Metal electrode (M)
Electrolyte solution
(S)
+ Positive charge
+
+
–
– Negative charge
+
–
Solvent molecule
–
+
+
–
–
+
–
+
–
+
–
–
+
–
+
d
(a)
Δφ m/s (=Δψ m/s )
Δφ m/s – Δφ H/s (=Δψ m/s –ψ 1 )
d
Δφ H/s (=Δψ 1 )
0
x
(b)
42
Electrochemical Supercapacitors for Energy Storage and Delivery
FIGURE 2.3
(See color insert.) A schematic description where the double-layer potential drops.
1 dΔψ d(Δ −
ψ ψ 1 ) dψ 1
1
1
=
=
+
=
+
(2.4)
C d l
dq
dq
dq C H C diff
In Equation (2.4), C H is the differential capacitance of the Helmholtz layer
[Equation (2.5)] and C diff is the differential capacitance of the diffuse layer
[Equation (2.6)]:
Electrolyte solution
(S)
+ Positive charge
+
+
–
– Negative charge
+
–
Solvent molecule
–
+
+
–
–
+
–
+
–
+
–
–
+
–
+
d
(a)
Δφ m/s (=Δψ m/s )
Δφ m/s – Δφ H/s (=Δψ m/s –ψ 1 )
d
Δφ H/s (=Δψ 1 )
0
x
(b)
42
Electrochemical Supercapacitors for Energy Storage and Delivery
FIGURE 2.3
(See color insert.) A schematic description where the double-layer potential drops.
1 dΔψ d(Δ −
ψ ψ 1 ) dψ 1
1
1
=
=
+
=
+
(2.4)
C d l
dq
dq
dq C H C diff
In Equation (2.4), C H is the differential capacitance of the Helmholtz layer
[Equation (2.5)] and C diff is the differential capacitance of the diffuse layer
[Equation (2.6)]: