Heat conduction in the Frenkel-Kontorova model

Thermal rectification in mass-asymmetric one-dimensional anharmonic oscillator lattices with and without a ballistic spacer

In this work we perform a systematic analysis of various structural parameters that have influence on the thermal rectification effect, i.e. asymmetrical heat flow, and the negative differential thermal resistance -reduction of the heat flux as the applied thermal bias is increased- present in a one-dimensional, segmented mass-graded system consisting of a coupled nearest-neighbor harmonic oscillator lattice (ballistic spacer) and two diffusive leads (modeled by a substrate potential) attached to the lattice at both boundaries. At variance with previous works, we consider the size of the spacer as smaller than that of the leads. Also considered is the case where the leads are connected along the whole length of the oscillator lattice; that is, in the absence of the ballistic spacer. Upon variation of the system's parameters it was determined that the performance of the device, as quantified by the spectral properties, is largely enhanced in the absence of the ballistic spacer for the small system-size limit herein considered.

Thermal rectification in oscillator lattices with a ballistic spacer and next nearest-neighbor interactions

In this work we study the asymmetric heat flow, i.e., thermal rectification, of a one-dimensional, mass-graded system consisting of a coupled harmonic oscillator lattice (ballistic spacer) and two diffusive leads attached to the boundaries of the former with both nearest-neighbor and next nearest-neighbor (NNN) interactions. The latter enhance the rectification properties of the system and specially its independence on system size. The system presents a maximum rectification efficiency for a very precise value of the parameter that controls the coupling strength of the NNN interactions that depend on the temperature range wherein the device operates. The origin of this maximum value is the asymmetric local heat flow response corresponding to the NNN contribution at both sides of the lighter mass-loaded diffusive lead as quantified by the spectral properties. Upon variation of the system's parameters the performance of the device is always enhanced in the presence of NNN interactions.

Heterogeneous irradiated-pristine polyethylene nanofiber junction as a high-performance solid-state thermal diode

In this work, we demonstrate two types of heterogeneous irradiated-pristine polyethylene nanofiber junctions, ‘heavily-irradiated-pristine’ (HI-P) and ‘lightly-irradiated-pristine’ (LI-P) junctions, as high-performance solid-state thermal diodes. The HI-P junction rectifies heat flux in a single direction, while the LI-P junction shows dual-directional rectification under different working temperatures. We accurately model the phase transition of polyethylene nanofibers with a finite temperature range rather than a step function. The finite-temperature-range model suggests that the rectification factor increases with temperature bias and there is a minimum threshold of temperature bias for notable rectification. Besides, the finite-temperature-range model shows better prediction for the heat flow data from experiments, while the step function model tends to overestimate the rectification performance around the optimal length fraction of irradiation. Although both the models show that an optimal rectification occurs when the interface temperatures in the forward and the reverse biases are equal, the optimized rectification factor is determined by the temperature bias and the temperature range of phase transition. This work elucidates the influence of both the temperature bias and the temperature range of phase transition on thermal rectification performance, which could incredibly benefit the evaluation and design of thermal diodes.

Energy transport in harmonically driven segmented Frenkel-Kontorova lattices

In this work we study the energy transport in a one-dimensional system composed of two dissimilar Frenkel-Kontorova lattices connected by a time-modulated coupling and in contact with two heat reservoirs operating at different temperature by means of molecular dynamics simulations. There is a value of the driving frequency at which the heat flux takes its maximum value, a phenomenon termed thermal resonance. Structural modifications in the lattice strongly alter the way in which the external driving interacts with the phonon bands. The overlap of the latter in the harmonic regime of the model determines the frequency range wherein resonance emerges. Parameter dependencies by which the incoming heat flux can be directed to either of the heat reservoirs are examined as well. Our results may be conductive to further developments in designing thermal devices.

Thermal rectification in mass-graded next-nearest-neighbor Fermi-Pasta-Ulam lattices

We study the thermal rectification efficiency, i.e., quantification of asymmetric heat flow, of a one-dimensional mass-graded anharmonic oscillator Fermi-Pasta-Ulam lattice both with nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions. The system presents a maximum rectification efficiency for a very precise value of the parameter that controls the coupling strength of the NNN interactions, which also optimizes the rectification figure when its dependence on mass asymmetry and temperature differences is considered. The origin of the enhanced rectification is the asymmetric local heat flow response as the heat reservoirs are swapped when a finely tuned NNN contribution is taken into account. A simple theoretical analysis gives an estimate of the optimal NNN coupling in excellent agreement with our simulation results.

