Microlattices prepared by polymer waveguide technology

The microlattice shown at the right side of Figure 2 is a cellular solid that was developed by HRL with dimensions on the order of centimeters and absolute densities as low as 0.9 mg/cm³, which places it in the ultralightweight regime, defined as materials with densities below 10 mg/cm ^{Reference Wang, Evans, Dharmasena and Wadley3} . ^{Reference Schaedler, Jacobsen, Torrents, Sorensen, Lian, Greer, Valdevit and Carter35} This microlattice is composed of hollow metallic struts with widths of 100–500 μm and lengths of 1–4 mm; the wall thickness of the hollow cylindrical struts is on the order of 100–500 nm. ^{Reference Schaedler, Jacobsen, Torrents, Sorensen, Lian, Greer, Valdevit and Carter35}

Figure 2. Representative image of a microlattice fabricated using a three-dimensional array of self-propagating photopolymer waveguides. Reproduced with permission from Reference Reference Schaedler, Jacobsen, Torrents, Sorensen, Lian, Greer, Valdevit and Carter35. © 2011 American Association for the Advancement of Science.

Figure 2 shows a sample made using a polymer waveguide technique, a self-guided single-photon polymerization process using angled UV beams traveling through a mask that allows for fast throughput of macroscale sheets. ^{Reference Jacobsen, Barvosa-Carter and Nutt29,Reference Jacobsen, Barvosa-Carter and Nutt34} In the subsequent fabrication steps, the polymer scaffold is coated with a thin solid film, such as NiP or metallic glass. ^{Reference Rys, Valdevit, Schaedler, Jacobsen, Carter and Greer24,Reference Torrents, Schaedler, Jacobsen, Carter and Valdevit36} Removal of the polymer leaves a fully hollow structure composed of the deposited material. ^{Reference Schaedler, Jacobsen, Torrents, Sorensen, Lian, Greer, Valdevit and Carter35,Reference Torrents, Schaedler, Jacobsen, Carter and Valdevit36,Reference Valdevit, Godfrey, Schaedler, Jacobsen and Carter41} The waveguide technique allows easy adjustment of the angle and the number of bars connecting at a single node, illustrating the relationship between the mechanical properties and geometric parameters of ultralight hollow structures. ^{Reference Jacobsen, Barvosa-Carter and Nutt34}

This patterning technique can generate only certain unit-cell geometries, all of which deform under an applied load by bending, rather than stretching, the lattice bars. ^{Reference Montemayor, Meza and Greer42} This bending-mode deformation provides lower strength than stretching-mode deformation for any given density. ^{Reference Fleck, Deshpande and Ashby8,Reference Gibson and Ashby43}

Microlattices prepared by microstereolithography

Microarchitectures with dimensions similar to those of the microlattices just discussed have also been created using microstereolithography, shown in Figure 3 , which is an additive process with lattices created in a layer-by-layer fashion similar to 3D printing. ^{Reference Zheng, Lee, Weisgraber, Shusteff, DeOtte, Duoss, Kuntz, Biener, Ge, Jackson, Kucheyev, Fang and Spadaccini30} In contrast to the waveguide method, this technique is capable of producing a variety of different geometries, including the octet truss, which has sufficiently high nodal connectivity to be stretching-dominated. ^{Reference Deshpande, Ashby and Fleck7–Reference Deshpande, Fleck and Ashby9} Under uniaxial compression, hollow NiP or Al₂O₃ octet-truss microlattices have shown near agreement with the scaling of stiffness (E) and strength (σ) to the relative density ( $\bar \rho$ ) predicted by cellular-solids theory, namely, E ∝ ${\bar \rho ^m}$ and σ ∝ ${\bar \rho ^n}$ , with m = n = 1. Uniaxial compression experiments gave values of m = 1.1 and n = 1.2–2.7 for octet-truss microlattices with relative densities of $\bar \rho$ = 10^–4–10^–2, ^{Reference Zheng, Lee, Weisgraber, Shusteff, DeOtte, Duoss, Kuntz, Biener, Ge, Jackson, Kucheyev, Fang and Spadaccini30} where relative density ( $\bar \rho$ ) is the ratio of the volume contained within a unit cell to the volume of the unit cell. ^{Reference Fleck, Deshpande and Ashby8,Reference Gibson and Ashby43} These octet trusses have higher strength than the HRL microlattices, which is attributed to the stretching-dominated architectures of the former. ^{Reference Zheng, Lee, Weisgraber, Shusteff, DeOtte, Duoss, Kuntz, Biener, Ge, Jackson, Kucheyev, Fang and Spadaccini30,Reference Schaedler, Jacobsen, Torrents, Sorensen, Lian, Greer, Valdevit and Carter35}

Figure 3. Representative image of a microlattice fabricated by projection microstereolithography, a layer-by-layer technique capable of fabricating arbitrary, microscale, 3D structures with a resolution of ∼5 mm. Note: CAD, computer-assisted design. Reproduced with permission from Reference Reference Zheng, Lee, Weisgraber, Shusteff, DeOtte, Duoss, Kuntz, Biener, Ge, Jackson, Kucheyev, Fang and Spadaccini30. © 2014 American Association for the Advancement of Science.

Hollow microlattices produced by either polymer waveguides or microstereolithograhy have wall thicknesses in the size regime where material size effects have been observed, but the dimensions of their unit cells are too large to observe or capitalize on the size effects because their deformation behaviors can be fully described by structural mechanics, which is independent of material length scales. For example, if the microlattices were scaled up in a self-similar geometry, the mechanisms of deformation would be consistent with those of the microlattices at smaller scales. These microlattices offer many novel properties that result from the interaction of various structural length scales, such as their recovery and energy-absorption capabilities. It would not be appropriate to classify them as structural metamaterials because their properties can be fully described by classical mechanics.

Nanolattices prepared by direct-laser-writing two-photon lithography

Nanolattices fabricated by two-photon lithography (TPL) enable a size reduction by three orders of magnitude from microlattices while still being amenable to coating and scaffold removal. These architected materials have dimensions down to the nanoscale, with typical strut lengths of 3–20 μm, widths of 150–500 nm, and wall thicknesses of 5–600 nm. ^{Reference Montemayor and Greer37,Reference Montemayor, Meza and Greer42,Reference Meza and Greer44,Reference Jang, Meza, Greer and Greer45} Unlike microlattices, the individual building blocks that comprise nanolattices are small enough that they cannot be resolved by the human eye. Their mechanical properties depend on a combination of size-dependent material properties and structural responses and cannot be predicted solely by scale-free continuum theories. ^{Reference Montemayor and Greer37–Reference Gu and Greer39}

Nanolattices were first fabricated from a specific polymer using DLW TPL developed by Nanoscribe GmbH. ^{Reference Jang, Meza, Greer and Greer45} The two-photon method employs a 780-nm femtosecond pulsed laser focused into a small volume within the polymer (i.e., a voxel, or volume resolution element) with sufficient energy to cross-link the monomer and harden the material in that location through two-photon absorption. The ellipsoidal voxel can be rastered in three dimensions within a droplet of photoresist to create a polymer structure of arbitrary geometry, shown in Figure 4a. ^{Reference Fischer and Wegener31,Reference Sun and Kawata32} A variety of existing thin-film deposition techniques lend themselves to the coating of these polymer nanolattices. ^{Reference Meza, Das and Greer38,Reference Bauer, Hengsbach, Tesari, Schwaiger and Kraft40,Reference Montemayor, Meza and Greer42,Reference Meza and Greer44,Reference Jang, Meza, Greer and Greer45}

Figure 4. Schematic of (a) direct-laser-writing two-photon lithography (DLW TPL) and (b–e) representative images of nanolattices fabricated by this method: (b) hollow gold, (c) hollow alumina, (d) composite polymer/alumina, and (e) solid copper nanolattices. (a) Reproduced with permission from Reference Reference Montemayor, Meza and Greer42. © 2014 Wiley-Blackwell. (b) Reproduced with permission from Reference Reference Montemayor and Greer37. © 2015 The American Society of Mechanical Engineers. (c) Reproduced with permission from Reference Reference Meza and Greer44. © 2014 American Association for the Advancement of Science. (d) Reproduced with permission from Reference Reference Bauer, Hengsbach, Tesari, Schwaiger and Kraft40. © 2014 National Academy of Sciences. (e) Reproduced with permission from Reference Reference Gu and Greer39. © 2014 Elsevier.

