Measurement of Correlations between Low-Frequency Vibrational Modes and Particle Rearrangements in Quasi-Two-Dimensional Colloidal Glasses

We investigate correlations between low-frequency vibrational modes and rearrangements in two-dimensional colloidal glasses composed of thermosensitive microgel particles, which readily permit variation of the sample packing fraction. At each packing fraction, the particle displacement covariance matrix is measured and used to extract the vibrational spectrum of the “shadow” colloidal glass (i.e., the particle network with the same geometry and interactions as the sample colloid but absent damping). Rearrangements are induced by successive, small reductions in the packing fraction. The experimental results suggest that low-frequency quasilocalized phonon modes in colloidal glasses, i.e., modes that present low energy barriers for system rearrangements, are spatially correlated with rearrangements in this thermal system.

Figure 1

Particle displacement distribution when the packing fraction changes from 0.885 to 0.879. Inset (a) Real space distribution of particle displacements; brightness of a particle is proportional to the displacement magnitude. Inset (b) Real space distribution of change of ${\Psi }_6$ of the same region as inset (a); color change from black to red represents a change of ${\Psi }_6$ from 0 to 0.89, respectively.

Figure 2

Rearranging clusters and low-frequency modes at three different packing fractions studied, ranging from $\varphi =0.885$ to $\varphi =0.850$ from (a) to (c). Color contour plots indicate polarization magnitudes for each particle, summed over the lowest 30 modes. Circles indicate particles that moved more than 40 nm at each decompression step.

Figure 3

Projection coefficient ${\alpha }^2$ versus mode number. Different symbols represent ${\alpha }^2$ from different packing fraction steps. The eigenvectors are derived at packing fractions as indicated by the symbols, and the rearrangement vector is determined from the displacements of particles when the system is decompressed from the packing fraction indicated to the next highest value. The data are binned with a window of 5.

Figure 4

Comparison of soft spots and rearranging clusters at high packing fractions. Blue solid circles indicate particles belonging to rearranging clusters, defined as particles with displacements exceeding 40 nm; red empty circles are particles belonging to soft spots for $N_m=10$, $N_p=130$.