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Electrochemical Techniques
CHEM 269

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Course Contentz This course is designed to introduce the basics (thermodynamics
and kinetics) and applications (experimental techniques) ofelectrochemistry to students in varied fields, including analytical,physical and materials chemistry. The major course content will
include{ Part I Fundamentals
z Overview of electrode processes (Ch. 1)
z Potentials and thermodynamics (Ch. 2)
z Electron transfer kinetics (Ch. 3)
z Mass transfer: convection, migration and diffusion (Ch. 4)
z Doublelayer structures and surface adsorption (Ch. 13)
{ Part II Techniques and Applicationsz Potential step techniques (Ch. 5): chronoamperometry
z
Potential sweep methods (Ch. 6): linear sweep, cyclic voltammetryz Controlled current microelectrode (Ch. 8): chronopotentiometry
z Hydrodynamic techniques (Ch. 9): RDE, RRE, RRDE
z Impedance based techniques (Ch. 10): electrochemical impedancespectroscopy, AC voltammetry
z Grade: 1 midterm (30%); 1 final (50%); homework (20%)

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Chronoamperometry (CA)
E
t
E1 E2E3
E4
0
x
Co
Co*
t
x
Co
Co*
E
t
i
E2
E3
E4
0
i
E
iLIM,c
Sampledcurrentvoltammetry
Chronoamperometry

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CurrentPotential Characteristics
z Largeamplitude potential step
{Totally masstransfercontrolled{Electrode surface concentration ~ zero
{Current is independent of potential
z Smallamplitude potential changes{ i =iof
zReversible electrode processes
z Totally irreversible ET (Tafel region)R
Oo
C
C
nF
RTEE ln+=
( )( )
( )( ) ( )
=
'' 1,0,0
oo EERT
nF
R
EERT
nF
O
o etCetCnFAki

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Electrode Reactions
zMasstransfer control
zKinetic control
ObulkOsurf
Oads
Rads
Rsurf Rbulk
Osurf
Rsurf
electrode
Double layer
masstransfer
chemicalelectrontransfer

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Mass Transfer Issues
)()(
)()(
xvCx
xCD
RT
Fz
x
CDxJ jjj
jxjjj +
=
In a onedimension system,
In a threedimension system,
)()()()( rvCrCDT
FzrCDrJ jjj
jjjj
+=
diffusion migration convection
diffusioncurrent
migrationcurrent
convectioncurrent

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Potential Step under Diffusion Control
zPlanar electrode: O + ne R
zFicks Law2
2 ),(),(
x
txCD
t
txC OO
O
=
CO
(x,0) = CO
*
CO(0,t) = 0
LimCO(x,t) = CO*x
xD
s
OO
OesAs
CsxC
+= )(),(*
=
xD
s
OO
O
es
C
sxC 1),(
*
Laplacian transformation
0),0( =sCO
=
0
)()}({ dttFetFL st

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Cottrell Equation
z Frederick Gardner Cottrell (1877  1948) was born in Oakland, California. He received a B.S. in
chemistry from the University of California at Berkeley in 1896 and a Ph.D. from the University ofLeipzig in 1902.
z Although best known to electrochemists for the "Cottrell equation" his primary source of fame was asthe inventor of electrostatic precipitators for removal of suspended particles from gases. These devicesare still widely used for abatement of pollution by smoke from power plants and dust from cement kilnsand other industrial sources.
zCottrell played a part in the development of a process for the separation of helium from natural gas. Hewas also instrumental in establishing the synthetic ammonia industry in the United States duringattempts to perfect a process for formation of nitric oxide at high temperatures.
0
),(),0(
)(
=
==
x
OOO
x
txCDtJ
nFA
ti
0
),()(
=
=x
OO
x
sxCD
nFA
si
21
21
21 *
)(t
CnFADti
OO
=Reverse LT*
)(O
O Cs
D
nFA
si=
CO(0,t) = 0

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Depletion Layer Thickness
*
)(o
o
o C
t
DnFAi
=
tDt OO =)(
x
Co
Co*
t
tDO =
30 m
1 m
30 nm
at t =
1 s
1 ms
1 s

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Concentration Profile
= x
D
s
O
O
Oes
CsxC 1),(
*
=
= tD
xerfCtD
xerfcCtxCo
Oo
OO22
1),( **
In mathematics, the error function (also called the Gauss error function) is a
special function (nonelementary) which occurs in probability, statistics, materialsscience, and partial differential equations. It is defined as:

