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Nanographitic coating enables hydrophobicity in lightweight and strong microarchitected carbon

Metamaterials that are lightweight, stiff, strong, scalable and hydrophobic have been achieved separately through different materials and approaches, but achieving them in one material is an outstanding challenge. Here, stereolithography and pyrolysis are employed to create carbon microlattices with cubic topology and a strut width of 60–70 µm, with specific strength and stiffness of up to 468.62 MPa cm3 g−1 and 14.39 GPa cm3 g−1 at a density of 0.55 g cm−3, higher than existing microarchitected materials and approaching those of the strongest truss nanolattices. Subsequent fast Joule-heating then introduces a hierarchical nanographitic skin that enables hydrophobicity, with a water contact angle of 135 ± 2°, improving the hydrophilic response of pyrolytic carbon. As the Joule heating induced sp2-hybridization and nano-texturing predominantly affect the strut sheath, the effect on mechanical response is limited to a reduction in the distribution of compressive strength of as-pyrolyzed architectures by ~80% and the increase of the mean effective stiffness by ~15%. These findings demonstrate a technique to fabricate high strength, low density, and hydrophobic nanographite-coated carbon microlattices. Architectured materials are known for their mechanical properties, yet the addition of other functional properties would widen their applications range. Here, hydrophobicity is imparted to a high-strength carbon microlattice via a hierarchical nanographitic skin by rapid joule heating.

The field of mechanical metamaterials has particularly benefitted from the progress of reduced-scale manufacturing that has allowed the creation of architected materials with superior properties, mutually exclusive in traditional solids [19][20][21][22] . Such successful development comprises the realization of extremely deformable lattices constituted of brittle materials 23 , or simultaneously lightweight, stiff and strong architectures that exploit a hierarchical design 24 and the nanoscale strengthening effect 25,26 . The latter example has been achieved with carbon nanoarchitectures obtained by means of pyrolysis of polymeric lattices fabricated through two-photon lithography, which operates by cross-linking a liquid precursor resin voxel-by-voxel in a relatively slow process that prevents large-scale manufacturing. These carbon nanolattices have achieved the highest specific strength and stiffness (strength and stiffness to density ratio) ever attained for lightweight architected materials with densities below 1.0 g cm −3 , approaching the theoretical strength of the constituent material through a reduction of dimensions to the critical size of flaw insensitive solids [25][26][27] . On the other hand, carbon microlattices obtained via self-propagating photopolymer waveguides 28 and stereolithography (SLA) 29 show rapid prototyping of meso-and macroscale structures. However, their mechanical properties do not exceed those of traditional bulk materials, with specific strength limited to 53.68 MPa cm 3 g −1 , and specific stiffness bounded to 5.79 GPa cm 3 g −1 , thus not exploiting the advantages of an architected lattice design through additive manufacturing 28 . Therefore, one of the major challenges in metamaterial design is to simultaneously achieve high compressive mechanical properties and a fast, scalable fabrication.
Most of the studies on carbon architected materials have been focused on the synthesis and mechanical characterization [29][30][31][32][33][34] . The investigation of properties beyond the mechanical response could pave the pathway to multifunctional material design. Hydrophobicity, controlled through rational design of the lattice micro-texture, can be synergetic to the excellent mechanical performance of additively manufactured carbon lattices. The combination of hydrophobicity and strength in a single resistant material is sought for structural components exposed to extreme environments, to reduce wear and corrosion of lightweight systems in aerospace and maritime engineering, with applications ranging from anti-icing structures 35 to self-cleaning surfaces 36 . However, a simultaneous demonstration of these features is challenging. Currently, water repellent three-dimensionally fabricated structures are limited to planar arrays of microarchitectures 37 and soft lattices 38 , which do not guarantee durability and load-bearing capacity.
