Ultralow Thermal Conductivity and Mechanical Resilience of

Letter Cite This: Nano Lett. XXXX, XXX, XXX−XXX

pubs.acs.org/NanoLett

Ultralow Thermal Conductivity and Mechanical Resilience of Architected Nanolattices Nicholas G. Dou,† Robert A. Jagt,†,‡ Carlos M. Portela,† Julia R. Greer,† and Austin J. Minnich*,† †

Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, United States Faculty of Science and Engineering, University of Groningen, 9747 AG Groningen, The Netherlands

‡

Downloaded via KAOHSIUNG MEDICAL UNIV on July 19, 2018 at 14:43:05 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

S Supporting Information *

ABSTRACT: Creating materials that simultaneously possess ultralow thermal conductivity, high stiffness, and damage tolerance is challenging because thermal and mechanical properties are coupled in most fully dense and porous solids. Nanolattices can fill this void in the property space because of their hierarchical design and nanoscale features. We report that nanolattices composed of 24- to 182-nm-thick hollow alumina beams in the octet-truss architecture achieved thermal conductivities as low as 2 mW m−1 K−1 at room temperature while maintaining specific stiffnesses of 0.3 to 3 MPa kg−1 m3 and the ability to recover from large deformations. These nanoarchitected materials possess the same ultralow thermal conductivities as aerogels while attaining specific elastic moduli that are nearly 2 orders of magnitude higher. Our work demonstrates a general route to realizing multifunctional materials that occupy previously unreachable regions within the material property space. KEYWORDS: Multifunctional materials, octet-truss, 3ω, phonon transport, stiffness, recoverability catastrophically at 20 kPa of applied flexural or tensile stress.6,7 The fragility of aerogels is attributed to their “pearl necklace” structure that consists of secondary particles weakly connected at narrow neck regions. Some approaches to improving the mechanical properties of silica aerogels include increasing their density, which increases the connections between secondary particles;8 Oswald ripening or aging, where silica migrates to neck regions;9 and polymer reinforcement by copolymerization, cogellation, or conformal coating.10−12 The latter two methods widen the interparticle necks without substantially increasing the density, thereby raising the specific compressive modulus by up to an order of magnitude. The wider necks also cause an increase in thermal conductivity, with 41 mW m−1 K−1 reported for polyurea-encapsulated silica aerogels.13 The specific modulus and thermal conductivity are similarly correlated for organic and pyrolyzed carbon aerogels.14,15 Efforts to reduce the aerogel thermal conductivity without affecting the density have focused on opacification with carbon or TiO2, which inhibits radiative heat transfer.4,16

C

orrelations between material properties in different physical domains restrict the regions of property space that are accessible to typical materials. For example, lightweight materials that are both thermally insulating and mechanically stiff, which are desired as thermal protection or cryogenic insulation materials for space applications,1,2 are difficult to realize because the thermal conductivity and elastic modulus both increase with the strength of interatomic forces in fully dense solids. Porous solids, such as foams, achieve ultralow thermal conductivities of less than 100 mW m−1 K−1, but their specific modulus, or stiffness-to-density ratio, decreases precipitously as the relative density is reduced. Many porous solids fail catastrophically upon mechanical loading and cannot recover from large deformations. Creating materials that simultaneously possess ultralow thermal conductivity, high specific stiffness, and mechanical resilience remains an outstanding challenge. Aerogels are typically the first choice for materials with ultralow thermal conductivity,3 but their mechanical resilience is notoriously poor. The lightest monolithic silica aerogels with densities of about 80 kg m−3 have thermal conductivities of as low as 4 mW m−1 K−1 upon evacuation.4,5 These ultralight structures have a Young’s modulus of 1 MPa and fail © XXXX American Chemical Society

Received: March 23, 2018 Revised: July 3, 2018

A

DOI: 10.1021/acs.nanolett.8b01191 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters

Figure 1. (a) Fabrication process for hollow alumina nanolattices in a geometry suitable for thermal characterization with the 3ω method using two-photon lithography and atomic-layer deposition. (b) SEM cross-section showing the octet-truss architecture, the mesh top plate, and (inset) alumina pillars spanning the plate. (c) Optical microscope and (d) SEM images of the full sample geometry indicating the locations of current injection and voltage measurement. The length of the region between voltage probes that is characterized with the 3ω method is L = 1.5 mm. (e) Side view highlighting a ramp and (inset) a sacrificial beam. Scale bars are 1 mm for (c), 25 μm for (b, e), and 2 μm for the insets.

