Breakdown of Fourier's law in nanotube thermal conductors

Wet-spinning of carbon nanotube fibers: dispersion, processing and properties

Owing to the intrinsic excellent mechanical, electrical, and thermal properties of carbon nanotubes (CNTs), carbon nanotube fibers (CNTFs) have been expected to become promising candidates for the next-generation of high-performance fibers. They have received considerable interest for cutting-edge applications, such as ultra-light electric wire, aerospace craft, military equipment, and space elevators. Wet-spinning is a broadly utilized commercial technique for high-performance fiber manufacturing. Thus, compared with array spinning from drawable CNTs vertical array and direct dry spinning from floating catalyst chemical vapor deposition (FCCVD), the wet-spinning technique is considered to be a promising strategy to realize the production of CNTFs on a large scale. In this tutorial review, we begin with a summative description of CNTFs wet-spinning process. Then, we discuss the high-concentration CNTs wet-spinning dope preparation strategies and corresponding non-covalent adsorption/charge transfer mechanisms. The filament solidification during the coagulation process is another critical procedure for determining the configurations and properties for derived CNTFs. Next, we discuss post-treatment, including continuous drafting and thermal annealing, to further optimize the CNTs orientation and compact configuration. Finally, we summarize the physical property-structure relationship to give insights for further performance promotion in order to satisfy the prerequisite for detailed application. Insights into propelling high-performance CNTFs production from lab-scale to industry-scale are proposed, in anticipation of this novel fiber having an impact on our lives in the near future.

Polymeric Nanocomposites of Boron Nitride Nanosheets for Enhanced Directional or Isotropic Thermal Transport Performance

Polymeric composites with boron nitride nanosheets (BNNs), which are thermally conductive yet electrically insulating, have been pursued for a variety of technological applications, especially those for thermal management in electronic devices and systems. Highlighted in this review are recent advances in the effort to improve in-plane thermal transport performance in polymer/BNNs composites and also the growing research activities aimed at composites of enhanced cross-plane or isotropic thermal conductivity, for which various filler alignment strategies during composite fabrication have been explored. Also highlighted and discussed are some significant challenges and major opportunities for further advances in the development of thermally conductive composite materials and their mechanistic understandings.

1D and 2D Boron Nitride Nano Structures: A Critical Analysis for Emerging Applications in the Field of Nanocomposites

Boron nitride (BN) with its 1D and 2D nano derivatives have gained immense popularity in both the field of research and applications. These nano derivatives have proved to be one of the most promising fillers which can be incorporated in polymers to form nanocomposites with excellent properties. These materials have been around for 25 years whereas significant research has been done in this field for only the past decade. There are many interesting properties which are imparted to the nanocomposites wherein thermal stability, large energy band gap, resistance to oxidation, excellent thermal conductivity, chemical inertness, and exceptional mechanical properties are just a few worthy of mention. Hexagonal boron nitride (h-BN) was selected as the parent material by most researchers reviewed in this paper through which 2D derivative Boron nitride nanosheets (BNNS) and 1D derivative Boron nitride nanotubes (BNNTs) are synthesized. This review will focus on the in-depth properties of h-BN and further will concisely focus on BNNS and BNNTs for their various properties. A detailed discussion of the addition of BNNS and BNNTs into polymers to form nanocomposites, their synthesis, properties, and applications is followed by a summary determining the most suitable synthesizing processes and the materials, keeping in mind the current challenges.

Molecular heat transport across a time-periodic temperature gradient

The time-periodic modulation of a temperature gradient can alter the heat transport properties of a physical system. Oscillating thermal gradients give rise to behaviors such as modified thermal conductivity and controllable time-delayed energy storage that are not present in a system with static temperatures. Here, we examine how the heat transport properties of a molecular lattice model are affected by an oscillating temperature gradient. We use analytical analysis and molecular dynamics simulations to investigate the vibrational heat flow in a molecular lattice system consisting of a chain of particles connected to two heat baths at different temperatures, where the temperature difference between baths is oscillating in time. We derive expressions for heat currents in this system using a stochastic energetics framework and a nonequilibrium Green's function approach that is modified to treat the nonstationary average energy fluxes. We find that emergent energy storage, energy release, and thermal conductance mechanisms induced by the temperature oscillations can be controlled by varying the frequency, waveform, and amplitude of the oscillating gradient. The developed theoretical approach provides a general framework to describe how vibrational heat transmission through a molecular lattice is affected by temperature gradient oscillations.

Thermal transport in a defective pillared graphene network: insights from equilibrium molecular dynamics simulation

Graphene-based hybrid nanostructures have great potential to be ideal candidates for developing tailored thermal transport materials. In this study, we perform equilibrium molecular dynamics simulations employing the Green-Kubo method to investigate the influence of topological defects in three-dimensional pillared graphene networks. Similar to single-layer graphene and carbon nanotubes, the thermal conductivity (k) of pillared graphene systems exhibits a strong correlation with the system size (L), following a power-law relation k ∼ Lα, where α ranges from 0.12 to 0.15. Our results indicate that the vacancy defects significantly reduce thermal conductivity in pillared graphene systems compared to Stone-Wales defects. We observe that, beyond defect concentration, the location of the defects also plays a crucial role in determining thermal conductivity. We further analyze the phonon vibrational spectrum and the phonon participation ratio to obtain more insight into the thermal transport in the defective pillared graphene network. In most scenarios, longitudinal and flexural acoustic phonons experience significant localization within the 15-45 THz frequency range in the defective pillared graphene system.

