Role Of Non-Uniform Confinement In Shape Transitions Of Semi-Stiff Polymers

New types of nanostructures are constantly being developed synthetically but are also found in biological systems. Specific examples include the production of carbon nanocones as well as the conical core in some viruses. Such conical structures can be used to investigate the role of non-uniform confinement on the stability of e.g. toroidal structures formed by semi-stiff circular polymers, such as DNA. In this communication we are interested in the principal features of the compaction process. Using an external field and a conical confinement we observe several distinct shape transitions from a circle-like shape to several toroidal-like loops for both a two-dimensional and a three-dimensional system. The thermodynamic stability of these toroidal-like structures was investigated by evaluating their relative free energies using Monte Carlo simulations in the Extended Ensemble in the case of a two-dimensional system and by observing a hysteresis of the compaction-extension curve for the three-dimensional case.