For example, Montemayor et al. ^{Reference Gibson and Ashby43} demonstrated the conformal sputtering of metals (Figure 4b), such as gold, onto different geometries of nanolattices as long as the relative density was below $\bar \rho$ ≈ 4%. ^{Reference Montemayor, Meza and Greer42} Meza and co-workers ^{Reference Montemayor and Greer37,Reference Montemayor, Meza and Greer42,Reference Meza and Greer44,Reference Jang, Meza, Greer and Greer45} and Bauer et al. ^{Reference Bauer, Hengsbach, Tesari, Schwaiger and Kraft40} successfully used atomic layer deposition to coat ∼5–60-nm-thick Al₂O₃ and TiN coatings onto polymer scaffolds, as shown in Figure 4c–d. After deposition, the initial polymer scaffold was exposed by slicing off two of the six faces of the sample using a focused ion beam and then removed by oxygen plasma etching. ^{Reference Montemayor and Greer37,Reference Meza, Das and Greer38,Reference Montemayor, Meza and Greer42,Reference Meza and Greer44,Reference Jang, Meza, Greer and Greer45} The TPL method allows the angled tubes of a nanolattice to have smooth surfaces, in contrast to the rough stair-step edges produced by microstereolithography.

The nanolattice struts produced by TPL have elliptical cross sections, where the ellipticity of the tubes decreases with the unit-cell angle, an artifact related to the fabrication process. ^{Reference Montemayor and Greer37,Reference Valdevit, Godfrey, Schaedler, Jacobsen and Carter41,Reference Gibson and Ashby43,Reference Meza and Greer44} Hollow gold nanolattices with an octahedral geometry were fabricated by DLW TPL, and their response to uniaxial compression as a function of unit-cell angle and wall thickness revealed that both the strength and stiffness can be increased by an order of magnitude by tuning the geometry for samples of constant relative density, ^{Reference Montemayor and Greer37} in contrast to the behavior predicted by cellular-solids theory, which assumes a constant strength and stiffness for a given relative density. ^{Reference Fleck, Deshpande and Ashby8,Reference Gibson and Ashby43} This study demonstrated that both geometrical effects, resulting from changes in unit-cell angle, and material size effects, which emerge from the combination of the atomic-level microstructure of the solid constituent with the particular nano-sized wall thickness, can be exploited to elicit novel mechanical properties that would not exist in a larger version of the structure. ^{Reference Montemayor and Greer37}

Hollow alumina (Al₂O₃) nanolattices with the octet-truss geometry with relative densities in the range of $\bar \rho$ = 10^–4–10^–1 recovered up to 98% of their initial height after uniaxial compressions in excess of 50%. ^{Reference Meza, Das and Greer38} Their ductile-like deformation and recoverability has been attributed to the ratio between the wall thickness (t) and the semi-major axis (a) of the hollow elliptical strut cross section. When t/a was less than ∼0.03, the nanolattices deformed by shell buckling and recovered after deformation; at greater t/a values, the nanolattices failed catastrophically with little to no recovery. ^{Reference Meza, Das and Greer38} The constituent Al₂O₃ is brittle, but as the wall thickness decreases to the nanometer regime, the Al₂O₃ contains fewer flaws (e.g., inclusions, voids, and pores) commonly described using Weibull statistics. The material size effect manifests itself here as proximity to ideality, allowing the production of higher-quality materials, containing very few flaws, at the nanometer scale. This, in turn, allows the structure to experience shell buckling and to recover at appropriate t/a ratios instead of fracturing at a flaw first, as would be the case for thicker-walled structures. ^{Reference Meza, Das and Greer38,Reference Jang, Meza, Greer and Greer45}