Thermal Conductivity Enhancement of Polymeric Composites Using Hexagonal Boron Nitride: Design Strategies and Challenges

With the integration and miniaturization of chips, there is an increasing demand for improved heat dissipation. However, the low thermal conductivity (TC) of polymers, which are commonly used in chip packaging, has seriously limited the development of chips. To address this limitation, researchers have recently shown considerable interest in incorporating high-TC fillers into polymers to fabricate thermally conductive composites. Hexagonal boron nitride (h-BN) has emerged as a promising filler candidate due to its high-TC and excellent electrical insulation. This review comprehensively outlines the design strategies for using h-BN as a high-TC filler and covers intrinsic TC and morphology effects, functionalization methods, and the construction of three-dimensional (3D) thermal conduction networks. Additionally, it introduces some experimental TC measurement techniques of composites and theoretical computational simulations for composite design. Finally, the review summarizes some effective strategies and possible challenges for the design of h-BN fillers. This review provides researchers in the field of thermally conductive polymeric composites with a comprehensive understanding of thermal conduction and constructive guidance on h-BN design.

A Buckling Analysis of Thermoelastic Micro/Nano-Beams Considering the Size-Dependent Effect and Non-Uniform Temperature Distribution

Thermoelastic buckling of micro/nano-beams subjected to non-uniform temperature distribution is investigated in this paper. The mechanical governing equation is derived based on the surface effect and mechanical non-local effect. The non-local heat conduction model is used to predict temperature distribution in micro/nano-beams. Therefore, the obtained analytical solution can be used to analyze the influence of both the mechanical and thermal small scale effects on buckling of thermoelastic micro/nano-beams. In numerical simulations, a critical thickness is proposed to determine the influence region of both mechanical and thermal small scale effects. The influence of a small scale effect on buckling of micro/nano-beams must be considered if beam thickness is less than the critical thickness. In the influence region of a small scale effect, a surface effect has strong influence on the size-dependent buckling behavior, rather than mechanical and thermal non-local effects. Moreover, combined small scale effects, i.e., a surface effect and both mechanical and thermal non-local effects, lead to a larger critical load. Additionally, the influence of other key factors on buckling of the micro/nano-beams is studied in detail. This paper provides theoretical explanation to the buckling behaviors of micro/nano-beams under a non-uniform temperature distribution load.

Energy transport between heat baths with oscillating temperatures

Energy transport is a fundamental physical process that plays a prominent role in the function and performance of myriad systems and technologies. Recent experimental measurements have shown that subjecting a macroscale system to a time-periodic temperature gradient can increase thermal conductivity in comparison to a static temperature gradient. Here, we theoretically examine this mechanism in a nanoscale model by applying a stochastic Langevin framework to describe the energy transport properties of a particle connecting two heat baths with different temperatures, where the temperature difference between baths is oscillating in time. Analytical expressions for the energy flux of each heat bath and for the system itself are derived for the case of a free particle and a particle in a harmonic potential. We find that dynamical effects in the energy flux induced by temperature oscillations give rise to complex energy transport hysteresis effects. The presented results suggest that applying time-periodic temperature modulations is a potential route to control energy storage and release in molecular devices and nanosystems.

Motion of localized disturbances in scalar harmonic lattices

We present analytical and numerical investigations of energy propagation in systems of massive particles that interact via harmonic (linear) forces. The particle motion is described by a scalar displacement, and the particles are arranged in a simple crystal lattice. For the systems under consideration we prove the conservation of the total energy flux analytically. Then, using a sample case of a square lattice, we confirm the analytical results numerically. We create disturbances of a special kind which can move with a predefined velocity with a minor change in their shape. We show that a clot of energy, associated with each disturbance, moves similarly to a free body of matter in classical mechanics. We also numerically study a simultaneous propagation of a number of energy clots as an analogy to the motion of point masses in the conventional mechanics of particles. The obtained results demonstrate that an energy flow in lattices can be described in terms of numerous separated energy bodies, making a step towards a linkage between lattice dynamics and the kinetic theory of heat transfer in solids.

Electron hopping heat transport in molecules

The realization of single-molecule thermal conductance measurements has driven the need for theoretical tools to describe conduction processes that occur over atomistic length scales. In macroscale systems, the principle that is typically used to understand thermal conductivity is Fourier's law. At molecular length scales, however, deviations from Fourier's law are common in part because microscale thermal transport properties typically depend on the complex interplay between multiple heat conduction mechanisms. Here, the thermal transport properties that arise from electron transfer across a thermal gradient in a molecular conduction junction are examined theoretically. We illustrate how transport in a model junction is affected by varying the electronic structure and length of the molecular bridge in the junction as well as the strength of the coupling between the bridge and its surrounding environment. Three findings are of note: First, the transport properties can vary significantly depending on the characteristics of the molecular bridge and its environment; second, the system's thermal conductance commonly deviates from Fourier's law; and third, in properly engineered systems, the magnitude of electron hopping thermal conductance is similar to what has been measured in single-molecule devices.

