Thermal Metamaterials Research Articles

Non-Fourier heat conduction in 2D thermal metamaterials

The challenge of achieving precise control over heat conduction has persisted for years. Recent advancements in thermal metamaterials have offered a promising avenue for addressing this challenge. Yet, predicting the behaviors of non-Fourier heat conduction within these metamaterials remains elusive. In this study, we leveraged the extended plane wave expansion method (EPWEM) to decipher the complex band structures inherent to two-dimensional (2D) thermal metamaterials. To ascertain the reliability of our approach, wave transmission in the time-domain and band structures derived from the finite element method (FEM) were juxtaposed against EPWEM results. Our findings revealed the presence of both directional and complete band-gaps in the complex band structures. Then a thermal bridge is predicted via the proposed complex band structure strategy and demonstrated numerically. By shedding light on non-Fourier heat conduction within thermal metamaterials, our analysis paves the way for groundbreaking applications in domains like laser hardening, laser cladding, metal additive manufacturing, and so on.

General deep learning framework for emissivity engineering

Wavelength-selective thermal emitters (WS-TEs) have been frequently designed to achieve desired target emissivity spectra, as a typical emissivity engineering, for broad applications such as thermal camouflage, radiative cooling, and gas sensing, etc. However, previous designs require prior knowledge of materials or structures for different applications and the designed WS-TEs usually vary from applications to applications in terms of materials and structures, thus lacking of a general design framework for emissivity engineering across different applications. Moreover, previous designs fail to tackle the simultaneous design of both materials and structures, as they either fix materials to design structures or fix structures to select suitable materials. Herein, we employ the deep Q-learning network algorithm, a reinforcement learning method based on deep learning framework, to design multilayer WS-TEs. To demonstrate the general validity, three WS-TEs are designed for various applications, including thermal camouflage, radiative cooling and gas sensing, which are then fabricated and measured. The merits of the deep Q-learning algorithm include that it can (1) offer a general design framework for WS-TEs beyond one-dimensional multilayer structures; (2) autonomously select suitable materials from a self-built material library and (3) autonomously optimize structural parameters for the target emissivity spectra. The present framework is demonstrated to be feasible and efficient in designing WS-TEs across different applications, and the design parameters are highly scalable in materials, structures, dimensions, and the target functions, offering a general framework for emissivity engineering and paving the way for efficient design of nonlinear optimization problems beyond thermal metamaterials.

Theoretical simulation and mechanisms of SmNiO3-based phase change metamaterial for mid-infrared dynamic thermal control

Dynamic thermal emission control has gained increasing attention across diverse fields. Among phase change materials (PCMs), SmNiO3 has attracted many interests because of its fast phase transition and non-volatile properties. However, constructing an emissivity modulation metamaterial with angle stability performance is still rather challenging. In this work, we propose three kinds of SmNiO3-based metamaterials for mid-infrared emissivity dynamic modulation, specifically a trapezoidal metamaterial consisting of alternating SmNiO3 and Si multi-layer thin films and two modified grating metastructures, realizing an average emissivity modulation Δεaver of 0.42–0.45 in 5–16 µm. It is confirmed that the magnetic resonance stimulated inside the metamaterial is because of the slow-light effect. This work provides theoretical fundamentals for the design of dynamic thermal control metamaterials and benefits applications in the fields of infrared emission modulation.

Deep Learning-Assisted Active Metamaterials with Heat-Enhanced Thermal Transport.

Heat management is crucial for state-of-the-art applications such as passive radiative cooling, thermally adjustable wearables, and camouflage systems. Their adaptive versions, to cater to varied requirements, lean on the potential of adaptive metamaterials. Existing efforts, however, feature with highly anisotropic parameters, narrow working-temperature ranges, and the need for manual intervention, which remain long-term and tricky obstacles for the most advanced self-adaptive metamaterials. To surmount these barriers, heat-enhanced thermal diffusion metamaterials powered by deep learning is introduced. Such active metamaterials can automatically sense ambient temperatures and swiftly, as well as continuously, adjust their thermal functions with a high degree of tunability. They maintain robust thermal performance even when external thermal fields change direction, and both simulations and experiments demonstrate exceptional results. Furthermore, two metadevices with on-demand adaptability, performing distinctive features with isotropic materials, wide working temperatures, and spontaneous response are designed. This work offers a framework for the design of intelligent thermal diffusion metamaterials and can be expanded to other diffusion fields, adapting to increasingly complex and dynamic environments.

