Nitrogen-Mediated Graphene Oxide Enables Highly Efficient Proton Transfer

Two-dimensional (2D) graphene and graphene oxide (GO) offer great potential as a new type of cost-efficient proton-exchange membranes (PEM) for electrochemical devices. However, fundamental issues of proton transfer mechanism via 2D membranes are unclear and the transfer barrier for perfect graphene are too high for practical application. Using ab initio molecular dynamic simulations, we screened the proton transfer barrier for different un-doped and nitrogen doped GO membranes, and clarified the corresponding transfer mechanisms. More significantly, we further identify that N-mediated GO can be built into a highly efficient PEM with a proton transfer rate of seven orders of magnitude higher than an un-doped case via. a proton relay mechanism between a ketone-like oxygen and a pyridine-like nitrogen across the vacancy site. The N-doped 2D GO is also impermeable to small molecules, and hence a highly efficient PEM for practical applications.


GO
The structures of different GOs are displayed in Figure S1. Five types of GOs are considered as shown in Figure S1 Figure S2. It can be seen from this figure that the most stable structures under oxygen enrichment are V1-O2 for mono-vacancy, V2-O3 for di-vacancy, T1-V4-O4 for the first type of tetra-vacancy and T2-V4-O4 for the second type of tetra-vacancy.
These structures are checked for proton transfer barriers as shown in Figure 3 of main text. T2-V4-O3 is also checked as the formation energy of 4 th O of this structure is not exothermic much.
For perfect graphene, the oxidization energy is endothermic, which is not considered for further investigation.
The structures of different N-doped GO are displayed in Figure S3. The N doping energy around vacancy is calculated as: 3 where i is the number of doped N atoms, ΔEd(iN) is the N doping energy, E(iN) is the total energy of N-doped graphene. E0 is the total energy of un-doped graphene, E(C) is the total energy per atom of perfect graphene. E(N2) is the total energy of an isolated N2 molecule. The doping energies for graphitic N and pyridinic N are shown in Figure S4, which indicates that the pyridinic N (V2-pN) is much more stable than graphitic N (V2-gN) around vacancy. Hence, only pyridinic N configurations are investigated for oxidization. Oxygen atoms are added to the vacancies until all the dangling C atoms are fully occupied. The oxidization energies are also shown in Figure S4. Further oxidization of oxidized C site is rather difficult as shown in Figure   S10 in the following. Hence, the most stable N-doped GO structures under oxygen enrichment are V2-N1O2, T1-V4-N2O2, T2-V4-N1O2 and T2-V4-N1O3, respectively. The corresponding proton transfer barriers are calculated and shown in Figure 4 in main text. Note here that the "V2" structures are actually mono-vacancies because one vacancy site is occupied by N dopant.

SI2. Proton Transfer Profiles for Perfect Graphene
The proton transfer free energy profiles for a perfect single layer graphene were also checked and shown in Figure S5. The proton is assumed to approach two possible pathways, via the center of the hexatomic ring (PG-h) or via attached to a carbon atom site (PG-C) of perfect graphene. The free energy barriers are large for both PG-h (>4.0 eV) and PG-C (>3.0 eV) cases under water solution. This also indicates that the PG-C pathway is more favorable. The proton transfer barrier for PG-h was also checked by the climbing image nudged elastic band (CI-NEB) calculation using a hydronium ion for a proton, and the results are shown in Figure S6

SI4. Pathways for Proton Transport via V2-N1O2 Structure
For the V2-N1O2 structure, the two ketone-like oxygens toward two opposite sides of the graphene plane and the doped nitrogen is in the plane as shown Figure 2(f) of the main text.
However, the proton does not directly transfer to the N site as expected. Here, the details of the most favorable pathway for proton transfer via V2-N1O2 structure is shown in Figure S8. As shown in this figure, the proton is a hydronium ion when it is far away from the membrane surface. As the hydronium ion approaching the surface, the proton first relayed from the hydronium ion to the ketone-like oxygen in one side of the surface. Then, this proton continues 12 to relay from the ketone-like oxygen site to N site which is in the surface plane. Due to the symmetry of this structure, the proton transfer to the opposite side of the membrane is the reverse process, i.e. the proton on the N site would first relay to the ketone-like oxygen and then transfer to the solution in the opposite site. The attachment and detachment barriers for MV-1N2O(k) are 0.31 eV and 0.32 eV, respectively. This is also shown in main text. Figure S8. Proton transport free energy profile for proton approaching the N site of the V2-N1O2 structure. The geometry structures of some important points along the transport pathway are also presented. Other water molecules are removed to make the structures clear. Actually the proton relays between water molecules from water solution to the surface of the membrane.

Structure
The barriers for molecule crossover are checked for the T1-V4-N2O2H1 structure. The H2/O2 crossover barriers were calculated and presented in Figure S9. It can be seen that the barriers are higher than 2.36 eV and 8.0 eV for H2 and O2, respectively. The O2 molecule would decompose after the distance is smaller than 1.0 Angstrom. Therefore, the molecules are almost impossible to crossover the membranes with such a small vacancy.
14 Figure S9. H2/O2 crossover free energy profile for the T1-V4-N2O2H1 structure. The distance between the center of molecule and center of the two N atoms in the surface is constraint.

Structure
For symmetric structures investigated, the proton transfer barriers are for proton transfer in solution of one side attaching to the target sites in the membrane surface. The corresponding barriers from opposite is not calculated because it should be the same due to the symmetry. If we extrapolate the complete transfer process, the barriers should be symmetrical for an attached proton to detach from the other side of the membrane. The figures for the complete permeation process for T2-V4-N1O2 structure are shown in Figure S10, from which we can see that the proton is easy to be trapped to the N site due to the large detachment barrier. Figure S10. Proton transport free energy profile and figures for the complete permeation process for T2-V4-N1O2 structure. The solid line is for calculated barrier, and the dash line is extrapolated to the other side due to the symmetry. The "d" is distance between proton and N atom.

SI7. Discussions for formation of V2-N1O2 structure
As indicated by previous study, the pyridinic N doped mono-vacancy is the most popular structures observed in experiments. 1 In the present study, this structure corresponding to V2-pN.
Under an environment with O2, the V2-pN structure can be oxidized to a cis-V2-N1O2 structure with a low barrier of 0.40 eV as shown in Figure S11. The two O atoms of the formed cis-V2-N1O2 structure are in the same side of graphene, which is thermodynamically less stable than the structure with two O atoms in opposite side trans-V2-N1O2 structure. The cis-V2-N1O2 structure will transfer to the trans-V2-N1O2 structure with a barrier about 0.68 eV as shown in Figure S12. And the total energy of trans-V2-N1O2 structure is 0.60 eV lower than cis-V2-N1O2 structure. However, further oxidization of trans-V2-N1O2 structure is rather difficult as shown in Figure S11. If another O2 approaching the highlighted C site of the V2-N1O2 structure, one CO2 is formed with a high barrier of about 4.0 eV. Hence, the V2-N1O2 structure is rather stable. Figure S11. The oxidization energies barriers for V2-pN and V2-N1O2 structures. The distance along horizontal axis is the distance between the center of an O2 molecule and the highlighted C atom (for V2-N1O2 structure) / center of the highlighted two C atoms (for V2-pN structure).