Fig. 8.

Qualitative free energy profiles along the proton conducting channel. The initial and final states of the proton (i.e., the centers of positive charge for these two states) are at X=0, and X=L, respectively. The two curves $G_{\mathrm{p}}^{\mathrm{d}}(\mathrm{X})\text{and}{G}_{\mathrm{p}}^{\mathrm{a}}(\mathrm{X})$ correspond to electron Oxidized (O) and Reduced (R) states, respectively. $\mathrm{\Delta }{G}_e^0\text{and}\mathrm{\Delta }{G}_p^0$ are the free energies of electron and proton (uphill) transfer, respectively, in the uncoupled reaction. For the slow proton diffusion case, the effective potential is the lower of the two curves for a given X. $\mathrm{\Delta }{G}_p^{†}$ is the activation free energy for such a reaction. Figure reprinted with permission from Ref. 42. Copyright 2003 World Scientific.