wall-thickness-to-beam-radius ratio t/r all play important roles in determining the stiffness, strength, and failure modes of the material.38 At the nanoscale, appropriate values for these dimensional ratios can greatly improve the mechanical resilience of nanolattices. Recoverability after global deformation is enabled through a combination of elastic beam buckling, shell buckling, and microfracture at the nodes.39 In the thermal domain, the relative density and intrinsic thermal transport properties of the constituent material control the effective thermal conductivity of nanolattices. The nanoscale features of hollow nanolattices can increase the boundary scattering of phonons and lower the thermal conductivity.35,40 At a fixed relative density, dimensional ratios r/l and t/r provide degrees of freedom for tuning the mechanical properties with minimal impact on the thermal properties. In this work, we develop an experimental approach to characterize the thermal conductivity of nanolattices and demonstrate that nanolattices occupy a previously inaccessible region of thermomechanical property space. We focus on hollow-beam alumina nanolattices with the octet-truss architecture, showing that they combine ultralow thermal conductivities down to 2 mW m−1 K−1, high specific stiffnesses greater than 0.3 MPa kg−1 m3, and mechanical resilience in a single material. These structures retain comparable or lower

Inverse opals are another type of highly porous material with applications in photonics,17,18 sensing,19 catalysis,20 energy storage,21 biological tissue engineering,22 and many other fields.23 Mechanical studies of nickel inverse opals revealed their high specific strength and tunable specific modulus from 4 to 20 MPa kg−1 m3.24 A study of silicon inverse opals reported thermal conductivities of around 1000 mW m−1 K−1,25,26 which are significantly higher than those of aerogels and polymer foams. Other nanostructured materials, such as porous anodic aluminum oxide,27,28 3D nanowire networks,29,30 and certain 3D nanostructures,31 lack either ultralow thermal conductivity or structural rigidity. Nanolattices, composed of a periodic network of connected struts with nanoscale dimensions,32 have the potential to fill this gap in the property space by virtue of their hierarchical design33,34 and nanoscale features that decouple their thermal and mechanical properties.35 In the mechanical domain, lattice architecture and relative density set the effective elastic modulus of the material. For low densities (ρ < 10 kg m−3), the stiffness of solid-beam nanolattices scales linearly with density for stretching-dominated architectures and quadratically for bending-dominated architectures.36,37 Hollow-beam nanolattices exhibit more complex mechanical behavior in which the architecture, beam-radius-to-length ratio r/l, and B


Letter

Nano Letters

Figure 2. (a) Representative 3ω thermal response of the 81 nm wall thickness nanolattice versus driving frequency (symbols) along with the model-fitted curve (solid line) and ±20% bounds (shaded region). (b) Room-temperature thermal conductivity versus relative density depicting measured values (symbols), finite element simulations (solid line) of a representative unit cell (inset), a thermal conductivity model developed for cellular solids (dotted line),48 and our previous thermal resistance model (dashed line).35 (c) Measured thermal conductivity (symbols) versus temperature for three of the nanolattices along with finite element predictions (lines). Good agreement between simulations and experiments indicates that heat conduction occurs by diffusion.

photon lithography (TPL) and then conformally coat it with alumina using atomic layer deposition (ALD). We hollow out the structure by milling away sacrificial beams using a focused ion beam (FIB) and etching away the underlying polymer using oxygen plasma.38 We then deposit 100 nm of gold through an aligned shadow mask to create a metal line on top of the structure connected to four contact pads on the substrate. The resulting alumina nanolattice depicted in Figure 1c,d is 50 μm tall, 50 μm wide, and 3 mm long. A cross-section of the structure in Figure 1b shows the octet-truss architecture and the top plate, which is written as a mesh during TPL. Pores of the polymer mesh are filled during ALD, forming alumina pillars that provide channels for heat conduction through the plate after the polymer is etched away. A side view of the nanolattice in Figure 1e highlights one of the four ramps that allow electrical connection of the heater line to the contact pads. Also shown are the sacrificial beams through which the etchant plasma accesses the internal polymer in the nanolattice. The new geometry of our experiment requires a modified thermal model for interpreting the raw data. Recall that in the 3ω method a sinusoidal current is passed through the heater line at frequency ω, leading to Joule heating at 2ω. The resulting temperature rise is deduced from the measured voltage across the line at 3ω. The thermal frequency response is then fit to a heat diffusion model to extract the thermal conductivity of the nanolattice. The typical thermal model used for 3ω data reduction49 does not account for heat diffusion parallel to the heater line, which is significant for the bridge design due to the ultralow thermal conductivity of the nanolattice. We developed a custom thermal model for our nanolattice bridge samples that accurately captures the heat leakage along the metal heater line and in-plane conduction along the line. We present further justification and a detailed derivation of the nanolattice thermal model in the Supporting Information. We measured the thermal conductivity of six hollow alumina nanolattices with octet-truss unit cells of side length 25 μm,

