3.4 Surface Stress Versus Surface Charge Density or Potential …
99
upper d-band states just above the Fermi level of Pd, and thereby reducing the tensile
stress.
Furthermore, Feibelman [55] calculated g = −3.2 J m
−2 for the fcc-O (2 ×
2)/Pt (111) system corresponding to the oxygen adsorption of 1/4 monolayer on Pt
(111). Since the anodic charge density required for the formation of 1/4 oxygen
monolayer on Pt (111) is q a = 1.2 C m
−2 , the negative value of ζ g,q =
g
q a
= −2.7 V is estimated for the oxygen adsorption on Pt (111) surface [55]. The
minus sign of ζ g,q is consistent with the experimental results obtained in the oxygen
adsorption/desorption region by in situ dilatometry for the porous Pt electrode in
0.7 M NaF solution [49, 50] and by DSA/EIS for the (111)-textured Pt thin-film
electrode in 0.1 M HClO 4 solution [40]. Albina et al. [56] made the first-principles
electronic structure calculations based on density functional theory (DFT) with the
local density approximation (LDA) to obtain the values of ζ g,q for transition and
noble metals. The value of ζ g,q for a metal electrode with no surface charge (q = 0)
corresponding to potential of zero charge in electrolyte can be calculated from the
strain dependence of work function in vacuum [56]:
ζ g,q =
∂g
∂q
ε
=
1
e o
∂Φ
∂ε
q
,
(3.26)
where Φ is the work function (eV: 1.602 × 10
−19 J) and e o is the elementary charge
(1.602 × 10
−19 C). The values of ζ g,q = −1.0 and −0.98 V were calculated, respectively, for Pt (111) and Pd (111) electrodes, which are consistent with the experimental
results obtained in the electric double-layer region by in situ dilatometry for the nanoporous Pt and Pd electrodes in 0.7 M NaF solution [49–51, 53] and DECMA for the
(111)-textured Pd electrode in 0.01 M H 2 SO 4 solution [52, 54], indicating that the
value of ζ g,q for the metal electrode in the double-layer region, where the adsorption
effects are absent or negligible, is equivalent to that for the metal in vacuum.
The minus sign of ζ g,q in the electric double-layer region may be explained in
terms of electrocapillarity effect by Weissmüller’s group [37, 50, 56, 57] as follows:
(1) The excess electronic charge is localized on the uppermost surface due to large
electronic screening effect of fcc transition metal, (2) when the excess electronic
charge is negative, i.e., positive excess of electrons (q < 0) at potentials more
negative than E pzc , the electrostatic center of gravity of the surface Wigner–Seitz
cell shifts to promote an outward stretch of the ion cores [58], and (3) insofar as
the excess electronic charge does not enter the orbitals responsible for the bonding
between the surface atoms, the excess electronic charge is redistributed into the inplane bonds, which contributes to the increase in tensile surface stress g > 0, thereby
leading to the minus sign of ζ g,q . In the case where the excess electronic charge is
positive, i.e., negative excess of electrons (q > 0) at potentials more positive than
E pzc , the electrostatic center of gravity of the surface Wigner–Seitz cell shifts to
promote an inward contraction of the ion cores, and the negative excess of electronic
charge provides the decrease in tensile stress g < 0, thereby leading to the same
minus sign of ζ g,q .
99
upper d-band states just above the Fermi level of Pd, and thereby reducing the tensile
stress.
Furthermore, Feibelman [55] calculated g = −3.2 J m
−2 for the fcc-O (2 ×
2)/Pt (111) system corresponding to the oxygen adsorption of 1/4 monolayer on Pt
(111). Since the anodic charge density required for the formation of 1/4 oxygen
monolayer on Pt (111) is q a = 1.2 C m
−2 , the negative value of ζ g,q =
g
q a
= −2.7 V is estimated for the oxygen adsorption on Pt (111) surface [55]. The
minus sign of ζ g,q is consistent with the experimental results obtained in the oxygen
adsorption/desorption region by in situ dilatometry for the porous Pt electrode in
0.7 M NaF solution [49, 50] and by DSA/EIS for the (111)-textured Pt thin-film
electrode in 0.1 M HClO 4 solution [40]. Albina et al. [56] made the first-principles
electronic structure calculations based on density functional theory (DFT) with the
local density approximation (LDA) to obtain the values of ζ g,q for transition and
noble metals. The value of ζ g,q for a metal electrode with no surface charge (q = 0)
corresponding to potential of zero charge in electrolyte can be calculated from the
strain dependence of work function in vacuum [56]:
ζ g,q =
∂g
∂q
ε
=
1
e o
∂Φ
∂ε
q
,
(3.26)
where Φ is the work function (eV: 1.602 × 10
−19 J) and e o is the elementary charge
(1.602 × 10
−19 C). The values of ζ g,q = −1.0 and −0.98 V were calculated, respectively, for Pt (111) and Pd (111) electrodes, which are consistent with the experimental
results obtained in the electric double-layer region by in situ dilatometry for the nanoporous Pt and Pd electrodes in 0.7 M NaF solution [49–51, 53] and DECMA for the
(111)-textured Pd electrode in 0.01 M H 2 SO 4 solution [52, 54], indicating that the
value of ζ g,q for the metal electrode in the double-layer region, where the adsorption
effects are absent or negligible, is equivalent to that for the metal in vacuum.
The minus sign of ζ g,q in the electric double-layer region may be explained in
terms of electrocapillarity effect by Weissmüller’s group [37, 50, 56, 57] as follows:
(1) The excess electronic charge is localized on the uppermost surface due to large
electronic screening effect of fcc transition metal, (2) when the excess electronic
charge is negative, i.e., positive excess of electrons (q < 0) at potentials more
negative than E pzc , the electrostatic center of gravity of the surface Wigner–Seitz
cell shifts to promote an outward stretch of the ion cores [58], and (3) insofar as
the excess electronic charge does not enter the orbitals responsible for the bonding
between the surface atoms, the excess electronic charge is redistributed into the inplane bonds, which contributes to the increase in tensile surface stress g > 0, thereby
leading to the minus sign of ζ g,q . In the case where the excess electronic charge is
positive, i.e., negative excess of electrons (q > 0) at potentials more positive than
E pzc , the electrostatic center of gravity of the surface Wigner–Seitz cell shifts to
promote an inward contraction of the ion cores, and the negative excess of electronic
charge provides the decrease in tensile stress g < 0, thereby leading to the same
minus sign of ζ g,q .