physical and interfacial electrochemistry 2013 module...the term electrified interface (or double...
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Physical and Interfacial Physical and Interfacial Electrochemistry 2013
Lecture 5Electrode/solution
Interface+ -
Excess negativecharge density
Electrode
Potential
HelmholtzL Interface
Solution
+
+
+
+
--
--
s
Layer
Excess positivecharge density
xHDistance
ca. 0.6 nmCDL
The structure of the electrified interface
Th i f b di i il i f i l ifi d Al • The interface between two dissimilar interfaces is electrified. Almost all surfaces carry an excess electric charge.
• Hence when two dissimilar phases come into contact, charge separation occurs in the interfacial region which results in the generation of an occurs in the interfacial region which results in the generation of an interfacial potential difference or electric field.
The term electrified interface (or double layer region) is used to describe ythe arrangement of charges and oriented solvent dipoles at the interface between an electrode and an electrolyte . A simplistic picture of this region (termed the Helmholtz model) is presented in the figure outlined across. As we have seen this region is very thin The structure of the double layer we have seen this region is very thin . The structure of the double layer region can be pictured as a parallel plate capacitor with a plate separation of molecular dimension.
Excess negativeExcess negativecharge densityE field generated
Bottom line : an electricalDouble layer is set up at
++
--Excess positive
y pM/S interface.
++ -
Excess positivecharge density
Electro-neutrality is valid in bulk ysolution.
• Consider a metal electrode in contact with an aqueous solution containing salt (e.g KCl (aq)).
• The solution contains solvated charged ions and solvent dipoles.• Forces experienced by ions and solvent molecules in bulk of
solution are isotropic : spherical symmetry operates Ions and solution are isotropic : spherical symmetry operates. Ions and water molecules (on a time average) experience forces which are position and direction independent.Th i t li t f l t di l d iti d • There is no net alignment of solvent dipoles, and positive and negative ions are equally distributed throughout any volume element of the solution.
• Electroneutrality operates in bulk solution region very far from electrode surface.
Electroneutrality breaks downin surface region.
• What about the solution region next to the electrode surface?
• In this region forces experienced by ions and solvent dipoles are no longer isotropic and homogeneous. The forces are anisotropic because of the presence of the electrode phase.p p p
• New solvent structure, different from that of the bulk, develops because of the phase boundary.El t t lit b k d th l ti id f th • Electro-neutrality breaks down on the solution side of the interface.
• There will be a net orientation of solvent dipoles and a net pexcess charge in any volume element of the solution adjacent to the electrode surface.
• The solution side of the interface becomes electrified• The solution side of the interface becomes electrified.
Interfacial charge separation g pgenerates high interfacial E-field.
• Once the solution side of the interface becomes electrified (acquires a net or excess charge), an electric field will operate
th h b dacross the phase boundary.• Since the metallic phase contains charged particles, the latter will
respond to this E field.Th f l t ill f t d th • The free electrons will move away from or move towards the interface depending on the direction of the E field.
• Thus a net charge will be induced on the metal, which will be equal in magnitude and opposite in sign to that on the solution side of the in magnitude and opposite in sign to that on the solution side of the phase boundary.
• Thus charge separation occurs across the M/S interface, and this gives rise to an interfacial potential difference.gives rise to an interfacial potential difference.
• Typically the potential difference is ca. 1.0 V. However the spatial dimensions of the interface region are very small, typically 1 nm thick. Thus the electric field strength present at the M/S g pinterface will be typically 107 Vcm-1 which is very large.
Electrified interfaceElectrified interface.F l d fi iti • Formal definition. – Term electrified interface used to describe the arrangement of
charges and oriented solvent dipoles at the interface between an electrode and an electrolyte solutionelectrode and an electrolyte solution.
• We now present some simple approximate models to describe the properties of the electrified interface.W i th i l d l • We examine three simple models :– Helmholtz compact layer model– Gouy-Chapman diffuse layer model– Stern model .
• A key idea which we develop involves the representation of interfacial structure in terms of an electrical equivalent circuitqelement (specifically a single capacitor or series of capacitors).
• We initially adopt a simple pictorial description. This will be followed by a more quantitative mathematical analysis.fo owed y a more quant tat e mathemat ca ana ys s.
