The ${\omega }^3$ scaling of the vibrational density of states in quasi-2D nanoconfined solids

Abstract

Atomic vibrations play a vital role in the functions of various physical, chemical, and biological systems. The vibrational properties and the specific heat of crystalline bulk materials are well described by Debye theory, which successfully predicts the quadratic ${\omega }^2$ low-frequency scaling of the vibrational density of states (VDOS) in bulk ordered solids from few fundamental assumptions. However, the analogous framework for nanoconfined materials with fewer degrees of freedom has been far less well explored. Using inelastic neutron scattering, we characterize the VDOS of amorphous ice confined to a thickness of $\approx 1$ nm inside graphene oxide membranes and we observe a crossover from the Debye ${\omega }^2$ scaling to an anomalous ${\omega }^3$ behaviour upon reducing the confinement size $L$. Additionally, using molecular dynamics simulations, we confirm the experimental findings and also prove that such a scaling of the VDOS appears in both crystalline and amorphous solids under slab-confinement. We theoretically demonstrate that this low-frequency ${\omega }^3$ law results from the geometric constraints on the momentum phase space induced by confinement along one spatial direction. Finally, we predict that the Debye scaling reappears at a characteristic frequency ${\omega }_{\times }=vL/2\pi$, with $v$ the speed of sound of the material, and we confirm this quantitative estimate with simulations. This new physical phenomenon, revealed by combining theoretical, experimental and simulations results, is relevant to a myriad of systems both in synthetic and biological contexts and it could impact various technological applications for systems under confinement such as nano-devices or thin films.

v2: revised manuscript, matching the published version

References in corpus (12)

• Giant Phonon-induced Conductance in Scanning Tunneling Spectroscopy of Gate-tunable Graphene
• Universal law for the vibrational density of states of liquids
• Multiple reentrant glass transitions in confined hard-sphere glasses
• Fluids in Extreme Confinement
• Explaining the low-frequency shear elasticity of confined liquids
• Explaining the specific heat of liquids based on instantaneous normal modes
• Experimental Confirmation of the Universal Law for the Vibrational Density of States of Liquids
• Elastic Properties of Confined Fluids from Molecular Modeling to Ultrasonic Experiments on Porous Solids
• Low-frequency excess vibrational modes in two-dimensional glasses
• Universal $L^{-3}$ finite-size effects in the viscoelasticity of confined amorphous systems
• Diverging time scale in the dimensional crossover for liquids in strong confinement
• Does the boson peak survive in an ultrathin oxide glass?

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