Anomalous conduction in one-dimensional particle lattices: Wave-turbulence approach

One-dimensional particle chains are fundamental models to explain anomalous thermal conduction in low-dimensional solids such as nanotubes and nanowires. In these systems the thermal energy is carried by phonons, i.e., propagating lattice oscillations that interact via nonlinear resonance. The average energy transfer between the phonons can be described by the wave kinetic equation, derived directly from the microscopic dynamics. Here we use the spatially nonhomogeneous wave kinetic equation of the prototypical β-Fermi-Pasta-Ulam-Tsingou model, to study thermal conduction in one-dimensional particle chains on a mesoscale description. By means of numerical simulations, we study two complementary aspects of thermal conduction: in the presence of thermostats setting different temperatures at the two ends and propagation of a temperature perturbation over an equilibrium background. Our main findings are as follows. (i) The anomalous scaling of the conductivity with the system size, in close agreement with the known results from the microscopic dynamics, is due to a nontrivial interplay between high and low wave numbers. (ii) The high-wave-number phonons relax to local thermodynamic equilibrium transporting energy diffusively, in the manner of Fourier. (iii) The low-wave-number phonons are nearly noninteracting and transfer energy ballistically. These results present perspectives for the applicability of the full nonhomogeneous wave kinetic equation to study thermal propagation.

Analysis of ballistic transport and resonance in the α-Fermi-Pasta-Ulam-Tsingou model

Ballistic transport and resonance phenomena are elucidated in the one-dimensional α-Fermi-Pasta-Ulam-Tsingou (FPUT) model using an approach of computing thermal response functions. The existence of periodic oscillations in spatially sinusoidal temperature profiles seen in previous studies is confirmed. However, the results obtained using response functions enable a more complete understanding. In particular, it is shown that resonance involves beats between normal modes which tend to reinforce in a one-dimensional chain. Anharmonic scattering acts to destroy phase coherence across the statistical ensemble, and with increasing anharmonicity, transport is driven toward the diffusive regime. These results provide additional insight into anomalous heat transport in low-dimensional systems. Normal-mode scattering is also explored using time correlation functions. Interestingly, these calculations, in addition to demonstrating loss of phase coherence across an ensemble of simulations, appear to show evidence of so-called q-breathers in conditions of strong anharmonicity. Finally, we describe how the approach outlined here could be developed to include quantum statistics and also also first-principles estimates of phonon scattering rates to elucidate second sound and ballistic transport in realistic materials at low temperatures.

Nonmonotonic heat dissipation phenomenon in close-packed hotspot systems

Transient heat dissipation in close-packed quasi-two-dimensional nanoline and three-dimensional nanocuboid hotspot systems is studied based on the phonon Boltzmann transport equation. It is found that, counterintuitively, the heat dissipation efficiency is not a monotonic function of the distance between adjacent nanoscale heat sources but reaches the highest value when this distance is comparable to the phonon mean free path. This is due to the competition of two thermal transport processes: quasiballistic transport when phonons escape from the nanoscale heat source and the scattering among phonons originating from the adjacent nanoscale heat source.

Phonon hydrodynamics in crystalline materials

Phonon hydrodynamics is an exotic phonon transport phenomenon that challenges the conventional understanding of diffusive phonon scattering in crystalline solids. It features a peculiar collective motion of phonons with various unconventional properties resembling fluid hydrodynamics, facilitating non Fourier heat transport. Hence, it opens up several new avenues to enrich the knowledge and implementations on phonon physics, phonon engineering, and micro and nanoelectronic device technologies. This review aims at covering a comprehensive development as well as the recent advancements in this field via experiments, analytical methods, and state-of-the-art numerical techniques. The evolution of the topic has been realized using both phenomenological and material science perspectives. Further, the discussions related to the factors that influence such peculiar motion, illustrate the capability of phonon hydrodynamics to be implemented in various applications. A plethora of new ideas can emerge from the topic considering both the physics and the material science axes, navigating toward a promising outlook in the research areas around phonon transport in non-metallic solids.

Heat flux in chains of nonlocally coupled harmonic oscillators: Mean-field limit

We consider one-dimensional systems of all-to-all harmonically coupled particles with arbitrary masses, subject to two Langevin thermal baths. The couplings correspond to the mean-field limit of long-range interactions. Additionally, the particles can be subject to a harmonic on-site potential to break momentum conservation. Using the nonequilibrium Green's operator formalism, we calculate the transmittance, the heat flow, and local temperatures for arbitrary configurations of masses. For identical masses, we show analytically that the heat flux decays with the system size N as 1/N regardless of the conservation or not of the momentum and of the introduction or not of a Kac factor. These results describe, in good agreement, the thermal behavior of systems with small heterogeneity in the masses.

Unsteady ballistic heat transport in two-dimensional harmonic graphene lattice

We study the evolution of initial temperature profiles in a two-dimensional isolated harmonic graphene lattice. Two heat transfer problems are solved analytically and numerically. In the first problem, the evolution of a spatially sinusoidal initial temperature profile is considered. This profile is usually generated in real experiments based on the transient thermal grating technique. It is shown that at short times the amplitude of the profile decreases by an order magnitude and then it performs small decaying oscillations. A closed-form solution, describing the decay of the amplitude at short times is derived. It shows that due to symmetry of the lattice, the anisotropy of the ballistic heat transfer is negligible at short times, while at large times it is significant. In the second problem, a uniform spatial distribution of the initial temperature in a circle is specified. The profile is the simplest model of graphene heating by an ultrashort localized laser pulse. The corresponding solution has the symmetry of the lattice and many local maxima. Additionally, we show that each atom has two distinct temperatures corresponding to motions in zigzag and armchair directions. Presented results may serve for proper statement and interpretation of laboratory experiments and molecular dynamics simulations of unsteady heat transfer in graphene.