Bauer et al. also studied nonhollow Al₂O₃-coated polymer nanolattices fabricated using the DLW TPL method. ^{Reference Bauer, Hengsbach, Tesari, Schwaiger and Kraft40} They showed that most of the nanolattices failed because of brittle fracture, and the thinner Al₂O₃ coatings in the composite structures carried higher tensile stresses than their thicker counterparts prior to failure. For the thinnest Al₂O₃ coatings of 10 nm, microcracks and localized fracture were observed along the strut lengths, and the samples did not fail by fracture of the struts or nodes. ^{Reference Bauer, Hengsbach, Tesari, Schwaiger and Kraft40} Optimized honeycomb lattice composites, with rigid walls, outperformed existing engineering foams with a comparable density of 1 mg/cm³ by almost an order of magnitude, at compressive strengths of 280 MPa for the 50-nm Al₂O₃ case. ^{Reference Bauer, Hengsbach, Tesari, Schwaiger and Kraft40} Both the hollow and composite Al₂O₃ nanolattices achieve new strengths and stiffnesses for their given relative densities while eliciting many novel properties for brittle architected materials, such as recoverability, that result from both material and structural effects. ^{Reference Meza, Das and Greer38,Reference Bauer, Hengsbach, Tesari, Schwaiger and Kraft40}

The interplay of structural and material size effects has also been observed in lattices with solid metal struts as the constituent building blocks, created using extensions of the method employed for hollow nanolattices. In contrast to the nanolattices, the smallest length scale of the mesolattice is on the order of microns. ^{Reference Gu and Greer39} Monolithic (i.e., nonhollow) copper mesolattices with micron-sized struts and unit-cell sizes of 6 and 8 μm, shown in Figure 4e, were made by first using an inverse DLW TPL method to create a negative of the geometry by patterning in a positive-tone resist and then electroplating the metal into the exposed pores. ^{Reference Gu and Greer39} The polymer mold was subsequently removed to reveal a mesolattice with solid nodes and struts having diameters on the order of 2 μm. ^{Reference Gu and Greer39} The average grain size for electrochemically deposited copper was 2 μm, which enabled the grains to span the entire strut diameter.

These mesolattices had relative densities in the range of $\bar \rho$ = 0.4–0.8 and compressive yield strengths of 330 MPa, which is up to 80% higher than that of bulk copper (133 MPa). ^{Reference Gu and Greer39} For relative densities of 0.8, strengths of ∼330 MPa were observed as a result of the emergence of smaller-is-stronger material size effects in the micron-sized struts. ^{Reference Gu and Greer39} The mesolattice with architected small-scale copper struts outperformed bulk copper by a factor of up to 2.5 for relative densities of $\bar \rho$ > 0.6, when up to 40% of the material had been removed. This means that introducing architecture can significantly reduce the weight of the material while simultaneously strengthening it, a finding diametrically opposite to the predictions of classical theories. ^{Reference Gu and Greer39}

In addition to the geometries of structural metamaterials reviewed in this article, many researchers have begun developing and fabricating new geometries with unique properties. Polymer auxetic 3D materials (i.e., materials with a negative Poisson’s ratio) have been fabricated using the DLW TPL method. ^{Reference Bückmann, Stenger, Kadic, Kaschke, Frölich, Kennerknecht, Eberl, Thiel and Wegener46} Upon compression, typical materials expand in directions orthogonal to the loading axis; auxetic materials contract in these directions. ^{Reference Bückmann, Stenger, Kadic, Kaschke, Frölich, Kennerknecht, Eberl, Thiel and Wegener46} Pentamode materials—3D solid materials that, in principle, behave as fluids—have also been designed and fabricated with the TPL approach and provide novel properties in their unique ability to decouple the bulk and shear moduli. ^{Reference Kadic, Bückmann, Stenger, Thiel and Wegener47} This removes the coupling of shear and compression waves that can travel through a medium. ^{Reference Kadic, Bückmann, Stenger, Thiel and Wegener47} Both the auxetic and pentamode architectures have unique material properties that support their use in a variety of applications ranging from optical to structural systems. ^{Reference Bückmann, Stenger, Kadic, Kaschke, Frölich, Kennerknecht, Eberl, Thiel and Wegener46,Reference Kadic, Bückmann, Stenger, Thiel and Wegener47}

