Proton Coulomb Blockade Effect Involving Covalent Oxygen-Hydrogen Bond Switching

Instead of the canonical Grotthuss mechanism, we show that a knock-on proton transport process is preferred between organic functional groups (e.g., -COOH and -OH) and adjacent water molecules in biological proton channel and synthetic nanopores through comprehensive quantum and classical molecular dynamics simulations. The knock-on process is accomplished by the switching of covalent $\mathrm{O}─\mathrm{H}$ bonds of the functional group under externally applied electric fields. The proton transport through the synthetic nanopore exhibits nonlinear current-voltage characteristics, suggesting an unprecedented proton Coulomb blockade effect. These findings not only enhance the understanding of proton transport in nanoconfined systems but also pave the way for the design of a variety of proton-based nanofluidic devices.

Figure 1

Proton transport in the hHv1 proton channel. (a) Atomic model of the hHv1 proton channel. The hHv1 channel is shown as ribbons, with pore-lining residues displayed in licorice. A few water molecules and hydronium ions (${\mathrm{H}}_3{\mathrm{O}}^{+}$) inside the channel are shown by the VDW representation. (b) Density profile of water along the channel pore ($z$ axis). (c) Snapshots from a QM/MM simulation illustrating the proton transport process along the water chain via the Grotthuss mechanism. The right panel shows a schematic of the Grotthuss mechanism. (d) Time evolution of the distances between hydrogen atoms and surrounding oxygen atoms [see the top left panel in (g) for definitions] that participate in the knock-on process of proton transfer. (e) Time evolution of the number of hydrogen atoms ($N_{\text{H}}$) bonded to the oxygen atom of the E119 side chain (O2) and the oxygen atoms of two adjacent water molecules (O1 and O3). (f) Charge transfer between the E119 side chain and its surroundings during the knock-on process. (g) Snapshots from a QM/MM simulation showing the knock-on process of proton transport. The right panel shows a schematic of the knock-on process.

Figure 2

Knock-on proton transport through functionalized synthetic nanopores. (a) Proton transport through a functionalized graphene nanopore. The right panel shows the top view of the GRA-4O-2OH graphene nanopore, terminated with four oxygen atoms (red spheres) and two hydroxyl groups (red and white spheres). (b) Schematic of the knock-on and Grotthuss processes. (c) Positions of hydrogen atoms of hydroxyl groups (H1 and H2) and a proton (H3) involved in the knock-on process. Note that many knock-on processes under an electric field of $1.3\mathrm{V}/\mathrm{nm}$, shown in different colors, are identified in the simulation trajectory. (d) Energy barriers of proton penetration through the nanopore via the Grotthuss and knock-on processes, calculated with the DFT-NEB method.

Figure 3

Voltage dependence of proton transport through synthetic nanopores. (a) Recorded current through the GRA-4O-2OH nanopore as a function of the electric field at different proton concentrations. (b),(c),(d) Recorded currents through an oxygen-terminated pore (GRA-6O), a hydroxyl-terminated pore (GRA-5O-OH) and a pristine pore (GRA) as a function of the electric field at a proton concentration of 1.1 M. In (a) and (b), the solid lines show the results obtained with Eq. (2), while in (c) and (d), the dashed lines indicate linear fitting to the simulation data. The error bars represent the standard deviations of four subtrajectories out of a complete MD trajectory.

Figure 4

The underlying mechanism for the proton CB effect. (a) Equivalent circuit for the nanopore system. An analogy to quantum dots (QDs) is used to describe the nanopore for proton penetration. (b) The top panel shows a proton accompanied by charging energy ($E_{\mathrm{elec}}$) approaching the nanopore. The bottom panel shows the energy barrier $E_{\mathrm{kc}}$ of the knock-on proton transport process involving the breaking and formation of $\mathrm{O}─\mathrm{H}$ covalent bonds. The green circle represents the charge at the nanopore. (c) Equivalent energy-level diagram for proton CB. When the energy gap ($E_{\mathrm{CB}}$) is higher than the thermal energy ($k_{\mathrm{B}}T$), proton conduction is suppressed (blocked state). A build-up in an electric field ($E_{\mathrm{EXT}}$) above $E_{\mathrm{CB}}$ allows for proton conduction (open state).