-Jones model [10,11,13], the Fermi-Pasta-Ulam-α-β model [14], the diatomic gas model [15,16], the diatomic Toda model [16], and so on. More importantly, so far direct experimental measurements have not provided solid evidence yet to support the predicted abnormality in real low-dimensional materials of finite sizes available.In one dimensional (1D) case, the heat conductivity, denoted by κ, is related to the HCAF, denoted by C(t), by the Green-Kubo formulaHere k B is the Boltzmann constant, L and T are, respectively, the size and the temperature of the system, and C(t) ≡ J(0)J(t) , with J(t) being the total heat current at time t and · representing the equilibrium ensemble average.…”

“…is the local current on the qth particle. Still taking the ith particle as the tagged particle, we have [3,12]…”

Key role of asymmetric interactions in low-dimensional heat transport

“…1(b) shows, the asymmetry degree of the L-J potential increases as the average potential energy U , and for a fixed U value it increases as the parameter pair (m, n) varies from (m, n) = (12,6) to (m, n) = (2, 1). We will focus on the case of (m, n) = (12,6), the most frequently adopted parameters in literatures, but also discuss other values of (m, n) when it is in order. In Fig.…”