Vibrational Phonon Modes of Two-Dimensional Soft-Particle Colloidal Crystals with Hard-Particle Dopants

We study the phonon modes of two-dimensional colloidal crystals consisting of random distributions of ``soft'' NIPA microgel particles and ``hard'' polystyrene particle dopants. Thus, the effective springs connecting nearest-neighbors are very stiff, very soft, or of intermediate stiffness, corresponding to three possible inter-particle potentials present in the crystals. We employ video microscopy to derive the phonon modes of corresponding ``shadow'' crystals with the same geometric configuration and interactions as the experimental colloidal system, but absent damping [1,2,3]. Long wavelength, Debye-like behavior is found at low frequencies, regardless of the number of hard polystyrene particles present in the crystal. Hard particles are primary participants at high frequencies, while soft spheres are primary participants at intermediate frequencies. [1] Chen \textit{et al}., PRL \textbf{105}, 025501 (2010). [2] Kaya \textit{et al}., Science \textbf{329}, 656 (2010). [3] Ghosh \textit{et al}. PRL \textbf{104}, 248305 (2010).