The hydrated structures of the proton exchange membranes were theoretically investigated using long-range corrected density functional theory [1,2] to make clear why perfluorinated polymer membrane Nafion is superior to other membranes in the proton conductivity at low humidity and consequently to reveal the proton conductance mechanism in low-humidity membranes, which are significant for anti-freezing. First, we compared the hydration structures of Nafion and multiblock sulfonated poly(arylene ether sulfone)s (SPE) hydrocarbon membranes for various hydration numbers. As a result, we found the relay mechanism of not protons but protonated water clusters between the sulfonic acid groups may contribute to the high proton conductivity of Nafion with less-hydrated sulfonic acid groups. In the relay mechanism (Fig.), protonated water clusters are relayed by the side chains through the doubly-hydrated sulfonic acid groups. We also examined the infrared (IR) spectrum calculations of Nafion to figure out its hydration structures at low humidity [4]. Consequently, we found that the experimental IR spectrum behaviour for various humidity conditions strongly supports the relay mechanism, because it is consistent only with the IR spectrum behaviour of the doubly-hydrated sulfonic acid groups, in which protons are detached beforehand. Based on the relay mechanism, we have also examined the proton conductance of state-of-the-art block co-polymer membranes that provide high proton conductance comparable to that of Nafion [5]: Sulfonated poly ketone (SPK) [6] and Sulfonated poly (p-phenylene) (SPP) [7] membranes. As a result, we found that these membranes have similar detachment abilities of protonated water clusters to that of Nafion, though they give slightly lower proton detachment abilities than that of Nafion. H. Iikura, T. Tsuneda, T. Yanai and K. Hirao, J. Chem. Phys. 115, 3540 (2001).T. Tsuneda, Density Functional Theory in Quantum Chemistry (Springer), (2014).R. K. Singh, T. Tsuneda, K. Miyatake and M. Watanabe, Chem. Phys. Lett. 608, 11 (2014).R. K. Singh, K. Kunimatsu, K. Miyatake, and T. Tsuneda, submitted.R. K. Singh, K. Miyatake, and T. Tsuneda, in preparation.T. Miyahara, T. Hayano, S. Matsuno, M. Watanabe, and K. Miyatake, ACS Appl. Mater. Interfaces 4, 2881 (2012).J. Miyake, T. Mochizuki and K. Miyatake, ACS Macro Lett. 4, 750 (2015). Figure 1