Anisotropic lattice expansion of three-dimensional colloidal crystals and its impact on hypersonic phonon band gaps

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Abstract
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.

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