The Vibration Modes In Two-dimension Colloidal Glasses

We experimentally investigated the correlation between local structures and phononmodes in quasi-2D colloidal glasses. The glass samples consist of thermo-sensitivepoly-N-isopropylacrylamide microgel (PNIPAM) particles, whose diameter can be tuned bysmall changes of sample temperature. A binary mixture of these particles is confinedbetween two coverslips to form a monolayer of quasi-2D glass. By changing the numberratio between large and small particles, the structure or the overall degree of disorder of thesamples can be systematically tuned. We employed video microscopy to record the motionof the colloidal particles in the sample for11minutes at a rate of60fps.The trajectories of individual particles are obtained by particle tracking software.Dynamical matrix is constructed using covariance matrix analysis, from which theeigenfrequency and eigenvector of vibrations are extracted. In this study, we focus on theevolution of the low-frequency quasi-localized phonon modes in glasses, as the systembecomes more and more disordered from the increased dopants. To compare results fromdifferent samples, we choose samples with packing indentical fraction at86%, and rescalethe eigenfrequencies by the median frequency of each sample. For the four doping levelinvestigated (2%,9%,29%,61%), the density of states at low frequencies increases withthe doping level, suggesting that the fraction of low frequency modes increases withdisorder, which is corroborated by the higher boson peaks at higher dopant fractions. Wemeasured the participation ratio of the obtained phonon modes, and found that the peak ofthe boson peak correspond to quasi-localized vibration modes, or soft modes. We examinedthe correlation between the soft modes and local structural parameters. Specifically, wecalculated the local orientational order parameter in our samples, and computed thecorrelation coefficients between the relative amplitude and the local orientational orderparameter for each mode. The soft modes are found to have a significantly negativecorrelation with the local orientational order parameter, which implies that soft modes areconcentrated in regions with poor local order. We calculated the structural fluctuation oflocal structure parameters. The local structure parameters are free volume, the number of particles’ neighbors and the local structural entropy. We also computed the correlationcoefficients between the relative amplitude and the structural fluctuation of local structureparameters for each mode. Samilarly, the soft modes are found to have a significantcorrelation with structural fluctuation of local structure parameter, which implies that softmodes are concentrated in regions with bigger structural fluctuation.We therefore conclude that the local disorder and the regions with bigger structuralfluctuation could be the structural origin of soft modes in glasses.