Photonic crystals: Optical properties of nano- and microarchitected materials

Three-dimensional photonic crystals (PhCs) are structures whose constituent materials exhibit a periodic variation in the refractive index in all three spatial dimensions. Because of this periodicity, certain 3D PhCs exhibit a full photonic bandgap (PBG), a range of frequencies for which incident light cannot propagate in any direction. ^{Reference Blanco, Chomski, Grabtchak, Ibisate, John, Leonard, Lopez, Meseguer, Miguez, Mondia, Ozin, Toader and van Driel48,Reference Noda, Tomoda, Yamamoto and Chutinan49} Other 3D PhCs have pseudo-stopbands that forbid light propagation in some, not all, crystallographic directions. ^{Reference Arsenault, Clark, von Freymann, Cademartiri, Sapienza, Bertolotti, Vekris, Wong, Kitaev, Manners, Wang, John, Wiersma and Ozin50} The functionalities of 3D PhCs can be divided into two categories: (1) static PhCs, which can guide, ^{Reference Rinne, García-Santamaría and Braun51,Reference Deubel, Wegener, Linden, von Freymann and John52} diffract, ^{Reference Maka, Chigrin, Romanov and Sotomayor Torres53} trap, ^{Reference Chen54} and amplify ^{Reference Vlasov, Luterova, Pelant, Hönerlage and Astratov55} light through structural design and the introduction of defects, and (2) dynamic PhCs, which can change the frequency of light they reflect by manipulation of their refractive index or periodic dimensions through chemical ^{Reference Arsenault, Puzzo, Manners and Ozin56} or physical ^{Reference Fudouzi and Sawada57} stimuli.

Designed defects, such as lines of modified elements that form waveguides, are necessary to support optical modes and allow for the propagation of frequencies that cannot otherwise exist in the surrounding PBG material, a crucial step toward the realization of PhC-based optical circuitry. ^{Reference Rinne, García-Santamaría and Braun51} Wegener and co-workers pioneered the use of DLW TPL and double inversion to generate “woodpile” PhC architectures that contain defect cavities and act as resonators. ^{Reference von Freymann, Ledermann, Thiel, Staude, Essig, Busch and Wegener58} Direct laser writing also enables the fabrication of arbitrarily complex micro- and nanostructures and has been exploited to generate chiral PhCs with polarization stopbands ^{Reference Thiel, Decker, Deubel, Wegener, Linden and von Freymann59} and 3D photonic quasicrystals ^{Reference Ledermann, Cademartiri, Hermatschweiler, Toninelli, Ozin, Wiersma, Wegener and von Freymann60} that exhibit novel photonic properties not available in strictly periodic structures.

Fabrication and characterization of tunable 3D PhCs is an area of increasing research interest. Most such structures are based on colloidal crystal arrays, although block copolymers have also been used because self-assembly can yield double-gyroid microdomain architectures under specific chemical conditions. ^{Reference Urbas, Maldovan, DeRege and Thomas61} Inverse-opal structures represent the most common type of 3D tunable PhCs. Arsenault et al. demonstrated an elastomeric inverse-opal structure capable of being reversibly tuned in the optical range when mechanically stretched. ^{Reference Arsenault, Clark, von Freymann, Cademartiri, Sapienza, Bertolotti, Vekris, Wong, Kitaev, Manners, Wang, John, Wiersma and Ozin50} Tunable inverse-opal PhCs have also been generated using various thermosensitive and chemosensitive materials. For example, Aizenberg and co-workers exploited the structural color inherent in silica inverse opals to develop sensors whose optical properties change in different solvents. ^{Reference Burgess, Mishchenko, Hatton, Kolle, Lončar and Aizenberg62}

Phononic crystals: Acoustic properties of nano- and microarchitected materials

Similarly to light in photonic crystals, mechanical waves, or phonons, can be modified in materials with periodically varying mechanical properties. ^{Reference Lee, Singer and Thomas63,Reference Maldovan64} This spatial periodicity causes interference between transmitted and reflected waves having wavelengths comparable to the periodicity of the structure and, consequently, alters the propagation of these phonons. ^{Reference Burgess, Mishchenko, Hatton, Kolle, Lončar and Aizenberg62,Reference Maldovan64} Structures that can manipulate phonons in this way are PnCs, and micro- and nanocomposites have been shown to create artificial acoustic dispersion and PnBGs similar to the PBGs in PhCs. ^{Reference Kushwaha, Halevi, Dobrzynski and Djafari-Rouhani65}

