SOME NOTES ON LOW-DIMENSIONAL ELASTIC THEORIES OF BIO- AND NANO-STRUCTURES

Abstract

The shapes of DNA, carbon nanotube (CNT) and vesicle are determined by the minimum of their elastic energy. Two central results about the low-dimensional elastic structure are reported here. Firstly, if the energy density of a one-dimensional structure is only related to its curvature, we generally find that a helix solution with the helix angle θ = ±π/4 will have zero total energy. Secondly, with the fixed length and radii, the helical multi-walled carbon nanotubes (MWNTs) and DNA will have the lowest energy when the helix angle θ = ±π/3.