Simple representation of electrode/solutioninterphase region : Helmholtz
Excess negativecharge density
El t dExcess negativecharge density
p gcompact layer model.
+ -
Electrode
+ -
charge density
Electrode
Potential
HelmholtzL
Solution
+
+
-- Solution
+
+
--
Layer
+
+
--
+
+
--
s
Excess positivecharge density Electric field
present at
Excess positivecharge density
xHDistance
ca. 0.6 nmCDL
pinterface
rCC 0
26020 cmFCDL Structure of thin doublelayer region modelled asa parallel plate capacitor
H
rHDL x
CC 0 a parallel plate capacitorwith a plate separation of molecular dimension.
Excess negativecharge density
ElectrodePotential
Numerical calculationsUsing the Helmholtz
d l
Solution
+
+
+ ---
HelmholtzLayer
Model.
HxE
+
+
+
--
s
Distance
We need the followingRelationships from basicPhysics.
Electric fieldStrength (Vm-1)
Excess positivecharge density
xHDistance
ca. 0.6 nmCDL
CHelmholtzCapacitance (Fm-2) • A fundamental problem is
l f h HC
f h d
InterfacialPotential difference (V)
assigning a value for thedielectric constant of thesolvent in the thin HelmholtzregionSurface charge density
on metal (Cm-2)
0 = permittivity of vacuum= 8 854 x 10-12 Fm-1
region.• Solvent structure in this regiondiffers considerably from that ofthe bulk solution.H id bl di l i i
H
rH x
C 0= 8.854 x 10 Fmr = dielectric constant ofsolution.
• Have considerable dielectric saturationeffects and so dielectric constant will be much lower than that associated with the bulk solution
Distance between platesof capacitor
with the bulk solution.• The dielectric constant may also varyrapidly with distance in interfaceregion.
65)(78)(
Helmholtzbulk
r
r
Potential Distribution in Helmholtz CompactLayerLayer.
Linear potentialp fil in c mp ct
)(x MPotential distribution obtainedusing the Poisson-Boltzmannequation which relates charge
profile in compactlayer.
equation which relates chargedensity and electrostatic potential .
d 2
HxS
rdx
02
Radius of solvatedion = xH
xIons treated as point charges.Hence can assume that excesscharge density between electrode
d 02
Mx 0charge density between electrodesurface and OHP is zero, hence = 0.
dxddx
02
SM
SH
x
xx
x
dxM
Hx
xx
xH
SMM
This simple Helmholtz picture is not complete since it predicts that the double layer capacitance is a constant independent of concentration and the potential applied to the electrode . Experiment has shown that the double layer capacitance varies with the latter layer capacitance varies with the latter quantities in a somewhat complex manner and so this simple picture of the double layer region must be
d f d k h modified to take this observation into account .Hence we conclude that a more elaborate model is requiredelaborate model is required.However the simple Helmholtz model will hold quite well for electrolyte concentrations greater than 0.5 M.
The diffuse double layerThe diffuse double layer.H d 3 D di t ib ti f h i ?• How does a 3-D distribution of charge arise?
• We have neglected the disordering effect of the thermal motion of the ions in the solution. This opposes the ordering m f pp gtendency due to operation of electrostatic forces in the interface region.
• Thermal and electrostatic forces results in an equilibrium The • Thermal and electrostatic forces results in an equilibrium. The excess charge density sS counterbalancing the excess charge density sM on the metal, is at a maximum close to the electrode
f It di i i h i i t ti l surface. It diminishes in an approximate exponential manner with increasing distance from the electrode surface, giving rise to a diffuse space charge layer adjacent to the electrode.
• Detailed analysis indicates that the thickness of the diffuse layer region will depend both on the potential applied t the electrode and on the concentration of ions present in the electrode, and on the concentration of ions present in the electrolyte solution.
