4
across the double layer at the PZC is dependent on the orientation of dipoles, including water molecules at the surface. The model of an electrical double layer as a
condenser with a fixed plane of charge in the electrolyte (inner layer) is due to
Helmholtz [5]. Gouy [6] and Chapman [7] took into account the ion concentration
gradient extending from the electrode surface into the solution (diffuse layer) caused
by the charge in the double layer. Stern [8] modified this model by taking into
account that the finite size of ions results in a limiting distance of closest approach
to the electrode surface. The double-layer capacitance is a series combination of the
compact and diffuse layers, and the total capacitance of the metal–solution interface
C is given by:
1
1
1
2
2
/
/
/
C
C
C
M
s
=
+
−
−
(1.5)
where C M−2 and C 2−S are the capacitances between the metal and the outher
Helmholtz plane and for the diffuse ionic layer, respectively. C 2−S passes through the
minimum at the PZC value. The measurement of the differential double-layer
capacitance is used for the determination of E PZC . At high positive charges, anions
lose their solvation. This causes a decrease of the distance of closest approach and
consequently a large increase of C M−2 . At high negative charges, the corresponding
effect is small.
The potential of zero charge is related to the modified (electrochemical) work
function for electrons in the electrode since zero charge conditions are required for
determination of both quantities. (The Kelvin probe measures the disappearance of
excess charge.) The Fermi level of an electrode at E PZC correlates with the work
function, Φ. The relationship:
E PZC
const
= − +
Φ
(1.6)
holds for transition metals. For sp metals, the slope is not unity because of the
metal-dependent water orientation. Deviations from Eq. (1.6) may arise from different dipole structure and ion adsorption at the metal–electrolyte interface. The work
function as well as the PZC depends on the crystal orientation. Early studies were
done using Hg electrode, which provided a smooth, clean surface. Figure 1.2 shows
the double-layer capacitance of Hg in NaF at 25 °C, as a function of E − E PZC.
Recent double-layer studies have been done with single crystal surfaces [9]. The
coverage of specifically adsorbed anions, such as halides, can be large, and their
effects on adsorption of other species and the kinetics of reactions can cause considerable decrease and, in some cases, a complete inhibition (See Chap. 4). Figure 1.3a
shows the differential capacitance of Au(100) surface in KBr solution [9], Fig. 1.3b
voltammetry curve for Au(100) in KBr, and Fig. 1.3c a scanning tunneling microscopy (STM) image of Br adlayer at E = 0.4 V on Au(100) [10].
Differential capacitance of Au(100) as a function of potential shows a strong
potential dependence in agreement with voltammetry curve showing sharp spikes
indicating phase transitions in the Br adlayer. Figure 1.3c shows the STM image of
a high-coverage quasi-hexagonal c(2 × 2)R45° commensurate structure at potentials
1 Short Introduction to the Science of Electrocatalysis
across the double layer at the PZC is dependent on the orientation of dipoles, including water molecules at the surface. The model of an electrical double layer as a
condenser with a fixed plane of charge in the electrolyte (inner layer) is due to
Helmholtz [5]. Gouy [6] and Chapman [7] took into account the ion concentration
gradient extending from the electrode surface into the solution (diffuse layer) caused
by the charge in the double layer. Stern [8] modified this model by taking into
account that the finite size of ions results in a limiting distance of closest approach
to the electrode surface. The double-layer capacitance is a series combination of the
compact and diffuse layers, and the total capacitance of the metal–solution interface
C is given by:
1
1
1
2
2
/
/
/
C
C
C
M
s
=
+
−
−
(1.5)
where C M−2 and C 2−S are the capacitances between the metal and the outher
Helmholtz plane and for the diffuse ionic layer, respectively. C 2−S passes through the
minimum at the PZC value. The measurement of the differential double-layer
capacitance is used for the determination of E PZC . At high positive charges, anions
lose their solvation. This causes a decrease of the distance of closest approach and
consequently a large increase of C M−2 . At high negative charges, the corresponding
effect is small.
The potential of zero charge is related to the modified (electrochemical) work
function for electrons in the electrode since zero charge conditions are required for
determination of both quantities. (The Kelvin probe measures the disappearance of
excess charge.) The Fermi level of an electrode at E PZC correlates with the work
function, Φ. The relationship:
E PZC
const
= − +
Φ
(1.6)
holds for transition metals. For sp metals, the slope is not unity because of the
metal-dependent water orientation. Deviations from Eq. (1.6) may arise from different dipole structure and ion adsorption at the metal–electrolyte interface. The work
function as well as the PZC depends on the crystal orientation. Early studies were
done using Hg electrode, which provided a smooth, clean surface. Figure 1.2 shows
the double-layer capacitance of Hg in NaF at 25 °C, as a function of E − E PZC.
Recent double-layer studies have been done with single crystal surfaces [9]. The
coverage of specifically adsorbed anions, such as halides, can be large, and their
effects on adsorption of other species and the kinetics of reactions can cause considerable decrease and, in some cases, a complete inhibition (See Chap. 4). Figure 1.3a
shows the differential capacitance of Au(100) surface in KBr solution [9], Fig. 1.3b
voltammetry curve for Au(100) in KBr, and Fig. 1.3c a scanning tunneling microscopy (STM) image of Br adlayer at E = 0.4 V on Au(100) [10].
Differential capacitance of Au(100) as a function of potential shows a strong
potential dependence in agreement with voltammetry curve showing sharp spikes
indicating phase transitions in the Br adlayer. Figure 1.3c shows the STM image of
a high-coverage quasi-hexagonal c(2 × 2)R45° commensurate structure at potentials
1 Short Introduction to the Science of Electrocatalysis