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Electrochemical Techniques
CHEM 269
Course Content This course is designed to introduce the basics (thermodynamics
and kinetics) and applications (experimental techniques) of electrochemistry to students in varied fields, including analytical, physical and materials chemistry. The major course content will include Part I Fundamentals
Overview of electrode processes (Ch. 1)
Potentials and thermodynamics (Ch. 2)
Electron transfer kinetics (Ch. 3)
Mass transfer: convection, migration and diffusion (Ch. 4)
Double-layer structures and surface adsorption (Ch. 13)
Part II Techniques and Applications Potential step techniques (Ch. 5): chronoamperometry
Potential sweep methods (Ch. 6): linear sweep, cyclic voltammetry
Controlled current microelectrode (Ch. 8): chronopotentiometry
Hydrodynamic techniques (Ch. 9): RDE, RRE, RRDE
Impedance based techniques (Ch. 10): electrochemical impedance spectroscopy, AC voltammetry
Grade: 1 mid-term (30%); 1 final (50%); homework (20%)
Chronoamperometry (CA)
E
t
E1 E2
E3
E4
0
x
Co
Co*
t
x
Co
Co*
E –
t
i
E2
E3
E4
0 t
i
E
iLIM,c
Sampled-current
voltammetry
Chronoamperometry
Current-Potential Characteristics
Large-amplitude potential step
Totally mass-transfer controlled
Electrode surface concentration ~ zero
Current is independent of potential
Small-amplitude potential changes
i =iof
Reversible electrode processes
Totally irreversible ET (Tafel region) R
Oo
C
C
nF
RTEE ln
''1
,0,0
oo EERT
nF
R
EERT
nF
Oo etCetCnFAki
Electrode Reactions
Mass-transfer control
Kinetic control
O’bulk O’surf
Oads
Rads
R’surf R’bulk
Osurf
Rsurf
ele
ctro
de
Double layer
mass transfer
chemical electron transfer
Mass Transfer Issues
)()(
)()(
xvCx
xCD
RT
Fz
x
CDxJ jjj
jxjjj
In a one-dimension system,
In a three-dimension system,
)()()()( rvCrCDRT
FzrCDrJ jjj
jjjj
diffusion migration convection
diffusion current
migration current
convection current
Potential Step under Diffusion Control
Planar electrode: O + ne R
Fick’s Law 2
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
Oes
CsxC 1),(
*
Laplacian transformation
0),0( sCO
0
)()}({ dttFetFL st
Cottrell Equation
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 of Leipzig in 1902.
Although best known to electrochemists for the "Cottrell equation" his primary source of fame was as the inventor of electrostatic precipitators for removal of suspended particles from gases. These devices are still widely used for abatement of pollution by smoke from power plants and dust from cement kilns and other industrial sources.
Cottrell played a part in the development of a process for the separation of helium from natural gas. He was also instrumental in establishing the synthetic ammonia industry in the United States during attempts 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
Depletion Layer Thickness
*
)(o
o
o Ct
DnFAi
tDt OO )(
x
Co
Co*
t
tDO=
30 mm
1 mm
30 nm
at t =
1 s
1 ms
1 ms
Concentration Profile
xD
s
OO
Oes
CsxC 1),(
*
tD
xerfC
tD
xerfcCtxC
oO
oOO
221),( **
In mathematics, the error function (also called the Gauss error function) is a
special function (non-elementary) which occurs in probability, statistics, materials
science, and partial differential equations. It is defined as:
Sampled Current Voltammetry
Linear diffusion at a planar electrode