A more sophisticated picture (termed the Gouy-Chapman model) assumes that the excess
Gouy-Chapman model of diffuse double layer.
p p ( y p )charge density on the solution side of the interface can be represented in terms of a three dimensional space charge region . This is presented schematically in the figure presented below . This charge distribution arises as follows . It is reasonable to suppose that the disordering forces arising from the thermal energy of the ions should oppose the ordering g g gy pp gtendency induced in the interphase region by electrostatic forces . Consequently instead of considering a simple compact layer (termed the Helmholtz layer) these thermal and electrostatic forces are assumed to result in an equilibrium , in which the excess charge density S counterbalancing the charge density M on the metal, is at a maximum close to the y S g g y M ,electrode surface, and would diminish in an exponential manner with increasing distance from the electrode surface, thereby giving rise to a diffuse layer adjacent to the electrode . Detailed analysis indicates that the thickness of the latter region will depend on the potential applied to the electrode and on the concentration of ions in the electrolyte . p pp y
E lectrod e
E x cess n egative ch arged en sity
In the Gouy-Chapmanmodel of the interfaceregion, it is assumedthat the excess charge
-+
+ ---
--
--
-- -
-
that the excess chargedensity on the solution side of the interfacecan be represented interms of a threedimensional space charge.
-
--
+
+
+
-
--
-- ----- -
-
-
s
dimensional space charge.
E xcess p ositivech a rg e d en sity
x
ca. 1 -10 nm
L DS o lu tion
Diffuse layer thicknessOHP
Gouy-Chapman model of diffuse doublelayer
E ti h
layer.
r
BD
rDDL Tk
zeL
CC
0
00
hh
2cosh
DM
Electrode
Excess negative chargedensity
DD
rD
r
CCL
00,
0000
cosh
coshcosh
Valid when 0 is
DM
-+
+ -- -
--
-- -
- D
rD L
C 00, Valid when 0 is
small.
0
At potential ofZero charge:
0-+
+
-
-
-- ----- -
-
-
1cosh0
0
0
00
rC 0 --+ - - s
xSolution
DD L
C 0,
Excess positivecharge density ca. 1-10 nm
LDSolution
0sinh4 Dd LzecL D b L h
0sinh4 Dd Lzec
Charge density in diffuse layer
LD = Debye Length.Measures diffuse layerthickness.
Diffuse layer thickness.The diffuse layer thickness is called the Debye
Note that the Debye Length varies inversely with the square root of the electrolyte concentration . Hence as the solution becomes more concentrated the thickness of the diffuse y y
Length and is given the symbol LD. In many books this is denoted as 1/ .For a z,z electrolyte the Debye length is given by the expression across.
becomes more concentrated the thickness of the diffuse layer decreases . For instance for a simple 1-1 electrolyte such as NaCl at 298 K, LD = 30.5 nm when c = 10-4 mol dm-3
. However when c is increased to 0.1 mol dm-3 the Debye length decreases to 0.96 nm .g y p
Evaluation of the constants gives auseful expression for computation.
2/10
2/1
RTTkB
We recall this concept when we discussed the DH theory of Ion/ion interactions.
220
22 22
cFz
RTcezTkL rB
D
T111036
2/19106.9 cLD
cT
zL r
D103.6
1e-8
m mol m-3
or mM L D/m 1e-9
Note that the DebyeLength increases as
1 10 100 10001e-10
Length increases asthe ionic concentrationdecreases. The diffuselayer thickness will be greatest for the most dilute
c/mol m-3
1 10 100 1000greatest for the most dilute solutions.
(1,1) electrolyte, water r = 78, T = 298K
The Poisson-Boltzmann equation (I).From classical electrostatics we use the Poisson equation whichrelates the dielectric displacement vector D and the local volumedensity of charge (the number of charges per unit volume)density of charge (the number of charges per unit volume).
permittivitypermittivity of vacuum
ED
Dr 0
permittivity of vacuum
1120 10x854.8 Fm
E dielectric constant
Divergence electric fieldDivergenceoperator
electric fieldvector
Electric field vector E can be related to the electrostatic potential p using basic physics.
E
2
Gradient operatorThis is the form of the Poissonequation which relates the charge densityand the electrostatic potential.
The Poisson-Boltzmann equation (II).