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Sampled Current Voltammetry
z Linear diffusion at a planar electrode
zReversible electrode reaction{Stepped to an arbitrary potential
),0(
),0(
ln tC
tC
nF
RT
EER
Oo
+= ( )[ ]o
R
O
EEnftC
tC
== exp),0(
),0(
2
2
),(),(x
txCDt
txC OOO= 2
2
),(),(x
txCDt
txC RRR=
CO(x,0) = CO*
LimCO(x,t) = CO*x
CR(x,0) = CR* = 0
LimCR(x,t) = CR* = 0x

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Flux Balance
xD
s
OO OesAs
CsxC
+= )(),(
*
xD
s
RR
esBsxC
= )(),(
0),(),(
=
+
x
txCD
x
txCD RR
OO
Incoming flux Outgoing flux
0),(),(
=
+
x
sxCD
x
sxCD R
R
O
O
0)()( = sBDs
sAD
s
RO
)()()( sAsAD
DsB
O
R ==
xD
s
RResAsxC
= )(),(

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IE at any Potential
( )[ ]oR
O EEnftC
tC== exp
),0(
),0(
xD
s
s
CR
RO esxC
+
=
1
),(*
+=
11),(
*
xD
s
s
CO
RO esxC
),0(
),0(
sC
sC
R
O=
)()(*
sAsAs
CO =+
+=
1)(
*
sCO
sA
0
),(
=
=
x
OO
x
txCnFADi
( ) +=
1
)(2
12
1
21 *
t
CnFADti
OO

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Shape of IE Curve
( ) ( ) +=
+=
11)(
21
21
21 *dOO i
t
CnFADti
At very negative potentials, 0, and i(t) id
+
+=
)(
)(lnln'
ti
tii
nF
RT
D
D
nF
RTEE d
O
Ro
y
EE1/2
Slope n
E1/2 Waveshape analysis

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CA Reverse Technique
E
t
EiEr
Ef
0
( ) +=
1)(
21
21
21 *
t
CnFADti
OOf
+
+
+=
21
21
21
)1(
11
"1
1
'1
1)(
*
tt
CnFADti
OOr
or EEnf = exp"
of EEnf = exp'
=
ttCnFADti OOr 11)(
21
21 *
r
f
r
f
f
rt
t
t
t
ii =
when =0 and =
rfr
ti
i
=
11tr tf=

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SemiInfinite Spherical Diffusion
+
=
r
trC
rr
trCD
t
trC OOO
O ),(2),(),(
2
2
+=
oOO rt
CnFADti11
)(2
12
12
1 *
2
1
2
1
21 *
)(
t
CnFADti
OO
=
CO(r,0) = CO*
CO(r0,t) = 0
LimCO(r,t) = CO*r
boundary
conditions
+=
o
OO
rt
CnFADti11
)(
2
1
2
12
1 *
Cottrell equation

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Ultramicroelectrode
zRadius < 25 m, smaller than the diffusion layer
zResponse to a large amplitude potential step
{First term: short time (effect of doublelayer charging
{
Second term: steady state
+=
o
OO
rt
CnFADti11
)(
2
1
2
12
1 *
**
4OoOo
OO
ssCrnFD
r
CnFADi ==

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t
i
issplanar
electrode
spherical
electrode
21
21
21 *
)(t
CnFADti
OO
=
+=
oOO rt
CnFADti 11)(2
12
121 *

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Amperometric glucose sensor based on platinumiridium
nanomaterials
Peter HoltHindle, Samantha Nigro, Matt Asmussen and Aicheng Chen
Electrochemistry Communications, 10 (2008) 14381441
z This communication reports on a novel amperometric glucose sensor based onnanoporous PtIr catalysts. PtIr nanostructures with different contents of iridiumwere directly grown on Ti substrates using a onestep facile hydrothermal methodand were characterized using scanning electron microscopy and energy dispersiveXray spectroscopy. Our electrochemical study has shown that the nanoporous Pt
Ir(38%) electrode exhibits very strong and sensitive amperometric responses toglucose even in the presence of a high concentration of Cl and other commoninterfering species such as ascorbic acid, acetamidophenol and uric acid, promisingfor nonenzymatic glucose detection.

