Heat conduction in a three-dimensional momentum-conserving anharmonic lattice

Thermal rectification in three-dimensional mass-graded anharmonic oscillator lattices

In this work we study the thermal rectification efficiency, i.e., asymmetric heat flow, of a three-dimensional mass-graded anharmonic lattice of length N and width W by means of nonequilibrium molecular dynamics simulations. The obtained rectification, which is of the same order of magnitude as that of the corresponding one-dimensional lattice, saturates at low values of the aspect ratio W/N, consistent with the already known behavior of the corresponding heat fluxes of the homogeneous system under analogous conditions. The maximum rectification is obtained in the temperature range wherein no rectification could be obtained in other one-dimensional systems, as well as in the corresponding one-dimensional instance of the model studied herein.

Heat current flows across an interface in two-dimensional lattices

Heat current J that flows through a few typical two-dimensional nonlinear lattices is systematically studied. Each lattice consists of two identical segments that are coupled by an interface with strength k_{int}. It is found that the two-universality-class scenario that is revealed in one-dimensional systems is still valid in the two-dimensional systems. Namely, J may follow k_{int} in two entirely different ways, depending on whether or not the interface potential energy decays to zero. We also study the dependence of J on lattice width N_{Y} and transverse interaction strength k_{Y}. Universal power-law decay or divergence is observed. Finally, we check the equipartition theorem in the systems since it is the basis of all our theoretical analyses. Surprisingly, it holds perfectly even at the interface where there is a finite temperature jump, which makes the system far from equilibrium. However, the equipartition of potential energy, which is observed in one-dimensional systems, is no longer satisfied due to the interaction between different dimensions.

Heat conduction in a three-dimensional momentum-conserving fluid

Size dependence of energy transport and the effects of reduced dimensionality on transport coefficients are of key importance for understanding nonequilibrium properties of matter on the nanoscale. Here, we perform nonequilibrium and equilibrium simulations of heat conduction in a three-dimensional (3D) fluid with the multiparticle collision dynamics, interacting with two thermal walls. We find that the bulk 3D momentum-conserving fluid has a finite nondiverging thermal conductivity. However, for large aspect ratios of the simulation box, a crossover from 3D to one-dimensional (1D) abnormal behavior of the thermal conductivity occurs. In this case, we demonstrate a transition from normal to abnormal transport by a suitable decomposition of the energy current. These results not only provide a direct verification of Fourier's law, but also further confirm the validity of existing theories for 3D fluids. Moreover, they indicate that abnormal heat transport persists also for almost 1D fluids over a large range of sizes.

Resonance phonon approach to phonon relaxation time and mean free path in one-dimensional nonlinear lattices

We extend a previously proposed resonance phonon approach that is based on the linear response theory. By studying the complex response function in depth, we work out the phonon relaxation time besides the oscillating frequency of the phonons in a few one-dimensional nonlinear lattices. The results in the large wave-number-k regime agree with the expectations of the effective phonon theory. However, in the small-k limit they follow different scaling laws. The phonon mean free path can also be calculated indirectly. It coincides well with that derived from the anharmonic phonon approach. A power-law divergent heat conduction, i.e., the heat conductivity κ depends on lattice length N by κ∼N^{β} with β>0, then is supported for the momentum-conserving lattices. Furthermore, this approach can be applied to diatomic lattices. So obtained relaxation time quantitatively agrees with that from the effective phonon theory. As for the mean free path, the resonance phonon approach can detect both the acoustic and the optical branches, whereas the anharmonic phonon approach can only detect a combined branch, i.e., the acoustic branch for small k and the optical branch for large k.

Divergent and Ultrahigh Thermal Conductivity in Millimeter-Long Nanotubes

Low-dimensional materials could display anomalous thermal conduction that the thermal conductivity (κ) diverges with increasing lengths, in ways inconceivable in any bulk materials. However, previous theoretical or experimental investigations were plagued with many finite-size effects, rendering the results either indirect or inconclusive. Indeed, investigations on the anomalous thermal conduction must demand the sample length to be sufficiently long so that the phenomena could emerge from unwanted finite-size effects. Here we report experimental observations that the κ's of single-wall carbon nanotubes continuously increase with their lengths over 1 mm, reaching at least 8640  W/mK at room temperature. Remarkably, the anomalous thermal conduction persists even with the presence of defects, isotopic disorders, impurities, and surface absorbates. Thus, we demonstrate that the anomalous thermal conduction in real materials can persist over much longer distances than previously thought. The finding would open new regimes for wave engineering of heat as well as manipulating phonons at macroscopic scales.

Stretch diffusion and heat conduction in one-dimensional nonlinear lattices

For heat conduction in one-dimensional (1D) nonlinear Hamiltonian lattices, it has been known that conserved quantities play an important role in determining the actual heat conduction behavior. In closed or microcanonical Hamiltonian systems, the total energy and stretch are always conserved. Depending on the existence of external on-site potential, the total momentum can be conserved or not. All the momentum-conserving lattices have anomalous heat conduction except the 1D coupled rotator lattice. It was recently claimed that "whenever stretch (momentum) is not conserved in a 1D model, the momentum (stretch) and energy fields exhibit normal diffusion." The stretch in a coupled rotator lattice was also argued to be nonconserved due to the requirement of a finite partition function, which enables the coupled rotator lattice to fulfill this claim. In this work, we will systematically investigate stretch diffusion and heat conduction in terms of energy diffusion for typical 1D nonlinear lattices. Contrary to what was claimed, no clear connection between conserved quantities and heat conduction can be established. The actual situation might be more complicated than what was proposed.

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.

