Electrochemical Methods
MCHV C5060
Libuše Trnková
litrn@seznam.cz
 Introduction
 From Potentiometry (equilibrium) to Polarography
and Voltammetry (dynamics)
Reduction and Oxidation, Redox Potentials, Overpotential,
Electrode system, Cells, Reversibility and Irreversibility)
 Electrochemical Methods ( potentiostatic techniques)
(Voltammetry-CV, LSV, AC, NPV, DPV, SWV, Coulometry)
Fundamentals and Application Basic Equations, Double Layer,
Overpotential
 Hyphenated Methods (with electroanalysis)
(EIS - Electrochemical impedance spectra, HPLC with ED
SE – Spectroelectrochemistry, QCMB - Quarz Crystal
Microbalance, AFM – Atomic Force Microscopy)
Outline
1. A. J. Bard, Electroanalytical Chemistry, Marcel Dekker, N.Y. , 1970
2. J. Dvořák, J. Koryta: Elektrochemie, Academia, Praha, 1975
3. J. Zýka et al.: Analytická příručka, 3rd ed. SNTL, Praha, 1979
4. J. Koryta: Iontově selektivní elektrody, Academia, Praha, 1984
5. J. Wang: Analytical Electrochemistry, VCH Publishers, N.Y., 1984, 1994
10. J. Barek, K. Štulík, F. Opekar: Elektroanalytická chemie, Uč. Texty UK, 2005
6. Ch.M.A.Brett, A.M.O.Brett: Electrochemistry, Oxford, 1993
7. P. Klouda: Moderní analytické metody, P.K., Ostrava, 1994
9. K. Markušová: Elektrochemické metódy, PF UPJŠ, Košice, 2003
8. J.O´M. Bockris, A.K.M.Reddy: Modern Electrochemistry 1,2A,2B, Plenum
Press, N.Y. 1998
11. F. Scholtz: Electroanalytical methods, Spriner, Berlin/Heidelberg,2002.
Books and Monograph Series
Introduction
4
Distribution of EAM
based on electrode processes
Ox + ne  Red
based on electrical properties of
analyte solutions
conductivity
conductometry
capacitance
dielectrometry
current is non-zero
dynamic
electrochemistry
the analyte concentration
practically does not change
by electrolysis
voltammetry (polarography)
amperometry
the analyte is converted
qualitatively by electrolysis
coulometry; electrogravimetry,
current is very low
equilibrium
electrochemistry
(potentiometry)
Some Terms - Potentiometry
 Galvanic cell
 Electrolytic cell
 Reduction
 Oxidation
 Half Reactions
 Redox Couple
 Anode
 Cathode
 Standard Electrode Potential
Introduction
0
redox redox
RT
E E ln Q
zF
 
0 Ox
redox redox
Red
RT a
E E ln
zF a
 
Nernst equation
equilibrium
electrochemical potential; thermodynamic functions (rG rS rH)
activity; activity coefficients, product of solubility, solubility
Ox
+ ze Red
0
redoxzFE
ln K
RT

0
redoxE
equilibrium constant
Ion selective electrodes, potentiometric titrations
Zn(s)|ZnSO4(aq)||CuSO4(aq)|Cu(s)
Electrochemical cells
Eo
Cu2+/Cu= +0.34VEo
Zn2+/Zn= -0.76V
galvanic vs. electrolytic
Potentiometry - sample
Potentiometry
0 059+
0
Ag Ag / Ag
E E . log Ag
    Nernst equation
Ag e Ag

+
Ag / Ag In aqueous solution of NH3
3 3 22Ag NH Ag( NH ) 

equilibrium constant
 
 
3 2 8
2
3
6 10f
Ag NH
K .
Ag NH


 
  
  
 
 32 2
3
1
0 059 0 059+
0
Ag Ag / Ag
f
E E . log . log Ag NH
K NH

   
 
The potential shift due to the complex agent
The determination of:
 the constant complexity
 NH3, organic amines, other ligands
(concentration or activity)
 Standard electrode potential (Eo or Eø)
- relative to a standard hydrogen electrode (SHE)with Eo = 0V (a =1)
 Normal redox potential (Enormal or En)
- relative to a normal hydrogen electrode (NHE - potential of a Pt
electrode in 1 M acid solution, not aH
+=1 (1,18M)
 Absolute redox potential (Eabs)
- is the difference in electronic energy between a point inside the metal
electrode (Fermi level) and a point outside the electrolyte (an electron at
rest in a vacuum). The absolute electrode potential of SHE = 4.44±0.02 V at 25oC
 Formal redox potential (Eo´ or E f) Ox + ze-= Red
the effect of pH and ionic strength Eo´
Redox potentials
… to understand and predict the electrochemistry of the chemical reactions.
 4 44 0 02M M
abs SHEE E . . V  
  
  
 
 
 
 
0 00 05916 0 05916 0 05916red red
Ox Ox
Red Red. . .
E E log E log log
z Ox z z Ox
 
 
    
