Fig. 3. Mechanism of the potential distribution at atomically-thin graphene interfaces.
a Vb0 responses as a function of Vt applied for multilayer graphene with various numbers of layers as indicated in the figure. Both reservoirs were filled with 0.01 M KCl. The empty symbols are the experimental data. The solid lines are the predictions using Vb0 = Vt/[1 + (εS/εg)·(d/dHK+)] with different εS as the fitting parameters. For simplicity, only the fittings at positive Vt are shown. Inset shows the best εS being used, with the error bars representing the uncertainty. Note that the effective thickness of monolayer graphene is assumed zero as defined in the text. Therefore, no εS is needed to fit the monolayer graphene data. The arrow indicates the dielectric constant ~80 of bulk water. b The decay of Ib0 and Vb0 with increasing number of graphene layers. Error bars are S.T.D., estimated from at least three different devices in each thickness. c Schematic of the potential drop Φ at the top and bottom interfaces, in the case when Ib = 0. For simplicity, only the Stern layers are shown, with their boundaries indicated by the green dashed lines. The slopes of Φ in the two Stern layers are equal (in their absolute values) and are different than that in graphite, depending on the ratio of dielectric constant εS/εg. The purple and green balls represent ions of different hydration sizes, while the dark gray balls represent carbon atoms. The sizes of the blurred blue spheres around the ions indicate the relative sizes of hydrated ions.