Heat transport in nonlinear lattices free from the umklapp process

We construct one-dimensional nonlinear lattices having the special property such that the umklapp process vanishes and only the normal processes are included in the potential functions. These lattices have long-range quartic nonlinear and nearest-neighbor harmonic interactions with/without harmonic onsite potential. We study heat transport in two cases of the lattices with and without harmonic onsite potential by nonequilibrium molecular dynamics simulation. It is shown that the ballistic heat transport occurs in both cases, i.e., the scaling law κ∝N holds between the thermal conductivity κ and the lattice size N. This result directly validates Peierls's hypothesis that only the umklapp processes can cause the thermal resistance while the normal ones do not.

Phonon-engineered extreme thermal conductivity materials

Materials with ultrahigh or low thermal conductivity are desirable for many technological applications, such as thermal management of electronic and photonic devices, heat exchangers, energy converters and thermal insulation. Recent advances in simulation tools (first principles, the atomistic Green's function and molecular dynamics) and experimental techniques (pump-probe techniques and microfabricated platforms) have led to new insights on phonon transport and scattering in materials and the discovery of new thermal materials, and are enabling the engineering of phonons towards desired thermal properties. We review recent discoveries of both inorganic and organic materials with ultrahigh and low thermal conductivity, highlighting heat-conduction physics, strategies used to change thermal conductivity, and future directions to achieve extreme thermal conductivities in solid-state materials.

Analytical results for a minimalist thermal diode

We consider a system consisting of two interacting classical particles, each one subject to an on-site potential and to a Langevin thermal bath. We analytically calculate the heat current that can be established through the system when the bath temperatures are different, for weak nonlinear forces. We explore the conditions under which the diode effect emerges when inverting the temperature difference. Despite the simplicity of this two-particle diode, an intricate dependence on the system parameters is put in evidence. Moreover, behaviors reported for long chains of particles can be extracted, for instance, the dependence of the flux with the interfacial stiffness and type of forces present, as well as the dependencies on the temperature required for rectification. These analytical results can be a tool to foresee the distinct role that diverse types of nonlinearity and asymmetry play in thermal conduction and rectification.

Ultrahigh Convergent Thermal Conductivity of Carbon Nanotubes from Comprehensive Atomistic Modeling

Anomalous heat transport in one-dimensional nanostructures, such as nanotubes and nanowires, is a widely debated problem in condensed matter and statistical physics, with contradicting pieces of evidence from experiments and simulations. Using a comprehensive modeling approach, comprised of lattice dynamics and molecular dynamics simulations, we proved that the infinite length limit of the thermal conductivity of a (10,0) single-wall carbon nanotube is finite but this limit is reached only for macroscopic lengths due to a thermal phonon mean free path of several millimeters. Our calculations showed that the extremely high thermal conductivity of this system at room temperature is dictated by quantum effects. Modal analysis showed that the divergent nature of thermal conductivity, observed in one-dimensional model systems, is suppressed in carbon nanotubes by anharmonic scattering channels provided by the flexural and optical modes with polarization in the plane orthogonal to the transport direction.

Microscopic Theory of Fluctuating Hydrodynamics in Nonlinear Lattices

The theory of fluctuating hydrodynamics has been an important tool for analyzing macroscopic behavior in nonlinear lattices. However, despite its practical success, its microscopic derivation is still incomplete. In this work, we provide the microscopic derivation of fluctuating hydrodynamics, using the coarse-graining and projection technique; the equivalence of ensembles turns out to be critical. The Green-Kubo (GK)-like formula for the bare transport coefficients are presented in a numerically computable form. Our numerical simulations show that the bare transport coefficients exist for a sufficiently large but finite coarse-graining length in the infinite lattice within the framework of the GK-like formula. This demonstrates that the bare transport coefficients uniquely exist for each physical system.

Revisiting the problem of crystallisation and melting of selenium

In this paper, we study the structure of the solid selenium (Se) formed by the vapor deposition method. We provide direct visual evidence that faceted crystal-like shapes obtained from vapor phase deposition are a self-assembly of linear strands that have a persistence length of 10μm. These strands are held together by weak forces and can easily be separated. These chains occasionally get entangled to form chiral structures and often meander about destroying long range orientation and translation order in a continuous manner. Moreover, it is easy for the long strands of linear chains to slide past the neighboring ones, and hence the system has a large concentration of disinclination like defects in addition to the defects caused by the entanglement of the chains. Like organic polymers, the obtained Se structures also exhibit a spread in the melting temperature. This spread is closely related to the density of the sub-structures present in the system. The infrared imaging shows that these structures heat up in an inhomogeneous manner and the cross polarized images show that the process of melting initiates in the bulk.

Heat transport and surface functionalization in nanocomposites of boron nitride nanotubes and polyethylene

This work explores the possibility for improving heat transport in a polymeric, electrical insulating material, such as polyethylene, by adding boron nitride nanotubes - a heat superdiffusive material. We use molecular dynamics simulations to study the nanocomposites formed by addition of the nanotubes to both amorphous and crystalline polyethylene, and also investigate the effect of surface functionalization using a silane coupling agent, which, being covalently attached to both the nanofiller and the polymer matrix, facilitates the heat transport between them. Even though transport is shown to deteriorate in each simulation when the coupling agents are added, they are expected to favor the nucleation of the crystalline regions about the nanotubes, thus significantly boosting heat conduction in the material along their direction.

