44
Electrochemical Supercapacitors for Energy Storage and Delivery
In general, the Helmholtz layer can be treated as a linear capacitor. In a
theoretical model of the electric double-layer, the compact Helmholtz layer
is generally treated as an ideal capacitor with a fixed thickness (d), and its
capacitance is considered unchanging with the potential drop across it.
Therefore, the capacitance of the Helmholtz layer can be treated as a constant if the temperature, the dielectric constant of the electrolyte solution
inside the compact layer, and its thickness are fixed. However, if the specific
ion adsorption happened on the electrode surface, the dielectric constant of
the electrolyte solution inside the compact layer may be affected, leading to
non-linear behavior of the Helmholtz layer. This will be discussed more in
a later section.
In a theoretical model, the diffuse layer appears more complicated.
According to the definition in Chapter 1, the diffuse layer capacitor should
be treated as a nonlinear rather than linear capacitor because its capacitance is dependent on the electrode potential. Figure 2.6 shows the differential capacitance of a graphite electrode as a function of an electrode
70
80
90
C/μF·cm
–2
100
110
A
B
s
s
+0.5
0
–0.5
–1.0
E/V vs NHE
FIGURE 2.6
Capacity-potential curves for edge orientation of stress-annealed pyrolytic graphite in 0.5 M
H 2 SO 4 and 1 M NaOH at 25°C and 1000 Hz without hood. (A) 0.5 M H 2 SO 4 . ( —) potentials going
positive, (— —) potentials going negative from +0.1 V, (—·—·—·) potentials going negative from
+0.4 V, (··········) potentials going negative from +0.8 V. (B) 1 M NaOH. (—) potentials going positive, (— —) potentials going negative from –0.4 V, (— ·— ·—·) potentials going negative from
–0.2 V, (··········) potentials going negative from +0.2 V. (Source: Randin, J. P. and E. Yeager. 2001.
Electroanalytical Chemistry and Interfacial Electrochemistry, 58, 313–322. With permission.)
Electrochemical Supercapacitors for Energy Storage and Delivery
In general, the Helmholtz layer can be treated as a linear capacitor. In a
theoretical model of the electric double-layer, the compact Helmholtz layer
is generally treated as an ideal capacitor with a fixed thickness (d), and its
capacitance is considered unchanging with the potential drop across it.
Therefore, the capacitance of the Helmholtz layer can be treated as a constant if the temperature, the dielectric constant of the electrolyte solution
inside the compact layer, and its thickness are fixed. However, if the specific
ion adsorption happened on the electrode surface, the dielectric constant of
the electrolyte solution inside the compact layer may be affected, leading to
non-linear behavior of the Helmholtz layer. This will be discussed more in
a later section.
In a theoretical model, the diffuse layer appears more complicated.
According to the definition in Chapter 1, the diffuse layer capacitor should
be treated as a nonlinear rather than linear capacitor because its capacitance is dependent on the electrode potential. Figure 2.6 shows the differential capacitance of a graphite electrode as a function of an electrode
70
80
90
C/μF·cm
–2
100
110
A
B
s
s
+0.5
0
–0.5
–1.0
E/V vs NHE
FIGURE 2.6
Capacity-potential curves for edge orientation of stress-annealed pyrolytic graphite in 0.5 M
H 2 SO 4 and 1 M NaOH at 25°C and 1000 Hz without hood. (A) 0.5 M H 2 SO 4 . ( —) potentials going
positive, (— —) potentials going negative from +0.1 V, (—·—·—·) potentials going negative from
+0.4 V, (··········) potentials going negative from +0.8 V. (B) 1 M NaOH. (—) potentials going positive, (— —) potentials going negative from –0.4 V, (— ·— ·—·) potentials going negative from
–0.2 V, (··········) potentials going negative from +0.2 V. (Source: Randin, J. P. and E. Yeager. 2001.
Electroanalytical Chemistry and Interfacial Electrochemistry, 58, 313–322. With permission.)