Reversible electrode reaction
Stepped to an arbitrary potential
),0(
),0(ln
tC
tC
nF
RTEE
R
Oo o
R
O EEnftC
tC exp
),0(
),0(
2
2 ),(),(
x
txCD
t
txC OO
O
2
2 ),(),(
x
txCD
t
txC RR
R
CO(x,0) = CO*
LimCO(x,t) = CO* x∞
CR(x,0) = CR* = 0
LimCR(x,t) = CR* = 0 x∞
Flux Balance
xD
s
OO
OesAs
CsxC
)(),(*
xD
s
RResBsxC
)(),(
0]),(
[]),(
[ 00
xx
x
txCD
x
txCD R
RO
O
Incoming flux Outgoing flux
0)()( sBD
ssA
D
s
RO
)()()( sAsAD
DsB
O
R
xD
s
RResAsxC
)(),(
I-E at any Potential
o
R
O EEnftC
tC exp
),0(
),0(
xD
s
s
C
RRO esxC
1),(
*
11),(
*
xD
s
s
C
O
R
Oe
sxC
),0(
),0(
sC
sC
R
O
)()(*
sAsAs
CO
1)(
*
s
CO
sA
0
),(
x
OO
x
txCnFADi
1)(
21
21
21 *
t
CnFADti
OO
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
E E1/2
Slope n
E1/2 Wave-shape analysis
CA Reverse Technique
E
t
Ei Er
Ef
0 t
1)(
21
21
21 *
t
CnFADti
OOf
21
21
21
)1(
11
"1
1
'1
1)(
*
tt
CnFADti
OOr
t
or EEnf exp" o
f EEnf exp'
tt
CnFADti
OOr
11)(
21
21 *
t
r
f
r
f
f
r
t
t
t
t
i
i
t
when ’ =0 and ” =∞
rf
r
ti
i t
11tr – tf = t
Semi-Infinite Spherical Diffusion
r
trC
rr
trCD
t
trC OOO
O ),(2),(),(
2
2
oOO rt
CnFADti11
)(2
12
12
1 *
21
21
21 *
)(t
CnFADti
OO
CO(r,0) = CO*
CO(r0,t) = 0
LimCO(r,t) = CO* r∞
boundary
conditions
oOO rt
CnFADti11
)(2
12
12
1 *
Cottrell equation
Ultramicroelectrode
Radius < 25 mm, smaller than the diffusion layer
Response to a large amplitude potential step
First term: short time (effect of double-layer charging
Second term: steady state
oOO rt
CnFADti11
)(2
12
12
1 *
**
4 OoOo
OOss CrnFD
r
CnFADi
t
i
iss planar
electrode
spherical
electrode
21
21
21 *
)(t
CnFADti
OO
oOO rt
CnFADti11
)(2
12
12
1 *
Amperometric glucose sensor based on platinum–iridium
nanomaterials
Peter Holt-Hindle, Samantha Nigro, Matt Asmussen and Aicheng Chen
Electrochemistry Communications, 10 (2008) 1438-1441
This communication reports on a novel amperometric glucose sensor based on nanoporous Pt–Ir catalysts. Pt–Ir nanostructures with different contents of iridium were directly grown on Ti substrates using a one-step facile hydrothermal method and were characterized using scanning electron microscopy and energy dispersive X-ray spectroscopy. Our electrochemical study has shown that the nanoporous Pt–Ir(38%) electrode exhibits very strong and sensitive amperometric responses to glucose even in the presence of a high concentration of Cl− and other common interfering species such as ascorbic acid, acetamidophenol and uric acid, promising for nonenzymatic glucose detection.
(a) Chronoamperometric responses of S0, S1, S2 and
S3 measured at 0.1 V in 0.1 M PBS (pH 7.4) +0.15 M
NaCl with successive additions of 1 mM glucose (0–
20 mM). (b) The corresponding calibration plots.
(a) S0: Pt–Ir(0%), (b) S1: Pt–Ir(22%), (c) S2: Pt–Ir(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.
Interference Study
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.
Pt–Ir(0%)
Pt–Ir(38%)
Electroanalysis 1997, 9, 619.
Microelectrode Voltammetry
Fig. 1 Plot showing cyclic voltammograms recorded for a series of 25 mm Pt microelectrodes recorded at 2 mV/s in a solution containing 10 mM K3[Fe(CN)6] in Sr(NO3)2 at 25 mm under anaerobic conditions. The insert in the figure shows a SEM image of the 93 mC HI-ePt modified microelectrode recorded after the experiments were performed. The scale bar on the SEM represents 10 mm.