Anomalous diffusion and Noether's second theorem

Despite the fact that conserved currents have dimensions that are determined solely by dimensional analysis (and hence no anomalous dimensions), Nature abounds in examples of anomalous diffusion in which L∝t^{γ}, with γ≠1/2, and heat transport in which the thermal conductivity diverges as L^{α}. Aside from breaking of Lorentz invariance, the true common link in such problems is an anomalous dimension for the underlying conserved current, thereby violating the basic tenet of field theory. We show here that the phenomenological nonlocal equations of motion that are used to describe such anomalies all follow from Lorentz-violating gauge transformations arising from Noether's second theorem. The generalizations lead to a family of diffusion and heat transport equations that systematize how nonlocal gauge transformations generate more general forms of Fick's and Fourier's laws for diffusive and heat transport, respectively. In particular, the associated Goldstone modes of the form ω∝k^{α}, α∈R are direct consequences of fractional equations of motion.

Regulating heat conduction of complex networks by distributed nodes masses

Developing efficient strategy to regulate heat conduction is a challenging problem, with potential implication in the field of thermal materials. We here focus on a potential thermal material, i.e. complex networks of nanowires and nanotubes, and propose a model where the mass of each node is assigned proportional to its degree with [Formula: see text], to investigate how distributed nodes masses can impact the heat flow in a network. We find that the heat conduction of complex network can be either increased or decreased, depending on the controlling parameter [Formula: see text]. Especially, there is an optimal heat conduction at [Formula: see text] and it is independent of network topologies. Moreover, we find that the temperature distribution within a complex network is also strongly influenced by the controlling parameter [Formula: see text]. A brief theoretical analysis is provided to explain these results. These findings may open up appealing applications in the cases of demanding either increasing or decreasing heat conduction, and our approach of regulating heat conduction by distributed nodes masses may be also valuable to the challenge of controlling waste heat dissipation in highly integrated and miniaturized modern devices.

Equilibration of sinusoidal modulation of temperature in linear and nonlinear chains

The equilibration of sinusoidally modulated distribution of the kinetic temperature is analyzed in the β-Fermi-Pasta-Ulam-Tsingou chain with different degrees of nonlinearity and for different wavelengths of temperature modulation. Two different types of initial conditions are used to show that either one gives the same result as the number of realizations increases and that the initial conditions that are closer to the state of thermal equilibrium give faster convergence. The kinetics of temperature equilibration is monitored and compared to the analytical solution available for the linear chain in the continuum limit. The transition from ballistic to diffusive thermal conductivity with an increase in the degree of anharmonicity is shown. In the ballistic case, the energy equilibration has an oscillatory character with an amplitude decreasing in time, and in the diffusive case, it is monotonous in time. For smaller wavelength of temperature modulation, the oscillatory character of temperature equilibration remains for a larger degree of anharmonicity. For a given wavelength of temperature modulation, there is such a value of the anharmonicity parameter at which the temperature equilibration occurs most rapidly.

Heat conduction in two-dimensional momentum-conserving and -nonconserving gases

Compared to that for two-dimensional (2D) lattices, our understanding of heat conduction in 2D gases is still limited. Here we study heat conduction behavior of 2D gas systems with momentum-conserving and -nonconserving interparticle interactions by using the nonequilibrium and equilibrium molecular dynamics methods. For the momentum-conserving system, we find that when the dimensionality of the system is changed from 2D to quasi-one-dimensional (quasi-1D), the heat conductivity κ diverges with the system size L as κ∼lnL (the theoretical prediction for 2D systems) for a short L and shows, in the thermodynamic limit, a tendency to κ∼L^{1/3} like that predicted in 1D fluids. This suggests that the dimensional-crossover effect of heat conduction exists in 2D systems with conserved momentum. In contrast, for the momentum-nonconserving system, as L increases, finite heat conductivity independent of L is observed. These findings are in agreement with the predictions given by hydrodynamic theory and thus further confirm the validity of the theory in 2D gases.

Universal scaling for recovery of Fourier's law in low-dimensional solids under momentum conservation

Dynamic renormalization group (RG) of fluctuating viscoelastic equations is investigated to clarify the cause for numerically reported disappearance of anomalous heat conduction (recovery of Fourier's law) in low-dimensional momentum-conserving systems. RG flow is obtained explicitly for simplified two model cases: a one-dimensional continuous medium under low pressure and incompressible viscoelastic medium of arbitrary dimensions. Analyses of these clarify that the inviscid fixed point of contributing the anomalous heat conduction becomes unstable under the RG flow of nonzero elastic-wave speeds. The dynamic RG analysis further predicts a universal scaling of describing the crossover between the growth and saturation of observed heat conductivity, which is confirmed through the numerical experiments of Fermi-Pasta-Ulam β (FPU-β) lattices.

Coexistence of Ballistic and Fourier Regimes in the β Fermi-Pasta-Ulam-Tsingou Lattice

Commonly, thermal transport properties of one-dimensional systems are found to be anomalous. Here, we perform a numerical and theoretical study of the β-Fermi-Pasta-Ulam-Tsingou chain, considered a prototypical model for one-dimensional anharmonic crystals, in contact with thermostats at different temperatures. We give evidence that, in steady state conditions, the local wave energy spectrum can be naturally split into modes that are essentially ballistic (noninteracting or scarcely interacting) and kinetic modes (interacting enough to relax to local thermodynamic equilibrium). We show numerically that the well-known divergence of the energy conductivity is related to how the transition region between these two sets of modes shifts in k space with the system size L, due to properties of the collision integral of the system. Moreover, we show that the kinetic modes are responsible for a macroscopic behavior compatible with Fourier's law. Our work sheds light on the long-standing problem of the applicability of standard thermodynamics in one-dimensional nonlinear chains, testbed for understanding the thermal properties of nanotubes and nanowires.

