“…An increase in EW results in the larger sulfonate-sulfonate separation, and thus hinders proton transport through hydrophilic channels (Allahyarov and Taylor, 2011). Theoretical and computational analyses, such as molecular dynamics (MD) simulations and ab initio simulations, have been used extensively to investigate proton transport properties including electroosmosis in Nafion membranes and thin films (Feng et al, 2012, Feng and Voth, 2011, Jorn et al, 2012, Petersen and Voth, 2006, Petersen et al, 2005, Tse et al, 2013, Seeliger et al, 2005, Spohr et al, 2002, Cui et al, 2007, Jang et al, 2004, Wang et al, 2011a, Karo et al, 2010, Knox and Voth, 2010, Komarov et al, 2013, Spohr, 2007, Mabuchi and Tokumasu, 2014, Wescott et al, 2006, Tuckerman et al, 1995, Eikerling et al, 2008, Kornyshev and Spohr, 2009, Choe et al, 2008, Yan et al, 2008, Aochi et al, 2016, Kurihara et al, 2017. However, extensive simulations using ab initio methods for a larger number of atoms, where systems reproduce nanostructured Nafion morphology and water domains with reliable statistics, have been limited because of the high computational cost of such simulations.…”