In this work, we present an approach based on pyrolysis and Joule heating to create lightweight 3D microarchitected carbon that combines superior mechanical performances and considerable hydrophobicity. The former process is mainly responsible for the advanced structural features, while the latter predominately enhances the water contact angle. Through an anisotropic unit cell topology, the specific strength and stiffness reached 468. 62 MPa cm 3 g −1 and 14.39 GPa cm 3 g −1 , outperforming all existing meso-and microlattices and attaining values that approach those of the strongest open-cell nanoarchitected materials developed up to date, despite presenting strut width and length two orders of magnitude larger. We show that Joule heating transforms the mainly amorphous as-pyrolyzed microarchitectures into glassy/ nanographitic carbon core/shell morphologies. We prove that the lattice architecture converts the hydrophilic pyrolytic carbon into a hydrophobic material with a water contact angle of 103 ± 12°, and the Joule heating induces a porous nanographitic skin that further enhances the contact angle to 135 ± 2°, thus approaching superhydrophobicity. Since the fast Joule heating process mainly affects the strut surface, the changes in structural response in Joule heated lattices are limited to a reduction of the distribution of compressive strengths by~80% while preserving the remarkable mean failure stress, and to an increase of the average effective stiffness by~15%. On the one hand, the heat-induced defect-rich nanoporous surface mitigates scattering of the failure stress and controls the onset of catastrophic failure; on the other hand, it prevents the Joule heated architectures from reaching the highest strength recorded in aspyrolyzed lattices. These results demonstrate a feasible methodology to create nanographite-coated microstructured carbon, with promising applications in extreme environments.

Results
Additive manufacturing and material characterization of carbon microlattices. The Digital Light Processing (DLP) SLA 3D-printed polymeric lattices were obtained from a transparent PR-48 photoresist resin. Subsequently, they were subjected to pyrolysis that yielded fully dense carbon microlattices, associated with an isotropic 66% linear and 97% volumetric shrinkage ( Supplementary Fig. 1). The Joule heating process after pyrolysis did not affect the lattice microarchitecture (Fig. 1a, b and Supplementary Fig. 2), which presented cubic unit cells, dimensions of~200 μm, strut width of 60-70 μm and a density of 0.55 g cm −3 . Further details on the fabrication process can be found in the "Method" section.
Scanning electron microscopy (SEM) images in Fig. 1c, d show that SLA introduced imperfections in the architected microstructure, designed initially with cubic unit cells with constant beam width. The manufactured lattices presented an orientationdependent strut width, with beams deposited parallelly to the printer platform that resulted~20% wider than the ones built along the vertical direction. The relative density was calculated for both types of lattices, showing ρ= 0.30 ± 0.01 for as-pyrolyzed and ρ= 0.28 ± 0.01 for Joule-heated microlattices, within the limit of true cellular solids. Furthermore, SEM images at progressive magnification conveyed that the features present in the originallysculpted polymer lattices were preserved throughout the heat treatments (Fig. 1c, d). The 7-9 μm-separated grooves that populated each beam constituted the traces of layer-by-layer SLA. The texture of as-pyrolyzed samples appeared smooth, while Joule-heated specimens presented sporadically located micropores, with diameter lower than 2 μm, and homogeneously distributed nanopores, with diameter smaller than 50 nm (Fig. 1c, d).
Atomic force microscopy (AFM) characterized changes in the surface roughness introduced by the Joule heating treatment. AFM images at low magnification on 40 μm × 40 μm areas revealed that the groove depth on the surface of as-pyrolyzed samples presented a root mean square (RMS) of 661 ± 114 nm (Fig. 2a, left column), while high magnification over 300 nm × 300 nm regions proved the smoothness of the surface of as-pyrolyzed carbon, with protrusions limited to an RMS value of 5.26 ± 2.24 nm (Fig. 2a, right column). Joule heating treatment increased surface roughness to an RMS of 734 ± 44 nm and created micropores, visible from low magnification images (Fig. 2b, left column). At the nanoscale, roughness became nearly fourfold, with an RMS value of 19.07 ± 9.36 nm, as a result of nanopores developed through Joule heating (Fig. 2b, right column).