We now need to evaluate the charge density . The volume densityof charge is obtained by adding together the product of the chargeqj and concentration cj of each ionic species j in the solution next toqj and concentration cj of each ionic species j in the solution next tothe electrode surface.
eczcq
Ion valence
j
jjj
jj eczcq
fundamental chargeWe use the Boltzmann equation of statistical mechanics to obtain arelationship between the local counterion concentration cj and the bulkconcentration cj
. To do thisjwe need to evaluate thework wj done in bringingthe ion from a reference
Tkw
ccB
jjj exp
point at infinity , up to a point distance rfrom the electrode surface. Weassume that this work is purely
Tkrez
cc jjj
)(exp
electrical in nature. )()( rezrqrw jjj
TkB
jj
The Poisson-Boltzmann equation (III).TkL B
D 211
We are now in a position to write down the PB equation.This is a fairly complicatedequation to solve from first
r )(1)(2
cze 2Debye Length, z,z electrolyte
q f m fprinciples. The exact form ofthe differential equation dependson the geometry.W sh ll ss m l t l t
j
jjj
rez
recz
e p1
)()(2
We shall assume a z,z electrolytesuch as KCl or NaCl.The geometry determines the formthat the 2 operator takes.
j B
jjj Tk
ecz
exp
zzz l tp
A planar geometry is used formacroelectrodes, whereas a sphericalgeometry is adopted forultramicroelectrodes
ccc
zzz z,z valentelectrolyte
zezezecxd 2ultramicroelectrodes.
d 2
2
Planar geometry
Tkzezec
Tkze
Tkzezec
dxxd
BB
sinh2
expexp2
drdr
drd
r
dx2
22
2
1
TkB
Tkze
Tkzezec
drdr
drd
r
expexp1 2
2
The PB equationis solved for drdrr
Spherical geometry
Tkzezec
TkTkdrdrr
B
BB
sinh2
is solved for .
Detailed analysis utilising electrostatic theory and statistical mechanics (Albery 1975) shows that
zek TB2
x( y )the normalised potential distribution in the diffuse layer is given by :
2 210tanh tanh exp
k Tzek T
B
B
2
200
LD
In short one uses the Poisson equation of electrostatics which relates the electrostatic potential to the charge distribution generating it
0 p
p g g gand the Boltzmann distribution law of classical statistical mechanics which describes the way that ions are distributed throughout the diffuse layer to develop a hybrid equation called the Poisson-
The variation of normalised potential with normalised distance for various values of 0 computed using the full PB expression is presented in the next l d l h d
p y qBoltzmann (PB) equation which is then solved using standard mathematical techniques to obtain the expression outlined above. This procedure is well described in many of the books dealing with
slide. Below 0 = 1 we note that decays exponentially with distance . For 0 > 5 and a limiting curve is obtained . We note also that decays to zero when is
h h h h y g
fundamental physical electrochemistry .
In the full PB expression above denotes the electrostatic potential at any distance in the diffuse layer and is the electrostatic potential at
greater than 3 . This means that the strong electric field of the electrode is contained within a distance of ca. 3LDfrom the electrode .
diffuse layer, and 0 is the electrostatic potential at the surface of the electrode . For small values of the normalised potential we write that and the potential distribution within the diffuse layer decays according to the following simple
tanh
layer decays according to the following simple exponential relationship :
0 exp
12dPoisson/Boltzmann equation : planar surface.
02sinh21
2
2
dd
Large surface potential
00 0
exptanh2 1Neglect compact layer
0
exp2tanhtanh2 01
ze
Normalised potential Normaliseddistance
Tk
zeTk
B
B
2
2
00
x
Lx
D
Full solution of PB equation
exp0
Variation of electrostaticpotential with distance
q
potential with distancein the diffuse layer region.The potential is effectivelyexponentially decaying with
Small surfacepotentialDebye-Huckelexponentially decaying with
distancefrom solid surface.
Thickness ofDiffuse layer
yapproximation
The Poisson Boltzmann equation (IV).
• The PB equation fully describes the pertinent electrical propertiesof the diffuse layer . However it can only be solved analytically fora few special situations For the most general cases a numericala few special situations. For the most general cases a numericalsolution has to be adopted.• The PB equation for flat planar surfaces can be rigorously solved forz,z electrolytes.z,z electrolytes.• This cannot be done rigorously for spherical surfaces. Approximatesolutions of varying degrees of accuracy have been produced.•A reasonable approach valid both for planar and spherical interfacespp p pinvolves the Debye-Huckel approximation, which results in the transformation of the PB equation into a linear form as indicated below. This approximation will beppvalid provided that the potential at the surface of the electrodeis not too large.
