Controlling the Energy Flow in Nonlinear Lattices: A Model for a Thermal Rectifier

Abstract

We address the problem of heat conduction in 1-D nonlinear chains; we show that, acting on the parameter which controls the strength of the on site potential inside a segment of the chain, we induce a transition from conducting to insulating behavior in the whole system. Quite remarkably, the same transition can be observed by increasing the temperatures of the thermal baths at both ends of the chain by the same amount. The control of heat conduction by nonlinearity opens the possibility to propose new devices such as a thermal rectifier.In recent years a renewed attention has been directed to the energy transport in dynamical systems, a problem which has been denoted by Peierls as one of the outstanding unsolved problems of modern physics [1]. These efforts mainly focused on the possibility to derive the Fourier law of heat conduction on purely dynamical grounds without recourse to any statistical assumption [2][3][4][5][6][7][8][9][10][11]. In spite of relevant progresses, several problems remain open and we are still far from a complete understanding [5][6][7][8][9][10][11].In this paper we investigate a different and important problem namely the possibility to control the energy transport inside a nonlinear 1D chain connecting two thermostats at different temperatures. We show that we can parametrically control the heat flux through the system by acting on a small central part of the chain. Even more interestingly, we show that it is possible to adjust the heat flux by varying the temperatures of both thermostats, keeping constant the temperature difference. Thus we provide a simple mechanism to change the properties of the system, from a normal conductor obeying Fourier law, down to an almost perfect insulator. Controlling heat conduction by nonlinearity opens new possibilities, such as the design of a lattice that carries heats preferentially in one direction, i.e. a thermal rectifier.We consider the Hamiltonianwhich describes a chain of N particles with harmonic coupling of constant K and a Morse on-site potential V n (y n ) = D n (e −αnyn − 1) 2 . This model was introduced for DNA chains where m is the reduced mass of a base pair, y n denotes the stretching from equilibrium position of the hydrogen bonds connecting the two bases of the n-th pair and p n is its momentum [12][13][14]. In the context of the present study, model (1) can simply be viewed as a generic system of anharmonic coupled oscillators, the onsite potential arising from interactions with other parts of the system, not included in the model. The Morse potential is simply an example of a highly anharmonic soft potential, which has a frequency that decreases drastically when the amplitude of the motion increases.In this paper we consider the out-of-equilibrium properties of model (1) by numerically simulating the dynamics of the N particle chain, coupled, at the two ends, with thermal baths at different temperatures T 1 and T 2 . We thermalize at T 1 and T 2 the first and the last L particles by using Nosé-Hoover thermostats chains [15,16],...

From Thermal Rectifiers to Thermoelectric Devices

“…However if the translational invariance is broken by a substrate potential, so that momentum is not a constant of the motion, a simple one-dimensional lattice of harmonically coupled particles subjected to an external at low T at high T potential, known as a Klein-Gordon model, can show a well defined thermal con-ductivity while allowing an easy analysis of the properties of the system. Such a lattice can form the basis for a thermal rectifier [141].…”

Multimode quantized thermal conductance tuned by electric field in a composite polymer

“…Recently, Cao et al [19] has proposed an approach to realize field-dependent multimode quantized thermal conductance by introducing both harmonic and anharmonic couplings [20][21][22] to a quantum wire. By stretching or compressing the wire, phononic band structures are tuned and multiple phononic channels are opened one by one.…”

Heat conduction in one dimensional systems: Fourier law, chaos, and heat control

“…Actually a model of thermal rectifier has been recently proposed [13] in which the heat can flow preferentially in one direction. Although this model is far away from a prototype realization, it is based on a mechanism of very general nature and, as such, is suitable of improvement and may eventually lead to real applications.…”

“…[13], there is a new crucial element which allows to improve the efficiency by more than two orders of magnitude.…”

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