Existing literature on pyrolyzed carbon nano-and microarchitected materials suggests that the atomic-scale structures of nanolattices fabricated by two-photon lithography 25 , microlattices manufactured through self-propagating photopolymer waveguide 28 , and microarchitectures produced by SLA 29 , are all glassy carbon, a class of sp 2 -hybridized carbon. Figure 3a and Supplementary Fig. 3 compare Raman spectra collected from the skin and inner core of the beams obtained from both types of microlattices. The spectra indicated a skin-core structure that resembles the morphology of polyacrylonitrile (PAN)-derived carbon fibers 39 , where the outer shell contains more sp 2hybridized carbon and less amorphous carbon than the inner core does. As-pyrolyzed samples presented a moderately sp 2hybridized surface, evidenced by the distinguished D and G peaks and the indiscernible 2D, D + D′ and 2D′ peaks that form a broad single peak at 2800 cm −1 . The internal core of the beams, on the other hand, shows only a shallow split between D and G peaks since the integrated intensity of amorphous carbon component at 1505 cm −1 surpasses that of G peak 40 . This observation suggests that pyrolyzing the PR48 photoresist polymer at 1000°C produces mainly amorphous carbon with a low degree of sp 2 -hybridization. In the Joule-heated specimens, although the fraction of sp 2 -hybridized carbon generally increased throughout the microstructure, the different composition between the surface and the core of the beams remained. The inner core after Joule heating presented a moderately sp 2 -hybridized carbon, similar to the as-pyrolyzed skin. The surface of the beams, on the other hand, contained features of emerging nanocrystalline graphites. The relative area intensity of G peak to amorphous carbon peak nearly doubled compared to the as-pyrolyzed skin ( Supplementary Fig. 4), deepening the valley between G and D peaks [41][42][43][44] . Furthermore, separate second-order peaks, namely 2D (2690 cm −1 ), D + D′ (2930 cm −1 ) and 2D′ (3190 cm −1 ), visible only in Joule-heated skin, imply the presence of defect-rich graphitic structures 41,45,46 ( Supplementary Fig. 5). The D peak higher than the nominal G peak (G and D′ treated as a single peak at 1600 cm −1 ) for this case also suggests nanographites crystallized from the amorphous matrix 47 .
HRTEM imaging visualized the structural changes induced by Joule heating at an atomic scale. Although Joule-heated carbon was still mainly non-crystalline, stacks of graphene sheets became conspicuous, with a distinguishable peak from (002) direction in the Fast Fourier Transformation (FFT) pattern (Fig. 3b, c and Supplementary Fig. 6). Joule-heated carbon locally presented 10 nm-long clusters of assembled graphene sheets spaced at 3.4-3.7 Å (Fig. 3d). In the FFT pattern, the orientation of (002) spacing became anisotropic, and its intensity increased, proving the alignment of graphene sheets and the formation of crystallites. The densification associated with graphitization of noncrystalline carbon, testified by the higher density of graphite, 2.23 g cm −3 , than that of amorphous carbon, 1.8-2.0 g cm −3 , was likely the cause of micro-and nanopores formation after Joule heating (Figs. 1 and 2). A similar roughening of the surface of carbon fibers by Joule heating has been reported, associated with graphitization of amorphous carbon 48 .
At the initial contact, the 0.7 μl water droplet spontaneously spread over the surface of the as-pyrolyzed plates and microlattices. A different response was observed for Joule-heated microlattices, where the initial contact area was approximately one order of magnitude smaller than on the as-pyrolyzed samples ( Fig. 4a and Supplementary Movie 1). At equilibrium, the contact interface areas were 1.70 ± 0.31 mm 2 for as-pyrolyzed plates, 1.14 ± 0.25 mm 2 for as-pyrolyzed microlattices, and 0.61 ± 0.03 mm 2 for Joule-heated microarchitectures.
The contact angles were measured along the parallel (θ // ) and perpendicular (θ?) directions defined by the SLA-induced grooves ( Fig. 4b and Supplementary Table 1). The presence of Characterization of constituent carbon by Raman spectroscopy and TEM. a Raman spectra collected with an incident wavelength λ = 514 nm from the skin and the inner core of the beams reveal that the as-pyrolyzed samples are mainly constituted of amorphous carbon, while Joule heating increased the degree of sp 2 -hybridization and introduced a defect-rich nanographitic skin. Representative diffraction patterns and TEM images of as-pyrolyzed (b) and Joule-heated (c) carbon. Inset spectra with diffraction patterns indicate the grayscale intensity of diffraction rings for each crystallographic direction. d A high-resolution TEM (HRTEM) image of Joule-heated carbon containing nanocrystalline graphite and its FFT pattern. Circles highlight the nanocrystals that are~10 nm long, with graphene sheets spaced at~3.4-3.7 Å. The inset reports the intensity of the FFT diffraction ring for graphite (002), which increases along the direction where graphene sheets are stacked. Scale bars are 10 nm.
the grooves in carbon plates led to anisotropic contact angles, with θ // = 76 ± 3°and θ?= 85 ± 18°. The significant standard deviation of θ?, as opposed to the tight distribution of θ // , suggests the presence of thermodynamically unstable airgaps between the droplet and the grooved surface. In as-pyrolyzed microarchitectures, the lattice structure introduced hydrophobicity through a Cassie-Baxter state, showing θ // = 100 ± 12°and θ?=106 ± 12°. The microstructure also reduced the orientationdependent wetting response, proving that additive manufacturing can effectively modulate the water contact angle of architected materials.
