Equilibrium Configurations of Lipid Bilayer Membranes and Carbon Nanostructures

The present article concerns the continuum modelling of the mechanical behaviour and equilibrium shapes of two types of nano-scale objects: fluid lipid bilayer membranes and carbon nanostructures. A unified continuum model is used to handle four different case studies. Two of them consist in representing in analytic form cylindrical and axisymmetric equilibrium configurations of single-wall carbon nanotubes and fluid lipid bilayer membranes subjected to uniform hydrostatic pressure. The third one is concerned with determination of possible shapes of junctions between a single-wall carbon nanotube and a flat graphene sheet or another single-wall carbon nanotube. The last one deals with the mechanical behaviour of closed fluid lipid bilayer membranes (vesicles) adhering onto a flat homogeneous rigid substrate subjected to micro-injection and uniform hydrostatic pressure.