Energy Dissipation for Nanometer Sized Acoustic Oscillators

Abstract

Ultrafast laser excitation of nanostructures causes rapid heating that can excite vibrational modes that map onto the expansion coordinates. These modes lose energy by radiating sound waves into the environment. Recent experiments have focused on how liquid viscosity and associated viscoelasticity affect the energy dissipation process. In this Perspective we give an overview of the continuum mechanics theory used to describe the damping of the vibrational modes in solid and liquid environments and describe recent experimental measurements of damping. The theory focuses on the breathing modes of spheres, infinite cylinders, and infinite plates, as these are the most relevant to experiments and can be described analytically. We examine the differences between different shapes and how the relaxation times depends on the dimensions of the nanostructures. In particular, a complicated behavior occurs at sizes where the frequency of the vibrational modes becomes comparable to the relaxation time in the environment. In this regime the quality factors for the breathing modes can be used to estimate environmental relaxation times, providing unique information about the properties of materials at nanoscale dimensions.

Compressible viscoelasticity of cell membranes determined by gigahertz-frequency acoustic vibrations

“… [46] . This system has been used to investigate the viscous and viscoelastic properties of simple liquids, including water, glycerol, and their mixtures [47] , [48] .…”

“…At low vibrational frequencies, radiation of sounds waves is the dominant effect (inviscid limit) and damping is controlled by the acoustic impedance of the liquid. As the frequency increases, liquid viscosity effect becomes important, and the vibrational lifetimes start to decrease [48] . Finally, when the period of the vibrational motion approaches the liquid relaxation time, the vibration triggers a viscoelastic response in the liquid.…”

Ultrafast nano generation of acoustic waves in water via a single carbon nanotube

“…Specifically, the effect of intrinsic damping, i.e. viscous and viscoelastic damping [9] , [61] , a yet open issue in the present frequency range, will need to be addressed. Indeed, intrinsic damping might hamper water oscillations frequencies greater than that of the MWCNT fundamental mode.…”

Vibrational Anharmonicity and Energy Relaxation in Nanoscale Acoustic Resonators

“…However, good agreement between the experimental and calculated quality factors can be achieved for the n = 3 mode by adding internal damping: that is, by calculating a total quality factor by 1/Q tot = 1/Q sub + 1/Q int , where Q sub is the damping due to radiation of sound waves into the substrate (which is obtained from eq 2) and Q int is the internal damping contribution. 20 The dashed lines in Figure 4 show Q tot for the fundamental and n = 3 overtone for a value of Q int = 150. Using this value for Q int brings the experiments and calculations into good agreement for the n = 3 mode; however, the agreement between the experiments and calculations is now slightly worse for the fundamental mode.…”

“…These results can be accounted for by a continuum mechanics model that consists of an organic "spacer" layer between the substrate and the nanoplate, and a second organic layer on top of the nanoplate. 12,20 This work provides important insights into controlling nanoplate vibrational quality factors, which is potentially useful for the development of nanoelectromechanical devices for sensing applications. The samples in the experiments were prepared by drop casting a nanoplate solution onto a glass coverslip.…”