Oscillatory characteristics of metallic nanoparticles inside lipid nanotubes

Abstract

This study is concerned with the oscillatory behavior of metallic nanoparticles, and in particular silver and gold nanoparticles, inside lipid nanotubes (LNTs) using the continuum approximation along with the 6-12 Lennard-Jones (LJ) potential function. The nanoparticle is modeled as a dense sphere and the LNT is assumed to be comprised of six layers including two head groups, two intermediate layers and two tail groups. To evaluate van der Waals (vdW) interactions, analytical expressions are first derived through undertaking surface and volume integrals which are then validated by a fully numerical scheme based on the differential quadrature (DQ) technique. Using the actual force distribution between the two interacting molecules, the equation of motion is directly solved utilizing the Runge-Kutta numerical integration scheme to arrive at the time history of displacement and velocity of the inner core. Also, a semi-analytical expression incorporating both geometrical parameters and initial conditions is introduced for the precise evaluation of oscillation frequency. A comprehensive study is conducted to gain an insight into the influences of nanoparticle radius, LNT length, head and tail group thicknesses and initial conditions on the oscillatory behavior of the metallic nanoparticles inside LNTs. It is found that the escape velocity and oscillation frequency of silver nanoparticles are higher than those of gold ones. It is further shown that the oscillation frequency is less affected by the tail group thickness when compared to the head group thickness.