2.potentials, kinetics, and d orbitals: featuring e and ec mechanisms note to alanah: importance of...
TRANSCRIPT
2.Potentials, Kinetics, and d Orbitals:Featuring E and EC mechanisms
Note to alanah: importanceOf the fast electron transferEffect of iron aqueous for -Ubiquitous – total iron Environment, aquated etc
Ox*Oxsurf
Redsurf
Red*
Homogeneous Electron transferHere a self exchange
HeterogeneousElectron transfer
Fe CN e Fe CN63
64
Fe CN Fe CN Fe CN Fe CN63
64
64
63
* *
Solution diffusionSolvent reorganizationBond reorganizationPotential field effects (charge on
surfaces)
The two are related processes
k11
ko
1. Electron “hops” max ~ 14 angstroms
can be accompanied by surface oxidation
diffusionOx*Oxsurf
RedsurfNa+
migration
Distance ElectricField extends from Surface into solution
k
Diffusion red
Red*
Precursor
HomogeneousElectron transfer
HeterogeneousElectron transfer
Product
If we control migration have no precursor have no product reaction have adequate compensating charge movement have no electrode surface alterations then:
k
diffusionOx*Oxsurf
Redsurf
HeterogeneousElectron transfer
Reversible, semi-infinite linear diffusion- reversible – electron transfer is “instantaneous- semi-infinite – bulk solution width is much greater than width of
solution near the electrode surface which has been affected- linear diffusion – material diffuses perpendicular towards the electrode
(no radial diffusion)
Fe CN e Fe CN63
64
Extends “infinitely”
Region “perturbed”By the electrode
What happens when the system is NOT reversible?
k
DnF
RT
o
1 2
1 2
1 2
1/
/
/
Stretches the duck, 1 0
0 0 1.
-1.00
-0.80
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
0 0.2 0.4 0.6 0.8 1 1.2 1.4
V
Cu
rren
t
Simulation of 1e reversible systemA=1cm2, v=1V/s, D= 1x105 cm2/s, Cox=1mole/L, alpha=0.5; Eo=0.8 V
k (cm/s)= 1x104
10.01 0.001 0.0001
What controls whether or not the electronTransfer is “reversible”?
Use Example Metal Complex Chemistry
Image: A Van der Ven and G. Ceder, p 47 in Lithium Batteries Science and Technology, Nazri and Pistoia, eds., Kluwer, 2004
Eg d orbitals on central metal lie in the pathOf incoming octahedrally Oriented ligands
T2g d orbitals on theCentral metal lieSomewhat out of The path of the Incoming octahedrallyOriented ligands
http://vinobalan.tripod.com/sitebuildercontent/sitebuilderpictures/picture1.gif
Images of electronDensity of d orbitals
z
x
y
x
y
+
z
z
x
y
+
z
x
y
yz
+
z
x
y
xy
+
z
x
yxz
+
Cl-
Cl-
Cl-Cl-
Cl-
Incoming Cl-see little e
Incoming Cl-bumps into d orbital e
1. Initially all orbitals same energy2. Incoming anion interacts with d orbitals3. Energy levels change due to the interaction4. 3 orbitals move down in energy5. 2 move up
z
x
y
+
z
x
y
xy
+
z
y
+
z
z
x
y
+
Cl-Cl-
Cl-
Cl-
Image: A Van der Ven and G. Ceder, p 47 in Lithium Batteries Science and Technology, Nazri and Pistoia, eds., Kluwer, 2004
Eg d orbitals on central metal lie in the pathOf incoming octahedrally Oriented ligands
T2g d orbitals on theCentral metal lieSomewhat out of The path of the Incoming octahedrallyOriented ligands
Cl-
N..
Greater Orbital Splitting with Nitrogencharge dense lone pair (localized)
z2
z
z
x
y
+
z
z
x
y
+
D orbital energy in absenceof ligands
Suppose it is :NH3 instead of Cl-
What do you think will happen?