A significant reduction of the wettability was observed in Jouleheated samples, where the contact angles increased to θ // = 135 ± 3°and θ?=135 ± 1°. The average contact angles rose by 35°and 29°for parallel and perpendicular directions, respectively, thus exceeding the gain observed between as-pyrolyzed plate and aspyrolyzed microlattice. The increased hydrophobicity stemmed from the effects of the Joule heating treatment, which introduced a porous nanographitic skin. Highly sp 2 -hybridized carbon presents a contact angle higher than 90°even in the absence of surface porosity 52 , improving the hydrophobic response of amorphous carbon. Moreover, the development of a surface porosity reduces the solid fraction of the water-carbon interface, governed by nanopores at a submicron scale. Therefore, the combination of sp 2 -hybridization with the development of a hierarchical lattice texture allowed both θ // and θ? to achieve a mean value of 135°without discernable anisotropy. Although the present results were yet to achieve superhydrophobicity (θ > 150°), which could be obtained by increasing the power input for Joule heating that leads to higher degree of sp 2 -hybridization, they demonstrate a simple process to significantly increase the water contact angle without employing fluorination process 53 , plasma-enhanced chemical vapor deposition (PECVD) 50 or nanoengineered coatings 54,55 .
Micro-and nanomechanical characterization. The mechanical properties of as-pyrolyzed and Joule-heated carbon microlattices were investigated through uniaxial compression experiments (Fig. 5a, b and Supplementary Movie 2). Eight specimens of each type of samples were compressed, with the average densities of 0.553 ± 0.015 g cm −3 and 0.552 ± 0.021 g cm −3 , for as-pyrolyzed and Joule-heated microlattices, respectively. Engineering stressstrain data presented an initial toe region caused by misalignment, roughness and imperfection in the manufactured specimens. They revealed that all samples failed catastrophically and brittly at similar remarkable compressive stresses, with a significant variation in the compressive strength of the as-pyrolyzed samples, 151.26 ± 54.53 MPa, and with a much tighter distribution for Joule-heated microlattices, 152.92 ± 11.21 MPa (Supplementary Table 2). The structural stiffness of each type of architectures was calculated from the linear elastic region of the stress-strain curves and resulted in 4.82 ± 0.61 GPa for the aspyrolyzed samples and 5.50 ± 0.97 GPa for the Joule-heated specimens. The different mechanical responses obtained for the two types of lattices became negligible on the core of the beam when subjected to nanoindentation tests (Fig. 5c). The Young's moduli E c of core materials were calculated to be 25.38 ± 2.75 GPa for aspyrolyzed and 25.35 ± 2.01 GPa for Joule-heated samples (Supplementary Table 3), similar to Young's moduli of disordered carbon materials 56,57 . Figure 5d shows the material property map for compressive strength versus density of the developed carbon microlattices, together with various structural materials and high-strength truss micro-2,7,28-30,58-60 and nanolattices 25,26,61 . Compression experiments indicate that both types of microlattices fail brittly at virtually the same average stress of~152 MPa, which is stronger by one order of magnitude than the compressive strength of carbon aerogels 58 , and by a factor of 2-3 than that of conventional structural materials, for the same density. The strength achieved in this work represents the highest value ever recorded for microstructured solids, and approaches that of pyrolytic carbon 25,26 and SiOC 61 nanoarchitectures, which are the strongest truss lattices fabricated up to date, reaching up tõ 550 MPa, for the same density 61 . Figure 5e, f reports the specific compressive strength and specific Young's modulus of the carbon microlattices in the context of high-strength micro-and nanoarchitectures, compared through their characteristic strut width. The plots convey that the fabricated carbon architectures possess specific strength and stiffness more than one order of magnitude higher than those of nickel 2 , carbon 29 , graphene-aerogel 30 , and alumina 59 microlattices, and 2-7 times greater than SiOC 7 , vitreous carbon 28 , and alumina coated polymer 60 microlattices. Currently, only pyrolytic carbon and SiOC nanolattices synthesized by using two-photon lithography have similar or higher specific compressive properties, attainable through size effects at the strut width of hundreds of nanometers, which corresponds to the critical size for material flaw insensitivity [25][26][27]61 . Considering Griffith's law for brittle materials and assuming that the intrinsic length scale (critical flaw size, a c ) is on the same order as the extrinsic one (characteristic length of the lattice, d), the specific strength for lattices composed of the same constituent material scales as σ* ∝ d −0.5 . In contrast to strength, the stiffness of lattice architectures is not affected by size-effects, and the reduction of the length scale of micro and nanolattices has not been proven to enhance rigidity. The plot of the compressive strength normalized by the stiffness of the constituent material, reported as a function

σ /ρ
Strength, (MPa) σ * Density, (g cm ) ρ of the relative density for several high-strength lattices (Supplementary Fig. 7), further testifies the significant ultimate stress achieved by the carbon microarchitectures, outperforming all existing microlattices and approaching the strongest open-cell nanostructured materials ever realized. However, our microlattices present strut width and unit cell size two-orders of magnitude higher than those nanostructured solids. Therefore, the manufactured lattices prove that their remarkable strength and stiffness are compatible with a more scalable fabrication towards mesostructured solids. The unique mechanical properties of the fabricated microlattices are attributed to the combination of the manufacturing process and the anisotropic unit cell topology, where the former guarantees a high-quality pyrolytic carbon, while the latter ensures stiffness and strength through a high proportion of struts aligned with the loading direction 62 .
