To test whether these small energy barriers are special cases for Pt surface or general phe- nomena on different metallic surfaces, the minimum energy path of proton transfer from hydronium to O* atom is also calculated on Au, Cu, Ni and Al (111) surfaces. The results of reaction energy and activation energy are listed in Table 4.6, where the stability of O∗ relative to OH∗is also calculated, defined as the energy changesδEO∗→OH∗of the following
reaction:
O∗+1
2H2→OH
∗ (4.17)
In Table 4.6, there is a clear tendency that when the stability of O* relative to OH* increases as δEO∗→OH∗ becomes more positive, both the reaction energies and activation
energies of the corresponding PCET also become more positive. On Au (111) surface, there is a large negative reaction energy and almost zero activation energy for proton transfer to O∗, while on Al (111) surface, the activation energy is relatively high. From the analysis of minimum energy path, it shows that most of the activation energies on Al, Ni and Pt come from the barrier to move O∗atom from fcc hollow site to bridge site at the transition state, instead of the proton transfer process inside the hydrogen bond network. Furthermore, even for Al the activation energy is only 0.3 eV larger than the reaction energy. So it is suitable to use the positive reaction energy as the approximate value of the activation energy in PCET, as long as the proton (hydronium) is close to the electrode surface.
However, as mentioned above, these DFT+NEB studies only reveal the dynamics of PCET near the electrode surface; a full PCET path is completed if we also consider how the proton is transferred from hydronium in the bulk electrolyte to hydronium near the surface.
Table 4.6: Reaction energy δE and reaction energy Ea of PCET to O∗ near Au,
Ni, Pt, Cu and Al (111) surface by using the configuration shown in Fig. 4.12 (c)
(H3O(H2O)2+O∗→OH∗+(H2O)3). δEO∗→OH∗ is the reaction energy of Eq. 4.17.
δE [eV] Ea[eV] δE (O∗+12H2→OH∗)[eV]
Al 0.10 0.39 1.05
Ni 0.03 0.23 -0.20
Pt 0.20 0.24 -0.52
Cu -0.81 0.00 -0.79
Au -1.00 0.04 -1.34
Figure 4.16: Reaction path of proton-coupled electron transfer (PCET) A∗ + H+ + e−→
AH∗. Here QPT is the activation free energy for proton transferred from the hydronium in
the bulk electrolyte to the hydronium near electrode surface;δG is the reaction free energy
of the whole reaction; H+∗means proton is in the hydronium close to the electrode surface; β is symmetric factor and usuallyβ ≈ 12[7, 78, 79, 80].
Usually this process requires excess energy, because the solvation field surrounding this hydronium would change and the electric field applied on this hydronium also changes. When electrode potential U increases, such excess energy would also increase, because more positive U results from more positive excess charges on the electrode surface, which would increase the repulsive energy between hydronium and electrode surface. So here we propose a hypothesis of PCET dynamics, as shown in Fig. 4.16: when proton is transferred from the hydronium in the bulk electrolyte to the hydronium near electrode surface, the activation free energy QPTchanges with electrode potential U as the following equation
QPT=β(U−U0)e (4.18)
where U0 is the electrode potential at which QPT = 0, and β is called symmetry factor,
defined in Section 2.2.3. For most cases in experiments, β ≈ 12[7, 78, 79, 80]. Then the proton is transferred to surface adsorbates A∗ and meet the electron from the electrode. According to the above calculations and discussions, if this step is down-hill in free energy, there is no extra activation free energy; otherwise, the extra activation free energy equals the total free energy difference in this step. Thus, the total activation energy of whole PCET can be summarized as
Q = QPT=β(U−U0)e if δG<QPT
= δG=δG0+ (U−U0)e otherwise (4.19)
BecauseδG can be negative at low U (high overpotential) and positive at high U (low
overpotential), the change of Q can have different linear relations with the change of U : δQ =βδU e at low U butδQ =δU e at high U . For electrochemical ORR, the reaction rate
ofδG as Q in Nøskov’s model is a good approximation[94].
However, for the activation free energy of PCET at low U , the exact physical mean-
ing of β is unclear. There are two possible explanations. The first explanation depends
on partial electron transfer: when the hydronium comes close to electrode surface, it may not be still at +1 charge state; as the calculations in Sec 4.2.1 shown, part of one electron charge, such asβe− withβ <1, may already transfer to the near-surface hydronium; as a result, when electrode potential changes byδU , the free energy of PCET’s initial state and
transition state, in which hydronium is close to the surface, may change by -δU e and -(1-
β)·δU e, respectively; thus, their difference, defined as activation free energy Q, changes by
(-(1-β)·δU e) - (-δU e) =β·δU e, soβ can be defined as symmetry factor. The second pos- sible explanation is from the potential distribution in the electrical double layer structures. As shown in Section 2.2.2, when hydronium comes close to the surface, the electrostatic potential is different from the bulk electrolyte far away; thus, when electrode potential
changes by δU , the electrostatic potential surrounding the near-surface hydronium may
change by (1-β)δU ; as a result, the free energy of PCET’s initial state and transition state
may change by -δU e and -(1-β)·δU e so that the corresponding Q changes by their differ-
ence, β·δU e. Both mechanisms are possible and a detailed analysis depends on a correct
description on electronic structures and potential profile of electrode-electrolyte interface, which will be discussed in Section 5.2.