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(a) Chronoamperometric responses of S0, S1, S2 and
S3 measured at 0.1 V in 0.1 M PBS (pH 7.4) +0.15 MNaCl with successive additions of 1 mM glucose (0
20 mM). (b) The corresponding calibration plots.
(a) S0: PtIr(0%), (b) S1: PtIr(22%), (c) S2: PtIr(38%). (d) EDX
spectra of samples S0 and S2. Insert: the enlarged portion of the
EDX spectrum of samples S0 and S2 between 9.0 and 12.0 keV.

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Interference Study
z Chronoamperometric curves of S0 and S2 recorded in 0.1 M PBS+0.15 M NaCl with successive additions of 0.2 mM UA, 0.1 mM AP,
0.1 mM AA and 1 mM Glucose at 60 second intervals under the
applied electrode potential 0.1 V.
PtIr(0%)
PtIr(38%)

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Electroanalysis 1997, 9, 619.

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Microelectrode Voltammetry
Fig. 1 Plot showing cyclicvoltammograms recorded for a
series of 25 m Pt microelectrodesrecorded at 2 mV/s in a solutioncontaining 10 mM K3[Fe(CN)6] inSr(NO3)2 at 25 m underanaerobic conditions. The insert in
the figure shows a SEM image ofthe 93 C HIePt modifiedmicroelectrode recorded after theexperiments were performed. Thescale bar on the SEM represents
10 m.
zElectrochemical reduction of oxygen on mesoporous platinum microelectrodes

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Chronocoulometry (CC)
21
21
21 *
)(
t
CnFADti
OO
=
ADSDLO
O QQtCnFAD
tQ ++= 21
21
21 *
)(
Cottrell Equation (at large potential steps)
Doublelayer charging
Surface adsorbed species nFA*
Q
t1/2intercept

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Reverse CC
( )
=> 2
12
1
21
21 *
)(
ttCnFAD
tQOO
d
Q t1/2t <
t >
( )
+=>=> 2
12
12
1
21
21 *
)()()(
ttCnFAD
tQQtQOO
dr
So the net charge removed in the reverse step is

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Potential Sweep Techniques
O
R
C
x

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Nernstian Processes
zO + ne R
zE(t) = Ei  vt
( ) ( )tSEvtERT
nFtf
tC
tC oi
R
O =
== 'exp)(
),0(
),0(
tetS
=)(RTnFv=
2
2
),(),(x
txCDt
txC OOO=
xD
s
OO
OesA
s
CsxC
+= )(),(*
Laplacian transformation

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0
),(),0(
)(
=
==
x
OOO
x
txCDtJ
nFA
ti
dtiDnFA
CtCt
O
OO =
0
* 21
))((1
),0(
nFA
if
)()(
=
dtfD
CtCt
O
OO = 0
* 21
))((1),0(
dtfDtC
t
RR =
0
21
))((
1
),0(

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( ) ( )tSEvtERTnFtftC tCo
iR
O =
== 'exp)(),0(),0(
21
21
21
)())((
))((*
0
+=
OR
Ot
DDtS
Cdtf
1)(
)())((
*
0
21
21
+=
tS
CDnFAdti OO
t
R
O
D
D=
z Let z = t so that t = z/

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Let z t so that t z/
zAt t = 0, z = 0, and at t = , z =
dzztzgdtf
tt
=
00
21
21
))(())((
)(1))((
*
0
21
21
ts
DCdzztzg
OOt
+=
)(1
1))((
0
21
tsdzztz
t
+=
OOOO DnFAC
ti
DC
zgz
**
)()()( ==
)(* tDnFACi OO = RTnFv=

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Numerical SimulationsLinear Sweep / Cyclic Voltammetry

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Key Features For Reversible Reactions
z i v1/2 for linear diffusion
zPeak current at 1/2
(st) = 0.4463,thus iP = (2.69 105)n3/2ADO1/2CO*v1/2
zPeak potentials{EP = E1/2 1.109(RT/nF)
{EP/2 = E1/2 + 1.09(RT/nF)
{EP EP/2= 2.20(RT/nF)
{E1/2 = EP,a + EP,c/2
EP/2
E1/2

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Totally Irreversible Reactions
O + ne R
( ) ( )bt
if
vtRT
nFEE
RT
nF
oEE
RT
nF
of ekeekekk
oi
o
,
''
===
( ) ( )tCkx
txCDnFA
iOf
x
OO ,0
,
0
=
==
)(* btbDnFACi OO =
vtEE i =
( ) )(21
21* btRT
FvDnFACi OO
=
K F t

