Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928...
Transcript of Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928...
![Page 1: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/1.jpg)
927
Lecture #13 of 17
![Page 2: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/2.jpg)
928
Q: What was in this set of lectures?
A: B&F Chapter 2 main concepts:
● “Section 2.1”: Salt; Activity; Underpotential deposition
(UPD)
● Section 2.3: Transference/Transport numbers; Liquid-
junction potentials
● Sections 2.2 & 2.4: Donnan potential; Membrane potentials;
pH meter; Ion-selective electrodes (ISEs)
![Page 3: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/3.jpg)
929
1900 20001920 1940 1960 1980
1933 – Arnold Beckman markets first pH electrode in Fullerton, CA for measuring acidity of lemon juice…
the Beckman G
1905 Walter Nernst proposes3rd Law of Thermodynamics; In Bern, Einstein describes PE effect,Brownian motion, and Special Rel.
Nernst wins Nobel Prize
1906 – Max Cremer discovers that athin glass membrane separating two solutions develops a potential related to the difference in pH between them
1920’s – Duncan MacInnes & Malcolm Dolediscover a glass suitable for glass pH electrodes…
Nernst dies
1961 – Pungor & Hallos-Rokosinyi invent solid membrane ISE
… little innovation for 30 years!
1967 - Ross demonstrates first liquid membrane electrode
1966 – Frant and Ross describe the F–-selective electrode
~110 years of Ion-Selective Electrodes (ISEs)…RECALL FROM LAST TIME…
![Page 4: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/4.jpg)
930the breakthrough discovery of Ernö Pretsch (ETH Zürich)…
6+ orders of magnitude more?!?!?!?! …
It’s real, general, and new, after 91 years!
… How did he do it?
http://www.pretsch.ethz.ch/EP/Pretsch.htmlSokalski, …, Pretsch, J. Am. Chem. Soc., 1997, 119, 11347
![Page 5: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/5.jpg)
931What did Ernö Petsch do?
… a “simple” idea…
… replace the inner filling solution of the ISE with a metal ion buffer!
Sokalski, …, Pretsch, J. Am. Chem. Soc., 1997, 119, 11347
![Page 6: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/6.jpg)
932What’s a metal ion buffer?
… Well, first of all, what’s a H+ (pH) buffer?
a weak acid a weak base
… Henderson–Hasselbalch equation
𝐾a =H3O+ A−
HA
H3O+ =𝐾a HA
A−
pH = − log H3O+ = p𝐾a + log
A−
HA
HA + H2O A– + H3O+
make these large…
… which fixes [H3O+]
… even at a small value
![Page 7: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/7.jpg)
933Case in point: Phosphate = three equilibria, three buffers
![Page 8: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/8.jpg)
934
EDTA EDTA–metal chelate
What’s a metal ion buffer? Just like it sounds…
Y4– + Mn+ [MY](n – 4)+
![Page 9: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/9.jpg)
935
EDTA EDTA–metal chelate
What’s a metal ion buffer? Just like it sounds…
Y4– + Mn+ [MY](n – 4)+
𝐾MY =MY 𝑛−4 +
Y4− M𝑛+ make these large…
… which fixes [Mn+]
… even at a small value
![Page 10: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/10.jpg)
936
EDTA EDTA–metal chelate
What’s a metal ion buffer? Just like it sounds…
Y4– + Mn+ [MY](n – 4)+
𝐾MY =MY 𝑛−4 +
Y4− M𝑛+
pM = − log M𝑛+ = −p𝐾MY + logY4−
MY 𝑛−4 +
M𝑛+ =MY 𝑛−4 +
Y4− 𝐾MY
make these large…
… which fixes [Mn+]
… even at a small value
![Page 11: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/11.jpg)
937
pM
… buffering of Mn+ occurs after
the equivalence point… Why?
no buffering here…
(started with Mn+ in solution)
pM = − log M𝑛+ = −p𝐾MY + logY4−
MY 𝑛−4 +
![Page 12: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/12.jpg)
938KMY is adjustable based on pH… here is data for Ca2+
![Page 13: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/13.jpg)
conventional ISE
939… so, what does a metal ion buffer have to do with an ISE?
filling solution, [Mn+] = 10-4 M
leaked Mn+, [Mn+] ≈ 10-6 M
… so you can’t detect anything
lower than this!