Although some unit cell topologies were indicated as quasiisotropic in pioneering studies, recently it has been proven that almost all of the micro and nanoarchitectures considered in Fig. 5d-f are anisotropic 63,64 . The Zener ratio a r depends on the relative density ρ and quantifies the degree of anisotropy for unit cells with cubic symmetry, where a r = 1 corresponds to an isotropic configuration, while a r < 1 and a r > 1 indicate that the unit cell presents the highest stiffness along <100> and <111 >, respectively. Whilst the former response can be found in cubic unit cell and the latter in octet architectures, which represent the most investigated topology up to date, both geometries are anisotropic ( Supplementary Fig. 8). The ideal chosen topology possess a r = 0.22, while less anisotropic octet microlattices with a r = 1.56 for a similar relative density and unit cell dimensions 33 , obtained through the presented manufacturing process, showed average stiffness and strength that were~50% and~80% of that of the as-pyrolyzed microlattices, thus proving the advantages of the cubic topology over a stretching dominated geometry when employed in a non-slender lattice and subjected to preferential loading directions. Beyond open-cell three-dimensional lattices, although the design of architected metamaterials has relied on highly anisotropic geometries, as nano-honeycombs 25 , to achieve exceptional mechanical properties, very recent studies have theorized 65 and experimented 66 almost isotropic architectures capable of achieving the Hashin-Shtrikman upper bound through closed-cell topologies governed by different deformation and failure mechanisms. While the average failure stress remained unchanged after Joule heating, the standard deviation drastically reduced by~80%. The heat treatment notably diminished the strength of the bestperforming as-pyrolyzed sample, but also increased the ultimate stress of the worst-performing as-pyrolyzed one. The reduced variability and the preserved average strength offered structural reliability, traditionally sought during the manufacturing process to improve the knowledge of mechanical properties and perform a probabilistic design with greater confidence 67 . The unchanged mean strength suggests that both types of microlattices globally failed via the same mechanism of catastrophic failure at the structural flaws within the material, and phenomenologically convey that Joule heating suppressed failure initiation at stresses significantly distant from the average failure stress. The combination of additive manufacturing and material reconfiguration through carbonization of polymeric precursor implies the development of various defects such as cracks, pores, and voids, all of which serve as locations of stress concentrations during mechanical loading (Supplementary Fig. 9). The stochastic signature of failure stresses in the as-pyrolyzed samples is assumed to be a result of a broad distribution of such flaws of different sizes and orientations throughout the microlattice. In Joule-heated samples, failure initiates at more tightly distributed surface flaws, significantly reducing the strength variability of as-pyrolyzed microlattices. On the one hand, the Joule heating process annealed the pre-existing critical flaws, preventing failure significantly below the average strength. On the other hand, it relieved the compressive residual stresses caused by the pyrolysis of the photoresists 68 , which can prevent crack propagation, and introduced surface defects, thus reducing the highest strengths recorded for as-pyrolyzed lattices. Therefore, the porous sheath is believed to contribute to the narrow deviation of compressive strength, suggesting surface nanoporosity as the preferred location where brittle failure is triggered. This hypothesis is proven by the relationship between the critical semi-elliptical surface flaw size a c and the failure strength of brittle material σ f , given by a c = K IC 2 /(π σ f 2 ), where K IC = 0.91 MPa√m is the carbon fracture toughness 57,69 . The bulk fracture strength of glassy carbon is size-dependent 70 , and it increases with a reduction of strut size because of the lower probability of finding a critical flaw. Assuming a fracture strength of 1.5-2.5 GPa, similarly to the values measured for pyrolytic glassy carbon fibers of 5 μm diameter 71 , the critical flaw size results~40-120 nm, which corresponds to the dimension of the measured surface nanoporosity (Fig. 3).
Apart from its contribution to the reduced strength variability, Joule heating did not significantly improve structural properties: the average failure stress remained unchanged, and the mean lattice stiffness marked a moderate increase of~15%. Other thermal processes, such as standard annealing at temperatures above 2000°C, would be more effective than Joule-heating in improving mechanical features, although they would not guarantee a significant hydrophobic response. The porous nanographitic sheath is likely the cause of the increase in the average lattice stiffness from as-pyrolyzed specimens. The aspyrolyzed microlattices were assumed to be homogeneously constituted of non-crystalline pyrolytic carbon owning elastic modulus of 25.38 GPa as from core nanoindentation, with negligible stiffness difference between the core and the skin of the beams. Finite element analysis of pyrolytic carbon microlattices predicted Young's modulus of 4.79 GPa ( Supplementary  Fig. 10), consistent with the micromechanical experimental measurements. The SLA-induced corrugations were not included in the numerical model as simulations revealed that the effect of the bidirectional traces of SLA on stiffness was negligible ( Supplementary Fig. 11). Nanoindentation on the internal core of Joule-heated samples revealed the same bulk stiffness as in aspyrolyzed specimens, while the beam texture prevented a reliable measurement of the elastic modulus of the skin. However, the porous nanocrystalline morphology of Joule-heated sheath suggested an increased stiffness when compared to that of the non-crystalline strut core 39 . Numerical analyses indicated that the homogenized Young's modulus of Joule-heated carbon increased to 29.19 GPa, a response attributed to the combined stiffening effects of the porosity 72 and nanographitic layers 73-75 that developed on the skin of Joule-heated microlattices.

Discussion
The paradigm for the development of lightweight metamaterials with superior mechanical performances has been the capitalization of strengthening size effects through the reduction of the lattice structural elements to the nanoscale, which inherently hinders a scalable fabrication. Furthermore, the simultaneous realization of a lightweight, strong, stiff, and hydrophobic single material has remained a challenge that prevents the application of these complementary properties in a crossfunctional solid.
We created a microarchitected carbon that combines excellent mechanical performances and remarkable hydrophobicity. Through a combination of SLA and pyrolysis, we manufactured carbon microlattices with strut width of 60-70 μm, cubic unit cell size of~200 μm and density of 0.55 g cm −3 . Although the unit cell topology was not optimized, the developed anisotropic architectures attained a specific strength up to 468.62 MPa cm 3 g −1 , and a specific stiffness as high as 14.39 GPa cm 3 g −1 . The specific mechanical properties exceeded those of all existing meso-and microlattices, and they approached the stiffest and strongest nanoarchitectures realized so far 25,26,61 , albeit possessing unit cell dimensions two orders of magnitude larger and allowing faster creation of strong architectures. This work also demonstrated how to engender hydrophobicity in carbon-based materials through rational design of the lattice architecture, showing a facile technique to approach superhydrophobicity via Joule heatinginduced graphitization and development of a hierarchical lattice surface. Whilst the effect of the heat treatment predominantly altered the strut sheath, thus enabling noteworthy contact angles, it did not improve significantly the mechanical response, which arises from the bulk and could be further enhanced through other treatments. Nevertheless, we found Joule heating to preserve the mean strength while reducing its variability, and simultaneously increasing the lattice rigidity through a skin stiffened by porous nanographite. Compared to thermal treatment in a standard tube furnace, Joule heating can achieve higher temperatures, enables further graphitization, is faster and consumes less energy. However, the treatment might also induce undesired effects which, depending on the application, can hinder the mechanical response. This includes surface nanoporosity that could prevent the constituent carbon material from attaining the theoretical maximum strength, the removal of residual stresses which can cause the loss of the highest compressive strength values of aspyrolyzed carbon, and inhomogeneous heat distribution that could cause edge effects in large samples.
The combination of lightweight, strength, stiffness, and hydrophobicity makes nanographite-coated carbon microlattices potential candidates as a tunable multifunctional material for extreme environments, with applications ranging from water purification membranes 76 to structural elements of vehicles where load-bearing and ice-inhibiting surfaces are required 77 .

