1. - Gouy – Chapman Model + electrostatics k T (Boltzman) Thermal
Randomization
The number of carriers in a given energy plane (distance away
from electrode) is found to be:
electrostatic
thermal
charge on e-
Bulk carrier # concentration
The potential profile is:
In all
cases
For a 1:1 electrolyte (~e.g. NaF, CaSO4)
is potential
at electrode
mol/L
inverse thickness of diffuse layer

2. Use unsimplified equation k−1 is often called the Debye Length
1.0
effectively linear
exponential
Ah, the outer Helmholtz Plane!

3. Too large a Cd and too fast a change! Why does Gouy – Chapman Fail?
1:1 electrolyte
***Figure ***
Chem. Rev , 441
***Figure ***
Too large a Cd and too fast a change!
Why does Gouy – Chapman Fail?
The model assumes that the ions are point
charges. As increases, the separation between
the metal and charged electrolyte decreases to 0.
Not Realistic!
Stern’s Modification Accounts for
1. Finite ionic size
2. Additional radial increase due to
solvation of ions

4. - Thus, must have plane of closest approach! +
For diffuse layer only!!!
“x2” OHP
1.0
This is the compact layer.
Get linear drop of
Diffuse Layer
Recall capacitance
is inversely additive!
compact
OHP
Exactly what we saw from Helmholtz.

5. - - Effects of Double Layer on ET Reactions O+ C+ O- C+ O+ O- O+ O+ O+
attracts
repels - - O+
C+ O+
O+ O+ O+ C+
O+ O+
C+ O+ O+ C+ O- O-
vs. x2
OHP
Thus apparent concentration of Oz is “similar” to that of the
electrolyte. That is to say we have an electrostatic driving
force attracting the cationic O or repelling anionic O.
If is + , then cationic O repelled and anionic O attracted.
So,
So, we will see changes in
i0 and k0 at different [SE]
and [Oz]*, which is what
prompted this study/theory.
Note NO absolute
value of charge.
z is the signed
charge on O.

6. So, Oz does not experience , but .
Linear Decay of , à là Helmholtz
OHP
140
120
100 80 60 40 20
Diffuse Layer,
exponential decay of mV
OHP
So, Oz does not experience , but
So, must correct for:
1. electrostatic effects on
2. electrostatic effects on E in rate equations from Chp. 3.
Recalling:
Totally irreversible reaction of O R
kf >>> kb
+ne
corrections so
Frumkin
Correction
This is the apparent rate constant.

7. Of course, x2, and thus, , vary with electrolyte size/type.
Examples:
Mg(ClO4)2
0.025
-63.0 12
0.40
0.25
-41.1
2.7
0.38
means
delocalized
and
“An”
The [ ] at x2 is being depleted due
to interactions.
Of course, x2, and thus, , vary with electrolyte size/type.
Also, we have assumed NO specific adsorption of SE anions,
O, or R.
Thus, the Frumkin Correction is limited, but it works well in
most cases.