The hydrated structures of the proton exchange membranes were theoretically investigated using long-range corrected density functional theory to make clear why perfluorinated polymer membrane Nafion is superior to other membranes in the proton conductivity at low humidity. For exploring the possibility of the proton conductance in the vehicle mechanism with low hydration numbers, we examined the relay model of protonated water clusters between the sulfonic acid groups in Nafion and concluded that this relay model may contribute to the high proton conductivity of Nafion with less-hydrated sulfonic acid groups. (c) 2014 Elsevier B.V. All rights reserved.