Approximate form
22 Planar
xx expexp
DH approximationpprox mate form
Of potential distribution
22
2
dxdPlanar
geometry
DLx expexp 00 Tkze B
Charge density in diffuse layer region.If the potential applied to
00
1
ddxxD
If the potential applied tothe metal surface is smallwe can assume a linearapproximation and
For a z,z electrolyte the local charge density is given by
pp
00sinh
2sinh22exp2exp
zeczec
0 0 0
4
zec
D
Debye Length
0
2sinh2 dzecD sinhd
0
22
0
2
24
cez
Tkzezec
B
0
0
sinh2sinh2
dzec
D
N t th t th i f
sinh
sinh
dd
d
00
2
Tkcez
B
0 sinh
0cosh4
0
zec
D
Note that the sign of Dis opposite to that of 0.Hence a positive 0 impliesthat negative ions are attracted
0sinh40
zec
that negative ions are attractedto interface and vice versa.
We define the differential
Diffuse Layer capacitance CD
We define the differentialcapacitance of thediffuse layer as
00
22
sinh2
BD d
dTkcezC
000 2
dd
Tkze
dd
ddC D
B
MDD
22
0
22
cosh2
BTkcez
i h4 zec
Charge density within diffuse layer is
022
2cosh2
BB Tkze
Tkcez 0sinh
D
W ll th t D b L th (diff
0
0
cosh2
cosh
D
B
CTk
ze
Tk11
We recall that Debye Length (diffuselayer thickness is
cez 222 0cos DC
CD depends on potential.It is not constant
cTk
zeL B
D 211
Tkcez
B
2
It is not constant.
Variation of diffuse layercapacitance withcapacitance with potential.
How good is the diffuse layerTheory in practice ?Theory in practice ?
Diffuse layer model also appliesf ll d l l / l for colloidal particle/solution interface.Double layer modelling still beingP f d t h l l t Performed at research level to various degrees of sophistication.
We can also compute the distribution of ions in the diffuse layer (Albery 1975) . Now ions
ithi th diff l t ll f th
In the former expressions the function f(0) will depend on the sign of the potential applied to th l t d di t within the diffuse layer are not all of the same
sign . The charge density on the electrode is balanced by an accumulation of charges of opposite sign (termed counter ions) and by a d fi it f h f th i (t d
the electrode according to :
00 00 ln tanh
2f
deficit of charges of the same sign (termed co-ions) compared with their concentrations in the bulk solution region . Now the ion distribution in the diffuse layer is given by the B lt di t ib ti l
00 00 ln tanh
2f
Boltzmann distribution law :
cc
zek TB
exp exp
2
These expressions, although complex, carry an important message . In simple terms they state that almost all the charge on the metal is balanced by the accumulation of counter ions
(1)c k TB
It is possible to show that (Albery 1975) the co-ion (labeled +) and the counter-ion (labeled
balanced by the accumulation of counter- ions and relatively little by the expulsion of co-ions . The counter-ions therefore enjoy a greater significance than the co-ions .
- ) distributions are given by the following expression :
cf
tanh2 1
This breakdown in the electroneutrality is outlined in the figure presented in the next slide for various values of 0 . Here eqn.1 and eqn.2. have been used . It is clear that even for quite small values of 0 the counter-ion and co-ion concentrations in the diffuse layer will exhibit significant
c
f
cc
f
tanh
coth
0
20
212
concentrations in the diffuse layer will exhibit significant deviations from their bulk solution values where electro-neutrality is maintained . We note that for > 5 electro-neutrtality is restored . For instance for 0 = 0.5 the concentrations are altered by a factor of 3 . For larger
(2)
values of 0 the concentration of the repelled co-ions approach zero in the interphase region near the electrode surface whereas the concentration of the attracted counter-ion is many times its value in the bulk solution .
Electroneutrality breakdownin diffuse layer region :
Counter ion excess
2 1t h fc
in diffuse layer regionPlanar surface.
02
02
1coth
2tanh
fc
fc
02 f
c
2tanhln0 0
00 f
2tanhln0 0
00 f
Counterion concentration increasesclose to charged solid surface and co-ion C i d l ticlose to charged solid surface and co-ionconcentration decreases close tocharged surface.
Co-ion depletion
Typical variation of CDL with applied potential.Hg/aqueous KCl interface.
Modern models incorporatingspecific adsorption of ions
Capacitance maximum
in the inner compactlayer, allied witha model for thewater structurewater structurein the inner layerexplain thecapacitance maximum
Constant capacityRegion.g
Explained byHelmholtz model
Capacitance minimum
Explained byGouy-Chapmanmodel
Stern model of the interface region.