CN->NO2->en>NH3>NCS->H2O>F->OH->Cl->SCN->S2->Br->I-
Strong field Weak field
OH->Cl->SCN->S2->Br->I-
Weak Field
CN->NO2->en>NH3>NCS-
Strong Field
10Dq10Dq
6Dq (2*6=+12)
4Dq (3*4= -12)
eg
t2g
OH->Cl->SCN->S2->Br->I-
Weak Field
CN->NO2->en>NH3>NCS-
Strong Field
6Dq
4Dq
eg
t2g
Co: 3d74s2
Co3+: 3d6 Co2+: 3d7
Co t e Co t etg tg g3 6 2 6 1
( ) Co t e e Co t etg g tg g
3 4 2 2 5 2
( )
Crystal Field Splitting alsoAffects the self exchange rate
http://vinobalan.tripod.com/sitebuildercontent/sitebuilderpictures/picture1.gif
z
x
y
Co t e Co t etg tg g3 6 2 6 1
( )
Reduction requires insertionOf an electron in an eg orbitalWhich is directly in the pathOf an incoming ligand. ThisRequires that the ligand moveOut (bond lengthening) in Order to avoid electrostaticrepulsion
OH->Cl->SCN->S2->Br->I-
Weak Field
CN->NO2->en>NH3>NCS-
Strong Field
6Dq
4Dq
eg
t2g
Cr: 3d54s14po
Cr2+: 3d4Cr3+: 3d3
Cr t e C r tg g3
23 2
24
( ) Cr t e C r t etg tg g
3 3 2 3 13
( )
One electron in an orbitalIn the path of an incomingLigand – implies bond length changes
Strong Field predicted)
Cr t e C r tg g3
23 2
24
( )
Cr t e C r t etg tg g3 3 2 3 13
( )
Co t e Co t etg tg g3 6 2 6 1
( )
Co t e e Co t etg g tg g3 4 2 2 5 2
( )
Fe t e F e ttg tg3 5 2 6
( )
Fe t e e Fe t etg g tg g3 3 2 2 4 2
( )
Ru t e Ru ttg tg3 5 2 6
( )
Ru t e Ru ttg tg3 5 2 6
( )
Weak Field (predicted)
H2O (actual)
Cr t e C r t etg tg g3 3 2 3 13
( )
Mn t e e M n t etg g tg g3 3 1 2 3 2
( )
Fe t e e Fe t etg g tg g3 3 2 2 4 2
( )
Co t e Co t etg tg g3 6 2 5 2
( )
Predict that the bond length changesRequired for the Co3+ reduction should have an effect on the rate of electron transfer because not only does the electronHave to get there it has to arrive at a timeWhen the bond has fluctuated to a lengthThat it can be accepted.
A A A Ared ox
k
ox red* *
11Self Exchange constant homogeneous
electron transfer
D orbitals in Ru (larger and with more electrons) are more greatly perturbed thereforeLarger Dq therefore less movement of electrons into path of ligand
Note effect of having to move electrons in path of ligand for Co!
fast
Ox*Oxsurf
Redsurf
Red*
Homogeneous Electron transferHere a self exchange
HeterogeneousElectron transfer
Fe CN e Fe CN63
64
Fe CN Fe CN Fe CN Fe CN63
64
64
63
* *
Solution diffusionSolvent reorganizationBond reorganizationPotential field effects (charge on
surfaces)
k11ko
The electron transfer self exchange rate can be predicted from Marcus Theory
A A A Ared ox
k
ox red* *
11
Self Exchange constantHomogeneous electrontransfer
k K A A n el
G
RTf
, * ex p
Precursor equilibriumConstant
Nuclear frequency factor = frequency of attempts onThe energy barrier associated with bond vibrations andSolvent motion
Electron tunneling (related to distanceThe electron can “hop”
Activation energy
A A A Ared ox red ox* *
1 and 1Not “11” as 1 speciesReacts with itself
HomogeneousElectron transferHere a self Exchange rate
G
F E E w wf
i oo
o r
i o
4
1
2
M3+
L
LL
L
M2+
L
LL
L
Work to bring3+ to vicinity of 2+
Internal reorganizationEnergy for bond lengthchanges
External reorganizationEnergy for moving solventMolecules around different charges
Radius change ofOverall moleculeIs minimal
So energy to reorganize solvent Around the complex is similar
Energy to alterBond lengths within theComplex accounts forMost of the differences
How does the Homogeneous Electron Transfer RateRelate to the heterogeneous electron transfer rate?
Vo (Cotton 2nd Ed)
1.840.77-1.59-0.41-0.25-0.37
Kevin M. Rosso and James R. Rustad, JPC A 2000, 104, 6718: Ab Initio Calculation Of Hmogeneous Outer Sphere Electron Transfer Rates: Application to M(OH2)6
2+/3+ Redox Couple.
