Emergence of solid-like Debye scaling in the vibrational density of states of liquids under nanoconfinement
Yuanxi YuSha JinXue FanMona SarterDehong YuMatteo BaggioliLiang Hong
Yuanxi YuSha JinXue Fan
At frequencies higher than the inverse of the structural relaxation time $\tau$, the dynamics of liquids display several solid-like properties, including propagating collective shear waves and emergent elasticity. However, in classical bulk liquids, where $\tau$ is typically of the order of 1 ps or less, this solid-like behavior remains elusive in the low-frequency region of the vibrational density of states (VDOS). Here, we provide compelling evidence for the emergent solid-like nature of liquids at short distances through inelastic neutron scattering measurements of the low-frequency VDOS in liquid water and glycerol confined within graphene oxide membranes. In particular, upon increasing the strength of confinement, we observe a transition from a liquid-like VDOS (linear in the frequency $\omega$) to a solid-like behavior (Debye law, $\sim\omega^2$) in the range of $1$-$4$ meV. Molecular dynamics simulations confirm these findings and reveal additional solid-like features, including propagating collective shear waves and a reduction in the self-diffusion constant. Finally, we show that the onset of solid-like dynamics is pushed towards low frequency along with the slowing-down of the relaxation processes upon confinement, and that the scale at which solidity emerges is qualitatively compatible with k-gap theory and the concept of gapped momentum states. Our results provide convincing experimental evidence of the continuity between liquids and solids, as originally advocated by Frenkel and Maxwell, and a deeper understanding of the dynamics of liquids across a wide range of length scales.