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, (NN) over bar, but only weakly on the number of particles in each glassy cluster. In particular, the median phonon frequency, omega(med), is constant for (NN) over bar < 2 and then grows linearly with <(NN)over bar> for (NN) over bar > 2. This behavior parallels concurrent observations about local isostatic structures, which are absent in clusters with (NN) over bar < 2 and then grow linearly in number for <(NN)over bar> > 2. Thus, cluster vibrational properties appear to be strongly connected to cluster mechanical stability, and the scaling of omega(med) with (NN) over bar is reminiscent of the jamming transition. Simulations of random networks of springs corroborate observations.