thermal conductivity compared to that of aerogels while achieving specific elastic moduli nearly 2 orders of magnitude higher. Low-density nanolattices can recover from compressive strains of more than 20%, which would result in the catastrophic failure of typical aerogels. Further reductions in thermal conductivity could be achieved by exploiting classical size effects. This work demonstrates a general route to designing and performing the thermal characterization of novel multifunctional nanoarchitected materials with property combinations that are extremely difficult to realize in conventional solids. Measuring the thermal conductivity of nanolattices is challenging due to their ultralow thermal conductivity, complex geometry, and fabrication constraints. Conventional thermal characterization methods such as hot wire41,42 and laser flash43 are not applicable because samples that cover the required macroscale area would take a prohibitively long time to fabricate. The thermal penetration depth of typical optical pump−probe techniques44,45 in thermally insulating materials limits the experimental sensitivity to about a micrometer below the sample surface, which is too shallow for nanolattices whose unit cells span several micrometers. The ultralow thermal conductivity of nanolattices results in poor sensitivity of the experimental signal to the nanolattice thermal conductivity for the most straightforward adaptations of the 3ω method,46 such as writing the sample on top of the heater line.47 We developed a new approach to measure the thermal conductivity of nanolattices that uses the 3ω method46 with a unique bridgelike sample design. The new design minimizes the structure size while maintaining excellent experimental sensitivity. Performing thermal measurements of our nanolattice bridge samples requires a reconsideration of the usual fabrication process for nanolattices and of the established thermal model for 3ω data analysis. We fabricated alumina nanolattices in the bridge configuration using the process outlined in Figure 1a. Our bridge design features a mesh top plate and side ramps that facilitate patterning of the heater line and electrical contacts required for the 3ω measurement. We first create a three-dimensional polymer scaffold using twoC


Letter

Nano Letters circular beams of radius 1.8 μm, and wall thicknesses from 24 to 182 nm, which have relative densities ranging from 0.5 to 4%. Experiments were conducted at temperatures from 95 to 300 K and at pressures in the 10−6 Torr range. Figure 2a shows the 3ω frequency response for the 81 nm wall thickness nanolattice at room temperature plotted with the best fit curve and model-generated curves for thermal conductivity deviations of ±20%, illustrating experimental sensitivity to the thermal conductivity of the nanolattice. Room-temperature thermal conductivities of six nanolattices versus relative density are shown in Figure 2b. The 20% error bars reflect uncertainty in the fitting procedure as well as uncertainty in the nanolattice dimensions caused by fabrication imperfections. Earlier work revealed that the ALD-deposited alumina is amorphous,38 so we expect the heat transport to occur by diffusion and the thermal conductivity to follow classical effective medium theories. To test this hypothesis, we performed finite element method (FEM) simulations on the representative unit cell shown in the inset of Figure 2b using the thermal conductivity of amorphous alumina reported in the literature.50 The measured 3ω data are consistent with the predictions of FEM and a thermal conductivity model developed for cellular solids.48 For low relative densities below about 1%, a simple thermal resistor model gives a good approximation.35 Both the resistor and cellular models depend only on the relative density, which suggests that small fabrication-induced imperfections, such as thickness nonuniformities and beam waviness, have little impact on thermal conductivity. The temperature-dependent thermal conductivities of three nanolattices with wall thicknesses of 36, 81, and 182 nm are also in reasonable agreement with FEM simulations, as depicted in Figure 2c. We attribute the offset of the 36 nm experimental data from simulation results to uncertainty in the bulk thermal conductivity of alumina, uncertainty in the true lattice dimensions, and structural imperfections. All of the nanolattices exhibit the same trend of increasing thermal conductivity with increasing temperature, which matches reported measurements of amorphous alumina thin films50 and resembles those of many other amorphous bulk solids.51 The similarity of these temperature dependences suggests that phonon transport occurs by diffusion and classical size effects are not significant. The observed diffusive transport behavior is consistent with the expectation that vibrational mean free paths are on the order of the interatomic spacing in amorphous alumina.52 The complete set of thermal conductivity measurements is presented in Supporting Information Figure S2. We also measured the elastic modulus and deformation characteristics of the same nanolattices tested thermally. We performed uniaxial compression experiments on 5 × 5 × 5 lattices to 50% strain at a rate of 0.001 s−1 in a G200 XP Nanoindenter (Agilent Technologies). Representative stress− strain curves for each nanolattice geometry are shown in Supporting Information Figure S3. From these data, we calculate the Young’s modulus as the slope of the linear loading regime and the effective strength as the stress at the initial instability or at the point of catastrophic failure, depending on the failure mechanism. The stiffnesses and strengths extracted from the compression experiments are plotted in Supporting Information Figures S4 and S5. Several identical samples were compressed to estimate the average mechanical properties for each geometry. The measured stiffnesses and strengths of nanolattices exhibit density scalings of E ∝ ρ1.91 and σy ∝ ρ1.75,