Change in M-OBond length (Ɓ)
0.96 0.137 0.17 0.12 0.085
The results shown here indicate that the rate of electron transfer, ket, is mostAffected by the bond length changes required because of movement of electrons in and out of the eg d orbitals
Charge transport in micas: The kinetics of FeII/III electron transfer in the octahedral sheet, Keven M. Rosso and Eugene S. Ilton, . J of Chemical Physics, 119, 17, 9207
An extreme example of the inner sphere work required is to reduce an iron containing crystal
Hydroxyl group at apex (trans)
Hydroxyl group at “waist” (cis)
Calculate the self exchange Of FeII to FeIII from the M1 And M2 sites using a cluster
Oxidation involves removal of an electron from an Fe 3dt2g orbitalNuclear coordinates in the cluster respond by contraction of the atoms
M1 site ContractionOn oxidation
M2 site Contraction onoxidation
i
M2/M2 2.01eVM1/M2 1.07eV
Notice the high value of the inner reorganization energy
A A A Ared ox
k
ox red* *
11
Self Exchange constantHomogeneous electrontransfer
A e Aox
k
red
o
Heterogeneous
Electron transfer
k Zk
Zo elso
11
1 2
ln
/
Where Zel is a collision frequency factorRelating to the number of electrode surfaceCollisions required to produce a successful Orientation, generally taken to be 103 to 104 cm/s
ZkT
mso ln 2
Zsoln is a solution collisional factor estimatedFrom the thermal velocity of the reaction moleculesAnd their effective mass. Typical values are 1011 to 1012 1/Ms
Can relate the homogeneous self exchange rate constant to the heterogeneous rate constant
diffusionOx*Oxsurf
Redsurf
HomogeneousElectron transfer
HeterogeneousElectron transfer
Red
k Zk
Zo elso
11
1 2
ln
/
k
DnF
RT
o
1 2
1 2
1 2
1/
/
/
1 2 1 2 1 2 1 2
1/ / / /
k
D nF
RT
o
=7.0; 0.25
“rounds”; spreads; decreases
Try this one
What is the a) Heterogeneous electron transfer rate constant, ko (with units)b) homogeneous self exchange electron transfer rate constant, k11, (with units)
of a compound ifn=1Epc= -0.632 V vs SCEEpa= -0.420 V vs SCEAt a scan rate of 100 mV/sAt 25oCFor a compound with D = 1.6x10-6 cm2/s and a reduced mass of 625 g/M?
Values of some constants:
k=1.38065x10-23J/KR=8.31447 J/mol KF=9.64853x104C/mole of eF/RT = 38.92/V
Vkgm
s A
kgm
s C
J
CC As
Jkgm
s
2
3
2
2
2
2
diffusionOx*Oxsurf
RedsurfNa+
migration
HeterogeneousElectron transfer
What happens when there is little salt- affects migration of compound- affects compensating charge
3 mM Fe(CN)63/4- 100 mV/s at ITO
-3
-2
-1
0
1
2
3
-0.4-0.200.20.40.60.8
V vs AgCl
mil
liA
mp
s
0.01 M NaCl
0.3 M NaCl
0.05 M NaCl
0.1 M NaCl
0.5 M NaCl
0.7 M NaCl
-1.00E+00
-8.00E-01
-6.00E-01
-4.00E-01
-2.00E-01
0.00E+00
2.00E-01
4.00E-01
6.00E-01
8.00E-01
0 0.2 0.4 0.6 0.8 1 1.2 1.4V
curr
ent
Simulation of 1e reversible systemA=1cm2, ket=1x104 cm/s k, D= 1x105 cm2/s, Cox=1mole/L, alpha=0.5; Eo=0.8 V, 1V/s
R (ohms) 0 0.05 0.1 0.2 0.3 0.4 0.7
Note!!!effect of poor charge compensation looks like the effect of a slow electron transfer rate!!!
diffusionOx*Oxsurf
Redsurf
k
Diffusion red
Red*
Precursor
Product
k
What happens if there is a coupled chemical reaction?
diffusionOx*Oxsurf
Redsurf
Diffusion red
Red*
Product
k
The rate of the conversion to the product is faster than theRate of re-oxidation
Co en e Co en E lectrochem ica l reaction
Co en Co en en Chem ica l reactionfa st
33
32
32 2
k P n nkT
g
kT
geA B
molecu le A m olecu le B
E
RTA
2 8 8
, ,
orientation Collision frequencyFraction of molecules withEnough energy to break bond
Rate constant factors areorientation of a successful collisioncollisional frequencyand fraction of molecules (atoms) colliding with enough energy to break
their own bonds
Rate constant for ligand “on”: it is the removal of other ligands on the central atom
Rate constant for ligand on
Rate constant for ligand “off”:fraction of molecules with enough energy to break bond,
expect more successful “off” with lower bond to central atomthat is, 2+ vs 3+
Cr: 3d54s14po
Cr2+: 3d4Cr3+: 3d3
10Dq
Generally true that the Dq values are Larger for the oxidized state of the metal thanFor the lower charged reduced state of the metal
As a result we normally predict thatThe Crystal Field Stabilization EnergyExperienced due to ligand binding toThe metal ion is larger for the trivalentAs compared to the divalent metal.