Size effects on thermal rectification in mass-graded anharmonic lattices

In this work we study the thermal rectification efficiency of a one-dimensional mass-graded anharmonic oscillator lattice at large system sizes. A modest increase in rectification is observed. When the magnitude of the mass gradient scales with the system size, the aforementioned effect increases substantially. This result can be unmistakeably attributed to an asymmetry in the local temperature profile obtained for the employed parameter values.

Van der Waals interaction-tuned heat transfer in nanostructures

Interfaces usually impede heat transfer in heterogeneous structures. Recent experiments show that van der Waals (vdW) interactions can significantly enhance thermal conductivity parallel to the interface of a bundle of nanoribbons compared to a single layer of freestanding nanoribbon. In this paper, by simulating heat transfer in nanostructures based on a model of nonlinear one-dimensional lattices interacting via van der Waals interactions, we show that the vdW interface interaction can adjust the thermal conductivity parallel to the interface. The efficiency of the adjustment depends on the intensity of interactions and temperature. The nonlinear dependence of the conductivity on the intensity of interactions agrees well with experimental results for carbon nanotube bundles, multi-walled carbon nanotubes, multi-layer graphene, and nanoribbons.

Nonstationary heat conduction in one-dimensional models with substrate potential

The paper investigates nonstationary heat conduction in one-dimensional models with substrate potential. To establish universal characteristic properties of the process, we explore three different models: Frenkel-Kontorova (FK), phi4+ (φ(4)+), and phi4- (φ(4)-). Direct numeric simulations reveal in all these models a crossover from oscillatory decay of short-wave perturbations of the temperature field to smooth diffusive decay of the long-wave perturbations. Such behavior is inconsistent with the parabolic Fourier equation of heat conduction and clearly demonstrates the necessity for hyperbolic corrections in the phenomenological description of the heat conduction process. The crossover wavelength decreases with an increase in the average temperature. The decay patterns of the temperature field almost do not depend on the amplitude of the perturbations, so the use of linear evolution equations for the temperature field is justified. In all models investigated, the relaxation of thermal perturbations is exponential, contrary to a linear chain, where it follows a power law. The most popular lowest-order hyperbolic generalization of the Fourier law, known as the Cattaneo-Vernotte or telegraph equation, is also not valid for the description of the observed behavior of the models with the substrate potential, since the characteristic relaxation time in an oscillatory regime strongly depends on the excitation wavelength. For some of the models, this dependence seems to obey a simple scaling law.

Double negative differential thermal resistance induced by nonlinear on-site potentials

We study heat conduction through one-dimensional homogeneous lattices in the presence of the nonlinear on-site potentials containing the bounded and unbounded parts, and the harmonic interaction potential. We observe the occurrence of double negative differential thermal resistance (NDTR); namely, there exist two regions of temperature difference, where the heat flux decreases as the applied temperature difference increases. The nonlinearity of the bounded part contributes to NDTR at low temperatures and NDTR at high temperatures is induced by the nonlinearity of the unbounded part. The nonlinearity of the on-site potentials is necessary to obtain NDTR for the harmonic interaction homogeneous lattices. However, for the anharmonic homogeneous lattices, NDTR even occurs in the absence of the on-site potentials, for example, the rotator model.

Heat conduction in deformable Frenkel-Kontorova lattices: thermal conductivity and negative differential thermal resistance

Heat conduction through the Frenkel-Kontorova lattices is numerically investigated in the presence of a deformable substrate potential. It is found that the deformation of the substrate potential has a strong influence on heat conduction. The thermal conductivity as a function of the shape parameter is nonmonotonic. The deformation can enhance thermal conductivity greatly, and there exists an optimal deformable value at which thermal conductivity takes its maximum. Remarkably, we also find that the deformation can facilitate the appearance of the negative differential thermal resistance.

