Mathematical modelling for equilibrium configurations of concentric gold nanoparticles

Nanotechnology is a promising research area, and it is believed that the unique properties of molecules at the nano-scale will benefit mankind especially in the medical exploration. Here we utilize an applied mathematical modelling to investigate spherical and cylindrical concentric structures of gold nanoparticles, with the aim of maximising the free space for which to improve amount of drug or gene to bind on the nanoparticle surfaces and deliver to the target cells. The energy between two gold molecules is modelled by the 6–12 Lennard-Jones potential function, and the total potential between two layers for such particles is calculated using the continuous approximation. On minimising the energy function, the radii for five layers for the concentric sphere and likewise for the cylinder are presented. Further, the equilibrium spacing between any two layers is predicted to lie in the range 2.94–2.96 Å, for both concentric structures. There are at present no experimental or simulation results for comparison with the theoretical equilibrium configurations for concentric gold nanoparticles predicted by this study.