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been given and plotted: the open cell potential 0 V, the equilibrium po-
tential 1.23 V, and the lowest potential. Under the lowest potential, the
free energy changes of all of the elementary steps are negative or zero,
which are depend on the specific nanomaterials. The difference between
the lowest potential and the equilibrium (1.23 V) is termed as the theo-
retical overpotential, which is an important indicator to evaluate the
electrochemical catalytic activity of materials. We found that the lowest
potential of H 2 O splitting on the outside and inside of TiO 2 NTs is 1.68
and 2.23 V, respectively, and that of inside NTAs is 2.36 V, which all
correspond to the first step on the three kinds of nanostructures. Based
on the thermodynamic point of view from the Gibbs free analysis, the
rate-limiting step is to obtain the OH from the dissociation of the first
H 2 O on both TiO 2 NTs and NTAs. The overpotential of H 2 O splitting on
the outside and inside of TiO 2 NTs is 0.45 and 1.0 V, respectively and that
of inside NTAs is 1.13 V. We found that the overpotential of H 2 O splitting
on the outside of NTs is nearly the same as that of RuO 2 (0.37 eV), 93 which
is one of the best known inorganic catalysts for H 2 O splitting or O 2
evolution. While for H 2 O splitting on the inside of either TiO 2 NTs or
NTAs, the overpotential is much larger than that on the outside of NTs,
which is even larger than that on TiO 2 (110) surface. 90,91,94 The large
overpotential of H 2 O splitting on the inside of TiO 2 NTs or NTAs are
probably caused by the small diameter nanotubes. The effect of tube
diameter as well as defects and dopants on the performance of H 2 O
splitting needs to be investigated.
3.3.2 Water splitting on doped TiO 2 nanotube arrays. It was found
that the overpotentials for water splitting on pure TiO 2 NTAs are relatively
higher. In order to reduce the overpotentials, the catalytic properties of
TiO 2 NTAs are tuned by N, F, Pt momodoping or codoping. The calcu-
lated free energies of the intermediates on the N-doped, F-doped, Pt-
deposited, Pt loaded N-doped and Pt loaded F-doped TiO 2 NTAs (denoted
as N-TNTAs, F-TNTAs, Pt/TNTAs, Pt/N-TNTAs and Pt/F-TNTAs, respect-
ively) under different applied potentials are presented in Fig. 22. The
open cell and equilibrium potential is still 0 and 1.23 V, respectively. It is
observed that at the open cell potential (0 V) the free energy change of
every step is positive and uphill for all the doped TiO 2 NTAs. Even
the lower potential threshold (1.23 V) is not sucient to make all the
elementary steps thermodynamically facile. Note that although the
Pt/F-TNTAs (Fig. 22e) may be considered to split water at 1.23 V better,
the second and the third steps give rise to free energy differences and the
trend of free energy still goes uphill. The lowest potential and theoretical
overpotential is 2.31 and 1.08 V on N-TNTAs (Fig. 22a), respectively. The
overpotential is nearly the same as that on the pristine NTAs (1.13 V). It is
seen that the rate-determining step with the highest free energy change is
the third step for N-TNTAs. Nevertheless, it is the first step for the pris-
tine NTAs. Although N-doping increases the free energy of the third step
reaction (from 1.63 to 2.31 eV), N-doping reduces the free energy of the
dissociation of the first H 2 O (from 2.36 to 0.19 eV). In thecase of F-TNTAs
(Fig. 22b), it is apparent that the oxidation will be prohibited by the
 
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