Gouy Chapman Model

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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 11 electrolyte (e.g. NaF, CaSO4)
is potential at electrode
mol/L
inverse thickness of diffuse layer
2
Use unsimplified equation
1.0
effectively linear
exponential
0
Ah, the outer Helmholtz Plane!
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11 electrolyte
Figure 12.3.5
Chem. Rev. 1947 41, 441
Figure 12.3.1
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! Sterns Modification Accounts for
1. Finite ionic size 2. Additional
radial increase due to solvation of
ions
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Thus, must have plane of closest approach!
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For diffuse layer only!!!
x2 OHP
1.0
This is the compact layer. Get linear drop of
.
Diffuse Layer
compact OHP
Recall capacitance is inversely additive!
Exactly what we saw from Helmholtz.
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Effects of Double Layer on ET Reactions
attracts
repels
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O C O O O O C O O O O C
O O C O O O O
C O- C O- C O- C O-
O- O- O- 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.
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Linear Decay of , à là Helmholtz
OHP
140 120 100 80 60 40 20 0
10 20 30
40 50 60 70
80
Diffuse Layer, exponential decay of
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 gtgtgt kb
ne
corrections
so
Frumkin Correction
This is the apparent rate constant.
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Examples
Mg(ClO4)2
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.
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Adsorption Effects on Cyclic Voltammetric
Traces Non Specific Adsorption Long-range
electrostatic forces perturb the distribution of
ions near the electrode surface. Specific
Adsorption Strong interaction between the
adsorbate (Ads) and the electrode material causes
the formation of an adlayer on the electrode
surface. Need a way to relate 1.
Concentration of Ads, 2. Activity of Ads
in solution, 3. Energy of Adsi and Adsi in
solution (i) Must assume A. No Ads Ads
interactions B. Homogeneous surface C.
Maximum surface concentration
0Bulk activity
Adsorbed on surface
Then,
or
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Langmuir Adsorption Isotherm
interactions btw. Ads.
(one monolayer)
Langmuir Adsorption Isotherm
- interactions btw. Ads.
(For a neat analysis, see JACS (1997) 119
10763-10773) How describe Ads
interactions? Frumkin
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Au
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