General three-dimensional thermal illusion metamaterials

Abstract Thermal illusion aims to create fake thermal signals or hide the thermal target from the background thermal field to mislead infrared observers, and illusion thermotics was proposed to regulate heat flux with artificially structured metamaterials for thermal illusion. Most theoretical and experimental works on illusion thermotics focus on two-dimensional materials, while heat transfer in real three-dimensional (3D) objects remains elusive, so the general 3D illusion thermotics is urgently demanded. In this study, we propose a general method to design 3D thermal illusion metamaterials with varying illusions at different sizes and positions. To validate the generality of the 3D method for thermal illusion metamaterials, we realize thermal functionalities of thermal shifting, splitting, trapping, amplifying and compressing. In addition, we propose a special way to simplify the design method under the condition that the size of illusion target is equal to the size of original heat source. The 3D thermal illusion metamaterial paves a general way for illusion thermotics and triggers the exploring of illusion metamaterials for more functionalities and applications.

Introduction of Asymmetry to Enhance Thermal Transport in Porous Metamaterials at Low Temperature

Introducing porosity with different degrees of disorder has been widely used to regulate thermal properties of materials, which generally results in decrease of thermal conductivity. We investigate the thermal conductivity of porous metamaterials in the ballistic transport region by using the Lorentz gas model. It is found that the introduction of asymmetry and Gaussian disorder into porous metamaterials can lead to a strong enhancement of thermal conductivity. By dividing the transport process into ballistic transport, non-ballistic transport, and unsuccessful transport processes, we find that the enhancement of thermal conductivity originates from the significant increase ballistic transport ratio. The findings enhance the understanding of ballistic thermal transport in porous materials and may facilitate designs of high-performance porous thermal metamaterials.

Two-scale data-driven design for heat manipulation

Data-driven methods have gained increasing attention in computational mechanics and design. This study investigates a two-scale data-driven design for thermal metamaterials with various functionalities. To address the complexity of multiscale design, the design variables are chosen as the components of the homogenized thermal conductivity matrix originating from the lower scale unit cells. Multiple macroscopic functionalities including thermal cloak, thermal concentrator, thermal rotator/inverter, and their combinations, are achieved using the developed approach. Sensitivity analysis is performed to determine the effect of each design variable on the desired functionalities, which is then incorporated into topology optimization. Geometric extraction demonstrates an excellent matching between the optimized homogenized conductivity and the extraction from the constructed database containing both architecture and property information. The designed heterostructures exhibit multiple thermal meta-functionalities that can be applied to a wide range of heat transfer fields from personal computers to aerospace engineering.

Variable Thermal Conductivity Metamaterials Applied to Passive Thermal Control of Satellites

Abstract Active materials like the proposed variable thermal conductivity metamaterial enable new thermal designs and low-cost, low-power, passive thermal control. Thermal control of satellites conventionally requires active thermal control systems that are expensive, large, inefficient, energy-intensive, and unavailable for CubeSats. The high-temperature operation case is the thermal system’s primary design consideration for CubeSats. The thermal path is designed to reject as much heat as possible to ensure the system does not overheat. In other cases, such as during a power anomaly, the oversized thermal path results in rapid cooling, culminating in mission failure due to thermal limits on the electronics or batteries. Improving the thermal control of CubeSats can enable new thermally challenging missions, increase satellite longevity, and increase mission success rate by controlling the dynamic thermal environment. The materials available for thermal management are inherently limited, but new engineered materials provide unique opportunities to change how satellites adapt to thermal loads. This paper investigates using an adaptive metamaterial designed to passively change its thermal conductivity as a function of temperature to meet the needs of the satellite. The thermal performance of a CubeSat is evaluated with a variable thermal conductivity metamaterial located in the critical thermal path from the satellite to the radiator. The system’s performance using two metamaterial configurations is compared to a baseline copper thermal path. Multiple satellite thermal operation cases are investigated to determine the operation ranges, and the metamaterial’s performance in various conditions is quantified.

Inverse Design and Experimental Verification of Metamaterials for Thermal Illusion Using Genetic Algorithms

Thermal metamaterials offer a promising avenue for creating artificial materials with unconventional physical properties, such as thermal cloak, concentrator, rotator, and illusion. However, designs and fabrication of thermal metamaterials are of challenge due to the limitations of existing methods on anisotropic material properties. We propose an evolutionary framework for designing thermal metamaterials using genetic algorithm optimization. Our approach encodes unit cells with different thermal conductivities and performs global optimization using the evolution-inspired operators. We further fabricate the thermal functional cells using 3D printing and verify their thermal illusion functionality experimentally. Our study introduces a new design paradigm for advanced thermal metamaterials that can manipulate heat flows robustly and realize functional thermal metadevices without anisotropic thermal conductivity. Our approach can be easily applied to fabrications in various fields such as thermal management and thermal sensing.