Heat-current correlation loss induced by finite-size effects in a one-dimensional nonlinear lattice

The Green-Kubo formula provides a mathematical expression for heat conductivity in terms of integrals of the heat-current correlation function, which should be calculated in the thermodynamic limit. In finite systems this function generally decreases, i.e., it decays faster than it does in infinite systems. We compared the values of the correlation function in a one-dimensional purely quartic lattice with various lengths, and found that this loss is much smaller than is conventionally estimated. By studying the heat diffusion process in this lattice, we found that, in contrast to the conventional belief, the collisions between sound modes do not noticeably affect the current correlation function. Therefore, its loss being surprisingly small can be well understood. This finding allows one to calculate the heat conductivity in a very large system with desirable accuracy by performing simulations in a system with much smaller size, and thus greatly broadens the application of the Green-Kubo method.

Temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with a soft on-site potential

The temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with soft on-site potential (soft-KG) are investigated systematically. Similarly to the previously studied hard-KG lattices, the existence of renormalized phonons is also confirmed in soft-KG lattices. In particular, the temperature dependence of the renormalized phonon frequency predicted by a classical field theory is verified by detailed numerical simulations. However, the thermal conductivities of soft-KG lattices exhibit the opposite trend in temperature dependence in comparison with those of hard-KG lattices. The interesting thing is that the temperature-dependent thermal conductivities of both soft- and hard-KG lattices can be interpreted in the same framework of effective phonon theory. According to the effective phonon theory, the exponents of the power-law dependence of the thermal conductivities as a function of temperature are only determined by the exponents of the soft or hard on-site potentials. These theoretical predictions are consistently verified very well by extensive numerical simulations.

Validity of Fourier's law in one-dimensional momentum-conserving lattices with asymmetric interparticle interactions

We have numerically studied heat conduction in a few one-dimensional momentum-conserving lattices with asymmetric interparticle interactions by the nonequilibrium heat bath method, the equilibrium Green-Kubo method, and the heat current power spectra analysis. Very strong finite-size effects are clearly observed. Such effects make the heat conduction obey a Fourier-like law in a wide range of lattice lengths. However, in yet longer lattice lengths, the heat conductivity regains its power-law divergence. Therefore, the power-law divergence of the heat conductivity in the thermodynamic limit is verified, as is expected by many existing theories.

Heat conduction of symmetric lattices

Heat conduction of symmetric Frenkel-Kontorova (FK) lattices with a coupling displacement was investigated. Through simplifying the model, we derived analytical expression of thermal current of the system in the overdamped case. By means of numerical calculations, the results indicate that: (i) As the coupling displacement d equals to zero, temperature oscillations of the heat baths linked with the lattices can control magnitude and direction of the thermal current; (ii) Whether there is a temperature bias or not, the thermal current oscillates periodically with d, whose amplitudes become greater and greater; (iii) As d is not equal to zero, the thermal current monotonically both increases and decreases with temperature oscillation amplitude of the heat baths, dependent on values of d; (iv) The coupling displacement also induces nonmonotonic behaviors of the thermal current vs spring constant of the lattice and coupling strength of the lattices; (v) These dynamical behaviors come from interaction of the coupling displacement with periodic potential of the FK lattices. Our results have the implication that the coupling displacement plays a crucial role in the control of heat current.

Logarithmic divergent thermal conductivity in two-dimensional nonlinear lattices

Heat conduction in three two-dimensional (2D) momentum-conserving nonlinear lattices are numerically calculated via both nonequilibrium heat-bath and equilibrium Green-Kubo algorithms. It is expected by mainstream theories that heat conduction in such 2D lattices is divergent and the thermal conductivity κ increases with lattice length N logarithmically. Our simulations for the purely quartic lattice firmly confirm it. However, very robust finite-size effects are observed in the calculations for the other two lattices, which well explain some existing studies and imply the extreme difficulties in observing their true asymptotic behaviors with affordable computation resources.

Crossover from Fermi-Pasta-Ulam to normal diffusive behavior in heat conduction through open anharmonic lattices

We study heat conduction in one-, two-, and three-dimensional anharmonic lattices connected to stochastic Langevin heat baths. The interatomic potential of the lattices is double-well type, i.e., V(DW)(x)=k(2)x(2)/2+k(4)x(4)/4 with k(2)<0 and k(4)>0. We observe two different temperature regimes of transport: a high-temperature regime where asymptotic length dependence of nonequilibrium steady state heat current is similar to the well-known Fermi-Pasta-Ulam lattices with an interatomic potential, V(FPU)(x)=k(2)x(2)/2+k(4)x(4)/4 with k(2),k(4)>0, and a low-temperature regime where heat conduction is most likely diffusive normal, satisfying Fourier's law. We present our simulation results for different temperature regimes in all dimensions.

Thermal conduction and interface effects in nanoscale Fermi-Pasta-Ulam conductors

We perform classical nonequilibrium molecular dynamics simulations to calculate heat flow through a microscopic junction connecting two larger reservoirs. In contrast to earlier papers, we also include the reservoirs in the simulated region to study the effect of the bulk-nanostructure interfaces and the bulk conductance. The scalar Fermi-Pasta-Ulam (FPU) model is used to describe the effects of anharmonic interactions in a simple manner. The temperature profile close to the junction in the low-temperature limit is shown to exhibit strong directional features that fade out when temperature increases. Simulating both the FPU chain and the two bulk regions is also shown to eliminate the nonmonotonous temperature variations found for simpler geometries and models. We show that, with sufficiently large reservoirs, the temperature profile in the chain does not depend on the details of thermalization used at the boundaries.