Methods
Fabrication. Polymer lattices were prepared by 3D printing a transparent photoresist resin (PR-48) in a DLP SLA Amber Autodesk 3D printer, using a layer thickness of 25 μm. Each lattice had a periodic three-dimensional pattern of 600 μm-wide cubic unit cells with a beam width of 200 μm and a length of 400 μm. Dimensions of specimens are reported below as thickness × width × length by the number of unit cells, where SLA layers were deposited along the width direction, and the bottom-most anchoring layer was designed to be thicker in order to sustain the microlattice during printing. Specimens for mechanical characterization were composed of 4 × 8 × 14 unit cells. Specimens for contact angle measurements were designed to provide an area for a droplet of deionized (DI) water to deposit without reaching the edge of the lattices, containing 4 × 10 × 24 unit cells. In order to assess the influence of the architected geometry on the water contact angle, plates were fabricated with an area equivalent to 20 × 19 unit cells. The additive manufactured samples were post-cured under sunlight for a day. The thicker anchoring layer was removed using a razor blade to prevent geometry distortion during pyrolysis, thus reducing by one the number of unit cells along the width of the samples.
The polymeric microlattices were pyrolyzed under vacuum of <50 mtorr in a 22 mm diameter fused quartz tube set in a Lindberg tube furnace, model 54357. During pyrolysis, the furnace temperature was differentially increased to yield fully dense carbon lattices and to prevent trapping of gasified components. The temperature was first elevated to 300°C and kept constant for 4 h, then raised to 400°C and held constant for 1 h, followed by the final carbonizing step at 1000°C for 4 h, with all heating rates performed at 10°C min −1 .
After pyrolysis, the carbon microlattices were cooled down to room temperature, the vacuum was removed, and the samples were transferred to a cylindrical custommade apparatus ( Supplementary Fig. 12), where Joule heating was performed. The as-pyrolyzed lattices were clamped between a pair of gold-plated copper electrodes that came in contact with the 4 × 7 unit cell surfaces and were suspended in a cylindrical glass jar. After purging the chamber with 100 cm³ min −1 of argon flow for a minute, we applied current for 10 min to produce a power density of 10-12 kW g −1 . The argon flow was maintained at 100-400 cm 3 min −1 , depending on the sample size, to preserve the integrity of the material.
Manufacturing imperfections against the original CAD model arose during additive fabrication. The strut width in the generated lattices was dependent on orientation, with d 1 and d 2 that identify the beams deposited parallelly or perpendicularly to the printer platform, while l represents the unit cell size. Therefore, the microlattices relative density ρ is formulated as where the first and second terms account for the beam and node relative density, respectively. The relative density was calculated for three different samples of both types of lattices by averaging the measured characteristic lengths, providing ρ = 0.30 ± 0.01 for as-pyrolyzed and ρ = 0.28 ± 0.01 for Joule-heated microlattices.

Material characterization.
Atomic-level microstructures of the lattices before and after Joule heating treatment were investigated using Raman spectroscopy (Renishaw M1000 Micro Raman Spectrometer System), SEM (Thermo-Fisher Versa 3D DualBeam), Transmission Electron Microscopy (TEM, Thermo-Fisher, Tecnai TF-30), and AFM (Brucker Dimension Icon). Raman spectra were collected with a green laser (wavelength λ = 514 nm). The internal core of the beam was inspected through Raman laser by removing 2 μm of the external surface with an abrasive sheet containing 0.3 μm alumina powder (Buehler, FiberMet Abrasive Discs). SEM and TEM samples were prepared by cleaving the carbon microlattices, collecting pieces of the generated debris, manually grinding them between two glass slides, and transferring the ground powder onto a copper TEM grid using carbon support (Pacific Grid Tech). The debris of specimens failed during micromechanical testing were analyzed with SEM, showing that the core of the beams was fully dense, while micropores developed only on the surface. AFM PeakForce Tapping (PFT) mode was used to characterize the surface roughness of each sample at three different locations by using a silicon probe with a tip radius r tip = 2 nm (Brucker SCANASYST-AIR). AFM scans were obtained on 40 μm × 40 μm regions at a frequency of 0.1 Hz, and on 300 nm × 300 nm areas at a rate of 2 Hz.
Contact angle measurements. The water contact angle was measured by a contact angle goniometer (Kyowa Kaimen Kagaku DM-301) equipped with a PTFE-coated 28-gauge needle. Samples were mounted onto a movable stage with a 9 × 24 unit cell surface (microlattices) or 19 × 19 unit cell surface (plates) facing toward the needle. The stage was elevated until the sample entered in contact with the 0.7 μl droplet of DI water (diameter > 500 μm) dispensed from the needle. Subsequently, the stage was retracted to detach the droplet from the syringe (Supplementary Movie 1). The contact angles were measured at equilibrium along the parallel (θ // ) and perpendicular (θ?) directions defined by the SLA-induced grooves. The evaporation time of dispensed water droplets was recorded, showing a decrease of~20% from monolithic plates to microlattices. Five measurements per sample were conducted, in a laboratory environment with a temperature of 27°C and 60% relative humidity.