which are significantly better than the density scalings for aerogels, as seen in Supporting Information Figure S5. For the lowest-density nanolattices (24 nm wall thickness, 0.5% relative density), we performed additional in situ experiments using an InSEM (Nanomechanics Inc.) nanoindenter, where cyclic loading to 20% strain allowed recoverability and deformation modes to be observed. Figure 3a depicts the stress−strain data for cyclic compression of a 24

Figure 3. (a) Stress and strain recorded during a six-cycle compression test of a 24 nm wall thickness nanolattice. Curves are labeled with the cycle number. SEM images (b) before, (c) during, and (d) after the test show 98% recovery. The circular marker in (a) indicates the stress and strain of the partially compressed nanolattice shown in (c). Close-up images (insets) illustrate the contribution of beam buckling, shell buckling, and fracture. Scale bars are 50 μm for (b−d) and 10 μm for insets.

nm wall thickness nanolattice. Images of the structure before, during, and after the test are shown in Figure 3b−d. After yielding, the nanolattice experiences bursts of strain that correspond to layer-by-layer collapse. This serrated deformation signature is characteristic of competing failure modes: brittle fracture of tube walls, hollow beam buckling, and local shell buckling.38 The strain bursts are caused by noncatastrophic brittle fracture of the ceramic walls at nodes, while the mechanism of recoverable deformation is elastic shell buckling as shown in Figure 3c. Adapting the analysis by Meza et al.38 to circular hollow beams, we find that shell buckling is expected to dominate when the wall-thickness-to-beam-radius ratio is less than σ ij t yz jj zz = f 3(1 − ν 2) E k r {crit

while beam buckling is expected to occur when the beamradius-to-length ratio is less than D


Letter

Nano Letters

1 ij r yz jj zz = 2π k l {crit

σf E

more pronounced in low-density structures that also have the lowest thermal conductivities because of the more favorable density scalings for stretching-dominated nanolattices over stochastic aerogels. The nanolattices provide the added benefit of tunable mechanical properties, which can be decoupled from thermal properties by fixing the relative density and changing characteristic ratios r/l and t/r. This work demonstrates that hollow alumina nanolattices simultaneously achieve ultralow thermal conductivity, high stiffness and strength, and the ability to recover from large compressive strains by exploiting architecture and nanoscale feature sizes. A wider range of physical properties are attainable by modifying the lattice architecture, structural dimensions, and constituent material. Our results imply that thermal conductivity depends primarily on relative density via the resistor35 or cellular48 models, with a weaker dependence on lattice topology. Mechanical stiffness can be increased by introducing additional levels of hierarchy39 or decreased by using a bending-dominated architecture48 while simultaneously preserving ultralow thermal conductivity by keeping the relative density constant. The thermal conductivity could be decreased by creating multilayered walls to increase phonon interfacial scattering, which should not strongly affect the stiffness for a given relative density. Current micro- and nanofabrication techniques can readily produce these more sophisticated designs. Further developments in scalable manufacturing methods54,55 are needed to create macroscale nanolattices with dimensions (unit cell size, beam radius, and wall thickness), structural fidelity, and material quality comparable to those of existing processes. Once scaled-up, the nanolattices could have potential applications as structural thermal insulation for cryogenic storage tanks, cryogenic feed lines, and reusable surface insulation on launch vehicles and other spacecraft. Our work shows a general strategy for designing and characterizing nanoarchitected materials that occupy regions of property space that are challenging to access with conventional materials.

