The development of artificial transmembrane channels that are capable of transporting ions, water and small molecules across cell membrane is crucial for applications in drug delivery and gene therapy. In this paper, we determine the interaction between ions and artificial channels in order to understand the mechanisms underlying the selection and transport of ions through the channels. Particularly, the concept of suction energy is employed to determine the interaction of ions (Na+, Cl−, Ca2＋, K+) and cylindrical and hourglass shaped channels made from polyethylene terephthalate (PET). Based on this concept, we find critical pore sizes for cylindrical and hourglass shaped channels that can be used for selective separation of positive charged ions. Further, we find that coating PET channel with different materials can reduce these values of the critical pore sizes. These results are also confirmed by molecular dynamics studies. The main contribution of this work is mathematical expressions for the interaction energy as a function of ion type, channel structure and size of the channel, and this method can be applied to study other pores with different shapes and sizes.