![Page 14: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/14.jpg)
940… so, what does a metal ion buffer have to do with an ISE?
conventional ISE
filling solution,
[Mn+]free = 10-10 M
leaked Mn+,
[Mn+] ≈ 10-12 M
… and so
~1012 M can
be detected!
with metal ion buffer
![Page 15: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/15.jpg)
941
THANK YOU, Ernö!
http://www.pretsch.ethz.ch/EP/Pretsch.htmlSokalski, …, Pretsch, J. Am. Chem. Soc., 1997, 119, 11347
the breakthrough discovery of Ernö Pretsch (ETH Zürich)…
![Page 16: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/16.jpg)
942
Q: What’s in this set of lectures?
A: B&F Chapter 13 main concepts:
● Section 1.2.3: Double layer structure
● Sections 13.1 & 13.2: Gibbs adsorption isotherm;
Electrocapillary / Surface excess /
Lippmann’s equation; Point of Zero
Charge
● Section 13.3: Models: Helmholtz, Gouy–Chapman
(Poisson–Boltzmann), GC–Stern
● Section 13.5: Specific adsorption
![Page 17: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/17.jpg)
943the charge on an electrode, qM, is compensated by the
accumulation of oppositely charged ions in solution: qM = –qS
… we want to understand the details of how these metal–solution
interfaces are structured…
… the bulk solution region
is called the quasi-neutral
region in semiconductors
![Page 18: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/18.jpg)
944in polar solvents, all charged surfaces possess a common structure…
anion (e.g. Cl–)
specifically
adsorbed anion; also
called contact
adsorption; polarized
with δ+ near the
electrode
water
qM < 0
(IHP) (AKA compact layer, Helmholtz layer, or
Stern layer)
+ –
![Page 19: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/19.jpg)
945… cations have strongly coordinated waters that exchange slowly…
cation (e.g. Na+)
(OHP)
![Page 20: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/20.jpg)
946… the (second) layer of solution extending from the OHP that has a
composition perturbed from bulk is called the diffuse layer
… follows a Poisson–
Boltzmann distribution…
![Page 21: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/21.jpg)
947
… this is the same idea
behind derivation of the
Debye–Hückel equation
(to obtain activity
coefficients based on the
ionic strength) and the
Donnan equation (to
obtain the electric
potential difference
across a membrane |
solution interface)…
… the general idea for
each is that diffusive
(thermal) transport
(Boltzmann) is equal
and opposite to drift
(electrostatic) transport
(Poisson/Gauss)
… the (second) layer of solution extending from the OHP that has a
composition perturbed from bulk is called the diffuse layer
… follows a Poisson–
Boltzmann distribution…
![Page 22: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/22.jpg)
948
Notice particularly the following:
1) A layer of oriented waters covers the surface…
… water orientation (O or H) is dictated by the surface charge
2) Anions shed their primary hydration layers and directly adsorb
onto the surface. This is called “specific adsorption”… with an
exception being F–
3) In general, cations do not specifically adsorb; their primary
hydration layers are too strongly attached (by the ion–dipole
interaction) to be shed at room temperature. This is an example
of “nonspecific adsorption”… with an exception being (CH3)4N+
![Page 23: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/23.jpg)
949the persistence of water molecules within the first hydration layer is
illustrated by the water exchange rate from ions…
Girault, Analytical and Physical Electrochemistry, Marcel Dekker, 2004, Figure 3.13
![Page 24: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/24.jpg)
950
I–
Cl–
Br–
>1010
Girault, Analytical and Physical Electrochemistry, Marcel Dekker, 2004, Figure 3.13
the persistence of water molecules within the first hydration layer is
illustrated by the water exchange rate from ions…
![Page 25: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/25.jpg)
951
excess charge (density)
in solution
charge (density)
on metal
σM = –σS
The electrode carries a charge, qM, and a surface change density σM
(σM = qM/A). The total charge (density) of the system is zero, and so…
![Page 26: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/26.jpg)
952
Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure 1.2.2
qM < 0 qM > 0
σM = –σS
The electrode carries a charge, qM, and a surface change density σM
(σM = qM/A). The total charge (density) of the system is zero, and so…
![Page 27: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/27.jpg)
953
Bockris and Reddy, Vol. 2, Plenum Publishing, 1977, Figure 7.46
… now, what is excess solution charge? There is a technical name
for this… it is called the (Gibbs) Surface Excess, Γ
(mol cm-2)
![Page 28: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/28.jpg)
954… now put it all together, and what do we have? …
… where R is in a reference system, and S is in the actual system
![Page 29: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/29.jpg)
955
differential
excess
free energy γ =𝜕𝐺
𝜕𝐴surface
tension
… where R is in a reference system, and S is in the actual system
… and at constant temperature and constant pressure…
… now put it all together, and what do we have? …
![Page 30: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/30.jpg)
956
total
differential
… where R is in a reference system, and S is in the actual system
… and at constant temperature and constant pressure…
… now put it all together, and what do we have? …
![Page 31: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/31.jpg)
957
total
differential
… and setting the two forms of the differential eqn equal to each other…
surface
excess
= Gibbs Adsorption Isotherm
−𝑑γ =
𝑖
Γ𝑖 𝑑 𝜇𝑖
… now put it all together, and what do we have? …
(mol cm-2)
![Page 32: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/32.jpg)
the surface tension (units: energy/area, typically
J m-2 or N m-1… these are identical)
958… now put it all together, and what do we have?
… we won’t derive it, but by recasting the electrochemical potential
difference between the electrodes as the change in applied potential…
… we have the electrocapillary equation (B&F pp. 537–538)…
γ =𝜕𝐺
𝜕𝐴
−𝑑γ = σ𝑀𝑑𝐸 +
𝑖
Γ𝑖 𝑑𝜇𝑖
![Page 33: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/33.jpg)
the surface excess concentration
of species i (units: moles/area),
and sometimes called the Gibbs
surface excess
959
−𝑑γ = σ𝑀𝑑𝐸 +
𝑖
Γ𝑖 𝑑𝜇𝑖
… now put it all together, and what do we have?
… we won’t derive it, but by recasting the electrochemical potential
difference between the electrodes as the change in applied potential…
… we have the electrocapillary equation (B&F pp. 537–538)…
![Page 34: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/34.jpg)
the chemical potential of species i
960
… but where is the electric potential term?
−𝑑γ = σ𝑀𝑑𝐸 +
𝑖
Γ𝑖 𝑑𝜇𝑖
… now put it all together, and what do we have?
… we won’t derive it, but by recasting the electrochemical potential
difference between the electrodes as the change in applied potential…
… we have the electrocapillary equation (B&F pp. 537–538)…
![Page 35: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/35.jpg)
the change in potential
between the WE and the RE
961
−𝑑γ = σ𝑀𝑑𝐸 +
𝑖
Γ𝑖 𝑑𝜇𝑖
… now put it all together, and what do we have?
… we won’t derive it, but by recasting the electrochemical potential
difference between the electrodes as the change in applied potential…
… we have the electrocapillary equation (B&F pp. 537–538)…
![Page 36: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/36.jpg)
962
… so measurement of the surface tension of the electrode as a
function of its potential is a direct way to get at its surface charge
(density), σM. This is called Lippmann's Equation:
σ𝑀 = −𝑑γ
𝑑𝐸𝜇𝑖
−𝑑γ = σ𝑀𝑑𝐸 +
𝑖
Γ𝑖 𝑑𝜇𝑖
We want to know this…
… now put it all together, and what do we have?
… we won’t derive it, but by recasting the electrochemical potential
difference between the electrodes as the change in applied potential…
… we have the electrocapillary equation (B&F pp. 537–538)…
(recall that this means constant chemical potential of all species)
![Page 37: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/37.jpg)
… so measurement of the surface tension of the electrode as a
function of its potential is a direct way to get at its surface charge
(density), σM. This is called Lippmann's Equation:
963
σ𝑀 = −𝑑γ
𝑑𝐸𝜇𝑖
−𝑑γ = σ𝑀𝑑𝐸 +
𝑖
Γ𝑖 𝑑𝜇𝑖
We want to know this…
… or better yet, qM
… or better yet, qS
… now put it all together, and what do we have?