Nanomechanical and micromechanical characterization. Nanoindentation was performed on lattice nodes using a nanoindenter (Agilent, G200) equipped with a diamond Berkovich indenter tip. As-pyrolyzed and Joule-heated core samples were mounted on an SEM stub using a graphite paste, and they were indented to a depth of 1 μm at the loading and unloading rates of 2 mN s −1 . From the loaddisplacement curves, the Young's modulus E c was calculated as 78 is the reduced Young's modulus, S is the gradient of the load-displacement curve at the maximum depth of indentation, A = 24:675 h 2 c þ 0:562 h c þ 0:003216 is the indentation area for the Berkovich indenter tip, h c = 1 μm is the depth of indentation, β = 1.081 is the constant for the Berkovich indenter tip, E i = 1143 GPa is the Young's modulus of the diamond indenter 79 , ν i = 0.0691 and ν s = 0.21 are the Poisson's ratios of the diamond indenter 79 and pyrolytic carbon specimen 80 , respectively. For micromechanical characterization, compression tests on all microlattices were carried out on an electromechanical testing frame (Instron, 5569). The load was applied at a nominal rate of 2.5 μm s −1 on the 7 × 14 unit cells sample surface until failure (Supplementary Movie 2), while the displacement was measured with a laser extensometer (Electronic Instrument Research, LE-01) interfaced with the electromechanical apparatus for data synchronization. Eight specimens for both as-pyrolyzed and Joule-heated samples were compressed, with the load-displacement curve obtained. The engineering stress-strain curve was calculated by normalizing the measured force by the lattice cross-section and the compressive displacement by the sample height (Fig. 5a, b and Supplementary Table 2). The microlattice Young's modulus was determined from the linear-elastic portion of the stress-strain curve after the initial toe region, whereas the compressive strength represents the maximum stress achieved before brittle failure.
Finite element analysis. The microlattice geometry obtained from SEM images was generated with SolidWorks 2018 (Dassault Systèmes) and imported in the finite element software Abaqus 2018 (Dassault Systèmes). The lattice was discretized with 1.2 million tetrahedral elements with Young's modulus E c = 25.38 GPa measured through nanoindentation, and Poisson ratio ν = 0.21 (ref. 80 ). The as-pyrolyzed microlattices were assumed to be entirely constituted of amorphous pyrolytic carbon possessing uniform stiffness E c . Starting from the experimentally measured average effective stiffness of the Joule-heated lattices, the homogenized Young's modulus of the Joule-heated carbon was calculated through numerical analysis as 29.19 GPa ( Supplementary Fig. 10), where the increase in elastic modulus is attributed to the stiffening effect of the~1-1.5 μm thick porous nanographitic skin [72][73][74][75] . Displacement was imposed on the microlattice top surface while the resultant force was acquired, with boundary conditions imposed on the bottom surface. The lattice stiffness was obtained from the engineering stress-strain curve calculated through the compressive force-displacement relationship.
In order to assess the influence of SLA-induced corrugations, finite element simulations were performed on as-pyrolyzed uncorrugated and corrugated unit cells, showing that the effective stiffness varied by only 3.52% ( Supplementary  Fig. 11), thus justifying the choice of neglecting the bidirectional SLA traces in the full computational model. The topology of the corrugation was acquired from SEM images, generated with SolidWorks 2018 and imported in Abaqus 2018.
The quantification of the degree of anisotropy for unit cells with cubic symmetry was obtained through the Zener ratio a r ¼ 2C 44 , where C ij represents the non-null components of the forth-order elastic stiffness tensor, written in Voigt notation. The Zener ratio of the ideal cubic topology was calculated through finite element simulations, and compared with that computed for the octet geometry, which represents the most investigated topology 25,26,33,59,61 , for relative densities ρ lower than 40%. For each relative density, two analyses were sufficient to define a r . The first allows obtaining C 11 and C 12 by imposing a normal strain along <100> to a laterally constrained unit cell, while the second gives C 44 when shear strains are applied to two adjacent faces of the unit cell 81 .

Data availability
The main data that support the findings of this study are available within the Article and its Supplementary Information. Additional data are available from the authors on reasonable request.