Phonon spectra, nearest neighbors, and mechanical stability of disordered colloidal clusters with attractive interactions

We investigate the influence of morphology and size on the vibrational properties of disordered clusters of colloidal particles with attractive interactions. Spectral features of the vibrational modes are found to depend strongly on the average number of nearest neighbors, NN̄, but only weakly on the number of particles in each glassy cluster. In particular, the median phonon frequency, ω_med, is constant for NN̄<2 and then grows linearly with NN̄ for NN̄>2. This behavior parallels concurrent observations about local isostatic structures, which are absent in clusters with NN̄<2 and then grow linearly in number for NN̄>2. Thus, cluster vibrational properties appear to be strongly connected to cluster mechanical stability, and the scaling of ω_med with NN̄ is reminiscent of the jamming transition. Simulations of random networks of springs corroborate observations.