In this paper, the dynamic behavior of nano-oscillators constructed from lysozyme molecule inside titania nanotubes is investigated. The continuum approximation along with the classical Lennard–Jones and Coulomb potential functions is adopted to mathematically model the van der Waals (vdW) and electrostatic interactions between lysozyme molecule and titania nanotubes, respectively. Based on the analytical expression for the total interaction force, the equation of motion is solved numerically to obtain the time histories of position and velocity of lysozyme enzyme. Furthermore, a semi-analytical expression based on the conservation ofmechanicalenergylawisderivedtoaccuratelyevaluatetheoscillationfrequencyofsystemasafunctionofgeometricalparameters, electric charges of molecules and initial conditions. Numerical results are presented to examine the effects of net charge of lysozyme and size of nanotube (length and radius) on the total interactions of the underlying mechanism. It is found that the electrostatic interactions dominate the vdW ones. A comparative study is also conducted to examine the effect of net charge of lysozyme on its oscillatory motion inside titania nanotubes. Numerical results indicate that the lysozyme with negative net charge is repulsed from the nanotube, while the lysozyme with positive net charge is allowed to oscillate inside the titania nanotubes with frequencies in the gigahertz range. It is further demonstrated that lysozyme molecule with positive net charge produces higher frequencies inside titania nanotubes compared to the lysozyme molecule with zero net charge.