Electrochemical reduction of oxygen on mesoporous platinum microelectrodes
Chronocoulometry (CC)
21
21
21 *
)(t
CnFADti
OO
ADSDLOO QQt
CnFADtQ 2
1
21
21 *
)(
Cottrell Equation (at large potential steps)
Double-layer charging
Surface adsorbed species nFAG*
Q
t1/2 intercept
Reverse CC
2
12
1
21
21 *
)( t
t ttCnFAD
tQOO
d
Q t1/2 t < t
t > t
2
12
12
1
21
21 *
)()()( tt
ttt ttCnFAD
tQQtQOO
dr
So the net charge removed in the reverse step is
Potential Sweep Techniques
O
R
C
x
Nernstian Processes
O + ne R
E(t) = Ei - vt
tSEvtERT
nFtf
tC
tC oi
R
O
'exp)(
),0(
),0(
tetS )(RT
nFv
2
2 ),(),(
x
txCD
t
txC OO
O
xD
s
OO
OesAs
CsxC
)(),(*
Laplacian transformation
0
),(),0(
)(
x
OOO
x
txCDtJ
nFA
ti
ttt
dtiDnFA
CtCt
O
OO
0
* 21
))((1
),0(
nFA
if
)()(
tt
ttt
dtfD
CtCt
O
OO
0
* 21
))((1
),0(
ttt
dtfD
tCt
R
R
0
21
))((1
),0(
tSEvtERT
nFtf
tC
tC oi
R
O
'exp)(
),0(
),0(
21
21
21
)())((
))((*
0
OR
Ot
DDtS
Cdtf
ttt
1)(
)())((
*
0
21
21
ttt
tS
CDnFAdti OO
t
R
O
D
D
Let z = t so that t = z/
At t = 0, z = 0, and at t = t, z = t
ttt
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 RT
nFv
Numerical Simulations Linear Sweep / Cyclic Voltammetry
Key Features For Reversible Reactions
i v1/2 for linear diffusion
Peak current at 1/2(st) = 0.4463,
thus iP = (2.69 105)n3/2ADO1/2CO*v1/2
Peak 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
Totally Irreversible Reactions
O + ne R
bt
if
vtRT
nFEE
RT
nF
oEE
RT
nF
of ekeekekk
oi
o
,
''
tCk
x
txCD
nFA
iOf
x
OO ,0
,
0
)(*
btbDnFACi OO
vtEE i
)(21
21* bt
RT
FvDnFACi OO
Key Features
At 1/2(bt) = 0.4958,
Peak potential
|EP – EP/2|= 1.857(RT/nF)
212
1
lnln780.0'
RT
Fv
k
D
Fn
RTEE
o
oP
O
21
21
21
*5)1099.2( vDnACi OOP
'* exp277.0 o
Po
OP EERT
FknFACi
Reversible vs Irreversible Reactions
Cyclic Voltammetry
Current reflects the combined contributions from Faradaic processes and double-layer charging
For chemically reversible reactions, iP,a = iP,c
(independent of v)
Peak splitting DEP = |EP,a – EP,c|=2.3RT/nF
DEP = 59/n mV at 298 K, or
at steady state, 58/n mV.
Reversible vs Kinetically Slow Reactions
DEp = constant DEp decreases with increasing k
DEp increases with increasing sweep rate
Cyclic voltammogram of [Cu(pic)2].2H2O in DMF solution
Bispicolinate Copper (II)
The separation between them, DEp, exceeds
the Nernstian requirement of 59 mV
expected for a reversible one-electron
process. This value increases from DEp =
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
Fig. 1 Cyclic voltammetry (100 mV s 1) of: (a) 1 in CH2Cl2 containing 0.1 M Bu4NPF6; (b) a poly-1 coated Pt electrode in acetonitrile containing 0.1 M Et4NClO4.
