4.3 Changes in Surface Stress during UPD
111
of q c is obtained from the integration of the corresponding cyclic voltammogram,
referred to zero at 0.80 V (SHE). In Fig. 4.4, the relationship between g and q c
consists of three linear (I), (III), and (V), and two plateau (II) and (IV) domains.
In the linear (I) domain with a slope of −1.19 V, no UPD of Pb but adsorption of
perchlorate ions takes place on the Au (111) electrode. As explained in Sect. 3.4 of
Chap. 3, the surface stress–surface charge density coefficient ζ g,q =
∂g
∂q
takes a minus
sign for the Au (111) electrode in the electric double-layer region [22]. The negative
slope of ζ g,q =
g
q c
= −1.19 V in the linear (I) domain is consistent with the minus
sign of ζ g,q for the Au (111) electrode in the electric double-layer region. The plateau
(II) domain where surface stress takes a maximum corresponds to the transition from
the anion adsorption phase to the Pb-UPD phase. In the linear (III) domain with a
slope of 0.55 V, the Pb-UPD proceeds on the Au (111) electrode. The plateau (IV)
domain where the hump of surface stress appears corresponds to a structural change
of the UPD layer. In the linear (V) domain with a slope of 0.58 V, the Pb-UPD still
proceeds until reaching to the UPD monolayer. The positive slopes of 0.55 V in the
linear (III) domain and of 0.58 V in the linear (V) domain are characteristic of the
Pb-UPD on the Au (111) electrode.
The intersection of two extrapolated lines in the linear (I) and (III) domains
at q c = −0.94 C m
−2 may be regarded as the onset of the Pb-UPD. The
cathodic charge density at the cathodic limit potential of −0.24 V (SHE) is q c =
−4.66 C m
−2 . If the Pb-UPD monolayer is formed at −0.24 V (SHE), the cathodic
charge density required for the monolayer formation is (q c ) m = −3.72 C m
−2 .
The atomic density of an atomically flat Au (111) surface without reconstruction is
1.38 × 10
19 atoms m
−2 . Assuming the complete discharging of Pb
2+ (i.e., z = 2),
and the hexagonal close-packed (hcp) Pb monolayer, and taking the difference in
radius between Pb (r = 0.175 nm) and Au (r = 0.144 nm) atoms into account [12],
the cathodic charge density required for the formation of the Pb-UPD monolayer
on an atomically flat Au (111) surface is (q c ) m = −3.02 C m
−2 . If the surface
roughness of the (111)-textured Au film electrode is S r = 1.2, the experimental value
of (q c ) m in Fig. 4.4 is close to that theoretically derived.
The surface coverage θ Pb of Pb on the top abscissa of Fig. 4.4 is calculated from
the cathodic charge density by regarding as θ Pb = 1.0 at −0.24 V (SHE). The plateau
(IV) domain with the hump of surface stress associated with the structural change of
the Pb-UPD layer corresponds to θ Pb = 0.43 ∼ 0.80. Stafford and Bertocci [13] also
measured the changes in surface stress as a function of θ Pb on a (111)-textured Au
thin-film electrode in 0.1 M HClO 4 solution with 10
−2 M Pb (ClO 4 ) 2 and observed the
same plateau (IV) domain at θ Pb = 0.56 ∼ 0.86. According to Stafford and Bertocci
[13], the values of θ Pb determined by using an electrochemical quartz microbalance
(EQCM) in separated experiments were in good agreement with the coulometric
results. The average value of θ Pb at the plateau (IV) domain deviates each other by
θ Pb ≈ 0.1, which may result from the difference in ionic strength or activity of
Pb
2+ between the electrolytes used for experiments [12, 13].
111
of q c is obtained from the integration of the corresponding cyclic voltammogram,
referred to zero at 0.80 V (SHE). In Fig. 4.4, the relationship between g and q c
consists of three linear (I), (III), and (V), and two plateau (II) and (IV) domains.
In the linear (I) domain with a slope of −1.19 V, no UPD of Pb but adsorption of
perchlorate ions takes place on the Au (111) electrode. As explained in Sect. 3.4 of
Chap. 3, the surface stress–surface charge density coefficient ζ g,q =
∂g
∂q
takes a minus
sign for the Au (111) electrode in the electric double-layer region [22]. The negative
slope of ζ g,q =
g
q c
= −1.19 V in the linear (I) domain is consistent with the minus
sign of ζ g,q for the Au (111) electrode in the electric double-layer region. The plateau
(II) domain where surface stress takes a maximum corresponds to the transition from
the anion adsorption phase to the Pb-UPD phase. In the linear (III) domain with a
slope of 0.55 V, the Pb-UPD proceeds on the Au (111) electrode. The plateau (IV)
domain where the hump of surface stress appears corresponds to a structural change
of the UPD layer. In the linear (V) domain with a slope of 0.58 V, the Pb-UPD still
proceeds until reaching to the UPD monolayer. The positive slopes of 0.55 V in the
linear (III) domain and of 0.58 V in the linear (V) domain are characteristic of the
Pb-UPD on the Au (111) electrode.
The intersection of two extrapolated lines in the linear (I) and (III) domains
at q c = −0.94 C m
−2 may be regarded as the onset of the Pb-UPD. The
cathodic charge density at the cathodic limit potential of −0.24 V (SHE) is q c =
−4.66 C m
−2 . If the Pb-UPD monolayer is formed at −0.24 V (SHE), the cathodic
charge density required for the monolayer formation is (q c ) m = −3.72 C m
−2 .
The atomic density of an atomically flat Au (111) surface without reconstruction is
1.38 × 10
19 atoms m
−2 . Assuming the complete discharging of Pb
2+ (i.e., z = 2),
and the hexagonal close-packed (hcp) Pb monolayer, and taking the difference in
radius between Pb (r = 0.175 nm) and Au (r = 0.144 nm) atoms into account [12],
the cathodic charge density required for the formation of the Pb-UPD monolayer
on an atomically flat Au (111) surface is (q c ) m = −3.02 C m
−2 . If the surface
roughness of the (111)-textured Au film electrode is S r = 1.2, the experimental value
of (q c ) m in Fig. 4.4 is close to that theoretically derived.
The surface coverage θ Pb of Pb on the top abscissa of Fig. 4.4 is calculated from
the cathodic charge density by regarding as θ Pb = 1.0 at −0.24 V (SHE). The plateau
(IV) domain with the hump of surface stress associated with the structural change of
the Pb-UPD layer corresponds to θ Pb = 0.43 ∼ 0.80. Stafford and Bertocci [13] also
measured the changes in surface stress as a function of θ Pb on a (111)-textured Au
thin-film electrode in 0.1 M HClO 4 solution with 10
−2 M Pb (ClO 4 ) 2 and observed the
same plateau (IV) domain at θ Pb = 0.56 ∼ 0.86. According to Stafford and Bertocci
[13], the values of θ Pb determined by using an electrochemical quartz microbalance
(EQCM) in separated experiments were in good agreement with the coulometric
results. The average value of θ Pb at the plateau (IV) domain deviates each other by
θ Pb ≈ 0.1, which may result from the difference in ionic strength or activity of
Pb
2+ between the electrolytes used for experiments [12, 13].