We used the 1c24C system to characterize PT using our DP, where the added proton was always on one side of the DSG. The inclusion of a single proton in 1c24C enabled a direct comparison of D s in DSG versus SSG. PT was measured by tracking the center of excess charge (CEC), a method we developed to locate protons in graphanol . A detailed explanation of CEC in provided in the Methods section. We measured proton self-diffusion coefficients (D s ) by calculating the mean-square displacements (MSD) of the CEC for any given DP-MD simulation and relating the MSD to D s through the Einstein relation, where t is the simulation time, d is the number of dimensions (d = 2 in this case), and r CEC (t) is the location of the CEC at time t. We used the DP for DSG to measure D s in DSG and compared it to that computed for SSG . We set a fixed temperature of T = 800 K. There are two reasons for studying the system at such a high temperature: (1) sampling of more proton hopping events in a given simulation time and (2) evaluating the thermal stability of charged DSG. Our previous work with charged SSG showed that a poorly trained DP caused spurious H 2 O dissociation, where the CEC breaks away from the graphane layer. This phenomenon regularly occurred at high temperatures (≥ 800 K). We performed 50 independent DP-MD N V T -MD simulations at T = 800 K to collect sufficient data to provide good statistics. The production run for each simulation was for 250 ps (0.25 fs time steps) after being equilibrated for 20 ps at T = 800 K. Results for SSG from Achar et al. showed that an MD simulation timescale of 250 ps was sufficient to observe PT diffusion. There were no instabilities in any of these simulations. This was tested by calculating the root mean squared displacement (RMSD) of O atoms in the last MD step frame with respect to the first MD step frame. We found the the RMSD over all independent runs to be 0.53 ± 0.09 Å, which suggests that the O atoms did not detach from the graphane layer. Trajectories from these simulations were used to compute D s of the CEC to measure PT in DSG at T = 800 K. Our estimate of D s was 3.0 × 10 -8 ± 1.48 × 10 -8 m 2 /s, which is statistically indistinguishable from the SSG estimate of 3.3 × 10 -8 ± 1.5 × 10 -8 m 2 /s, of Achar et al. . The similarity in PT self-diffusivities means that inclusion of an additional layer of functionalization, as in DSG, does not impact value of the diffusivity or the mechanism of PT.