ALD alumina has a Young’s modulus of E = 164 GPa, a fracture strength of σf = 1.57 to 2.56 GPa, and a Poisson’s ratio of ν = 0.24,53 so the critical ratios for the nanolattices in this work are (t/r)crit = 0.016 to 0.026 and (r/l)crit = 0.016 to 0.020. The nanolattices with 24-nm-thick walls have characteristic ratios of t/r = 0.013 and r/l = 0.10, implying that recoverability can be attributed to shell buckling despite brittle failure occurring at some nodes, which is consistent with the in situ observations. The localization of cracks at the lattice nodes causes the stiffness of the nanolattices to decrease significantly throughout cyclic loading while still recovering to 98% of its original dimensions after each cycle. For subcritical t/r and r/l ratios, we expect that recoverable behavior can occur at strains of as large as 50%,38 which was not probed in this work. The recoverability of these nanolattices, whose unit cell size is 2 to 5 times larger than for previously studied structures,38 indicates that shell-buckling behavior is scale-independent if the defect concentration in the solid is low. We examine the multifunctional performance of these nanoarchitected materials on a plot of specific elastic modulus versus thermal conductivity, shown in Figure 4. Compared to

■

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.8b01191. Figure 4. Material property plot of specific modulus versus thermal conductivity. Dashed outlines indicate foams. For the same specific stiffness, nanolattices achieve an order of magnitude lower thermal conductivity than do polymer foams and porous ceramics used for space shuttle thermal protection systems. For the same thermal conductivity, nanolattices possess an almost 2 orders of magnitude higher specific stiffness compared to that of evacuated aerogels.

■

Sample fabrication, thermal experiments, mechanical experiments and simulations, 3ω thermal model, critical t/r and r/l ratios, and supplementary figures (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

the porous ceramics used for spacecraft thermal protection systems, the hollow alumina nanolattices have a similar specific modulus but almost an order of magnitude lower thermal conductivity. Compared to aerogels, the measured nanolattices have similar or lower thermal conductivity while achieving specific moduli of up to 2 orders of magnitude higher. Most aerogels also experience catastrophic failure under modest mechanical loads, while alumina nanolattices are more than an order of magnitude stronger at the same density, as illustrated in Supporting Information Figure S5b, and can exhibit recoverability and ductile-like deformation behavior. This improvement in the mechanical properties becomes even

ORCID

Nicholas G. Dou: 0000-0001-8199-5588 Austin J. Minnich: 0000-0002-9671-9540 Author Contributions

N.G.D. built the 3ω experiment, conducted the thermal measurements, and developed the thermal model. R.A.J. fabricated samples and assisted with thermal measurements. C.M.P. performed the mechanical measurements. J.R.G. and A.J.M. provided technical guidance and supervision. All authors contributed to writing the paper. E


Letter

Nano Letters Notes

silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres. Nature 2000, 405, 437. (18) Vlasov, Y. A.; Bo, X.-Z.; Sturm, J. C.; Norris, D. J. On-chip natural assembly of silicon photonic bandgap crystals. Nature 2001, 414, 289−293. (19) Scott, R. W. J.; Yang, S. M.; Chabanis, G.; Coombs, N.; Williams, D. E.; Ozin, G. A. Tin Dioxide Opals and Inverted Opals: Near-Ideal Microstructures for Gas Sensors. Adv. Mater. 2001, 13, 1468−1472. (20) Chen, J. I. L.; von Freymann, G.; Choi, S. Y.; Kitaev, V.; Ozin, G. A. Amplified Photochemistry with Slow Photons. Adv. Mater. 2006, 18, 1915−1919. (21) Esmanski, A.; Ozin, G. A. Silicon Inverse-Opal-Based Macroporous Materials as Negative Electrodes for Lithium Ion Batteries. Adv. Funct. Mater. 2009, 19, 1999−2010. (22) Choi, S.-W.; Xie, J.; Xia, Y. Chitosan-Based Inverse Opals: Three-Dimensional Scaffolds with Uniform Pore Structures for Cell Culture. Adv. Mater. 2009, 21, 2997−3001. (23) Stein, A.; Wilson, B. E.; Rudisill, S. G. Design and functionality of colloidal-crystal-templated materialsChemical applications of inverse opals. Chem. Soc. Rev. 2013, 42, 2763−2803. (24) Pikul, J. H.; Dai, Z.; Yu, X.; Zhang, H.; Kim, T.; Braun, P. V.; King, W. P. Micromechanical devices with controllable stiffness fabricated from regular 3D porous materials. J. Micromech. Microeng. 2014, 24, 105006. (25) Ma, J.; Sinha, S. Thermoelectric properties of highly doped ntype polysilicon inverse opals. J. Appl. Phys. 2012, 112, 073719. (26) Ma, J.; Parajuli, B. R.; Ghossoub, M. G.; Mihi, A.; Sadhu, J.; Braun, P. V.; Sinha, S. Coherent Phonon-Grain Boundary Scattering in Silicon Inverse Opals. Nano Lett. 2013, 13, 618−624. (27) Abad, B.; Maiz, J.; Ruiz-Clavijo, A.; Caballero-Calero, O.; Martin-Gonzalez, M. Tailoring thermal conductivity via threedimensional porous alumina. Sci. Rep. 2016, 6, 38595. (28) Martín, J.; Martín-González, M.; Fernández, J. F.; CaballeroCalero, O. Ordered three-dimensional interconnected nanoarchitectures in anodic porous alumina. Nat. Commun. 2014, 5, 5130. (29) Rauber, M.; Alber, I.; Müller, S.; Neumann, R.; Picht, O.; Roth, C.; Schökel, A.; Toimil-Molares, M. E.; Ensinger, W. Highly-Ordered Supportless Three-Dimensional Nanowire Networks with Tunable Complexity and Interwire Connectivity for Device Integration. Nano Lett. 2011, 11, 2304−2310. (30) Vlad, A.; Antohe, V.-A.; Martinez-Huerta, J. M.; Ferain, E.; Gohy, J.-F.; Piraux, L. Three-dimensional interconnected Nicore NiOshell nanowire networks for lithium microbattery architectures. J. Mater. Chem. A 2016, 4, 1603−1607. (31) Hong, S.; Park, J.; Jeon, S. G.; Kim, K.; Park, S. H.; Shin, H. S.; Kim, B.; Jeon, S.; Song, J. Y. Monolithic Bi1.5Sb0.5Te3 ternary alloys with a periodic 3D nanostructure for enhancing thermoelectric performance. J. Mater. Chem. C 2017, 5, 8974−8980. (32) Jang, D.; Meza, L. R.; Greer, F.; Greer, J. R. Fabrication and deformation of three-dimensional hollow ceramic nanostructures. Nat. Mater. 2013, 12, 893−898. (33) Schaedler, T. A.; Jacobsen, A. J.; Torrents, A.; Sorensen, A. E.; Lian, J.; Greer, J. R.; Valdevit, L.; Carter, W. B. Ultralight Metallic Microlattices. Science 2011, 334, 962−965. (34) Meza, L. R.; Greer, J. R. Mechanical characterization of hollow ceramic nanolattices. J. Mater. Sci. 2014, 49, 2496−2508. (35) Dou, N. G.; Minnich, A. J. Heat conduction in multifunctional nanotrusses studied using Boltzmann transport equation. Appl. Phys. Lett. 2016, 108, 011902. (36) Zheng, X.; Lee, H.; Weisgraber, T. H.; Shusteff, M.; DeOtte, J.; Duoss, E. B.; Kuntz, J. D.; Biener, M. M.; Ge, Q.; Jackson, J. A.; Kucheyev, S. O.; Fang, N. X.; Spadaccini, C. M. Ultralight, ultrastiff mechanical metamaterials. Science 2014, 344, 1373−1377. (37) Meza, L. R.; Phlipot, G. P.; Portela, C. M.; Maggi, A.; Montemayor, L. C.; Comella, A.; Kochmann, D. M.; Greer, J. R. Reexamining the mechanical property space of three-dimensional lattice architectures. Acta Mater. 2017, 140, 424−432.