Metal Aquo complexes
Dq Stabilizationcm-1 kJ/mol
V3+ 1800 174.5V2+ 1180 168.0
Cr3+ 1760 250.8Cr2+ 1400 100.3
Mn3+ 2100 150.1Mn2+ 750
Fe3+ 1400Fe2+ 1000
Co3+ 188Co2+ 71.5
0
500
1000
1500
2000
2500
V Cr Mn Fe
Dq
(cm
-1)
3+
2+x
Co3+
No return peak
By changing the scan rate the rateConstant for the following chemical reactionCan be measured
Co en e Co en E
Co en Co en en Ck
33
32
32 2
-7.00E-01
-5.00E-01
-3.00E-01
-1.00E-01
1.00E-01
3.00E-01
5.00E-01
7.00E-01
9.00E-01
-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
V
Cu
rren
t
V=0.5V/salpha=0.5ket=1e4K=1e4variable kf
-7.00E-01
-5.00E-01
-3.00E-01
-1.00E-01
1.00E-01
3.00E-01
5.00E-01
7.00E-01
9.00E-01
-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
V
Cu
rren
t
V=0.5V/salpha=0.5ket=1e4K=1e4variable kf
-7.00E-01
-5.00E-01
-3.00E-01
-1.00E-01
1.00E-01
3.00E-01
5.00E-01
7.00E-01
9.00E-01
-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
V
Cu
rren
t
V=0.5V/salpha=0.5ket=1e4K=1e4variable kf
-7.00E-01
-5.00E-01
-3.00E-01
-1.00E-01
1.00E-01
3.00E-01
5.00E-01
7.00E-01
9.00E-01
-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
V
Cu
rren
t
V=0.5V/salpha=0.5ket=1e4K=1e4variable kf
-7.00E-01
-5.00E-01
-3.00E-01
-1.00E-01
1.00E-01
3.00E-01
5.00E-01
7.00E-01
9.00E-01
-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
V
Cu
rren
t
V=0.5V/salpha=0.5ket=1e4K=1e4variable kf
-7.00E-01
-5.00E-01
-3.00E-01
-1.00E-01
1.00E-01
3.00E-01
5.00E-01
7.00E-01
9.00E-01
-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
V
Cu
rren
t
V=0.5V/salpha=0.5ket=1e4K=1e4variable kf
-7.00E-01
-5.00E-01
-3.00E-01
-1.00E-01
1.00E-01
3.00E-01
5.00E-01
7.00E-01
9.00E-01
-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
V
Cu
rren
t
V=0.5V/salpha=0.5ket=1e4K=1e4variable kf
-7.00E-01
-5.00E-01
-3.00E-01
-1.00E-01
1.00E-01
3.00E-01
5.00E-01
7.00E-01
9.00E-01
-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
V
Cu
rren
t
V=0.5V/salpha=0.5ket=1e4K=1e4variable kf
-7.00E-01
-5.00E-01
-3.00E-01
-1.00E-01
1.00E-01
3.00E-01
5.00E-01
7.00E-01
9.00E-01
-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
V
Cu
rren
t
V=0.5V/salpha=0.5ket=1e4K=1e4variable kf
-7.00E-01
-5.00E-01
-3.00E-01
-1.00E-01
1.00E-01
3.00E-01
5.00E-01
7.00E-01
9.00E-01
-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
V
Cu
rren
t
V=0.5V/salpha=0.5ket=1e4K=1e4variable kf
1e-5
1e4
1e11
A e A
A Bk f
A e A E G nFE
A B K G RT K
A e B E G nFE RT Ko
0
ln
ln'
Kinetically limited by following reaction
In equilibriumWith followingReaction Potential shiftsEASIER toreduce
Here are actualCurrent scales inWhich ip decreasesAs scan rate decreases
Here a dimensionless current parameter is defined which allows you to put all the currents on one scale
kV
s
k tim efo llow ing reaction erim en tex p
k RT
nF
Is large if k is large or time is large – both allowthe following reaction to proceed
Co en e Co en E
Co en Co en en Ck
33
32
32 2
In the linear region
n E ERT
nF
RT
nF
k RT
nFp
1 2 0 7 8 0
2/ . ln
Try a calculation
You acquire a series of voltammograms for 3 mM Co(en)33+ in 0.01 M NaCl/water at a
Pt electrode with a reference electrode of Ag/AgCl. The formal potential is known to be 0.5 V vs AgCl. You scan between 0.3 and 0.8 V at 10 mV/s. You observe a CV in which only a cathodic peak is present. The peak potential shifts with increasing scan rates to more positive potentials. You find that the Epc is 505 mV when the scan rate is 500V/s.
