CVD graphene synthesis

We used graphene having a grain size of ~100 μm (ref. 54) grown on copper foils by atmospheric pressure CVD54,55. The graphene was transferred using spin coating of poly(methyl methacrylate) (PMMA) followed by copper etching in a FeCl 3 solution and PMMA removal in acetone. The transfer was made onto clean fused silica substrates (ISP Optics, 1” diameter, QI-W-25-1, flatness 1 wave per inch at 633 nm) to fill ~1 cm2 with a single layer. Following annealing in a flow of 4% H 2 in Ar for 30 min at 300 °C, vibrational sum-frequency generation spectra showed no evidence for CH stretches56. Similar to the finding of water layers between graphene and mica by atomic force microscopy57, there is probably water located between the graphene samples and the fused silica substrates used here.

Scanning electron microscopy

SEM images were collected from the center of the graphene film. Graphene on an optical window was imaged using a Hitachi S-4800 scanning electron microscope (SEM) operating at 2 kV with a probing current of 10 μA and an Everhart–Thornley detector. Copper tape was used to reduce charging effects. Individual images were taken at × 1,200 magnification with 1,280 × 960 resolution. An array of 5 × 5 images (529 × 397 μm, pixel size 176 nm) was stitched together using Adobe Illustrator. Automatic brightness and contrast adjustment on each frame was carried out using the ‘auto adjust’ feature in Preview (Apple, Inc.). No other postedit feature or change was applied.

Aberration-corrected scanning transmission electron microscopy

To confirm the single-layer nature of graphene synthesized using the CVD method13, atomic-resolution STEM imaging was performed at room temperature with an aberration-corrected Nion UltraSTEM-100 (ref. 58) equipped with a cold field-emission electron source. The microscope was operated at 60 kV, which is below the knock-on damage threshold for graphene. The CVD-prepared graphene specimens were transferred to a SiN-supported silicon microchip transmission electron microscopy grid. Before STEM imaging, the specimen was heated at 160 °C in vacuum (10−5 torr) for 8 h to remove surface contamination. Following heating in vacuum, the specimen was immediately transferred to the UltraSTEM for ADF STEM imaging. The surface of the graphene still retains residual PMMA that was used in the transfer processes to the transmission electron microscopy grid as shown in Supplementary Fig. 26; however, there are large areas that are devoid of the PMMA, which made it feasible to directly image the lattice structure and confirm the single-layer nature using atomic-resolution STEM imaging. The images were filtered using a smoothing function in Digital Micrograph, and the contrast and brightness were adjusted to enhance the contrast of the graphene.

Aqueous solution and substrate preparation

The aqueous solutions were prepared with Millipore water, prepared the day before an experiment and left open to air overnight to equilibrate with atmospheric CO 2 and NaCl (Alfa Aesar, 99+%). The concentration of NaCl was confirmed using a conductivity meter (Fisher Traceable Conductivity and TDS meter, Fisher Scientific). Solution pH was adjusted with minimum amounts of dilute solutions of ~1 M NaOH (Sigma-Aldrich, 99.99%) and HCl (EMD ACS grade). The pH-jump experiments were carried out using a fused silica hemisphere (ISP Optics, 1” diameter, QU-HS-25) pressed against either a fused silica window (ISP Optics, 1” diameter, QI-W-25-1) or a CVD-prepared graphene film transferred onto a silica window in an experimental setup previously reported13,56. The hemisphere and the fused silica window were cleaned before experiments by first treating the surface of interest with NoChromix (Godax Laboratories) for 1 h, rinsing with Millipore water and then storing in Millipore water overnight for SHG experiments the next day. On the day of the experiment, the bare fused silica window and hemisphere were sonicated in methanol for 6 min, dried in a 110 °C oven for 30 min, oxygen plasma cleaned (Harric Plasma) on high for 30 s, and then stored in Millipore water until the experiment. The graphene samples were not cleaned with this procedure, but were instead cleaned by flushing with ~2 l of Millipore water before each experiment. Supplementary Note 9 describes the graphene characterization and analysis by Raman and ultraviolet–visible spectroscopy (Supplementary Fig. 16) prior and after the pH-jump experiments.

Flow system and flow cell

As shown in Fig. 1a, the graphene-on-fused silica sample or the silica window were clamped face down against a Viton O-ring on the Teflon flow cell13,56 so that the surface of interest was in contact with the aqueous phase. The fused silica hemisphere was then clamped on top of the window with a Millipore water layer in between in order to minimize the change of refractive index between the phases and to avoid the use of an index-matching fluid. Throughout the duration of the experiment, it was also necessary to maintain a ring of Millipore water around the bottom of the hemisphere in order to avoid evaporation of the sandwiched water layer. All of the experiments were completed with a 0.9 ml s−1 flow using variable flow peristaltic pumps as previously reported13,56. Using the flow system depicted in Fig. 1a, the pumps were switched to pull solutions from two different reservoirs. For the experiments reported here (excluding pKa experiments, see Supplementary Note 2), the two reservoirs contained 1 mM NaCl Millipore solutions adjusted to either pH 3 or 10. At the start and end of each pH-jump experiment, a 1 mM NaCl aqueous solution adjusted to pH 7 was pumped through the system, and the SHG signal was collected until it reached a steady state. It is assumed that the steady-state conditions were reached once the SHG signal remained at a stable intensity for a minimum of 300 s. After the system reached the steady state at pH 7, the flow was switched back and forth between the pH 3 and 10 aqueous solutions, each time allowing the SHG signal to reach steady state before switching to the next pH. After several pH 3 to 10 and pH 10 to 3 jumps were completed, the pH was adjusted back to pH 7, and the SHG signal was collected until the steady state was reached one last time. None of the liquid flow effects, reported for fused silica/water interfaces subjected to high shear rates59, were observed under the creeping flow conditions used here. Supplementary Note 10 and Supplementary Table 2 assess the flow dynamics in the cell.

Laser and detection system

A detailed description of our SHG setup has been described previously60,61,62,63. Briefly, we use a regeneratively amplified Ti:sapphire system (Hurricane, Spectra Physics) that operates at a kHz repetition rate to produce 120 fs pulses to pump an optical parametric amplifier (OPA-CF, Spectra Physics) tuned to produce 600 nm light. After exiting the OPA, the beam is then directed through a variable density filter to attenuate the pulse energy to either 0.3±0.05 μJ per pulse for bare silica studies or 0.15±0.05 μJ per pulse for graphene studies. The pulse energy used for the graphene films equates to a power density of 2.1(7) × 104 μJ cm−2 per pulse with a 30 μm focal spot, which is well below the damage threshold of graphene as previously reported13,56. At an angle just below total internal reflection, the p-polarized attenuated fundamental light is then directed through a fused silica hemisphere and focused at the graphene/water or silica/water interface. The reflected fundamental and second harmonic lights are directed through a Schott filter and a monochromator to remove any contributions at the fundamental frequency before amplification with a photomultiplier tube and detection using a gated single-photon counting system. Correct power dependencies and spectral responses are verified regularly, the SHG responses are well polarized, and sample damage does not occur13,56. Given that the SHG jump rates are independent of the mean stream velocity (Supplementary Note 1), we are confident that the acid–base reactions occurring at the fused silica surface are not mass transfer limited. Ultraviolet–visible and Raman spectra indicate that the samples are resistant to acid–base cycling under the conditions employed here.

Computer simulations

First-principles periodic DFT calculations were carried out to determine the lowest energy interfacial water/graphene, water/graphene/water/silica structures and the activation barriers for proton diffusion through these interfaces using the Vienna Ab Initio Simulation Package64,65. In the DFT calculations, the reaction systems were modelled by optimizing a water phase above and below a single-graphene sheet. The simulations were carried out in a 5 × 5 supercell comprised of 50 carbon atoms, extended infinitively in the x and y dimensions. A 15 Å gap was inserted between the graphene layer perpendicular to the surface. The gap was subsequently filled with enough water molecules to match the overall density of water at 1.0 × 103 kg m−3. The initial simulations were carried out with water on both sides of the graphene layer. The lower SiO 2 substrate was initially simplified by using additional water. Subsequent calculations were carried out with more realistic slabs comprised of water/graphene/water/SiO 2 substrates. The reaction rates and mechanisms of proton transfer through the graphene were described in the framework of transition state theory and within the harmonic approximation, which is robust for systems of high densities.

All of the calculations were carried out within the generalized gradient approximation using Perdew–Burke–Ernzerhof functional66 to treat exchange and correlation gradient corrections and projector augmented wave pseudopotentials67 to describe the electron–ion interactions. Plane wave basis sets with a cutoff energy of 400 eV were used to solve the Kohn–Sham equations for calculations for systems without water. Calculations for systems that include water solvation were carried out with cutoff energies for C and O of 283 eV. The surface Brillouin zone was sampled using a Monkhorst–Pack mesh of 3 × 3 × 1. All electronic energies were converged to within a tolerance of 1 × 10−5 eV. All of the atoms were allowed to relax in the geometry optimizations until the forces on each atom were <0.03 eV Å−1. Spin polarization was examined for all of the systems explored and applied when needed. Transition states were isolated using the nudged elastic band method44,45 together with the dimer method68. The nudged elastic band method was used to provide an initial transition state structure that was used in the subsequent dimer simulations to isolate the transition state. The reaction barrier was defined as the energy difference between the transition state and the reaction state minimum. The intrinsic barrier is defined as the energy gap between a transition state and its immediate reaction state. Given the importance of surface relaxation in atomically defected graphene layers69, all of our calculations on the single, di and quad carbon vacancy sites and the oxygen-terminated sites explicitly modeled surface relaxation (Supplementary Note 11 and Supplementary Figs 17–19).

The ReaxFF simulations were performed using the stand-alone ReaxFF implementation to study proton transfer through pristine graphene and graphene with di and quad vacancies. We then compared with results from long ab initio MD to validate predictions of force field in describing water/graphene systems (Supplementary Note 12 and Supplementary Fig. 20). In our simulations, we used a (6 × 6) periodic graphene sheet with water molecules placed in random configurations on either side of the graphene sheet. The dimensions of the simulation cell are 15.01 × 17.83 Å parallel to the sheet and 30 Å in the direction perpendicular to the sheet. All MD simulations have been performed in the canonical (NVT, constant number of atoms (N), constant volume (V) and constant temperature (T)) ensemble, with a time step of 0.25 fs using the Berendsen thermostat with a coupling time constant of 100 fs to control temperature of the entire system. To obtain the density plots in Fig. 3, we first divided the simulation cell into a mesh of cubic boxes with dimensions (0.30 × 0.30 × 0.30 Å). We then counted the number of times a particular atom type (for example, oxygen) was located in each of the grids through the entire length of simulation and normalized these numbers by the highest count recorded in any of the grids. We used these normalized values to obtain the resulting density plots in Fig. 3. The ReaxFF results reproduce the DFT results, described well in further detail in Supplementary Note 13 and Supplementary Figs 13 and 21–25.