Thermally driven hybrid metastructure for multi-functional surface acoustic wave engineering

Acoustic wave engineering through solid mediums are essential for improving or optimizing the performances of various platforms, such as biomedical and industrial applications. Metamaterials or metasurfaces have been recently developed to artificially manipulate the wave propagation passing through mediums. However, they only conduct one fixed function passively, determined by the structure design for the particular wavelength, and their fabrication involves high-cost and complex procedures. Here, we report a thermally driven hybrid metastructure (HMS) for actively controlling surface acoustic waves. The HMS is designed as the layered structure of a thermoresponsive polymer (TP), thermal metamaterials (TMs) and an intermediate layer (IL) made of silica aerogel. For providing multi-functions, TPs conduct the considerable elastic modulus changes and corresponding wave manipulation at a certain glass transition temperature while TMs enable the programmed heating configuration, and the IL mitigates thermal and acoustic wave interference. By introducing the IL, the entire energy of the propagating wave is captured at the interface and interference between the wave and thermal energy is prevented, which directly reflects the temperature control through the TMs into the TP heating configuration. Versatile functions of programmable wave engineering including omnidirectional wave focusing-collimation through modified Luneberg lenses, dual-functioning focusing-bifurcation, and double refraction through 3-phase wave steering are demonstrated using the proposed HMS implemented by the temperature gradient design of TMs. This work will inspire tunable and scalable platforms for active controls of wave propagation enabled by thermal energy as a driving force.

Autonomously Tuning Multilayer Thermal Cloak with Variable Thermal Conductivity Based on Thermal Triggered Dual Phase-Transition Metamaterial

Thermal cloaks offer the potential to conceal internal objects from detection or to prevent thermal shock by controlling external heat flow. However, most conventional natural materials lack the desired flexibility and versatility required for on-demand thermal manipulation. We propose a solution in the form of homogeneous multilayer thermodynamic cloaks. Through an ingenious design, these cloaks achieve exceptional and extreme parameters, enabling the distribution of multiple materials in space. We first investigate the effects of important design parameters on the thermal shielding effectiveness of conventional thermal cloaks. Subsequently, we introduce an autonomous tuning function for the thermodynamic cloak, accomplished by leveraging two phase transition materials as thermal conductive layers. Remarkably, this tuning function does not require any energy input. Finite element analysis results demonstrate a significant reduction in the temperature gradient inside the thermal cloak compared to the surrounding background. This reduction indicates the cloak’s remarkable ability to manipulate the spatial thermal field. Furthermore, the utilization of materials undergoing phase transition leads to an increase in thermal conductivity, enabling the cloak to achieve the opposite variation of the temperature field between the object region and the background. This means that, while the temperature gradient within the cloak decreases, the temperature gradient in the background increases. This work addresses a compelling and crucial challenge in the realm of thermal metamaterials, i.e., autonomous tuning of the thermal field without energy input. Such an achievement is currently unattainable with existing natural materials. This study establishes the groundwork for the application of thermal metamaterials in thermodynamic cloaks, with potential extensions into thermal energy harvesting, thermal camouflage, and thermoelectric conversion devices. By harnessing phonons, our findings provide an unprecedented and practical approach to flexibly implementing thermal cloaks and manipulating heat flow.

Design and Analysis of a Temperature-Sensitive Thermal Meta-Regulator Possessing Different Heat Distribution Modes

The control and regulation of thermal fields is of great significance in solving various thermal management problems in human life. Benefitting from the emerging space transformation technique and thermal meta-material, thermal meta-structures with unique thermal control capabilities have been rapidly developed in recent years. However, the exploration of the functional diversity of thermal meta-materials and structures is still inadequate; most related works are still limited to the single-field control effect and lack sensitivity to external environment changes. For the designed functional structures, observation and analysis of energy fluctuations and irreversible heat loss during the regulation process of the diffusive thermal field are also scare. Therefore, in this current work, we design a thermal meta-regulator (based on the space transformation theory) that is capable of differently distributing thermal energy according to the heat input direction and switching field control pattern with the change of ambient temperature. In addition to the common indicator of temperature, we also introduce the local entropy production rate and the total entropy production in the thermo-dynamic category to carry out entropy analysis of the energy processes involved in the thermal meta-regulator, making a multi-angle evaluation of the structural performance. Furthermore, we use the statistical response surface method to explore the comprehensive/interaction effect of multiple influencing factors on the thermal meta-regulator; the derived regression equations can be used to accurately predict the structural effects under different design schemes and temperature conditions. Our work further enriches the diversity and flexibility of thermal field manipulation manners and the demonstrated functions are also expected to be realized in other physical fields.

Effective Thermal Conductivity and Heat Transfer Characteristics of a Series of Ceramic Triply Periodic Minimal Surface Lattice Structure

Triply periodic minimal surface (TPMS) structures with high surface area, high porosity, complex pore channels, and pore size distribution have great potential for application in thermal metamaterials and thermal engineering applications. To demonstrate the possibility of the use of TPMS structures as thermal metamaterials, the thermal insulation properties and heat transfer mechanisms of TPMS structures are investigated in detail. The results show that modulation of the volume fraction to within 15% by a rational geometric design indicates the possibility to obtain excellent lightweight properties. The effective thermal conductivity is within 0.25 W m−1 K−1, which is much lower than this component, indicating that the TPMS structure is designed to reduce the effective thermal conductivity and provide a lightweight design. However, in a high‐temperature environment, reasonable structural parameters can shield the cavity radiation in the TPMS structure and play an effective role to provide high‐temperature thermal insulation. Finally, based on the relationship between structural parameters and thermal insulation performance, a dynamic density TPMS‐graded structure is proposed, which exhibits a better thermal insulation performance than the conventional TPMS structure both at room temperature and at high temperature.

Enhanced temperature-responsive functions of thermal metamaterials by interface engineering

A phase-change thermal metamaterial (PCTM) has attracted a lot of attention to implement responsive thermal functions that can be adaptable to ambient environments. Temperature responsive PCTMs consisting of aligned metal backbones and phase change materials (PCMs) are capable of transforming artificial heat paths enabled by rapidly transiting thermophysical characteristics at certain temperatures. However, fabricating the PCTMs essentially involves the interfacial boundaries of different materials such as metal and PCMs, thereby degrading thermal transport between them. Moreover, while the phase of the material is altered from solid to liquid or vice versa, the instability of the interfaces inevitably occurs. Herein, we report an interface engineering of PCTMs using layer-by-layer (LbL) coating layers and nanocomposite PCMs to improve the on/off switching transition of thermal functions manipulating the heat flux in response to a specific temperature. LbL-assembled ultra-thin interfaces (multi-walled carbon nanotube (MWCNT)-polyethylenimine (PEI) layers and MWCNT-PEI-Silane layers) as interfacial thermal resistance compensators and PCM nanocomposites using graphene nanoplatelets (GNPs) are incorporated into thermal shifters based on stainless steel backbones. The LbL interfaces reduce the physical voids and phonon scattering between PCMs and metal surfaces while the GNP fillers increase the thermal conductivity of the PCMs in solid phases. The engineered PCTMs highly amplify the on/off switching ratio of thermal shifter unit cells and enhance overall thermal functions of temperature responsive TM modules (shield, concentrator, diffuser, and inverter). This work can pave a way for feasible solutions of interfacial resistances and instability in TMs.

Non-Equilibrium Thermodynamics of Heat Transport in Superlattices, Graded Systems, and Thermal Metamaterials with Defects.

In this review, we discuss a nonequilibrium thermodynamic theory for heat transport in superlattices, graded systems, and thermal metamaterials with defects. The aim is to provide researchers in nonequilibrium thermodynamics as well as material scientists with a framework to consider in a systematic way several nonequilibrium questions about current developments, which are fostering new aims in heat transport, and the techniques for achieving them, for instance, defect engineering, dislocation engineering, stress engineering, phonon engineering, and nanoengineering. We also suggest some new applications in the particular case of mobile defects.

Engineering Heat Transport Across Epitaxial Lattice-Mismatched van der Waals Heterointerfaces.

Artificially engineered 2D materials offer unique physical properties for thermal management, surpassing naturally occurring materials. Here, using van der Waals epitaxy, we demonstrate the ability to engineer extremely insulating thermal metamaterials based on atomically thin lattice-mismatched Bi2Se3/MoSe2 superlattices and graphene/PdSe2 heterostructures with exceptional thermal resistances (70-202 m2 K/GW) and ultralow cross-plane thermal conductivities (0.012-0.07 W/mK) at room temperature, comparable to those of amorphous materials. Experimental data obtained using frequency-domain thermoreflectance and low-frequency Raman spectroscopy, supported by tight-binding phonon calculations, reveal the impact of lattice mismatch, phonon-interface scattering, size effects, temperature, and interface thermal resistance on cross-plane heat dissipation, uncovering different thermal transport regimes and the dominant role of long-wavelength phonons. Our findings provide essential insights into emerging synthesis and thermal characterization methods and valuable guidance for the development of large-area heteroepitaxial van der Waals films of dissimilar materials with tailored thermal transport characteristics.