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Key Features
zAt 1/2(bt) = 0.4958,
zPeak potential
{EP EP/2= 1.857(RT/nF)
+
+=212
1
lnln780.0'
RT
Fv
k
D
Fn
RTEE
o
oP
O
21
2
1
21
*5)1099.2( vDnACi OOP =
( )
= '* exp277.0 oPo
OP EE
RT
FknFACi
R ibl I ibl R ti

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Reversible vs Irreversible Reactions
C li V lt t

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Cyclic Voltammetry
z Current reflects the combinedcontributions from Faradaic
processes and doublelayercharging
z For chemically reversible
reactions, iP,a = iP,c(independent of v)
z Peak splitting{EP = EP,a EP,c=2.3RT/nF{EP = 59/n mV at 298 K, orat steady state, 58/n mV.
R ibl Ki ti ll Sl R ti

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Reversible vs Kinetically Slow Reactions
Ep = constant Ep decreases with increasing kEp increases with increasing sweep rate

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Cyclic voltammogram of [Cu(pic)2].2H2O in DMF solution
Bispicolinate Copper (II)
The separation between them, Ep, exceeds
the Nernstian requirement of 59 mVexpected for a reversible oneelectron
process. This value increases from Ep =0.11V at 0.05 V/s to 0.33 V at 5 V/s
indicating a kinetic inhibition of the electron
transfer process
Multistep Reactions

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Multistep Reactions
Fig. 1 Cyclic voltammetry (100 mV s 1) of: (a) 1 inCH2Cl2 containing 0.1 M Bu4NPF6; (b) a poly1coated Pt electrode in acetonitrile containing 0.1 MEt4NClO4.
1/20/1 +1/0
A low band gap conjugated metallopolymer
with nickel bis(dithiolene) crosslinks
Christopher L. Kean and Peter G. Pickup*
Chem. Commun., 2001.
Multistep Reactions

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Multistep Reactions
z Identify peak positions
z Identify peak pairing
zDeconvolution ofoverlapped
voltammetric peaks (A) Cyclic voltammogram at 0.05 V s1 of aGCE modified with KxFey[Ir(CN)6]z in 50 mMKCl/HCl. (B) Cyclic voltammogram after the
GCE was immersed in Cu2+ for 120 minutes
Voltammetric Responses of Adsorbed

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p
Speciesz Only adsorbed O and R are
electroactive (Nernstian reaction)
nFA
i
t
t
t
t RO
=
=
)()(
( )
==
=
'*
*
exp),0(
),0(
),0(
),0(
)(
)( o
R
O
RR
OO
RR
OO
R
O
EERT
nF
b
b
tCb
tCb
tC
tC
t
t
R
O
( )( )
*
'
'
exp1
exp)(
Oo
R
O
o
R
O
O
EERT
nF
b
b
EERT
nF
b
b
t
+
=
*22
4OP vA
RT
Fni =
2'
'*22
)(exp1
)(exp)(
+
=
=
o
R
O
o
R
OO
O
EE
RT
nF
bb
EERT
nF
bb
vA
RT
Fn
t
tnFAi
Key Features

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Key Features
z iP v (slope defines *)
z iP *zQads = nFA* (peak area)
zEP = Eo
zReversible reaction, peak
width at half maximummV
nnF
RTEP
6.9053.3,
21 ==
Physical Chemistry Chemical Physics DOI: 10.1039/b101561n
A ligand substitution reaction of oxocentred triruthenium complexes assembled as monolayers

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g y
on gold electrodes
Akira Sato , Masaaki Abe* , Tomohiko Inomata , Toshihiro Kondo , Shen Ye , Kohei Uosaki* and YoichiSasaki*
Cyclic voltammograms for monolayers of1 assembled onthe polycrystalline Au electrode in 0.1 M HClO4 aqueous
solution at 20oC in the electrode potential region between 
0.25 and + 0.85 V/s. Ag/AgCl. A platinum wire is used for
the counter electrode. Scan rate = 50, 100, 200 and 400
mV/s. Inset: A linear correlation of current intensities of the
anodic and cathodic waves (ipa and ipc, respectively) withthe scan rate.
* = 1.8 1010 mol/cm2

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PcFe
PcFe
WaveShape Analysis