-1/-2 0/-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
Identify peak positions
Identify peak pairing
Deconvolution of
overlapped
voltammetric peaks (A) Cyclic voltammogram at 0.05 V s−1 of a
GCE modified with KxFey[Ir(CN)6]z in 50 mM
KCl/HCl. (B) Cyclic voltammogram after the
GCE was immersed in Cu2+ for 120 minutes
Voltammetric Responses of Adsorbed
Species
Only adsorbed O and R are
electroactive (Nernstian reaction)
nFA
i
t
t
t
t RO
G
G
)()(
G
G
G
G '
*
*
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
)(O
o
R
O
o
R
O
O
EERT
nF
b
b
EERT
nF
b
b
t G
G
*22
4OP vA
RT
Fni G
2'
'*22
)(exp1
)(exp)(
G
G
o
R
O
o
R
OO
O
EERT
nF
bb
EERT
nF
bb
vA
RT
Fn
t
tnFAi
Key Features
iP v (slope defines G*)
iP G*
Qads = nFAG* (peak area)
EP = Eo’
Reversible reaction, peak
width at half maximum
mVnnF
RTEP
6.9053.3,
21 D
Physical Chemistry Chemical Physics DOI: 10.1039/b101561n
A ligand substitution reaction of oxo-centred triruthenium complexes assembled as monolayers
on gold electrodes
Akira Sato , Masaaki Abe* , Tomohiko Inomata , Toshihiro Kondo , Shen Ye , Kohei Uosaki* and Yoichi
Sasaki*
Cyclic voltammograms for monolayers of 1 assembled on
the 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) with
the scan rate.
G* = 1.8 10-10 mol/cm2
PcFe
PcFe
Wave-Shape Analysis
Question
- Reaction proceeds with a
simultaneous two-electron
transfer or two successive one-
electron reductions?
Controlled Current Techniques
Galvanostat
t
E
t
Classification
Constant-current chronopotentiometry
Programmed current chronopotentiometry
Cyclic chronopotentiometry
I
t
E
t
t
E
t1 t2
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
sxCD
x
OO
0
,
xD
s
O
OO
OesnFAD
si
s
CsxC
2
12
1
)(),(
*
xD
s
R
RRe
snFAD
sisxC
2
12
1
)(),(
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
*
t OnFAD
C
i
O
Sand equation
*
2
1OO CDAnFi
tt
Potential-Time Transient
),0(
),0(ln'
tC
tC
nF
RTEE
R
Oo
21
21
21
421
21
21
21
lnlnln'
t
t
nF
RTE
t
t
nF
RT
D
D
nF
RTEE
O
Ro
ttt
21
21
21
2),0( *
O
nFAD
itCtC OO
21
21
21
2),0(
R
nFAD
ittCR
Slope n
y
x
Reversible Reactions
Totally Irreversible Reactions
RneO
RT
EEnFtCnFAki
o
Oo
'
exp),0(
21
1,0
*
t
t
C
tC
O
O
21
21
21
2),0( *
O
nFAD
itCtC OO
21
1lnln*
'
t
t
nF
RT
i
knFAC
nF
RTEE
oOo
Quasi-Reversible Reactions
nfD
t
nFAC
inf
D
t
nFAC
i
i
i
RROOo
)1(exp2
1)exp(2
121
21
**
o
ROi
DCDCnFA
ti
nF
RT
RO
1112
21
21
21
21
**
S
mall
Double-Layer Effect
Most significant at the beginning or at the end of the charging step
if = i - idl
tACi dldl
Reverse Technique
For a reversible reactions, t2 = t1/3, i.e.,
maximum 1/3 of the R produced in the
forward step will be re-oxidized into O.
t
E
t1 t2
Anal. Chem. 1969, 41, 1806
Hydrodynamic Techniques
Advantages
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
jxjjj
diffusion migration convection
Theoretical Treatments
Convection maintains the concentrations
of all species uniform and equal to the bulk
values beyond a certain distance from the
electrode surface,
Within this layer (0 < x < ), no solution
movement occurs, and mass transfer is
purely diffusion.
Convective Diffusion Equation
)()()()( 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 For an incompressible fluid, continuity equation dictates that
the local volume dilation rate is zero
Navier-Stokes equation
Named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of viscous fluid substances such as liquids and gases.
The equation arises from applying Newton's second law to fluid motion, together with the assumption that the fluid stress is the sum of a diffusing viscous term (proportional to the gradient of velocity), plus a pressure term.
0 v
fvPdt
vdd ss
2
Pressure gradient
Stress tensor
Body force
Sir George Gabriel Stokes, 1st Baronet FRS (13
August 1819–1 February 1903), was a mathematician
and physicist, who at Cambridge made important
contributions 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 and
physicist who specialized in
mechanics.
The Navier-Stokes equation is one of the most useful sets of equations because they describe the physics of a large number of phenomena of academic and 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 a galaxy. As such, these equations in both full and simplified forms, are used in the design 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 they can be used to model and study magnetohydrodynamics.