Advanced Thermoelectric Design: From Materials and Structures to Devices

The long-standing popularity of thermoelectric materials has contributed to the creation of various thermoelectric devices and stimulated the development of strategies to improve their thermoelectric performance. In this review, we aim to comprehensively summarize the state-of-the-art strategies for the realization of high-performance thermoelectric materials and devices by establishing the links between synthesis, structural characteristics, properties, underlying chemistry and physics, including structural design (point defects, dislocations, interfaces, inclusions, and pores), multidimensional design (quantum dots/wires, nanoparticles, nanowires, nano- or microbelts, few-layered nanosheets, nano- or microplates, thin films, single crystals, and polycrystalline bulks), and advanced device design (thermoelectric modules, miniature generators and coolers, and flexible thermoelectric generators). The outline of each strategy starts with a concise presentation of their fundamentals and carefully selected examples. In the end, we point out the controversies, challenges, and outlooks toward the future development of thermoelectric materials and devices. Overall, this review will serve to help materials scientists, chemists, and physicists, particularly students and young researchers, in selecting suitable strategies for the improvement of thermoelectrics and potentially other relevant energy conversion technologies.

Dimensional crossover of thermal transport in quantum harmonic lattices coupled to self-consistent reservoirs

In this study, we investigate thermal transport in d-dimensional quantum harmonic lattices coupled to self-consistent reservoirs. The d-dimensional system is treated as a set of Klein-Gordon chains by exploiting an orthogonal transformation. For generality, the self-energy that describes the reservoir-system coupling is assumed to be a power function of energy Σ∝-iɛ^{n}, where n is limited to odd integers because of the reality condition. Total momentum conservation is violated for n=1 but otherwise preserved. In this approach, we show that for n=1, thermal conductivity remains finite in the thermodynamic limit and normal transport takes place for an arbitrary value of d. For n=3,5,7,⋯, however, thermal conductivity diverges and thermal transport becomes anomalous as long as d<n, whereas normal transport is recovered when d≥n. These criteria derived for quantum-mechanical lattices imply that normal transport emerges in high enough dimensions despite total momentum conservation and reinforce the prevailing conjecture deduced in the classical limit.

Thermal transport of carbon nanomaterials

The diversity of thermal transport properties in carbon nanomaterials enables them to be used in different thermal fields such as heat dissipation, thermal management, and thermoelectric conversion. In the past two decades, much effort has been devoted to study the thermal conductivities of different carbon nanomaterials. In this review, different theoretical methods and experimental techniques for investigating thermal transport in nanosystems are first summarized. Then, the thermal transport properties of various pure carbon nanomaterials including 1D carbon nanotubes, 2D graphene, 3D carbon foam, are reviewed in details and the associated underlying physical mechanisms are presented. Meanwhile, we discuss several important influences on the thermal conductivities of carbon nanomaterials, including size, structural defects, chemisorption and strain. Moreover, we introduce different nanostructuring pathways to manipulate the thermal conductivities of carbon-based nanocomposites and focus on the wave nature of phonons for controlling thermal transport. At last, we briefly review the potential applications of carbon nanomaterials in the fields of thermal devices and thermoelectric conversion.

Ballistic resonance and thermalization in the Fermi-Pasta-Ulam-Tsingou chain at finite temperature

We study conversion of thermal energy to mechanical energy and vice versa in an α-Fermi-Pasta-Ulam-Tsingou (FPUT) chain with a spatially sinusoidal profile of initial temperature. We show analytically that coupling between macroscopic dynamics and quasiballistic heat transport gives rise to mechanical vibrations with growing amplitude. This phenomenon is referred to as ballistic resonance. At large times, these mechanical vibrations decay monotonically, and therefore the well-known FPUT recurrence paradox occurring at zero temperature is eliminated at finite temperatures.

Understanding the Mechanical and Conductive Properties of Carbon Nanotube Fibers for Smart Electronics

The development of fiber-based smart electronics has provoked increasing demand for high-performance and multifunctional fiber materials. Carbon nanotube (CNT) fibers, the 1D macroassembly of CNTs, have extensively been utilized to construct wearable electronics due to their unique integration of high porosity/surface area, desirable mechanical/physical properties, and extraordinary structural flexibility, as well as their novel corrosion/oxidation resistivity. To take full advantage of CNT fibers, it is essential to understand their mechanical and conductive properties. Herein, the recent progress regarding the intrinsic structure-property relationship of CNT fibers, as well as the strategies of enhancing their mechanical and conductive properties are briefly summarized, providing helpful guidance for scouting ideally structured CNT fibers for specific flexible electronic applications.

Thermal-siphon phenomenon and thermal/electric conduction in complex networks

In past decades, a lot of studies have been carried out on complex networks and heat conduction in regular lattices. However, very little attention has been paid to the heat conduction in complex networks. In this work, we study (both thermal and electric) energy transport in physical networks rewired from 2D regular lattices. It is found that the network can be transferred from a good conductor to a poor conductor, depending on the rewired network structure and coupling scheme. Two interesting phenomena were discovered: (i) the thermal-siphon effect—namely the heat flux can go from a low-temperature node to a higher-temperature node and (ii) there exits an optimal network structure that displays small thermal conductance and large electrical conductance. These discoveries reveal that network-structured materials have great potential in applications in thermal-energy management and thermal-electric-energy conversion.