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WaveShape Analysis
Question
 Reaction proceeds with a
simultaneous twoelectrontransfer or two successive one
electron reductions?
Controlled Current Techniques

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Controlled Current Techniques
Galvanostat
t
E
Classification

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Classification
zConstantcurrent chronopotentiometry
zProgrammed current chronopotentiometry
zCyclic chronopotentiometry
I
t
E
t
t
E
t1 2
General Theory

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General Theory
CO(x,0) = CO*, CR(x,0) = 0
CO(,t) = CO*, CR(,t) = 0
xD
s
OO
OesAs
CsxC
+= )(),(
*
RneO +
( ) ( )
2
2 ,,
x
txCD
t
txC OO
O
=
( ) ( )2
2 ,,
x
txCD
t
txC RR
R
=
( ) ( )nFA
ti
x
txCD
x
OO =
=0
,
( ) ( )nFA
si
x
sxC
Dx
OO =
=0
,
xD
s
O
O
O
O
esnFAD
si
s
C
sxC
= 2121)(
),(
*
xD
s
RR
R
esnFAD
si
sxC
= 2121)(
),(
Sand Equation

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Sand Equation
xD
s
O
OO
OesnFAD
i
s
CsxC
=2
32
1
*
),(
=
tD
xxerfc
tD
xtD
nFAD
iCtxC
OO
O
OOO
24exp2),(
2*
21
21
21
2),0( *
O
nFAD
itCtC OO =
2
21
21
21
*
O
nFAD
C
i
O= Sand equation
*
2
1OO CDAnFi
=
PotentialTime Transient

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Potential Time Transient
),0(
),0(
ln
'
tC
tC
nF
RT
EE R
Oo
+=
21
21
21
421
21
21
21
lnlnln'
t
t
nF
RTE
t
t
nF
RT
D
D
nF
RTEE
O
Ro +=
+
+=
21
21
21
2),0( *
O
nFAD
itCtC OO =
21
21
212),0(
R
nFAD
ittCR =
Slope ny
x
Reversible Reactions
Totally Irreversible Reactions

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Totally Irreversible Reactions
RneO +
=RT
EEnFtCnFAki
o
Oo 'exp),0(
( ) 21
1,0*
=t
CtC
O
O
21
21
21
2),0( *
O
nFAD
itCtC OO =
+
=
21
1lnln*
'
t
nF
RT
i
knFAC
nF
RTEE
oOo
QuasiReversible Reactions

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Quasi Reversible Reactions
[ ]
nfD
t
nFAC
inf
D
t
nFAC
i
i
i
RROOo
)1(exp2
1)exp(2
121
21
**
+
=
+
+=o
ROi
DCDCnFA
tinF
RT
RO
1112
21
21
21
21
**
Small
DoubleLayer Effect

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Double Layer Effect
zMost significant at the beginning or at the
end of the charging stepz if= i  idl
t
ACi dldl
=
Reverse Technique

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q
zFor a reversible reactions, 2 = t1/3, i.e.,
maximum 1/3 of the R produced in theforward step will be reoxidized into O.
t
E
t1 2

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Anal. Chem. 1969, 41, 1806

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Hydrodynamic Methods

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Hydrodynamic Techniques

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zAdvantages
{A steady state is attained rather quickly
{Doublelayer charging does not enter the measurements
{Rate of mass transfer rate of diffusion alone
{Dual electrodes can be used to provide the same kind of
information that reverse techniques achieve
)()(
)()(
xvCx
xCD
RT
Fz
x
CDxJ
jjj
jxj
jj
+
=
diffusion migration convection
Theoretical Treatments

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zConvection maintains the concentrations
of all species uniform and equal to the bulkvalues beyond a certain distance from the
electrode surface,
zWithin this layer (0

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)()()()( rvCrCDRT
FzrCDrJ jjj
jjjj
+=
jjjjj
CvCDJt
C==
2
y
Cv
x
CD
t
C jy
jj
j
=
2
2
For a onedimensional system,
y
Velocity Profile

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z For an incompressible fluid, continuity equation dictates thatthe local volume dilation rate is zero
z NavierStokes equation
{Named afterClaudeLouis Navierand George GabrielStokes, describe the motion of viscous fluid substancessuch as liquids and gases.
{The equation arises from applying Newton's second law tofluid motion, together with the assumption that the fluidstress is the sum of a diffusing viscous term (proportionalto the gradient of velocity), plus a pressure term.
0= v
fvPdtvdd ss
++= 2
Pressuregradient
Stresstensor
Bodyforce