Heat conduction in driven Frenkel-Kontorova lattices: thermal pumping and resonance

Heat conduction through the Frenkel-Kontorova chain under the influence of an ac driving force applied locally at one boundary is studied by nonequilibrium molecular dynamics simulations. We observe the occurrence of thermal resonance, namely, there exists a value of the driving frequency at which the heat flux takes its maximum value. The resonance frequency is determined by the dynamical parameters of the model, which has been numerically explored. Remarkably, the heat can be pumped from the low-temperature heat bath to the high temperature one by suitably adjusting the frequency of the ac driving force. By examining effects of the driving amplitude on heat conduction, we show that the amplitude threshold for nonlinear supratransmission is absent when the system is in contact with heat baths, namely, the heat flux smoothly increases with the increasing of amplitude.

Heat conduction and reversed thermal diode: the interface effect

The important role of interface collisions on the thermal-diode effect, of the two-segment lattices is studied. In the high-average temperature region, it is found that the thermal-diode effect may be significantly weaken and even annihilated. In the low-temperature region, where the thermal diode is inhibited in the collisionless case, an interesting reversed thermal diode is achieved. These behaviors are interpreted in terms of phonon-band mixing induced by interface collisions. The regime where a reversed thermal diode can be observed by resorting to the dependence of the heat current on the average temperature, and a critical temperature exists. The results proposed in this paper reveal that thermal-diode effect can be qualitatively influenced if the interface collisions could not be neglected.

Transition from the exhibition to the nonexhibition of negative differential thermal resistance in the two-segment Frenkel-Kontorova model

An extensive study of the one-dimensional two-segment Frenkel-Kontorova (FK) model reveals a transition from the counterintuitive existence to the ordinary nonexistence of a negative-differential-thermal-resistance (NDTR) regime, when the system size or the intersegment coupling constant increases to a critical value. A "phase" diagram which depicts the relevant conditions for the exhibition of NDTR was obtained. In the existence of a NDTR regime, the link at the segment interface is weak and therefore the corresponding exhibition of NDTR can be explained in terms of effective phonon-band shifts. In the case where such a regime does not exist, the theory of phonon-band mismatch is not applicable due to sufficiently strong coupling between the FK segments. The findings suggest that the behavior of a thermal transistor will depend critically on the properties of the interface and the system size.

Scaling and the thermal conductivity of the Frenkel-Kontorova model

We have studied the dependence of the thermal conductivity kappa on the strength of the interparticle potential lambda and the strength of the external potential beta in the Frenkel-Kontorova model. We found that the functional relation can be expressed in a scaling form, kappa proportional, variantlambda;{32}/beta;{2} . This result is first obtained by nonequilibrium molecular dynamics. It is then confirmed by two analytical methods, the self-consistent phonon theory and the self-consistent stochastic reservoirs method. The thermal conductivity kappa is therefore a decreasing functon of beta and an increasing function of lambda.

Thermal rectifying effect in macroscopic size

We address the problem of the rectifying effect of heat conduction at macroscopic size. A design for a macroscopic thermal rectifier based on the macroscopic thermal conductivity of materials is introduced, and then realizations of the design are shown by numerical simulations and phenomenological estimations.

Asymmetric heat conduction through a weak link

We study the heat conduction of two nonlinear lattices joined by a weak harmonic link. When the system reaches a steady state, the heat conduction of the system is decided by the tunneling heat flow through the weak link. We present an analytical analysis by the combination of the self-consistent phonon theory and the heat tunneling transport formalism, and then the tunneling heat flow can be obtained. Moreover, the nonequilibrium molecular dynamics simulations are performed and the simulations results are consistent with the analytical predictions.

Asymmetric heat conduction in nonlinear lattices

In this Letter, we conduct an extensive study of the two-segment Frenkel-Kontorova model. We show that the rectification effect of the heat flux reported in recent literature is possible only in the weak interfacial coupling limit. The rectification effect will be reversed when the properties of the interface and the system size change. These two types of asymmetric heat conduction are governed by different mechanisms though both are induced by nonlinearity. An intuitive physical picture is proposed to interpret the reversal of the rectification effect. Since asymmetric heat conduction depends critically on the properties of the interface and the system size, it is probably not an easy task to fabricate a thermal rectifier or thermal diode in practice.