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the Air Force Office of Scientific Research (AFOSR) Multifunctional Materials program under grant no. FA9550-14-1-0266. J.R.G. acknowledges financial support from the Department of Defense (DoD) through the Vannevar Bush Faculty Fellowship, and C.M.P. acknowledges support from the Office of Naval Research (ONR) through grant no. N00014-16-1-2431. The authors thank Lucas R. Meza for useful discussions and fabrication assistance, the Kavli Nanoscience Institute at Caltech for providing clean room facilities and staff support, and Prof. Nathan S. Lewis for access to additional fabrication equipment.

■

REFERENCES

(1) Henson, G.; Jone, C. S., III. Aerospace Materials and Applications; American Institute of Aeronautics and Astronautics: Washington, D.C., 2017; Materials for Launch Vehicle Structures. (2) Arnold, S. M.; Cebon, D.; Ashby, M. F. Materials Selection for Aerospace Systems; National Aeronautics and Space Administration: Washington, D.C., 2012. (3) Kistler, S. S. The Relation between Heat Conductivity and Structure in Silica Aerogel. J. Phys. Chem. 1934, 39, 79−86. (4) Fricke, J.; Lu, X.; Wang, P.; Buttner, D.; Heinemann, U. Optimization of monolithic silica aerogel insulants. Int. J. Heat Mass Transfer 1992, 35, 2305−2309. (5) Lu, X.; Arduini-Schuster, M. C.; Kuhn, J.; Nilsson, O.; Fricke, J.; Pekala, R. W. Thermal Conductivity of Monolithic Organic Aerogels. Science 1992, 255, 971−972. (6) Gross, J.; Reichenauer, G.; Fricke, J. Mechanical properties of SiO2 aerogels. J. Phys. D: Appl. Phys. 1988, 21, 1447. (7) Woignier, T.; Phalippou, J. Mechanical strength of silica aerogels. J. Non-Cryst. Solids 1988, 100, 404−408. (8) Gross, J.; Fricke, J. Scaling of elastic properties in highly porous nanostructured aerogels. Nanostruct. Mater. 1995, 6, 905−908. (9) Hæreid, S.; Anderson, J.; Einarsrud, M. A.; Hua, D. W.; Smith, D. M. Thermal and temporal aging of TMOS-based aerogel precursors in water. J. Non-Cryst. Solids 1995, 185, 221−226. (10) Martin, J.; Hosticka, B.; Lattimer, C.; Norris, P. M. Mechanical and acoustical properties as a function of PEG concentration in macroporous silica gels. J. Non-Cryst. Solids 2001, 285, 222−229. (11) Wei, T.-Y.; Lu, S.-Y.; Chang, Y.-C. Transparent, Hydrophobic Composite Aerogels with High Mechanical Strength and Low HighTemperature Thermal Conductivities. J. Phys. Chem. B 2008, 112, 11881−11886. (12) Randall, J. P.; Meador, M. A. B.; Jana, S. C. Tailoring Mechanical Properties of Aerogels for Aerospace Applications. ACS Appl. Mater. Interfaces 2011, 3, 613−626. (13) Katti, A.; Shimpi, N.; Roy, S.; Lu, H.; Fabrizio, E. F.; Dass, A.; Capadona, L. A.; Leventis, N. Chemical, Physical, and Mechanical Characterization of Isocyanate Cross-linked Amine-Modified Silica Aerogels. Chem. Mater. 2006, 18, 285−296. (14) Lu, X.; Nilsson, O.; Fricke, J.; Pekala, R. W. Thermal and electrical conductivity of monolithic carbon aerogels. J. Appl. Phys. 1993, 73, 581−584. (15) Pekala, R. W.; Alviso, C. T.; LeMay, J. D. Organic aerogels: microstructural dependence of mechanical properties in compression. J. Non-Cryst. Solids 1990, 125, 67−75. (16) Lee, D.; Stevens, P. C.; Zeng, S. Q.; Hunt, A. J. Thermal characterization of carbon-opacified silica aerogels. J. Non-Cryst. Solids 1995, 186, 285−290. (17) Blanco, A.; Chomski, E.; Grabtchak, S.; Ibisate, M.; John, S.; Leonard, S. W.; Lopez, C.; Meseguer, F.; Miguez, H.; Mondia, J. P.; Ozin, G. A.; Toader, O.; Driel, H. M. v. Large-scale synthesis of a F