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Sir George Gabriel Stokes, 1st Baronet FRS (13
August 18191 February 1903), was a mathematician
and physicist, who at Cambridge made importantcontributions to fluid dynamics (including the Navier
Stokes equations), optics, and mathematical physics
(including Stokes' theorem). He was secretary, then
president, of the Royal Society.
ClaudeLouis Navier(10 February
1785 in Dijon 21 August 1836 in
Paris) was a French engineer andphysicist who specialized in
mechanics.
The NavierStokes equation is one of the most useful sets of equationsbecause they describe the physics of a large number of phenomena of academicand economic interest. They may be used to model weather, ocean currents,water flow in a pipe, flow around an airfoil (wing), and motion of stars inside agalaxy. As such, these equations in both full and simplified forms, are used in thedesign of aircraft and cars, the study of blood flow, the design of power stations,the analysis of the effects of pollution, etc. Coupled with Maxwell's equations theycan be used to model and study magnetohydrodynamics.
Rotating Disk Electrode (RDE)

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ss d
fvvP
ddt
vd ++= 2
1
0=dt
vd
At steadystate
...)32
()(3
2
+==
b
arFrvr
...)3
1()( 3 +++== abrGrv
( ) ( ) ...)63
1()(
4322
12
1+++==
baHvy
Kinematic
viscosity
a = 0.51023
b = 0.6159= (/v)1/2y
r
y
y = 0
vr
Uo
vy
Velocity Profiles

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zAt the electrode surface (y 0 or 0){vy = 0.513/21/2y2
{vr= 0.513/21/2ryzAt bulk solution (y )
{vr= 0{v = 0
{vy = Uo = 0.88447(v)1/2
vy
y
Uo
vr
y
r1
r2
r2 > r1
at y = 0, vy = 0 = vr, i.e., at
the electrode surface, no
convection, only diffusion
Hydrodynamic Boundary Layer

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zAt = (/v)1/2y = 3.6, vy = 0.8Uo, thecorresponding distance y
h= 3.6(v/)1/2
defined as the hydrodynamic boundary
layer thickness ()
zFor water, v = 0.01 cm2/s,{ at = 100 s1, yh = 36 nm
{ at = 104 s1, yh = 36 m
ConvectiveDiffusion Equation

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zAt steady state, dC/dt = 0
+
+
+
=
+
+
2
2
22
2
2
2 11
OOOOO
Oy
OOr
C
rr
C
rr
C
y
CD
y
Cv
C
r
v
r
Cv
At y = 0, CO = 0
limCO = CO*
CO is not a function of, i.e.,
y
2
2
0
==
OO CC
31
2
1
2
3
17.0
8934.0
*
0
=
= O
O
y
O
D
C
y
C
CvCDJt
C==
2
Levich Equation

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0=
=
y
OO
y
CnFADi
21
61
32
*, 62.0 OOcl CnFADi
=
**, O
O
OOOcl C
DnFACnFAmi
==
21
61
31
61.1
= OO D
Diffusion layer thickness
CurrentPotential Relationship

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( ) 2161
32
)0(62.0 * ==
yCCnFADi OOO
==
*,)0(
1
O
Ocl
C
yCii
==
*,)0(
1
R
Ral
C
yCii
+=
al
cl
ii
ii
nF
RTEE
,
,ln
21
i
E
and
Kinetic Effects

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=
===
clK
clOfOf
i
ii
i
iCEnFAkyCEnFAki
,,
* 11)()0()(
clK iii ,
111 += LevichKoutecky Equation
1/2
il,c
il,c 1/2
independent of

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Consideration In Experimental
Applications of RDE

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z Rotating rate must be sufficient large to
maintain a small diffusion layer at the
electrode surface, e.g., > 10 s1
(for water= 0.01 cm2/s and disk radius r1 = 0.1 cm)
z Potential scan rate must be small compared to
so that a steady state can be achieved,typically 20 mV/s
z Upper limit of is governed by the onset of
turbulent flow, generally < 2 105
/r12
{Flat electrode surface
{Electrode aligned to the center of the rotating rod
Rotating RingDisk Electrode (RRDE)

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z The difference between a rotating ringdiskelectrode (RRDE) and a rotating diskelectrode (RDE) is the addition of a second
working electrode in the form of a ringaround the central disk of the first workingelectrode. The two electrodes are separatedby a nonconductive barrier and connected
to the potentiostat through different leads.z To operate such an electrode it is necessary
to use a bipotentiostat.
Rotating RingDisk Electrode (RRDE)

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zThe disk current (RDE) is unaffected by
the presence of the ring electrode (current
or potential)
z In the case where the disk is open, the
electrode behaves as a rotating ringelectrode (RRE)
zWhen a potential is applied to the diskelectrode, the ring current varies (RRDE)
Rotating Ring Electrode (RRE)

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zDisk radius r1, inner radius r2, outer
radius r3,so the ring area
z In two independent measurements by
RDE and RRE
)( 222
3 rrA =
==
*,
)0(1
O
ORl
C
yCii
r1
r2
r3
32
32
31
32
31
33
==
r
r
r
r
i
i
D
R
( ) 21
61
32
32
*32
32,
62.0 OORl CDrrnFi
=
Collection Experiments
zDi k l t d (i ) O R

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zDisk electrode (iD): O + ne R{Disk potential is being scanned
zRing electrode (iR
): R O + ne{Ring potential is held at a positive enough position to
ensure that CR(y=0) 0
zCollection efficiencyN = iR
/iD
( ) ( )[ ] ( ) ( )( )[ ] +++++= 11111 32
32
FFFN
4
1
3
12arctan
2
3
1
1
ln4
3)(
313
1 3
+
+
+
+
=
F
1
3
1
2
=
rr
Collection Experiment

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At r1
= 0.187 cm, r2
= 0.200
cm and r3 = 0.332 cm,
N = 0.555, i.e., 55.5% of the
product generated at thedisk may be recovered by
the ring electrode
ED
i
iD
iR
Shielding Experiments
Di k l t d ( ) O R

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== 3
2
1,,, NiNiiio
lRDo
lRlR
ER
iD = 0iR
iR= NiD,l
Collection
Experiment
lDo
lR ii ,,3
2
=iR,l
Shielding
Experiment
zDisk electrode (iD): O + ne R{Disk potential is held at a constant position
zRing electrode (iR): O + ne R{Ring potential is being scanned
Shielding factor

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Collection Experiment

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N = 0.22,
cf. theoretical value 0.25
disk
ring
Electrochemical Impedance Spectroscopy
z Oh ' l d fi i t i

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z Ohm's law defines resistance interms of the ratio between voltageE and current I, I = E/R. While this
is a well known relationship, its useis limited to only one circuitelement  the ideal resistor.
z An ideal resistor has severalsimplifying properties:{ It follows Ohm's Law at all current and
voltage levels.
{ It's resistance value is independent offrequency.
{AC current and voltage signals thougha resistor are in phase with each other.
Inductor (coil)

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z The light bulb is a resistor. The wirein the coil has much lowerresistance (it's just wire), so what
you would expect when you turn onthe switch is for the bulb to glowvery dimly. Most of the currentshould follow the lowresistancepath through the loop.
z What happens instead is that whenyou close the switch, the bulb burnsbrightly and then gets dimmer.When you open the switch, the bulb
burns very brightly and then quicklygoes out.
z Example: viscous/viscoelastic thinfilms
Electrochemical Impedance

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z The real world contains circuit elements that exhibit much morecomplex behavior (inductors and capacitors, for instance). Theseelements force us to abandon the simple concept of resistance. Inits place we use impedance, which is a more general circuit
parameter. Like resistance, impedance is a measure of the ability ofa circuit to resist the flow of electrical current.
z Electrochemical impedance is usually measured by applying an ACpotential to an electrochemical cell and measuring the current
through the cell. Suppose that we apply a sinusoidal potentialexcitation. The response to this potential is an AC current signal,containing the excitation frequency and it's harmonics. This currentsignal can be analyzed as a sum of sinusoidal functions (a Fourierseries).
)sin()( tEte =)sin()( += tIti
Phase shift
Phase Shift

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zFor a pure resistor, i = e/R = (E/R)sin(t),so = 0
zFor a pure capacitor, q = Ce, so i = dq/dt
=CEcos(t) = CEsin(t+/2) , i.e., =
/2
RC Circuits (series)

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ze = eR + eC= i(R j/C) = iZ
zZ = R j/C{Z=[R2+1/(C)2]1/2
{tan() = 1/CR
R
Z
Impedance Plots