Heat conduction in harmonic chains with Lévy-type disorder

We consider heat transport in a one-dimensional harmonic chain attached at its ends to Langevin heat baths. The harmonic chain has mass impurities where the separation d between any two successive impurities is randomly distributed according to a power-law distribution P(d)∼1/d^{α+1}, being α>0. In the regime where the first moment of the distribution is well defined (1<α<2) the thermal conductivity κ scales with the system size N as κ∼N^{(α-3)/α} for fixed boundary conditions, whereas for free boundary conditions κ∼N^{(α-1)/α} if N≫1. When α=2, the inverse localization length λ scales with the frequency ω as λ∼ω^{2}lnω in the low-frequency regime, due to the logarithmic correction, the size scaling law of the thermal conductivity acquires a nonclosed form. When α>2, the thermal conductivity scales as in the uncorrelated disorder case. The situation α<1 is only analyzed numerically, where λ(ω)∼ω^{2-α}, which leads to the following asymptotic thermal conductivity: κ∼N^{-(α+1)/(2-α)} for fixed boundary conditions and κ∼N^{(1-α)/(2-α)} for free boundary conditions.

Energy and spin diffusion in the one-dimensional classical Heisenberg spin chain at finite and infinite temperatures

The energy and spin diffusion behaviors in the one-dimensional classical Heisenberg spin chain have been systematically investigated using the equilibrium diffusion method. The spatiotemporal autocorrelation functions for energy and spin are calculated at finite and infinite temperatures. As conserved quantities, the spreading of excess energy and spin can be used to determine their actual diffusion behaviors. At low temperatures, the energy diffusion shows almost ballistic behavior, and spin shows superdiffusion behavior for finite chain size. For energy diffusion, normal diffusion behavior can be obtained when the temperature is higher than 0.75. For spin diffusion, normal diffusion behavior is observed at infinite temperature.

Effects of Divacancy and Extended Line Defects on the Thermal Transport Properties of Graphene Nanoribbons

The effects of divacancy, including isolated defects and extended line defects (ELD), on the thermal transport properties of graphene nanoribbons (GNRs) are investigated using the Nonequilibrium Green's function method. Different divacancy defects can effectively tune the thermal transport of GNRs and the thermal conductance is significantly reduced. The phonon scattering of a single divacancy is mostly at high frequencies while the phonon scattering at low frequencies is also strong for randomly distributed multiple divacancies. The collective effect of impurity scattering and boundary scattering is discussed, which makes the defect scattering vary with the boundary condition. The effect on thermal transport properties of a divacancy is also shown to be closely related to the cross section of the defect, the internal structure and the bonding strength inside the defect. Both low frequency and high frequency phonons are scattered by 48, d5d7 and t5t7 ELD. However, the 585 ELD has almost no influence on phonon scattering at low frequency region, resulting in the thermal conductance of GNRs with 585 ELD being 50% higher than that of randomly distributed 585 defects. All these results are valuable for the design and manufacture of graphene nanodevices.

Effect of boundary chain folding on thermal conductivity of lamellar amorphous polyethylene

Thermal transport properties of amorphous polymers depend significantly on the chain morphology, and boundary chain folding is a common phenomenon in bulk or lamellar polymer materials. In this work, by using molecular dynamics simulations, we study thermal conductivity of lamellar amorphous polyethylene (LAPE) with varying chain length (L 0). For a short L 0 without boundary chain folding, thermal conductivity of LAPE is homogeneous along the chain length direction. In contrast, boundary chain folding takes place for large L 0, and the local thermal conductivity at the boundary is notably lower than that of the central region, indicating inhomogeneous thermal transport in LAPE. By analysing the chain morphology, we reveal that the boundary chain folding causes the reduction of both the orientation order parameter along the heat flow direction and the radius of gyration, leading to the reduced local thermal conductivity at the boundary. Further vibrational spectrum analysis reveals that the boundary chain folding shifts the vibrational spectrum to the lower frequency, and suppresses the transmission coefficient for both C-C vibration and C-H vibration. Our study suggests that the boundary chain folding is an important factor for polymers to achieve desirable thermal conductivity for plastic heat exchangers and electronic packaging applications.

Probing ballistic thermal conduction in segmented silicon nanowires

Ballistic heat conduction in semiconductors is a remarkable but controversial nanoscale phenomenon, which implies that nanostructures can conduct thermal energy without dissipation. Here, we experimentally probed ballistic thermal transport at distances of 400-800 nm and temperatures of 4-250 K. Measuring thermal properties of straight and serpentine silicon nanowires, we found that at 4 K heat conduction is quasi-ballistic with stronger ballisticity at shorter length scales. As we increased the temperature, quasi-ballistic heat conduction weakened and gradually turned into diffusive regime at temperatures above 150 K. Our Monte Carlo simulations illustrate how this transition is driven by different scattering processes and linked to the surface roughness and the temperature. These results demonstrate the length and temperature limits of quasi-ballistic heat conduction in silicon nanostructures, knowledge of which is essential for thermal management in microelectronics.

