Semimicroscopic theories are developed for the electronic work function and potential of zero charge (PZC) at graphene basal and edge planes, as well as metal/graphene (G/M) heterostructures. Our earlier curvature-dependent theory for the electrochemical work function (EWF) enables us to account for complexities arising from lower-dimensional graphene, its interaction with various metals, and dipolar solvents at the surface. The EWF directly links to PZC and the interfacial electron affinity ratio (Aad). Theory predicts the outer and inner WFs of SWCNTs, consistent with experimental values. The graphene edge WF is ∼2.3 times lower than the basal plane. G/M heterostructures exhibit WF reductions by a factor of 0.67–0.81 relative to metals and 0.7–0.9 relative to graphene. Surprisingly, the graphene edge PZC (−2.95 V) is far more negative than the basal plane (−0.18 V). Graphene coating shifts metal PZCs negatively, from −0.44 V for G/Pt(111) to −1.60 V for G/Cu(111). Dense G/M heterostructures display anomalous dual PZCs and amphoteric double layers, with metal-dependent PZC shifts from 0.98 V (for Pt) to 1.65 V (for Ni). In contrast, a sparse (or isolated) graphene flake on metal behaves as a surface composed of graphene basal and metal, producing smaller PZC shifts (10 mV for Ag to 720 mV for Pt). Finally, the theory captures the experimental data for the work functions and PZC for graphene and G/M heterostructures.
Mahajan et al. (Thu,) studied this question.