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logZ
log
log
/2
Bode plots
Zim
ZreR
increasing
Nyquist plots
RC Circuits (parallel)
+=+== Cjeeeei 1 Cj+= 11

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+=+== CjR
eZRZ
iC
CjRZ
+=
( ) ( )2
2
2 11
RC
CR
jRC
R
Z ++= ( ) RC=tan
Bode plots Nyquist plot
Equivalent Circuit for an Electrochemical Cell

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zRs: solution resistance
z
Cdl: doublelayer capacitancezRct: Chargetransfer resistance
zZW
: Warburg resistance (diffusion)
idl
if
if+idl
Kinetic Parameters from EIS
R C

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RS CSFaradaic branch
1=SC
+= ctS RR
=
R
R
O
O
DDnFA
2
1
),0( tC
E
OO
=
),0( tC
E
RR
=Masstransfer
terms
Kinetic Evaluation
RneO + Butler

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+=
oR
R
O
O
i
i
C
tC
C
tC
F
RT
**
),0(),0(
+
+=
RROO DCDCAF
RT
**2
11
2
o
ct
Fi
RTR =
*O
OFC
RT=
*R
RFC
RT=
oo
oct
SS ki
Fi
RTR
CR ==
1
ctR
2=fZ
at io (Rct 0)
= /4
Masstransfer
controlled
Butler
Volmer
equation
Randles Circuit
+ctR

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( ) ( )2
22
1
+++
+=
ctdldl
re
RCC
RZ
( )( ) ( )
22
2
2
1
1
+++
++
+=
ctdldl
dlctdl
im
RCC
CRCZ
LowFrequency Domain
0

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0
++=
ctreRRZ
+= dlim CZ
22
dlctreim CRRZZ22+=
Slope = 1
= /4
intercept
HighFrequency Domain
zW b t b i i ifi t i

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zWarburg term becomes insignificant, i.e.,
the ET reaction is under kinetic control
zThe equivalent circuit becomes
R
Rct
Cdl
222
1 ctdl
ctre
RC
RRZ
+
+=
222
2
1 ctdl
ctdlim
RC
RCZ
+=
22
2
22
=+
ctim
ctre
RZ
RRZ 2
ctR
Experimental Procedure
zStructural details of electrochemical Cell

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S uc u a de a s o e ec oc e ca Ce
z Impedance spectra
zDesign an equivalent circuit
zCurve fitting for kinetic parameters

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mercaptoacetic acid
(MAA) HSCH2COOH
mercaptopropionic

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mercaptopropionic
acid (MPA)
HSCH2CH2COOH
mercaptoundecanoic
acid (MUA)
HS(CH2)10COOH
mercaptobenzoic
acid (MBA)
HSC6H4COOH

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R
Rct
Cdl

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Fig. 2 Nyquist plots obtained with an Au polycrystalline electrode at 0.40 V vs. Hg/HgSO4 in electrolyte solution
containing 0.1 M NaNO3, and various concentrations of Sr(NO3)2. (A) Au coated with 1thioglycerol (TG); (B) Au
electrode coated with 1,4dithiothreitol (DTT).
Fig. 4 Normalized capacity of Au
coated electrodes, (A) DTT, (B) TG
as a function of metal ion
concentration

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Electrochemical Impedance Spectroscopy

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PseudoInductor Components

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The quartz crystal microbalance: a tool for probingviscous/viscoelastic properties of thin films
Tenan, M. A., Braz. J. Phys. vol.28 n.4, 405412. 1998
z The QCM consists basically ofan AT cut piezoelectric quartz

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an ATcut piezoelectric quartzcrystal disc with metallicelectrode films deposited on its
faces. One face is exposed tothe active medium. A drivercircuit applies an ac signal tothe electrodes, causing thecrystal to oscillate in a shear
mode, at a given resonancefrequency.
z Measured resonancefrequency shifts, f, areconverted into mass changesby the wellknown Sauerbreyequation.
EQCM
z The resonant mechanicalill ti b i ll fi d

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oscillations are basically fixedby the crystal thickness,whereas the damping dependson the characteristics of themounting and the surroundingmedium.
z The use of the QCM in a liquidmedium together withelectrochemical techniquesincreased enormously thepossibilities of this tool; and
hence electrochemical quartzcrystal microbalance, EQCM.