Radial breathing-mode frequency of elastically confined spherical nanoparticles subjected to circumferential magnetic field

• New formulation based on the nonlocal elasticity theory is proposed to investigate radial vibrations of the nanoparticles subjected to magnetic field.
• The influences of small scale and elastic foundation on the radial frequencies of several spherical nanoparticles are investigated.
• The transcendental equation for estimating the eigenfrequencies of the nanoparticles is developed.

Knowledge of the vibrational properties of nanoparticles is of fundamental interest since it is a signature of their morphology, and it can be utilized to characterize their physical properties. In addition, the vibration characteristics of the nanoparticles coupled with surrounding media and subjected to magnetic field are of recent interest. This paper develops an analytical approach to study the radial breathing-mode frequency of elastically confined spherical nanoparticles subjected to magnetic field. Based on Maxwell's equations, the nonlocal differential equation of radial motion is derived in terms of radial displacement and Lorentz's force. Bessel functions are used to obtain a frequency equation. The model is justified by a good agreement between the results given by the present model and available experimental and atomic simulation data. Furthermore, the model is used to elucidate the effect of nanoparticle size, the magnetic field and the stiffness of the elastic medium on the radial breathing-mode frequencies of several nanoparticles. Our results reveal that the effects of the magnetic field and the elastic medium are significant for nanoparticle with small size.

An analytical model is presented for studying the effects of a circumferential magnetic field on the radial breathing-mode frequency of a magnetically sensitive nanoparticle. The transcendental equation for estimating the frequency of the breathing-mode of the elastically confined nanoparticles is developed based on nonlocal continuum mechanics.Figure optionsDownload as PowerPoint slide