When Can the Elastic Properties of Simple Liquids Be Probed Using High-Frequency Nanoparticle Vibrations?

Abstract

Recent measurements on the gigahertz vibration of nanoparticles immersed in simple liquids, such as glycerol, show that the liquid's viscoelastic properties can significantly affect the nanoparticle's mechanical response. Here, we theoretically explore the high-frequency (elastic) limit of this phenomenon where the characteristic time scale for molecular relaxation in the liquid far exceeds the nanoparticle's vibration period. Paradoxically, we find that the effects of liquid elasticity (and viscosity) may not be visible in the nanoparticle's dynamic response in this high-frequency elastic limit—the response being identical to that of a macroscopic resonator in an inviscid fluid. A comprehensive mechanistic study reveals that the conditions for this unusual behavior are strongly dependent on the nanoparticle's vibration mode and the liquid's properties. A judicious choice of vibration mode is essential for interrogating the viscoelastic properties of simple liquids. Our findings explain recent measurements on nanowires and nanorods immersed in highly viscous liquids.

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