Structural, mechanical, and vibrational properties of particulate physical gels

Low-frequency vibrational states in ideal glasses with random pinning

Glasses exhibit spatially localized vibrations in the low-frequency regime. These localized modes emerge below the boson peak frequency ω_{BP}, and their vibrational densities of state follow g(ω)∝ω^{4} (ω is frequency). Here, we attempt to address how the localized vibrations behave through the ideal glass transition. To do this, we employ a random pinning method, which enables us to study the thermodynamic glass transition. We find that the localized vibrations survive even in equilibrium glass states. Remarkably, the localized vibrations still maintain the properties of appearance below ω_{BP} and g(ω)∝ω^{4}. Our results provide important insight into the material properties of ideal glasses.

Phonon transport properties of particulate physical gels

Particulate physical gels are sparse, low-density amorphous materials in which clusters of glasses are connected to form a heterogeneous network structure. This structure is characterized by two length scales, ξ s and ξ G: ξ s measures the length of heterogeneities in the network structure and ξ G is the size of glassy clusters. Accordingly, the vibrational states (eigenmodes) of such a material also exhibit a multiscale nature with two characteristic frequencies, [Formula: see text] and ω G, which are associated with ξ s and ξ G, respectively: (i) phonon-like vibrations in the homogeneous medium at [Formula: see text], (ii) phonon-like vibrations in the heterogeneous medium at [Formula: see text], and (iii) disordered vibrations in the glassy clusters at ω > ω G. Here, we demonstrate that the multiscale characteristics seen in the static structures and vibrational states also extend to the phonon transport properties. Phonon transport exhibits two distinct crossovers at frequencies ω* and ω G (or at wavenumbers of [Formula: see text] and [Formula: see text]). In particular, both transverse and longitudinal phonons cross over between Rayleigh scattering at [Formula: see text] and diffusive damping at [Formula: see text]. Remarkably, the Ioffe–Regel limit is located at the very low frequency of ω*. Thus, phonon transport is localized above ω*, even where phonon-like vibrational states persist. This markedly strong scattering behavior is caused by the sparse, porous structure of the gel.

Microscopic structural origin behind slowing down of colloidal phase separation approaching gelation

The gelation of colloidal particles interacting through a short-range attraction is widely recognized as a consequence of the dynamic arrest of phase separation into colloid-rich and solvent-rich phases. However, the microscopic origin behind the slowing down and dynamic arrest of phase separation remains elusive. In order to access microscopic structural changes through the entire process of gelation in a continuous fashion, we used core–shell fluorescent colloidal particles, laser scanning confocal microscopy, and a unique experimental protocol that allows us to initiate phase separation instantaneously and gently. Combining these enables us to track the trajectories of individual particles seamlessly during the whole phase-separation process from the early stage to the late arresting stage. We reveal that the enhancement of local packing and the resulting formation of locally stable rigid structures slow down the phase-separation process and arrest it to form a gel with an average coordination number of z = 6–7. This result supports a mechanical perspective on the dynamic arrest of sticky-sphere systems based on the microstructure, replacing conventional explanations based on the macroscopic vitrification of the colloid-rich phase. Our findings illuminate the microscopic mechanisms behind the dynamic arrest of colloidal phase separation, the emergence of mechanical rigidity, and the stability of colloidal gels.