This journal is © the Owner Societies 2014 Phys. Chem. Chem. Phys., 2014, 16, 8921--8926 | 8921 Cite this: Phys. Chem. Chem. Phys., 2014, 16, 8921 Anisotropic lattice expansion of three-dimensional colloidal crystals and its impact on hypersonic phonon band gaps† Songtao Wu,‡ a Gaohua Zhu,‡ a Jin S. Zhang, b Debasish Banerjee, a Jay D. Bass, b Chen Ling* a and Kazuhisa Yano* ac We report anisotropic expansion of self-assembled colloidal polystyrene–poly(dimethylsiloxane) crystals and its impact on the phonon band structure at hypersonic frequencies. The structural expansion was achieved by a multistep infiltration–polymerization process. Such a process expands the interplanar lattice distance 17% after 8 cycles whereas the in-plane distance remains unaffected. The variation of hypersonic phonon band structure induced by the anisotropic lattice expansion was recorded by Brillouin measurements. In the sample before expansion, a phononic band gap between 3.7 and 4.4 GHz is observed; after 17% structural expansion, the gap is shifted to a lower frequency between 3.5 and 4.0 GHz. This study offers a facile approach to control the macroscopic structure of colloidal crystals with great potential in designing tunable phononic devices. 1. Introduction Hypersonic phononic crystals (HPC) are materials with periodic variation in densities and/or elastic properties with submicron lattice constants. 1 With characteristic phonon band gaps at the hypersonic frequency regime (10 9 to 10 12 Hz), they have attracted growing interest recently due to potential applications in thermal management 2 and acousto-optic devices. 3 One of the most widely used approaches for the fabrication of HPC is lithography techniques. 4–8 A cost-effective and scalable alternative is a self-assembly method. Colloidal particles can self-assemble into periodic structure with their resulting physical properties precisely tunable depending on the fabrication approach and constituent material properties. 9–15 Over the last decade, self-assembled colloidal crystals have been utilized for numerous photonic applications. 9–11 Recently, Cheng and colleagues self- assembled the polystyrene colloidal crystals and reported direct observation of a complete phonon band gap at the hypersonic frequency regime after infiltrating a fluid with a similar refractive index. 16 A self-assembly method was also used to fabricate polystyrene–poly(dimethylsiloxane) composites, which represent the first solid–solid system with a hypersonic band gap. 17 Towards the practical applications of HPC, it is essential to achieve a precise control of its band gap in a predictable and reproducible way. For one- and two-dimensional phononic crystals, tunable band gaps were achieved by light triggered alteration of the elastic properties, 18 or by perturbing structural periodicity by introduction of defect layers, 19 or by structure deformation induced by solvent exposure. 8 Yet it is challenging to control the phonon band gap for a complicated 3-D phononic crystal in a convenient way. To the best of the authors’ knowledge, the experimental demonstration of band gap tuning was only reported by changing the elastic contrast of infiltrated fluids in the crystal lattice or by adjusting the lattice distances via replacing with different constituent particles. 16 The exploration of other new methods to control the band gap of 3D HPC remains desirable. Here we report a facile method to tune the self-assembled 3-D phononic crystal composite without replacing any of its constituents and study structural-dependent phononic properties. An evaporation-induced self-assembly method was employed to fabricate close-packed polystyrene (PS) colloidal crystals, which were later embedded into the poly(dimethylsiloxane) (PDMS) elastomer matrix. PDMS precursor liquid was infiltrated and then polymerized. After the polymerization, anisotropic lattice expansion was achieved, which transforms the original close- packed structure into a loose-packed one. The phonon dispersions of PS–PDMS crystals before and after expansion were recorded in a Toyota Research Institute of North America, Toyota Motor Engineering and Manufacturing North America, Inc., Ann Arbor, Michigan, 48105, USA. E-mail: chen.ling@tema.toyota.com b Department of Geology, University of Illinois at Urbana-Champaign, Urbana, Illinois, 61801, USA c Inorganic Materials Laboratory, Toyota Central R&D Labs. Inc., Nagakute, Aichi 480-1192, Japan. E-mail: k-yano@mosk.tytlabs.co.jp † Electronic supplementary information (ESI) available: Fitting of the reflectance spectrum. Derivation of vibration frequency from the spring-hard-sphere model. See DOI: 10.1039/c4cp00498a ‡ These authors contributed equally. Received 3rd February 2014, Accepted 13th March 2014 DOI: 10.1039/c4cp00498a www.rsc.org/pccp PCCP PAPER Published on 14 March 2014. Downloaded by Argonne National Laboratory on 10/07/2015 18:31:48. View Article Online View Journal | View Issue