• Neither the Helmholtz compact
• The Stern model is as follows. Next to the electrode we have a region of high electric field and low dielectric constant (r value • Neither the Helmholtz compact
layer model nor the Gouy-Chapman diffuse layer model is totally satisfactory.
w n n ( r uca. 6) with a row of firmly held counter ions. Beyond that there is an ionic atmosphere (the diffuse layer) where there is a
• In the GC model the solvated ions are modelled as point charges. This neglect of ion size i li ti I lit th
diffuse layer) where there is a balance between the ordering electrostatic force and disordering thermal motions. The dielectric constant is unrealistic. In reality the
solvated ion can only approach the electrode surface to a distance equal to its solvated
di
The dielectric constant increases rapidly with distance in this region.
• The electrical potential varies qradius a.
• Hence a more logical approach is to combine the features of h l h l
The electrical potential varies linearly with distance (ca. hydrated ion radius) within the inner compact layer and decreases in an approximate the Helmholtz and Gouy-
Chapman models. This was done by Stern.
decreases in an approximate exponential manner with distance within the diffuse layer, decaying to zero in the bulk solutionbulk solution.
Stern model of solid/solutioni h i
The Gouy-Chapman model of the double layer region assumes that ions behave like point h Thi l f i i i i
interphase region.
charges . This neglect of ionic size is not very realistic . Ions are hydrated in aqueous solutions and so the latter species can only approach the electrode to a distance equal to the radius of a hydrated ion . Consequently, a y q y,more logical approach is to combine the features of the Helmholtz and Gouy-Chapman models . This was done by Stern . Hence a better picture for the double layer is as follows Next to the electrode we have a region of high .Next to the electrode we have a region of high electric field and low dielectric constant with a row of firmly held counter-ions . Beyond that there is an ionic atmosphere (the diffuse layer) where there is a balance between the l t t ti f d d th l Consequently the interface region may now be electrostatic forces and random thermal
motions . This idea is presented in figure 2.6. The potential variation is also shown schematically . The potential varies linearly with distance within the inner compact layer
Consequently the interface region may now be represented in terms of a simple circuit model consisting of two capacitances labeled CH and CD in series . The total double layer capacitance CDL is therefore given by the following reciprocal p y
and decreases approximately exponentially with distance within the outer diffuse region . The line of demarcation between the compact and diffuse regions is called the Outer Helmholtz Plane (OHP)
therefore given by the following reciprocal expression. 1 1 1
C C CDL H D
Helmholtz Plane (OHP) .
CL
zek T LD
r
D
H
B
r
DH
0 0
2cosh coshC
xDLr
H 0
Stern model of solid/solutioninterphase region
CCC111
interphase region.
DHDL CCC
C CC CH CDCDL
Series arrangement of capacitors.
The smaller of the two capacitancesThe smaller of the two capacitanceswill determine the overall capacitance.If CH and CD are of very different sizethen the term containing the larger one
The diffuse layer capacitancewill predominate when the solution concentration is low.then the term containing the larger one
may be neglected.
Linear potentialVariation with di t
A reasonable model ofthe electrode/solutionA reasonable model ofthe electrode/solution distancethe electrode/solutioninterface.the electrode/solutioninterface.
The electrode/solutioni t f i d ll d
ExponentialV i ti finterface is modelled as
a series arrangement oftwo capacitors.This is an equivalent
Variation ofPotential withdistance
This is an equivalentcircuit representationof the interface.
From basic physics :DLHx
Compact layer
CCC111
CH CDCDL
p y
DHDL CCCSeries arrangement of capacitors.
Total capacitance Diffuse layer
Further elaborations on interfacial structure Hence in reality the situation at an
electrode/solution interface is quite complex We
The model for the double layer presented here is not at all sophisticated . Much work is currently underway to
electrode/solution interface is quite complex . We will not discuss these matters here . Instead we will present a picture of the currently accepted model of the interphase region in the figure presented in the next slide.p y y
develop better models for the interface region . For instance the inner layer capacity CH is independent of electrolyte concentration but it depends strongly on the charge density of the electrode and somewhat more weakly on temperature Negative ions may also de-
This is termed the BDM model (Bockris and Reddy 1970) . Note that it represents the situation on the solution side of the interface in terms of a triple layer . Many of the complicating features weakly on temperature . Negative ions may also de-
solvate and specifically adsorb on an electrode surface . This influences the potential distribution at the interface . There also will be an oriented layer of water molecules attached to the metal surface . This will give i t f t ti l
ay r . Many of th comp cat ng f atur s mentioned in the previous paragraph are illustrated . An Inner Helmholtz Plane (IHP) is defined and is regarded as the locus of the electrical centres of specifically adsorbed ions . A primary and secondary water layer is introduced with rise to a surface potential .