1. What is the value of the of rate constant for the following chemical reaction?2. What are the units of the rate constant?3. Is the value you obtained consistent with what we have discussed in class?
k RT
nF
F
RT V
3 8 9 2.
Co en e Co en E
Co en Co en en Ck
33
32
32 2
Consider the effect of 3+ and 2+ on Dq again
Dq Stabilizationcm-1 kJ/mol
V3+ 1800 174.5V2+ 1180 168.0
Cr3+ 1760 250.8Cr2+ 1400 100.3
Mn3+ 2100 150.1Mn2+ 750
Fe3+ 1400Fe2+ 1000
Co3+ 188Co2+ 71.5
Could we use this simple modelTo predict the formal potentials?
M e M EM
o3 23
/2
M L M L KM L
M LIII3 3
3
3
M L M L KM L
M LRT KII II
2 22
2
ln
M L e M L EML
3 23
/2
G rx
M L M L
K
M L
M LRT
KIII III
3 33
3
1 1
ln
nFEM
o3 /2
RT K IIIln
G nFE RT K RTKrx M
oII
III
3 2
1ln ln
G nFE RTK
Krx M
o II
III
3 2 ln
EG
nF
nFE RTK
K
nFML
o rxM
o II
III3 2
3 2
ln E E RTnF
K
KML
o
M
o II
III
3 2 3 2
ln
H2O EDTA H2O EDTA
Fe3+ 1.3x1025 Co 3+ 2.5X10 41
Fe2+ 2.1X1014 Co 2+ 2.0X1016
KIII/KII 6.19x1010 1.25x1025
Eo 0.771 0.12 1.92 0.36
Note,This doesn’t workVery well becauseThe interactionBetween mostLigand sites on Metal complexesAnd the centralMetal is not justelectrostaticShifts negative as predicted
E E RTnF
K
KML
o
M
o II
III
3 2 3 2
ln E E RT
nFK
KML
o
M
o III
II
3 2 3 2
lnOR
Electrostatic Charge Effects Show up In other places
Example is the potential shift of a cobalt sepulchrate complex When ion exchanged into an anionic film
J Phys Chem
Math Model
Cosep e Cosep ECoSep
o3 23
/2
Cosep XNa Cosep X Na KCosep X Na
Cosep NaXIII3 3
3
33
3
3 33 3
Cosep X Na Cosep XNa
K
Cosep NaX
Cosep X NaIII
33
33 3
33
33 31
Cosep XNa Cosep X Na KCosep X Na
Cosep NaXII2 2
2
23
2
2 22 2
Energy Term
Cosep X Na e Cosep X XNa ECoSepX
33
22
3 23
/
/2
G
E nFE
KRT
K
K RT K
nFE RTK
K
E
nFE RTK
K
nF
CoSep
o
CoSep
o
III III
II II
C oSep
o II
III
C oSepX
oCoSep
o II
III
3 3
3
3 23
3
1 1
/2 /2
/2
//2
/2
ln
ln
ln
ln
Cosep X Na e Cosep X XNa ECoSepX
33
22
3 23
/
/2
E
nFE RTK
K
nF
E ERT
nF
K
K
or
E ERT
nF
K
K
CoSepX
oCoSep
o II
III
C oSepX
o
CoSep
o II
III
C oSepX
o
CoSep
o III
II
3 23
3
3 23 3
3 23 3
//2
/2
//2 /2
//2 /2
ln
ln
ln
Cosep X Na e Cosep X XNa ECoSepX
33
22
3 23
/
/2
Neg attracts 3+More so largerThan KII
>1
neg
Bare electrode
In negatively charged clay