A number of unconventional phenomena can arise from phononic metamaterials, such as acoustic cloaking, ^{Reference Zhang, Xia and Fang66} wave filtering, ^{Reference Liu, Zhang, Mao, Zhu, Yang, Chan and Sheng67,Reference Ho, Cheng, Yang, Zhang and Sheng68} and acoustic damping. ^{Reference Babaee, Shim, Weaver, Chen, Patel and Bertoldi69} Two-dimensional PnCs have been fabricated with PnBGs in the sonic ^{Reference Vasseur, Deymier, Chenni, Djafari-Rouhani, Dobrzynski and Prevost70} (midgap frequency of 10²–10³ Hz), ultrasonic ^{Reference Montero de Espinosa, Jiménez and Torres71} (10⁴–10⁶ Hz), and even hypersonic ^{Reference Gorishnyy, Ullal, Maldovan, Fytas and Thomas72} (10⁹–10¹² Hz) ranges. Fabricating 3D PnCs with submicron periodicities to control high-frequency phonons with frequencies above 10¹² Hz remains a challenge.

Recently, 3D hypersonic PnCs were realized with polymer microspheres self-assembled into opal structures, ^{Reference Cheng, Wang, Jonas, Fytas and Stefanou73} and 3D mechanically tunable elastomeric PnCs with 980-nm lattice spacing were fabricated using interference lithography templating ^{Reference Jang, Ullal, Gorishnyy, Tsukruk and Thomas74} ( Figure 5 ). The submicron periodicity of these PnCs is comparable to the wavelengths of visible and near-infrared light, implying that these crystals can exhibit bandgaps for both hypersound and light. Akimov et al. used hypersound to modulate the period of a synthetic opal structure, consequently changing the spectral position and width of the structure’s photonic stopband—a demonstration of coupled photonic and phononic interactions. ^{Reference Akimov, Tanaka, Pevtsov, Kaplan, Golubev, Tamura, Yakovlev and Bayer75} Continued reduction of PnC periodicity to the nanometer scale promises to extend these structures to the terahertz regime, so that heat transport can be managed in a manner similar to photons and phonons. ^{Reference Maldovan76}

Figure 5. (a) Schematic of multibeam interference lithography and (b) representative scanning electron microscope image of a 3D polydimethylsiloxane/air phononic crystal structure fabricated via interference lithography template. (a) Reproduced with permission from Reference Reference Lee, Singer and Thomas63. © 2012 Wiley-VCH. (b) Reproduced with permission from Reference Reference Jang, Ullal, Gorishnyy, Tsukruk and Thomas74. © 2006 American Chemical Society.

Electrochemical devices based on 3D architectures

Three-dimensional periodically architected materials have been used to increase the efficiency of dye-sensitized solar cells (DSSCs). ^{Reference von Freymann, Kitaev, Lotsch and Ozin1,Reference Nishimura, Abrams, Lewis, Halaoui, Mallouk, Benkstein, van de Lagemaat and Frank77–Reference Guldin, Hüttner, Kolle, Welland, Müller-Buschbaum, Friend, Steiner and Tétreault79} Such materials can be porous, for sensitization and electrolyte infiltration, and can also improve light trapping. Properties of PhCs, including Bragg diffraction, PBG reflection, multiple scattering in disordered regions, and resonant modes, can greatly enhance the optical light path within the organic-dye active layer of DSSCs. This gives photons a higher probability of being absorbed in this layer, ^{Reference Nishimura, Abrams, Lewis, Halaoui, Mallouk, Benkstein, van de Lagemaat and Frank77–Reference Guldin, Hüttner, Kolle, Welland, Müller-Buschbaum, Friend, Steiner and Tétreault79} improving an efficiency that is limited, in part, because the organic dyes used in DSSCs are poor absorbers of red and near-infrared light. ^{Reference O’Regan and Grätzel80} Mihi et al. ^{Reference Mihi, Zhang and Braun78} increased DSSC power efficiency by using a porous PhC coupled to the working electrode. Guldin et al. ^{Reference Guldin, Hüttner, Kolle, Welland, Müller-Buschbaum, Friend, Steiner and Tétreault79} achieved similar results by fabricating a double-layer DSSC using titania inverse opals and mesoscopic block-copolymer-patterned titania. This structure allows for effective dye sensitization, electrolyte infiltration, and charge collection from both the mesoporous and PhC layers.

