Statistical mechanics of a polymer chain attached to the interface of a cone-shaped channel

A polymer chain confined in nano-scale geometry has been used to investigate the underlying mechanism of Nuclear Pore Complex (NPC), where transport of cargoes is directional. It was shown here that depending on the solvent quality (good or poor) across the channel, a polymer chain can be either inside or outside the channel or both. Exact results based on the short chain revealed that a slight variation in the solvent quality can drag polymer chain inside the pore and {\it vice versa} similar to one seen in NPC. Furthermore, we also report the absence of crystalline (highly dense) state when the pore-size is less than the certain value, which may have potential application in packaging of DNA inside the preformed viral proheads.