Emergence of Debye scaling in the density of states of liquids under nanoconfinement

Abstract: In the realm of nanoscience, the dynamic behaviors of liquids at scales beyond the conventional structural relaxation time, $\tau$, unfold a fascinating blend of solid-like characteristics, including the propagation of collective shear waves and the emergence of 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 density of states (DOS). Here, we provide evidence for the emergent solid-like nature of liquids at short distances through inelastic neutron scattering measurements of the low-frequency DOS 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 DOS (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. This nanoconfinement-induced transition, aligning with k-gap theory, underscores the potential of leveraging liquid nanoconfinement in advancing nanoscale science and technology, building more connections between fluid dynamics and materials engineering.