Letter

Nano Letters (38) Meza, L. R.; Das, S.; Greer, J. R. Strong, lightweight, and recoverable three-dimensional ceramic nanolattices. Science 2014, 345, 1322−1326. (39) Meza, L. R.; Zelhofer, A. J.; Clarke, N.; Mateos, A. J.; Kochmann, D. M.; Greer, J. R. Resilient 3D hierarchical architected metamaterials. Proc. Natl. Acad. Sci. U. S. A. 2015, 112, 11502−11507. (40) Sondheimer, E. H. The mean free path of electrons in metals. Adv. Phys. 1952, 1, 1−42. (41) Stålhane, B.; Pyk, S. Ny metod fö r bestäm ning av värmeledningskoefficienter. Teknisk Tidskrift 1931, 61. (42) Healy, J. J.; de Groot, J. J.; Kestin, J. The theory of the transient hot-wire method for measuring thermal conductivity. Physica B+C 1976, 82, 392−408. (43) Parker, W. J.; Jenkins, R. J.; Butler, C. P.; Abbott, G. L. Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity. J. Appl. Phys. 1961, 32, 1679−1684. (44) Paddock, C. A.; Eesley, G. L. Transient thermoreflectance from thin metal films. J. Appl. Phys. 1986, 60, 285−290. (45) Capinski, W. S.; Maris, H. J. Improved apparatus for picosecond pump-and-probe optical measurements. Rev. Sci. Instrum. 1996, 67, 2720−2726. (46) Cahill, D. G. Thermal conductivity measurement from 30 to 750 K: the 3ω method. Rev. Sci. Instrum. 1990, 61, 802−808. (47) Barako, M. T.; Roy-Panzer, S.; English, T. S.; Kodama, T.; Asheghi, M.; Kenny, T. W.; Goodson, K. E. Thermal conduction in vertically aligned copper nanowire arrays and composites. ACS Appl. Mater. Interfaces 2015, 7, 19251−19259. (48) Ashby, M. F. The properties of foams and lattices. Philos. Trans. R. Soc., A 2006, 364, 15−30. (49) Borca-Tasciuc, T.; Kumar, A. R.; Chen, G. Data reduction in 3ω method for thin-film thermal conductivity determination. Rev. Sci. Instrum. 2001, 72, 2139−2147. (50) Lee, S.-M.; Cahill, D. G.; Allen, T. H. Thermal conductivity of sputtered oxide films. Phys. Rev. B: Condens. Matter Mater. Phys. 1995, 52, 253−257. (51) Freeman, J. J.; Anderson, A. C. Thermal conductivity of amorphous solids. Phys. Rev. B: Condens. Matter Mater. Phys. 1986, 34, 5684−5690. (52) Cahill, D. G.; Pohl, R. O. Thermal conductivity of amorphous solids above the plateau. Phys. Rev. B: Condens. Matter Mater. Phys. 1987, 35, 4067−4073. (53) Berdova, M.; Ylitalo, T.; Kassamakov, I.; Heino, J.; Törmä, P. T.; Kilpi, L.; Ronkainen, H.; Koskinen, J.; Hæggström, E.; Franssila, S. Mechanical assessment of suspended ALD thin films by bulge and shaft-loading techniques. Acta Mater. 2014, 66, 370−377. (54) Divliansky, I.; Mayer, T. S.; Holliday, K. S.; Crespi, V. H. Fabrication of three-dimensional polymer photonic crystal structures using single diffraction element interference lithography. Appl. Phys. Lett. 2003, 82, 1667−1669. (55) Zheng, X.; Smith, W.; Jackson, J.; Moran, B.; Cui, H.; Chen, D.; Ye, J.; Fang, N.; Rodriguez, N.; Weisgraber, T.; Spadaccini, C. M. Multiscale metallic metamaterials. Nat. Mater. 2016, 15, 1100.

G


Ultralow Thermal Conductivity and Mechanical Resilience of

Recommend Documents