Energy and momentum diffusion in one-dimensional periodic and asymmetric nonlinear lattices with momentum conservation

The energy diffusion in one-dimensional (1D) momentum conserving nonlinear lattices usually exhibits anomalous superdiffusion, except the coupled rotator lattice with symmetric and periodic interacting potential which has normal energy diffusion corresponding to normal heat conduction. For nonperiodic 1D lattices with momentum conservation, it has been argued that the asymmetric potential can induce normal heat conduction. Later results indicate the observed normal behavior might be the finite size effect and the anomalous behavior will appear in the thermodynamical limit. Here we propose asymmetric and periodic 1D nonlinear lattices with momentum conservation. The energy and momentum diffusion behaviors will be investigated in detail and the same normal diffusion behaviors for both energy and momentum can be observed. These results confirm that the periodicity is the key for normal transport behavior in 1D momentum conserving lattices, whether the potential is symmetric or asymmetric.

Disorder limits the coherent phonon transport in two-dimensional phononic crystal structures

Recently, increasing efforts are being made to control thermal transport via coherent phonons in periodic phononic structures; however, the direct observation of coherent phonon transport is experimentally very difficult at ambient temperature, and the importance of coherent phonons to the total thermal conductivity has not been critically assessed to date. In this study, using the non-equilibrium molecular dynamics simulations, we studied coherent phonon transport in a C3N phononic crystal (CNPnC) structure at room temperature by changing the porosity. When the holes were randomly distributed to construct the disordered C3N (D-C3N) structure, the localization of the coherent phonons was revealed by the phonon transmission coefficient, phonon wave packet simulation, phonon participation ratio and spatial energy density, which led to a significant reduction in the thermal conductivity. Finally, the effects of the length, temperature and strain on the thermal conductivity of CNPnC and D-C3N have also been discussed. Our study provides a solid understanding of the coherent phonon transport behavior, which will be beneficial for phononic-related control based on coherent phonons.

Quantum thermal management devices based on strong coupling qubits

We study the performance of a thermal management device with small scales by considering a strong coupling between quantum qubits. A small change of the thermal current at the base will cause a great change to the thermal current at the emitter and collector, reaching its promise for large thermal amplification. The competition between the quantum coherence and the incoherence induces a significant variation in the amplification factor and consequently relates the thermal controls with quantum effects. The results obtained here will provide a feasible scheme for the realization of quantum thermal management devices.

Change of entropy for the one-dimensional ballistic heat equation: Sinusoidal initial perturbation

This work presents a thermodynamic analysis of the ballistic heat equation from two viewpoints: classical irreversible thermodynamics (CIT) and extended irreversible thermodynamics (EIT). A formula for calculating the entropy within the framework of EIT for the ballistic heat equation is derived. The entropy is calculated for a sinusoidal initial temperature perturbation by using both approaches. The results obtained from CIT show that the entropy is a non-monotonic function and that the entropy production can be negative. The results obtained for EIT show that the entropy is a monotonic function and that the entropy production is nonnegative. A comparison between the entropy behaviors predicted for the ballistic, for the ordinary Fourier-based, and for the hyperbolic heat equation is made. A crucial difference of the asymptotic behavior of the entropy for the ballistic heat equation is shown. It is argued that mathematical time reversibility of the partial differential ballistic heat equation is not consistent with its physical irreversibility. The processes described by the ballistic heat equation are irreversible because of the entropy increase.

Thermal echo in a finite one-dimensional harmonic crystal

An instant homogeneous thermal perturbation in the finite harmonic one-dimensional crystal is studied. Previously it was shown that for the same problem in the infinite crystal the kinetic temperature oscillates with decreasing amplitude described by the Bessel function of the first kind. In the present paper it is shown that in the finite crystal this behavior is observed only until a certain period of time when a sharp increase of the oscillation amplitude is realized. This phenomenon, further referred to as the thermal echo, occurs periodically, with the period proportional to the crystal length. The amplitude for each subsequent echo is lower than for the previous one. It is obtained analytically that the time-dependence of the kinetic temperature can be described by an infinite sum of the Bessel functions with multiple indices. It is also shown that the thermal echo in the thermodynamic limit is described by the Airy function.

Mode confinement, interface mass-smudging, and sample length effects on phonon transport in thin nanocomposite superlattices

We employ a semi-ab initio theoretical method to investigate mode confinement, interface mass-smudging, and sample length effects on phonon transport in thin nanocomposite superlattices. We present a detailed comparative study of numerical results showing the reduction in thermal conductivity due to each of these three effects for Si/Ge nanocomposite structures with planar superlattice (SL), embedded nanowire superlattice (NWSL), and embedded nanodot superlattice (NDSL) geometries. Importantly, it is found that any of these three types of thin period systems, with small amounts of interface mass smudging, can exhibit a room-temperature conductivity significantly lower than the SiGe alloy conductivity, providing strong evidence that they could be used as efficient thermoelectric materials. It is also found that the room-temperature conductivity of each of the nanocomposite superlattices shows a weaker sample size dependence than do the component bulk conductivities.

Derivation of fluctuating hydrodynamics and crossover from diffusive to anomalous transport in a hard-particle gas

A recently developed nonlinear fluctuating hydrodynamics theory has been quite successful in describing various features of anomalous energy transport. However, the diffusion and the noise terms present in this theory are not derived from microscopic descriptions but rather added phenomenologically. We here derive these hydrodynamic equations with explicit calculation of the diffusion and noise terms in a one-dimensional model. We show that in this model the energy current scales anomalously with system size L as ∼L^{-2/3} in the leading order with a diffusive correction of order ∼L^{-1}. The crossover length ℓ_{c} from diffusive to anomalous transport is expressed in terms of microscopic parameters. Our theoretical predictions are verified numerically.