Rotating Disk Electrode (RDE)
ss d
fvvP
ddt
vd
21
0dt
vd
At steady-state
...)32
()( 32
b
arFrvr
...)3
1()(3
a
brGrv
...)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
At the electrode surface (y 0 or 0)
vy = 0.513/21/2y2
vr = 0.513/21/2ry
At 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
At = (/v)1/2y = 3.6, vy = 0.8Uo, the
corresponding distance yh = 3.6(v/)1/2
defined as the hydrodynamic boundary
layer thickness ()
For water, v = 0.01 cm2/s,
at = 100 s-1, yh = 36 nm
at = 10-4 s-1, yh = 36 mm
Convective-Diffusion Equation
At steady state, dC/dt = 0
2
2
22
2
2
211
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
21
23
17.0
8934.0
*
0
O
O
y
O
D
C
y
C
CvCDJt
C
2
Levich Equation
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
21
61
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
clK
clOfOf
i
ii
i
iCEnFAkyCEnFAki
,,
* 11)()0()(
clK iii ,
111 Levich-Koutecky Equation
1/2
il,c
il,c 1/2
independent of
Consideration In Experimental
Applications of RDE
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)
Potential scan rate must be small compared to
so that a steady state can be achieved,
typically 20 mV/s
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)
The difference between a rotating ring-disk electrode (RRDE) and a rotating disk electrode (RDE) is the addition of a second working electrode in the form of a ring around the central disk of the first working electrode. The two electrodes are separated by a non-conductive barrier and connected to the potentiostat through different leads.
To operate such an electrode it is necessary to use a bipotentiostat.
Rotating Ring-Disk Electrode (RRDE)
The disk current (RDE) is unaffected by
the presence of the ring electrode (current
or potential)
In the case where the disk is open, the
electrode behaves as a rotating ring
electrode (RRE)
When a potential is applied to the disk
electrode, the ring current varies (RRDE)
Rotating Ring Electrode (RRE)
Disk radius r1, inner radius r2, outer
radius r3,so the ring area
In two independent measurements by
RDE and RRE
)(22
23 rrA
*,
)0(1
O
ORl
C
yCii
r1
r2
r3
32
32
31
32
31
33
r
r
r
r
i
i
D
R
2
1
6
13
23
2*3
232, 62.0 OORl CDrrnFi
Collection Experiments
Disk electrode (iD): O + ne R Disk potential is being scanned
Ring electrode (iR): R O + ne Ring potential is held at a positive enough position to
ensure that CR(y=0) 0
Collection efficiency N = iR/iD
11111 3
23
2
FFFN
4
1
3
12arctan
2
3
1
1
ln4
3)(
313
1 3
F
1
3
1
2
r
r
Collection Experiment
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 the
disk may be recovered by
the ring electrode
ED
i
iD
iR
Shielding Experiments
32
1,,, NiNiii olRD
olRlR
ER
iD = 0 iR
iR = NiD,l
Collection
Experiment
lDo
lR ii ,,3
2
iR,l
Shielding
Experiment
Disk electrode (iD): O + ne R
Disk potential is held at a constant position
Ring electrode (iR): O + ne R
Ring potential is being scanned
Shielding factor
Collection Experiment
N = 0.22,
cf. theoretical value 0.25
disk
ring
Electrochemical Impedance Spectroscopy
Ohm's law defines resistance in terms of the ratio between voltage E and current I, I = E/R. While this is a well known relationship, its use is limited to only one circuit element -- the ideal resistor.
An ideal resistor has several simplifying properties: It follows Ohm's Law at all current and
voltage levels.
It's resistance value is independent of frequency.
AC current and voltage signals though a resistor are in phase with each other.
Inductor (coil)
The light bulb is a resistor. The wire in the coil has much lower resistance (it's just wire), so what you would expect when you turn on the switch is for the bulb to glow very dimly. Most of the current should follow the low-resistance path through the loop.
What happens instead is that when you close the switch, the bulb burns brightly and then gets dimmer. When you open the switch, the bulb burns very brightly and then quickly goes out.
Example: viscous/viscoelastic thin films
Electrochemical Impedance
The real world contains circuit elements that exhibit much more complex behavior (inductors and capacitors, for instance). These elements force us to abandon the simple concept of resistance. In its place we use impedance, which is a more general circuit parameter. Like resistance, impedance is a measure of the ability of a circuit to resist the flow of electrical current.