The metal surface is also more complex than we have assumed . Because of the small electronic mass, electronic density can extend for a certain distance out
secondary water layer is introduced with considerably differing dielectric properties . The jury is still out on whether the BDM represents the true picture of the electrified interface region . The reader is referred to Bockris and Khan (1993)
d h i kl (1996( ) 1996(b)) f f h y
from the electrode surface . Typically the electronic density decreases exponentially with a decay length of ca. 0.05 nm . Since the electronic density of metals is high, this spill over will give rise to an appreciable negative excess charge outside the metal which for an
and Schmickler (1996(a) , 1996(b)) for further details on the current state of play .
negative excess charge outside the metal , which for an uncharged surface, must be balanced by an equal and opposite positive excess charge within the metal . This gives rise to a significant surface potential . The electric field in the double layer will distort the l t i dist ib ti d h th s f t ti l electronic distribution and change the surface potential .
This will in turn effect the magnitude of the Helmholtz capacity CH .
The BDM triple layerModel of the metal/solutionModel of the metal/solutionInterface.
One currently accepted model isOne currently accepted model isthe BDM model.It represents the situation onthe solution side of the interfacein terms of a triple layer.an inner helmholtz plane (IHP)is introduced and is regardedas the locus of the electrical centersas the locus of the electrical centersof specifically adsorbed ions.These anions are stronglyadsorbed onto the electrode
’
surface and are partiallydesolvated. This fact causes a reversal ofelectrostatic potential in the regionbetween the IHP and the OHP
xH
x’Hbetween the IHP and the OHP.A primary and secondary water layer isintroduced with differing dielectric properties.The primary water layer (r = 5) is located immediately adjacent to the metal electrode jsurface. The secondary water layer (er = 36) is located as a hydration sphere around a solvated cation and anion.
Polarizable and non-polarizable interfaces.
CDL Interfacial structure
RRCT
Electrode/solutioninterface
Electrical equivalentcircuitNo leakage of
Measures ETinterface circuit
Ideally Polarizable Interface : CTR
Charge acrossM/S interface
Measures ETAcross interface
y CTR
Ideally non-polarizable Interface: 0CTR
Charge transfer occursacross M/S interface
Simple equivalent circuit representation ofelectrode/solution interface region
CDLiC
electrode/solution interface region.
DL chargingcurrent
i
iC
RS
current Resistance ofsolution
Faradaiccurrent
iii RCT
iF
Solution
FC iii
ElectrodeDouble layer chargingcurrent always presentin addition toF d Faradaic current inelectrochemicalmeasurements.
Evaluation of CDL(and hence ic) always necessary
h kwhen makingkinetic measurementsat short timescales.
Experimental interrogation of pelectrode/solution interfaces.
• Conventional electrochemical techniques.– Based on measurement of current, potential and charge.– CV, RDV, RRDV, PSCA, CIS etc.– Applied both to macrosized and microelectrodes.
h d ll d l d– Theory, instrumentation , and practice well developed.– No direct information on microscopic structure of
electrode/solution interface.• Spectroscopic techniques• Spectroscopic techniques.
– Provides useful chemical information anout species at interfaces.– FTIR, Raman, UV/VIS, XPS, EXAFS, Ellipsometry, EC/NMR (new
technique very specialised limited application at present)technique, very specialised, limited application at present).• Scanning probe microscopy.
– High resolution topographical imaging of electrode surfaces with atomic resolution. Surface reactivity also probed with high spatial y p g presolution.
– STM, AFM, SECM.
R f t P A Ch i t A H tt T h i d M h iRefer to: P.A. Christensen, A. Hamnett, Techniques and Mechanismsin Electrochemistry, Chapman and Hall, UK, 1994 for details concerningSpectroscopic techniques.