The nano- and microscale constructs of architected materials have benefits beyond photonic properties for proposed silicon electrodes in lithium-ion batteries. ^{Reference Esmanski and Ozin81,Reference Xia, Gu and Greer82} (For more information on lithium-ion batteries, see the article in this issue by Crabtree et al.) Esmanski and Ozin ^{Reference Esmanski and Ozin81} and Pikul et al. ^{Reference Pikul, Gang Zhang, Cho, Braun and King83} extensively explored silicon inverse opals ( Figure 6 ), and Xia and co-workers ^{Reference Xia, Gu and Greer82} fabricated silicon nanolattices to study how macroporosity and architecture aid in accommodating the dramatic volume swings experienced by the silicon electrode as a result of lithium intercalation during cycling. ^{Reference Esmanski and Ozin81} The introduction of 3D architecture into silicon electrodes promises many advantages, including enhanced mechanical stability, minimal lithium diffusion distances and large surface areas for improved charge and discharge rate, control over porosity for superior electrolyte infiltration and increased cell capacity, and better electrical conductivity than can be obtained with electrodes based on particle aggregates requiring binders and additives. ^{Reference Esmanski and Ozin81,Reference Xia, Gu and Greer82}

Figure 6. Representative scanning electron microscope images at different magnifications of nanocrystalline silicon inverse opals templated from 480-nm silica spheres for use as negative electrodes in lithium-ion batteries. Reproduced with permission from Reference Reference Esmanski and Ozin81. © 2009 Wiley-VCH.

3D architected scaffolds for tissue growth

Human tissues are complex 3D structures that consist of cells and an extracellular matrix in which hierarchy can be found at multiple length scales. Tissue engineering is a growing field, and a great deal of research has focused on controlling cell alignment, differentiation, and proliferation and, eventually, tissue growth. ^{Reference Sun, Parker, Syoji, Wang, Lewis and Kaplan84} Aside from chemical cues, cell growth is highly dependent on substrate architecture, with physical properties such as geometry, pore size and connectivity, porosity, and stiffness playing significant roles in determining tissue development. ^{Reference Rumpler, Woesz, Dunlop, van Dongen and Fratzl85–Reference Karageorgiou and Kaplan87}

Architected materials allow for precise control over the microscale and mesoscale pore interconnectivity patterns of multilayered scaffolds, which can guide the alignment of cells into multicellular bundles—and eventually into tissues—and can provide mechanical cues for cell differentiation. ^{Reference Kolewe, Park, Gray, Ye, Langer and Freed88} In an effort to identify optimal conditions for bone-tissue growth, Sun et al. fabricated rigid silk/hydroxyapatite scaffolds with pore sizes in the range of 200–750 μm and assessed the differentiation and growth of human-bone-marrow-derived mesenchymal stem cells (hMSCs) on these substrates. ^{Reference Sun, Parker, Syoji, Wang, Lewis and Kaplan84} They found that hMSCs successfully grew onto and into the printed surfaces and organized into swirl-like structures resembling the cell orientation found in canals of human long bone. ^{Reference Sun, Parker, Syoji, Wang, Lewis and Kaplan84} Analogously, Kolewe et al. showed how neonatal rat heart cell attachment, elongation, and orientation can be dictated by altering the alignment of scaffold layers, the width of scaffold struts, and the gaps between offset struts ( Figure 7 ). ^{Reference Kolewe, Park, Gray, Ye, Langer and Freed88} These examples show that architected scaffold materials are useful not only for understanding cellular interactions with complex 3D environments, but potentially for generating functional tissues.

Figure 7. Representative confocal micrograph of neonatal rat heart cells cultured on multilayer poly(glycerol sebacate) scaffolds. Reproduced with permission from Reference Reference Kolewe, Park, Gray, Ye, Langer and Freed88. © 2013 Wiley-VCH.