… we won’t derive it, but by recasting the electrochemical potential
difference between the electrodes as the change in applied potential…
… we have the electrocapillary equation (B&F pp. 537–538)…
![Page 38: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/38.jpg)
… so measurement of the surface tension of the electrode as a
function of its potential is a direct way to get at its surface charge
(density), σM. This is called Lippmann's Equation:
964
Key Point: Measuring γ is easy if the electrode is a liquid…
We want to know this…
… or better yet, qM
… or better yet, qS… both q’s are the same
σ𝑀 = −𝑑γ
𝑑𝐸𝜇𝑖
−𝑑γ = σ𝑀𝑑𝐸 +
𝑖
Γ𝑖 𝑑𝜇𝑖
… now put it all together, and what do we have?
… we won’t derive it, but by recasting the electrochemical potential
difference between the electrodes as the change in applied potential…
… we have the electrocapillary equation (B&F pp. 537–538)…
![Page 39: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/39.jpg)
qm
965
Hg 2rc
qm = mass flow rate (kg/s)
http://gmwgroup.harvard.edu/
… thus, our window into the double layer structure is the dropping
mercury electrode (DME)… Seriously!
… since drop moves slowly, Fγ ≈ F(g)ravity (recall that Fg = mg = (qmtmax)g)
… and just before dropping…acceleration
due to gravity
(… recall that γ has units of N m-1)
B&F used “m,” butIUPAC prefers qm
![Page 40: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/40.jpg)
966… now, in a dropping mercury electrode, as the name implies…
Hg
glass
![Page 41: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/41.jpg)
967
Hg
glass
… now, in a dropping mercury electrode, as the name implies…
![Page 42: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/42.jpg)
968
Hg
glass
… now, in a dropping mercury electrode, as the name implies…
![Page 43: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/43.jpg)
969… what do we measure during this process?
glass
Hgr = 1 mm
… suppose the electrode is at a potential where σM = qM/A = 25 µC/cm2
… what is the surface charge, qM?
![Page 44: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/44.jpg)
970
Hgr = 2 mm
glass
… what do we measure during this process?
![Page 45: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/45.jpg)
971
Hgr = 2 mm
… so even though the potential is constant,
… and even though there is no Faradaic electrochemistry
occurring, the Hg droplet grows, and current flows to its surface…
… and this current is proportional to qM
glass
… what happens as the electrode grows?
![Page 46: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/46.jpg)
972
Hg
glass
… after it falls, off, the current drops to a small value…
… and then the process repeats…
… what happens as the electrode grows?
![Page 47: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/47.jpg)
973… okay, so let’s do an experiment… scan the potential (E) while
we measure the current in 0.1 M HCl…
Question: Why do the current
oscillations stop at -0.60V?
Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure 7.1.5
tmax
![Page 48: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/48.jpg)
974
Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure 7.1.5
tmax
the potential at
the point of zero charge
(pzc)
… okay, so let’s do an experiment… scan the potential (E) while
we measure the current in 0.1 M HCl…
![Page 49: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/49.jpg)
975
notice also that the phase of the current
oscillation inverts as E crosses the PZC…
Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure 7.1.5
… okay, so let’s do an experiment… scan the potential (E) while
we measure the current in 0.1 M HCl…
![Page 50: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/50.jpg)
976… a linear scan voltammogram acquired with a DME
(and therefore called a polarogram)
… DMEs are "self-cleaning"
CrO42- + 3e- + 4H2O
⇌ Cr(OH)3 + 5OH-
il
![Page 51: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/51.jpg)
977… look familiar? … It’s just this:
![Page 52: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/52.jpg)
978… okay, now going back to the case of 0.10 M HCl, let’s measure
the drop time, tmax, as a function of potential…
Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure 7.1.5
tmax
the potential at
the point of zero charge
(pzc)
![Page 53: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/53.jpg)
979… take the tmax versus E data and make a plot… and voila!…
clearly proportional to γ
… and recall…
σM = −𝑑γ
𝑑𝐸𝜇𝑖
![Page 54: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/54.jpg)
980
σM = −𝑑γ
𝑑𝐸𝜇𝑖
= 0
… take the tmax versus E data and make a plot… and voila!…
pzc
![Page 55: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/55.jpg)
981
Why is the surface tension largest
when the surface charge is smallest?
… take the tmax versus E data and make a plot… and voila!…
σM = −𝑑γ
𝑑𝐸𝜇𝑖
= 0
pzc
![Page 56: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/56.jpg)
982
Why is the surface tension largest
when the surface charge is smallest?
… the intermolecular
cohesive forces
between solvent
molecules is large
but…
… like charges
repel!
… take the tmax versus E data and make a plot… and voila!…
σM = −𝑑γ
𝑑𝐸𝜇𝑖
= 0
pzc
![Page 57: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/57.jpg)
983… okay, what can we do with this information? Well, a plot of
charge (q) versus potential (E) has a slope of… What?
![Page 58: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/58.jpg)
984
… but this is the integral / total capacitance… the capacitance that
applies for a given applied potential versus the pzc. For a real
capacitor, C is virtually E-independent, but that may not be (and in
fact, is not) true for an electrical double layer.
… in anticipation of this, let’s define a differential capacitance (Cd),
which is the correct term to use, as follows:
𝐶𝑑 =𝜕σM
𝜕𝐸= −𝜕2γ
𝜕𝐸2𝜇𝑖
… okay, what can we do with this information? Well, a plot of
charge (q) versus potential (E) has a slope of capacitance (C):
![Page 59: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/59.jpg)
985Let’s compare total capacitance (C) and differential capacitance
(Cd) as follows:
Ez is the potential at the pzc
![Page 60: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/60.jpg)
986… if we can measure γ, we can determine σM…
… and if we can determine σM, we can determine C…
… and all of this only works for liquid electrodes… Crazy!
σM = −𝑑γ
𝑑𝐸𝜇𝑖
![Page 61: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/61.jpg)
987… if we can measure γ, we can determine σM…
… and if we can determine σM, we can determine C…
… and all of this only works for liquid electrodes… Crazy!
σM = −𝑑γ
𝑑𝐸𝜇𝑖
… Aside: You can determine the pzc of a solid electrode using its capacitance
![Page 62: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/62.jpg)
988
H.H. Girault, Analytical and Physical Electrochemistry, EPFL Press, 2004, Figure 5.13
… here’s what the C vs. E data actually look like as a function of
concentration, for KF at a DME…
![Page 63: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/63.jpg)
989… data for NaF from B&F is qualitatively similar…
Flat? … Eh; not really.
Why were both of these
measured using fluoride
salts?
Grahame, Chem. Rev., 1947, 41, 441
![Page 64: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/64.jpg)
990
Grahame, Chem. Rev., 1947, 41, 441
… data for NaF from B&F is qualitatively similar…
Flat? … Eh; not really.
Why were both of these
measured using fluoride
salts?
In order to minimize
specific adsorption!
![Page 65: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/65.jpg)
991
For the purposes of this class, we want to understand
the microscopic origin of the most prominent features
of these Cd vs. E data:
a) A minimum in Cd exists at the pzc.
b) Cd is quasi-constant at potentials well positive and
well negative of the pzc.
c) This quasi-constant Cd is larger when E is (+) of pzc
than when it is (–) of pzc.
d) Cd increases with salt concentration at all potentials,
and the “dip” disappears.
![Page 66: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/66.jpg)
992… do you want to understand the details of Cd away from the pzc?
Do you want to understand the hump? There is a book for that…
John Bockris
Bockris, J. Chem. Educ., 1983, 60, 265
![Page 67: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/67.jpg)
993
Three traditional models for double layer structure:
1) Helmholtz
2) Gouy–Chapman (GC)
3) Gouy–Chapman–Stern (GCS)
… let’s take a look at each…
![Page 68: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/68.jpg)
994
… for a parallel plate capacitor, C
is independent of E because the
permittivity of the capacitor, εε0,
and its spacing, d, are both
independent of applied potential…
Models of Electrical Double Layer:
1) The Helmholtz Model: this is
the simplest possible model. It
postulates that ions (anions and
cations) occupy a plane a
distance, d, from the electrode
surface, and that the effective
"dielectric constant" operating in
the DL is potential independent:
http://www.cartage.org.lb/
d
![Page 69: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/69.jpg)
995… the Helmholtz model says that the electrical double layer acts
like, and looks like (rare in EChem), a parallel plate capacitor…
… Cd is therefore independent of E because the permittivity of the
capacitor, εε0, and its spacing, d, are both independent of applied
potential…
… Question: What Cd do we calculate for this model, using the known
"dielectric constant" (permittivity = IUPAC) of water?
![Page 70: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/70.jpg)
996… recall, here’s what the double layer really looks like…
![Page 71: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/71.jpg)
997… and here’s what the double layer looks like in the Helmholtz
approximation…
![Page 72: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/72.jpg)
998… and here’s what the double layer looks like in the Helmholtz
approximation…
now, what’s εr?
4Å = 0.4 x 10-9 m
![Page 73: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/73.jpg)
999… first, what’s εr for water? Well, that depends… can it rotate?
5.9
78.4
for water at 20 oC…
![Page 74: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/74.jpg)
1000… first, what’s εr for water? Well, that depends… can it rotate?
5.9
78.4
for water at 20 oC…
Scenario is where electric
field oscillates too quickly
for molecules to reorient
Scenario is where electric
field oscillates slow enough
that molecules do reorient
![Page 75: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/75.jpg)
1001
Answer: εr ≈ 78
(static relative permittivity)
4Å = 0.4 x 10-9 m
… and here’s what the double layer looks like in the Helmholtz
approximation…
![Page 76: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/76.jpg)
1002
4Å = 0.4 x 10-9 m
… and here’s what the double layer looks like in the Helmholtz
approximation…
Is this what is observed? Nope!… OK, now what?
![Page 77: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/77.jpg)
1003
4Å = 0.4 x 10-9 m
εr ≈ 6
… now, what if the water dielectric is saturated, and thus fixed?
… so that water cannot rotate…
… much more reasonable!
![Page 78: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/78.jpg)
1004… if the Helmholtz model is correct, we’d get this exactly:
σM = −𝑑γ
𝑑𝐸𝜇𝑖
![Page 79: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/79.jpg)
1005… here are electrocapillary data for various electrolytes…
… hey, you can already see that the Helmholtz Model fails a little…
… mostly on the left…
![Page 80: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/80.jpg)
1006
Notwithstanding, notice particularly the following:
a) the γ vs. E parabola is independent of salt…
at potentials negative of the pzc…
b) … but strongly dependent on salt positive of pzc…
c) … and pzc itself depends on the electrolyte…
… we’ll get to this later…
![Page 81: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/81.jpg)
1007… if C is dependent on potential, then the γ vs. E parabola will
be asymmetric…
… for example…
![Page 82: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/82.jpg)
1008
H.H. Girault, Analytical and Physical Electrochemistry, EPFL Press, 2004, Figure 5.13
… and a flat Cd is in no way observed… we need a more
sophisticated model…
![Page 83: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/83.jpg)
1009
H.H. Girault, Analytical and Physical Electrochemistry, EPFL Press, 2004, Figure 5.13
… and specifically one where the model of the double layer
captures these elements?
these Cd’s are
not constant
… and there is a minimum
in the Cd at the pzc…
![Page 84: Lecture #13 of 17 - UCI Department of Chemistryardo/echem/UCI-CHEM248... · Lecture #13 of 17. 928 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: ... Henderson–Hasselbalch](https://reader034.fdocuments.us/reader034/viewer/2022042804/5f58fd676d6a426b4e4087dd/html5/thumbnails/84.jpg)
1010
Three traditional models for double layer structure:
1) Helmholtz
2) Gouy–Chapman (GC)
3) Gouy–Chapman–Stern (GCS)
… let’s take a look at each…