DOI: 10.1002/adem.201300254 Design and Fabrication of Hollow Rigid Nanolattices via Two-Photon Lithography** By Lauren C. Montemayor, Lucas R. Meza and Julia R. Greer* Ordered cellular solids like the octet-truss and kagome lattices have been reported to have robust mechanical properties, for example a combination of high strength and fracture toughness. [1,2] The geometry of these structures enables creating materials with not only improved mechanical properties but also with low densities and high surface area to volume ratios. The ability to de-couple these historically coupled properties through architectural control in material design has the potential to push the envelope of existing materials in a variety of applications, from photovoltaic devices to hierarchical structural materials to materials for sustainable energy. [3,4] 3-Dimensional structures, whose global deformation is carried out by bending of the individual struts within the structure, are often referred to as bending-dominated struc- tures. Cellular solids whose overall deformation is carried out by stretching or compression of lattice members during loading are denoted as stretching-dominated structures. Stochastic foams with either open or closed cells represent an example of bending dominated structures whose compres- sive yield strength, s Y , has been proven to scale with the relative density,  r, as s Y / 0:3 r 3=2 s YS where s YS represents the yield strength of the parent solid. [3,5] The stiffness of such structures scales as E /  r 2 E S , where E S represents the stiffness of the parent solid. An example of a stretching-dominated structure is an octet-truss lattice, shown in Figure 1c, whose strength scales with the relative density as s Y / 0:3 rs YS and the stiffness scales as E / 0:3 rE S . [3] These scaling laws hold only for isotropic structures, i.e., whose unit cell has the anisotropy ratio, R ¼ 1, defined as width/height of a unit cell. [5] For isotropic geometries, stretching dominated structures have higher stiffness and strength compared to bending-dominated structures for a given relative density due to the linear relationship between relative density and both strength and stiffness. As a result, these types of ordered cellular solids are capable of outperforming the current open-cell foams, such as stochastic metallic foams. The relationship between fracture toughness and relative density for a 2-dimensional open-cell foam has the analytical form of K IC / s Y  r 2 while that for a stretching dominated structure is K IC / s Y  r. [1] In addition to strength, the stretching dominated structures also outperform the open-cell foams in terms of fracture toughness. Another example of an ordered structure is the so-called 2-dimensional kagome lattice shown in Figure 1b, which is a stretching periodic-bending dominated structure. In 2-dimensions, the stacked triangular unit cell is a stretching dominated structure but due to the tessellation pattern, the resulting lattice has a mechanism for bending at the nodes between unit cells. As a result, the overall lattice has both stretching and bending mechanisms; hence it is called a stretching periodic-bending structure. Its fracture toughness has been reported to scale as K IC / s Y  r 1=2 , rendering the kagome lattices to be tougher than the stretching and bending dominated geometries for low relative densities. [1] The higher fracture toughness offered by the kagome lattice in 2-dimensions, compared to other lattice geometries, make it is reasonable to expect similar advantages in a 3-dimensional kagome geometries. Evans et al. [6] have created a macro-scale version of the 3-dimensional kagome lattice but the structure was limited to a single unit cell in height. The 3-dimensional kagome unit cell presented in this paper can be tessellated to create lattices of multiple unit cells in height, thus providing a platform to fully study the mechanical behavior of the kagome lattice in 3-dimensions. If the high fracture toughness properties of the 2-dimensional geometry extend to the 3-dimensional kagome lattice, it will allow for the creation of nanostructured materials with the ability to inhibit crack propagation and increase damage tolerance of a structure for a given constituent material. [1,2] Ultra-lightweight small-scale hollow cellular structures have been fabricated using photolithographic techniques. [4,7–10] In contrast to traditional photolithography techniques, which typically produce 2-dimensional structures, Jacobsen et al. [9] created 3-dimensional structures by exposing a bulk volume of photoresist to collimated ultra-violet (UV) light through a mask. In their process, a 3D polymer waveguide was formed during exposure as a result of the change in index of refraction between the cured and uncured photoresist. The 3-dimensional geometry created by the polymer waveguide is fully defined by the lithographic mask pattern and by the [*] Prof. J. R. Greer, L. C. Montemayor, L. R. Meza 1200 E. California Blvd MC 309-81, Pasadena, CA 91125, USA E-mail: jrgreer@caltech.edu [**] The authors gratefully acknowledge the financial support from the Dow-Resnick Innovation Fund at Caltech and from the National Science Foundation through L.C.M.’s NSF Graduate Research Fellowship and J.R.G’s grant (CMMI-1234364). The authors acknowledge critical support and infrastructure provided by the Kavli Nanoscience Institute at Caltech. The authors would also like to thank Dongchan Jang for assistance in TEM sample preparation and analysis. 184 wileyonlinelibrary.com © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ADVANCED ENGINEERING MATERIALS 2014, 16, No. 2 COMMUNICATION