techniques - esp

7/29/2019 Techniques - ESP

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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 Double-layer 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 mid-term (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

Sampled-currentvoltammetry

Chronoamperometry


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Current-Potential Characteristics

z Large-amplitude potential step

{Totally mass-transfercontrolled{Electrode surface concentration ~ zero

{Current is independent of potential

z Small-amplitude 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

zMass-transfer 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 one-dimension system,

In a three-dimension 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 (non-elementary) 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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I-E 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 I-E 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 Wave-shape 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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Semi-Infinite 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 double-layer 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 Holt-Hindle, Samantha Nigro, Matt Asmussen and Aicheng Chen

Electrochemistry Communications, 10 (2008) 1438-1441

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 one-step facile hydrothermal methodand were characterized using scanning electron microscopy and energy dispersiveX-ray 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 HI-ePt 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)

Double-layer 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 double-layercharging

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 one-electron

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 poly-1coated 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 oxo-centred 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 10-10 mol/cm2


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PcFe

PcFe

Wave-Shape Analysis


53/116

Wave-Shape Analysis

Question

- Reaction proceeds with a

simultaneous two-electrontransfer 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

zConstant-current 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

=

Potential-Time 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



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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

Quasi-Reversible 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

Double-Layer Effect


61/116

Double Layer Effect

zMost significant at the beginning or at the

end of the charging stepz if= i - idl

t

ACi dldl

=

Reverse Technique


62/116

q

zFor a reversible reactions, 2 = t1/3, i.e.,

maximum 1/3 of the R produced in theforward step will be re-oxidized into O.

t

E

t1 2


63/116

Anal. Chem. 1969, 41, 1806


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65/116


66/116


67/116

Hydrodynamic Methods


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Hydrodynamic Techniques


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zAdvantages

{A steady state is attained rather quickly

{Double-layer 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


70/116

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


71/116

)()()()( rvCrCDRT

FzrCDrJ jjj

jjjj

+=

jjjjj

CvCDJt

C==

2

y

Cv

x

CD

t

C jy

jj

j

=

2

2

For a one-dimensional system,

y

Velocity Profile


72/116

z For an incompressible fluid, continuity equation dictates thatthe local volume dilation rate is zero

z Navier-Stokes equation

{Named afterClaude-Louis 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


73/116

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.

Claude-Louis Navier(10 February

1785 in Dijon 21 August 1836 in

Paris) was a French engineer andphysicist who specialized in

mechanics.

The Navier-Stokes 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)


74/116

ss d

fvvP

ddt

vd ++= 2

1

0=dt

vd

At steady-state

...)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


75/116

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


76/116

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 s-1, yh = 36 nm

{ at = 10-4 s-1, yh = 36 m

Convective-Diffusion Equation


77/116

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


78/116

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

Current-Potential Relationship


79/116

( ) 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


80/116

=

===

clK

clOfOf

i

ii

i

iCEnFAkyCEnFAki

,,

* 11)()0()(

clK iii ,

111 += Levich-Koutecky Equation

1/2

il,c

il,c 1/2

independent of


81/116


82/116


83/116

Consideration In Experimental

Applications of RDE


84/116

z Rotating rate must be sufficient large to

maintain a small diffusion layer at the

electrode surface, e.g., > 10 s-1

(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 Ring-Disk Electrode (RRDE)


85/116

z The difference between a rotating ring-diskelectrode (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 non-conductive barrier and connected

to the potentiostat through different leads.z To operate such an electrode it is necessary

to use a bipotentiostat.

Rotating Ring-Disk Electrode (RRDE)


86/116

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)


87/116

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


88/116

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


89/116

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


90/116

== 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


91/116


92/116

Collection Experiment


93/116

N = 0.22,

cf. theoretical value 0.25

disk

ring

Electrochemical Impedance Spectroscopy

z Oh ' l d fi i t i


94/116

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)


95/116

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 low-resistancepath 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


96/116

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


97/116

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)


98/116

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


99/116

log|Z|

log

log

/2

Bode plots

Zim

ZreR

increasing

Nyquist plots

RC Circuits (parallel)

+=+== Cjeeeei 1 Cj+= 11


100/116

+=+== 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


101/116

zRs: solution resistance

z

Cdl: double-layer capacitancezRct: Charge-transfer resistance

zZW

: Warburg resistance (diffusion)

idl

if

if+idl

Kinetic Parameters from EIS

R C


102/116

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-


103/116

+=

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

Mass-transfer

controlled

Butler

Volmer

equation

Randles Circuit

+ctR


104/116

( ) ( )2

22

1

+++

+=

ctdldl

re

RCC

RZ

( )( ) ( )

22

2

2

1

1

+++

++

+=

ctdldl

dlctdl

im

RCC

CRCZ

Low-Frequency Domain

0


105/116

0

++=

ctreRRZ

+= dlim CZ

22

dlctreim CRRZZ22+=

Slope = 1

= /4

intercept

High-Frequency Domain

zW b t b i i ifi t i


106/116

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


107/116

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


108/116

mercaptoacetic acid

(MAA) HSCH2COOH

mercaptopropionic


109/116

mercaptopropionic

acid (MPA)

HSCH2CH2COOH

mercaptoundecanoic

acid (MUA)

HS(CH2)10COOH

mercaptobenzoic

acid (MBA)

HSC6H4COOH


110/116

R

Rct

Cdl


111/116

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 1-thioglycerol (TG); (B) Au

electrode coated with 1,4-dithiothreitol (DTT).

Fig. 4 Normalized capacity of Au

coated electrodes, (A) DTT, (B) TG

as a function of metal ion

concentration


112/116

Electrochemical Impedance Spectroscopy


113/116

Pseudo-Inductor Components


114/116

The quartz crystal microbalance: a tool for probingviscous/viscoelastic properties of thin films

Tenan, M. A., Braz. J. Phys. vol.28 n.4, 405-412. 1998

z The QCM consists basically ofan AT cut piezoelectric quartz


115/116

an AT-cut 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 well-known Sauerbreyequation.

EQCM

z The resonant mechanicalill ti b i ll fi d


116/116

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.

techniques - esp

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