We investigate the influence of morphology and size on the vibrational properties of disordered clusters of colloidal particles with attractive interactions. From measurements of displacement correlations between particles in each cluster, we extract
vibrational properties of the corresponding shadow glassy cluster, with the same geometric configuration and interactions as the source cluster but without damping. Spectral features of the vibrational modes are found to depend strongly on the average number of nearest neighbors, $bar{NN}$, but only weakly on the number of particles in each glassy cluster. In particular, the median phonon frequency, $omega_{med}$, is essentially constant for $bar{NN}$ $<2$ and then grows linearly with $bar{NN}$ for $bar{NN}$ $>2$. This behavior parallels concurrent observations about local isostatic structures, which are absent in clusters with $bar{NN}$ $<2$ and then grow linearly in number for $bar{NN}$$>2$. Thus, cluster vibrational properties appear to be strongly connected to cluster mechanical stability (i.e., fraction of locally isostatic regions), and the scaling of $omega_{med}$ with $bar{NN}$ is reminiscent of the behavior of packings of spheres with repulsive interactions at the jamming transition. Simulations of random networks of springs corroborate observations and suggest that connections between phonon spectra and nearest neighbor number are generic to disordered networks.
The effects of particle shape on the vibrational properties of colloidal glasses are studied experimentally. Ellipsoidal glasses are created by stretching polystyrene spheres to different aspect ratios and then suspending the resulting ellipsoidal pa
rticles in water at high packing fraction. By measuring displacement correlations between particles, we extract vibrational properties of the corresponding shadow ellipsoidal glass with the same geometric configuration and interactions as the source suspension but without damping. Low frequency modes in glasses composed of ellipsoidal particles with major/minor axis aspect ratios $sim$1.1 are observed to have predominantly rotational character. By contrast, low frequency modes in glasses of ellipsoidal particles with larger aspect ratios ($sim$3.0) exhibit a mix of rotational and translational character. All glass samples were characterized by a distribution of particles with different aspect ratios. Interestingly, even within the same sample it was found that small-aspect-ratio particles participate relatively more in rotational modes, while large-aspect-ratio particles tend to participate relatively more in translational modes.
We conduct experiments on two-dimensional packings of colloidal thermosensitive hydrogel particles whose packing fraction can be tuned above the jamming transition by varying the temperature. By measuring displacement correlations between particles,
we extract the vibrational properties of a corresponding shadow system with the same configuration and interactions, but for which the dynamics of the particles are undamped. The vibrational spectrum and the nature of the modes are very similar to those predicted for zero-temperature idealized sphere models and found in atomic and molecular glasses; there is a boson peak at low frequency that shifts to higher frequency as the system is compressed above the jamming transition.