Electrochemical impedance is usually measured by applying an AC potential to an electrochemical cell and measuring the current through the cell. Suppose that we apply a sinusoidal potential excitation. The response to this potential is an AC current signal, containing the excitation frequency and it's harmonics. This current signal can be analyzed as a sum of sinusoidal functions (a Fourier series).
)sin()( tEte
)sin()( tItiPhase shift
Phase Shift
For a pure resistor, i = e/R = (E/R)sin(t),
so = 0
For a pure capacitor, q = Ce, so i = dq/dt
=CEcos(t) = CEsin(t+/2) , i.e., =
/2
RC Circuits (series)
e = eR + eC = i(R j/C) = iZ
Z = R j/C
|Z|=[R2+1/(C)2]1/2
tan( = 1/CR
R
Z
Impedance Plots
log|Z|
log
log
/2
Bode plots
Zim
Zre R
increasing
Nyquist plots
RC Circuits (parallel)
Cj
Re
Z
e
R
e
Z
ei
C
1
CjRZ
11
2
2
211
RC
CRj
RC
RZ
RCtan
Bode plots Nyquist plot
Equivalent Circuit for an Electrochemical Cell
Rs: solution resistance
Cdl: double-layer capacitance
Rct: Charge-transfer resistance
ZW: Warburg resistance (diffusion)
idl
if
if+idl
Kinetic Parameters from EIS
RS CS
Faradaic branch
1SC
ctS RR
R
R
O
O
DDnFA
2
1
),0( tC
E
OO
),0( tC
E
RR
Mass
transfer
terms
Kinetic Evaluation
oR
R
O
O
i
i
C
tC
C
tC
F
RT
**
),0(),0(
RneO
RROO DCDCAF
RT
**2
11
2
oct
Fi
RTR
*O
OFC
RT
*R
RFC
RT
oo
oct
SS ki
Fi
RTR
CR
1
ctR
2fZ
at io ∞ (Rct 0)
= /4
Mass-transfer
controlled
Butler-
Volmer
equation
Randle’s Circuit
2
22
1
ctdldl
ct
re
RCC
R
RZ
2
2
2
2
1
1
ctdldl
dlctdl
im
RCC
CRC
Z
Low-Frequency Domain
0
ctre RRZ
dlim CZ 22
dlctreim CRRZZ 22
Slope = 1
= /4
intercept
High-Frequency Domain
Warburg term becomes insignificant, i.e.,
the ET reaction is under kinetic control
The equivalent circuit becomes
R
Rct
Cdl
2221 ctdl
ctre
RC
RRZ
222
2
1 ctdl
ctdlim
RC
RCZ
22
2
22
ctim
ctre
RZ
RRZ 2
ctR
Experimental Procedure
Structural details of electrochemical Cell
Impedance spectra
Design an equivalent circuit
Curve fitting for kinetic parameters
mercaptoacetic acid
(MAA) HSCH2COOH
mercaptopropionic
acid (MPA)
HSCH2CH2COOH
mercaptoundecanoic
acid (MUA)
HS(CH2)10COOH
mercaptobenzoic
acid (MBA)
HSC6H4COOH
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
R
Rct
Cdl
Electrochemical Impedance Spectroscopy
Pseudo-Inductor Components
The quartz crystal microbalance: a tool for probing
viscous/viscoelastic properties of thin films
Tenan, M. A., Braz. J. Phys. vol.28 n.4, 405-412. 1998 The QCM consists basically of
an AT-cut piezoelectric quartz crystal disc with metallic electrode films deposited on its faces. One face is exposed to the active medium. A driver circuit applies an ac signal to the electrodes, causing the crystal to oscillate in a shear mode, at a given resonance frequency.
Measured resonance frequency shifts, Df, are converted into mass changes by the well-known Sauerbrey equation.
EQCM
The resonant mechanical oscillations are basically fixed by the crystal thickness, whereas the damping depends on the characteristics of the mounting and the surrounding medium.
The use of the QCM in a liquid medium together with electrochemical techniques increased enormously the possibilities of this tool; and hence electrochemical quartz crystal microbalance, EQCM.
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