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We investigate the influence of morphology and size on the vibrationalproperties of disordered clusters of colloidal particles with attractiveinteractions. From measurements of displacement correlations between particlesin each cluster, we extract vibrational properties of the corresponding"shadow" glassy cluster, with the same geometric configuration and interactionsas the "source" cluster but without damping. Spectral features of thevibrational modes are found to depend strongly on the average number of nearestneighbors, $\bar{NN}$, but only weakly on the number of particles in eachglassy cluster. In particular, the median phonon frequency, $\omega_{med}$, isessentially constant for $\bar{NN}$ $<2$ and then grows linearly with$\bar{NN}$ for $\bar{NN}$ $>2$. This behavior parallels concurrent observationsabout local isostatic structures, which are absent in clusters with $\bar{NN}$$<2$ and then grow linearly in number for $\bar{NN}$$>2$. Thus, clustervibrational properties appear to be strongly connected to cluster mechanicalstability (i.e., fraction of locally isostatic regions), and the scaling of$\omega_{med}$ with $\bar{NN}$ is reminiscent of the behavior of packings ofspheres with repulsive interactions at the jamming transition. Simulations ofrandom networks of springs corroborate observations and suggest thatconnections between phonon spectra and nearest neighbor number are generic todisordered networks.

Phonon Spectra, Nearest Neighbors, and Mechanical Stability of Disordered Colloidal Clusters with Attractive Interactions