Proton exchange membrane fuel cells enable clean and efficient energy, with many already commercially available. The comparatively low proton conductivity in the out-of-plane direction in GO membranes is problematic when considering fuel cell applications . Despite providing extra proton conducting sites, small molecule and polymer intercalators in these membranes are unable to permanently exist in interlayers due to weak interactions and ion transport inhibition from irregular conformation inside interlayers. Although intercalators are primarily designed to possess proton donor groups, protons hop among donors and acceptors along the hydrogen bond according to the Grotthuss mechanism . Chemical functionalization of GO membranes enhance water retention ability but leads to a substantial loss in mechanical strength, an increase in fuel crossover, and interlayer proton conducting sites that cannot sustain continuous proton transport due to a non-uniform distribution of epoxy and hydroxyl groups . Recently, a sulphate ion-intercalated 3D GO (3DSGO) membrane showed the highest proton conductivity and power density among all previously reported GO-based membranes . Given that the structural arrangement in 3DSGO is like that of Nafion, it may be possible to induce a permanent structural change in 3DSGO by the application of a strong electric field. Synthesis of a structurally modified 3DSGO membrane (or 'Graphenion' membrane) may contribute to understanding water percolation and proton transfer dynamics in membrane materials that have low water uptake and fast proton transfer. To this end, the method of thermodynamic integration can be used to describe the difference in Helmholtz free energies between a membrane with and without Coulomb interactions: