Electrified Interfaces
qmetal = -qsolution
charge neutrality!
Compact Layer = inner and outer Helmholtz planes
(electrostatic forces are very strong!)
Diffuse Layer = gradient of charge accumulation
(thermal agitation)
metal = qmetal/area (μC/cm2)
The excess charge on a metal is confined to the near surface region.
However, the balancing charge on the solution side of the interface
extends out into the solution with some thickness. (ionic zones in sol.)
Electrified Interfaces
metal = -(IHP + OHP + diffuse)
Structure of the electric double layer has
a major effect on electrode reaction
kinetics! (Faradaic reaction rates).
Species not specifically adsorbed
approach the OHP.
Φ2 – Φs is wasted!!
Φm – Φs is potential felt by analyte
 dy 
Field strength  dx  x  x 2 is critical!!
Electrified Interfaces
The solution side of the interface consists of a compact
layer (inner and outer Helmholtz layers) plus a diffuse layer.
Diffuse layer extends from the OHP to the bulk solution.
Ionic distribution influenced by ordering due to coulombic
forces and disorder caused by random thermal motion.
Qm + (QCL + QDL) = 0
Q = CE
QDL = CdlA(E-Epzc)
Qm = - (QCL + QDL)
(C = Farad E = voltage difference)
(A = area (cm2) Epzc = point of zero charge)
1/CTOT = 1/CCL + 1/CDL
CCL
CDL
Smallest value dominates
the interfacial capacitance
Chapter 13 – Electric Double Layer
A great deal of information about the electric double layer structure
(electrode /solution interfacial structure) comes from macroscopic
equilibrium measurements of surface tension and interfacial
capacitance.
Surface excesses and deficiencies
A
B
Interfacial zone
(few hundred angstroms)
ni = nSi - nRi
GR =(T, P, nRi)
GS = (T,P, A, nSi)
Real surface/interface has a
tendency to expand or contract
to minimize free energy.
Chapter 13 – Electric Double Layer
(GS/A) =  Change in free energy of the system as the area changes
- = Σ i μi
Gibbs Adsorption
Isotherm
μi = μi,ch + ziFΦ electrochemical free energy, includes
effects of large-scale electrical environment.
μi = (G/ni)T,P
i = ni/A
Surface excess concentration
Chapter 13 – Electric Double Layer
Lets consider the following electrochemical cell
Cu’/Ag/AgCl/K+, Cl-, M/Hg/Ni/Cu
M = -Fe
S = - M = F(K+ + Cl-)
Relative surface
excesses
K+(H2O) = K+ - (XKCl/XH2O)H2O
M(H2O) = M – (XM/XH2O)H2O
Electrocapillary
equation
- = ME_ + K+(H2O)μKCl + M(H2O)μM
Chapter 13 – Electric Double Layer
Measurement of surface tension, 
tmax = s
g=
m = g/s
Force down, weight, is counterbalanced by surface
tension acting around the circumference of the capillary
tip.
Weight of drop = gmtmax
Surface tension, , is a measure of the energy required to
produce a unit area of new surface. Doing this requires that
atoms or molecules previously in the bulk phase be
brought to the interface.
Example, water on a waxed (hydrophobic) surface tends to bead up. The
surface tension is very high as bringing water from the bulk of the drop to the
interface is costly energetically. The water molecule would rather remain
hydrogen bonded to other molecules. On the other hand, the surface tension is
low for water on a hydrophilic surface. Easy to spead out and wet. Forming a
new unit area is easy.
Chapter 13 – Electric Double Layer
ECM
M = -(/E_)μKCl, μM
Excess charge on the electrode is
equal to the slope of the
electrocapillary curve at any potential
tmax,s
Electrocapillary maximum, ECM
0
-0.5
-1.0
-1.5 -2.0
V vs. SCE
Slope of the curve is zero, point of zero
charge…..M = -S = 0
At more negative potentials, the surface has excess negative charge and at more
positive potentials excess positive charge. The units of positive charge
composing any excess repel each other, hence they counteract the ability of the
surface to contract.
Differential capacitance, ability of an
interface to store charge.
Cd = (M/E)
Chapter 13 – Electric Double Layer
Much of what is known about double layer structure comes
from studies at Hg-electrolyte interfaces.
• The metal is a liquid so the surface is free of grain
boundaries and defects.
• Large working potential window, particularly on the
negative potential end (Hg oxidizes a relaitively low
positive potentials (NHE)).
• Fresh, clean surface can be reproducibly and regularly
exposed (DME).
Chapter 13 – Electric Double Layer
ziFI (μC/cm2)
K+(H2O) = -(/μKF)E_, μM
Epzc
F-
+
K+
0.1 M KF Hg drop
K+
μKF = μ0KF + RTlnaKF
E-Epzc
FSimple electrostatics
K+(H2O) = -1/RT(/ln aKF)E_,μM
The relative surface excess can be evaluated at any potential, E, by
measuring the surface tension for several activities of KF. Surface
excess is given as mole/cm2. Curves look different for different
electrolyte species!!
Chapter 13 – Electric Double Layer
Chapter 13 – Electric Double Layer
Helmholtz
Gouy-Chapman
1
CTotal

1
CCompact
G-C-S
1

C DL
Chapter 13 – Electric Double Layer
  zi F ( ( x)  s ) 
Ci ( x)  Ci exp 

RT


 ( x)   zi FCi ( x)
i
Due to their dipole moments, the water molecules will compete with ions
for sites on the surface. Cations retain hydration layer. Anions will have
solvent shell partially or fully stripped and can form bonds with metal
atoms on surface.
Chapter 13 – Electric Double Layer
Predicts Ushaped C-E
profile!!
Chapter 13 – Electric Double Layer
Interfacial properties governed by the change present on the
electrode surface and the molar excesses present in the vacinity of
the electrode.
A. Helmholtz Model
Proposed two sheets of charge adjacent to one another – capacitor-like
behavior of the interface. Two sheets of opposite polarity – this is where
the idea of the double layer comes from.
Q = εεoV/d
Q/V = Cd = εεo/d
Predicts that Cd is constant
with potential, so either ε or
d muct be changing with E,
or a different model is
required.
Chapter 13 – Electric Double Layer
B. Gouy-Chapman Model
 Even though charge on the electrode is confined to the surface, the
same is not the case for the solution.
 It may take some significant thickness of solution to accumulate
enough charge to counterbalance M.
 Finite thickness arises because there is an interplay between tendency
of charge on the metallic phase to attract or repel carriers (ions) and the
tendency of thermal processes to randomize them.
 Diffuse layer model
  (E – Epzc and electrolyte concentration)
 Greatest concentration of excess ions would be when electrostatic
forces are most able to overcome thermal forces, while progressively
lesser concentrations would be found at greater distances.
ni = nio exp (-zieΦ/RT)
Φ is the electrostatic
potential (ΦM – ΦS)
Decreases with distance.
Chapter 13 – Electric Double Layer
ρ(x) = Σ nizie
Total charge stored in a lamina.
2Φ/x2 = (-e/εεo)Σ nioziexp(-zieΦ/kT)
Φ/x = -(8kTno/εεo) sinh (zeΦ/2kT)
tanh (zeΦ/4kT)/tanh (zeΦ0/4kT) = exp (-κx)
Φ = Φo exp (-κx)
Poisson-Boltzmann Eq. Shows
how the potential gradient
changes with charge stored in the
interfacial region
Symmetrical electrolyte, 1:1
no is the number conc. of each ion
Potential profile through the
diffuse layer
κ = (2nioz2e2/εεokT)1/2 = 3.29 x 107 z C*1/2
M = 11.7 C*1/2sinh (19.5zΦo)
Dilute solutions, 1:1 electrolyte, μC/cm2
C* = no/Na mole/cm3
(cm-1)
Chapter 13 – Electric Double Layer
Φ = Φo exp (-κx)
Cd = M/Φo = 228 zC*1/2 cosh(19.5zΦo)
Chapter 13 – Electric Double Layer
C. Stern Model
 G-C model predicts an unlimited rise in Cd with E because the ions are
not restricted with respect to location in solution.
 They are considered as point charges with no real size!
 Therefore, at high polarization potentials, the effective distance
between the metallic and solution charge zones decreases toward zero
and d increases.
 Ions in fact have a finite size (radius plus solvation sheath)
 Low electrolyte concentration and E near Epzc, the thickness of the
diffuse layer is large compared to x2. The diffuse layer would be more
compressed at very positive and negative E (relative to Epzc) and or at
high electrolyte concentrations.
Model takes into account aspects of both the Helmholtz and G-C models!
Chapter 13 – Electric Double Layer
Potential profile in the diffuse layer is given by
tanh (zeΦ/4kT)/tanh (zeΦ2/4kT) = exp (-κ(x-x2)
Charge on the solution side of the interface must be related to ni and Φ
M = -S = -εεo (Φ/x)x=x2 = (8kTεεonio)1/2 sinh(zeΦ2/2kT)
Taking /E, one gets the capacitance of the interface, Cd
1/Cd = x2/εεo + 1/{(2εεoz2e2nio/kT)1/2 cosh(zeΦ2/kT)}
1/Cd = 1/CH + 1/CD
governed by the smaller of the two
Near Epzc and low electrolyte concentration, V-shape profile expected.
Chapter 13 – Electric Double Layer
At large electrolyte
concentrations and or large
polarization potentials, CD
becomes large so it does
not contribute to Cd.
Chapter 13 – Electric Double Layer
Relationship between  (M & S), Φ and Cd
Specific Adsorption
 Specific versus nonspecific adsorption
 Non-specific adsorption provides no mechanism for the electrode
potential to vary with the electrolyte concentration.
 Surface tension plots diverge at E-Epzc > 0 due to specific anion
interactions with the surface.
 I- > Br- > Cl- > F- More polarizable, the greater the tendency to
specifically adsorb.
 Full or partial charge transfer with the electrode, but often the
negative charge is retained.
 Essentially, specific or contact adsorption of an anion makes the
surface potential more negative.
-
Chapter 13 – Electric Double Layer
1
RT
 E

  ln asalt
Concentration (M)


 M
Epzc (NaF)
Epzc (KI)
-0.472 V
-0.472 V
-0.480 V
-0.820 V
-0.720 V
-0.660 V
1.0
0.1
0.01
-
Esin – Markov Effect
Extension of the electrode.
Makes potential more
negative. More negative E
is required to compensate
with solution charge.
Specific adsorption increases as:
F- < BF4- < ClO4- < Cl- < Br- < I-
vs. SCE
Much of what is known about the
electric double layer structure
comes from many measurements:
1.
2.
3.
4.
5.
Cd and surface tension
Single crystal metals
UHV surface science methods
STM
Radio tracer studies
Chapter 13 – Electric Double Layer
Adsorption Isotherms
 Adsorption isotherm – relationship between i, ai, & E or qM
 aia = aib exp(-Go/RT) = βiaib
A. Langmuir Isotherm
 No interactions between adsorbed molecules.
 No heterogeneities in the surface sites.
 Monolayer coverage at saturation.
s
i/(s - i) = βiaib
Θ = i/s
Θ/(1-Θ) = βiaib
i = sβiCi/(1 + βiCi)
i
Conc.
Chapter 13 – Electric Double Layer
A. Frumkin Isotherm
 Interactions between adsorbed species can sometimes occur on a surface.
i/(s - i) exp (-2gi/RT) = βiaib
g
0, Langmuir isotherm approached
GoFrumkin = GoLangmuir - 2gi
g = expresses the way in
which coverage changes
adsorption energy of i.
((J/mol)/(mol/cm2))
g > 0 then interactions are
attractive.
g < 0 then interactions are
repulsive.
Rate of build-up of adsorbed layer depends on the rate of mass transport to
the surface.
i = sβiCi = sβiCi(0,t)
i(t) =  Di [Ci(x,t)/x]x=0 t
Chapter 13 – Electric Double Layer
Double Layer Effects on Reaction Rates
 ko  electrolyte composition
 Variation in potential in the double layer region
Oz + e-  Rz-1
A. z  0
io = nFAkoCo(1-)CR
Co(x2,t) = Cob exp (-zFΦ2/RT)
Surface concentration
greater than bulk.
B. Potential driving reactions is not ΦM – ΦS = Eappl, but rather ΦM – ΦS – Φ2
Effective potential is Eappl – Φ2
kt = ko exp [-(-z)FΦ2/RT]
io,t = io exp [-(-z)FΦ2/RT]