Deep-Learning-Enabled Intelligent Design of Thermal Metamaterials.

Thermal metamaterials are mixture-based materials that are engineered to manipulate, control, and process the flow of heat, enabling numerous advanced thermal metadevices. Conventional thermal metamaterials are predominantly designed with tractable regular geometries owing to the delicate analytical solution and easy-to-implement effective structures. Nevertheless, it is challenging to achieve the design of thermal metamaterials with arbitrary geometry, letting alone intelligent (automatic, real-time, and customizable) design of thermal metamaterials. Here, an intelligent design framework of thermal metamaterials is presented via a pre-trained deep learning model, which gracefully achieves the desired functional structures of thermal metamaterials with exceptional speed and efficiency, regardless of arbitrary geometry. It possesses incomparable versatility and is of great flexibility to achieve the corresponding design of thermal metamaterials with different background materials, anisotropic geometries, and thermal functionalities. The transformation thermotics-induced, freeform, background-independent, and omnidirectional thermal cloaks, whose structural configurations are automatically designed in real-time according to shape and background, are numerically and experimentally demonstrated. This study sets up a novel paradigm for an automatic and real-time design of thermal metamaterials in a new design scenario. More generally, it may open a door to the realization of an intelligent design of metamaterials in also other physical domains.

Observation of bulk quadrupole in topological heat transport

The quantized bulk quadrupole moment has so far revealed a non-trivial boundary state with lower-dimensional topological edge states and in-gap zero-dimensional corner modes. In contrast to photonic implementations, state-of-the-art strategies for topological thermal metamaterials struggle to achieve such higher-order hierarchical features. This is due to the absence of quantized bulk quadrupole moments in thermal diffusion fundamentally prohibiting possible band topology expansions. Here, we report a recipe for generating quantized bulk quadrupole moments in fluid heat transport and observe the quadrupole topological phases in non-Hermitian thermal systems. Our experiments show that both the real- and imaginary-valued bands exhibit the hierarchical features of bulk, gapped edge and in-gap corner states—in stark contrast to the higher-order states observed only on real-valued bands in classical wave fields. Our findings open up unique possibilities for diffusive metamaterial engineering and establish a playground for multipolar topological physics.

Space-Time Thermal Binary Coding by a Spatiotemporally Modulated Metashell

The recently proposed space-time-coding electromagnetic metasurface introduces the temporal dimension into artificial structure design, greatly expanding its digital application in information processing. However, the counterpart in thermal digital metamaterial is still lacking but compelling because the absence of temporal dimension prohibits synergetic modulation of thermal signal in time and space, thus limiting the capacity of information storage and the efficiency of information transmission with heat. Here, we introduce the temporal modulation into existing spatially variable thermal coding structures and propose a space-time thermal binary coding scheme. We design a category of coding units with time-dependent metashells so that they can switch their functionalities between cloaking and concentrating in time sequences. Integrating these identical units on a two-dimensional spatial array, we numerically show that this single metasurface can output various digital signal sequences composed of 0 and 1 in time and space dimensions. We further experimentally realize the temporal modulation with a rotatable concentric multilayered structure driven by a time-stepping motor. These results demonstrate a practical space-time strategy for thermal binary coding, provide a feasible prototype for spatiotemporal regulation of thermal signal, and promisingly open an alternative way for realizing information processing in diffusion systems.

Thermal metamaterials with nonconformal geometry

Thermal metamaterials have garnered significant attention for their potential to manipulate heat flow, leading to the development of various thermal metadevices such as thermal cloaks, concentrators, and rotators. However, the theoretical study of thermal metadevices with nonconformal geometry remains limited due to design and fabrication challenges. This letter proposes a method for designing and manufacturing nonconformal thermal metamaterials using the conformal discrete theory to simplify the anisotropic thermal conductivity tensors. The method involves 3D printing three thermal metadevices (a thermal cloak, concentrator, and rotator) with complex nonconformal geometry. Simulation and experimental results demonstrate the successful implementation of cloaking, concentrating, and rotating functionalities. Moreover, the thermal metadevices still maintained thermal functionality well under the condition of omnidirectional heat flow. This work provides guidance for the design and manufacture of nonconformal thermal metamaterials, as well as their potential applications in other fields such as electrics/magnetics, electromagnetics/optics, and acoustics.