POLAROGRAPHY/ VOLTAMMETRY
 Linear Sweep Voltammetry (LSV)
 Cyclic Voltammetry (CV)
 Normal Pulse Polarography/Voltammetry(NPP/NPV)
 Differential Pulse Polarography/Voltammetry(DPP/
DPV)
 Square Wave Voltammetry (SWV)
 Alternating Current (AC) Polarography /Voltammetry
 Elimination Polarography (EP)
 Elimination Voltammetry with Linear Scan(EVLS)
Dynamic electrochemistry
Red-Ox in electrochemistry
 the same reaction as in the chemistry? (often an analogous mechanism)
 continuous selection of potentials (selectivity in the generation of intermediates /
products
 continuous change of potential (order of electron transfer)
 acquisition of thermodynamic data (potentials or energy, ox., red., E1ox - E1red)
 different rate of potential changes or their modulation in real time
reversibility, kinetics, precursor, parallel and subsequent reactions, mechanism
electrode
positively chargednegatively charged
Red Ox
!!! reaction in a solution (homogeneous) X on a electrode surface(heterogeneous)
new dimension – a newest and most exciting part of electrochemistry
Electrode kinetics – dynamics in EAM
the electrode acts as an electron source and is termed a cathode
analyt reduction
the electrode acts as an electron sink and is termed an anode
Electrode kinetics
analyt oxidation
Electrode kinetics – dynamics in EAM
Historical polarograms
Polarography
I (μA)
I (μA)
E (mV)
E (mV)
the role of the supporting electrolyte (the indiferent electrolyte)!
problem - oxygen
in acidic solution
The Nobel Prize in Chemistry 1959
"for his discovery and development of the
polarographic methods of analysis"
Jaroslav Heyrovský
1890-1967
History
was an inventor of the polarographic method, father of
electroanalytical chemistry. His contribution to electroanalytical
chemistry can not be overestimated. All
voltammetry methods used now in electroanalytical
chemistry originate from polarography developed by him.
J. Heyrovský + M. Shikata (1924)
Instrumentation, common techniques
Two-electrode set
Three-electrode set
WE – working electrode
RE – reference electrode
(an electrode of the II. type!)
CE – counter electrode
(auxiliary)
WE – working electrode
RE – reference electrode
(an electrode of the II. type!)
Advantage of three-electrode set !
Instrumentation, common techniques
EcoTribo Polarograph
Polaro Sensors - Eco Trend
Prague, Czech Republic
Instrumentation, common techniques
Electrochemical
analyzer
AUTOLAB
Autolab
Ecochemie
Utrecht
The Netherlands
VA-Stand 663
Metrohm
Zurich
Switzerland
Autolab 20
Autolab 30
Dropping Mercury Electrode - DME Static Mercury Drop Electrode - SMDE
Hanging Mercury Drop Electrode - HMDE
Mercury electrode
sampling window
Mercury electrodes (DME, SMDE, HMDE)
Dropping Mercury Electrode - DME
Static Mercury Drop Electrode - SMDE
Hanging Mercury Drop Electrode - HMDE
 its liquid state at ambient temperature, renewable surface
 high purity material availability
 high conductivity
 high surface tension
 high overvoltage potential for hydrogen
 hydrophobic surface
 Hg(I) ions form sparingly soluble salts with many anions
 inertness chemically at low potentials (because of its)
 formation of amalgams with numerous metals (stripping)
 microelectrodes (Hg drop diameter smaller than a millimeter)
 reduction and oxidation of many simple and complex ions speciation
Ce(IV) + Ce(III), Cr(III)+Cr(II),Cr(IV)+Cr(III), Eu(III)+Eu(II),Fe(III)+Fe(II),Mo(VI)+Mo(V),
Sn(IV)+Sn(II),Ti(IV)+Ti(III)…..
 reduction and oxidation of numerous organic substances mechanism
azo, carbonyl, sulphide nitro, quinone, heteroaromatic compounds
a) ½ wave potential (E½) characteristic of Mn+ (E)
b) height of either average current maxima (i avg)
or top current max (i max) is ~ analyte concentration
c) i max is governed by:
rate of growth of DME > drop time (t, sec)
rate of mercury flow (m, mg/s)
diffusion coefficient of analyte (D, cm2/s)
number of electrons in process (z)
analyte concentration (c, mol/ml)
Ilkovič equations
(id)max = 0.706 z D1/2 m2/3 t1/6 c
(id)avg = 0.607 z D1/2 m2/3 t1/6 c
Residual currentHalf-wave potential
i max
i avg
Direct Current (DC) polarography
Half-wave potential, limited diffusion current
Mn+ + ne- +Hg = M(Hg) amalgam
Dionýz Ilkovič
1907 -1980 Slovensko
Electrode materials
• Carbon electrodes
- graphite of spectral quality
- glassy carbon (GC) or vitreous carbon (VC)
- graphite powder with liquid or solid binders
- carbon paste electrode
- carbon fibers, highly oriented pyrolytic graphite –
HOPG (basal hexagonal and edge one, at the edge plane
the electrode processes are usually much faster)
- paraffin impreganted graphite electrode (PIGE)
• Optically transparent electrodes (spectroelectrochemistry)
can be made by evaporating 10-100nm thick layers of Pt, Au, SnO2, TiO2,
Ag, Cu, Hg, C on glass or quartz substrates, grids
• metal, metal oxide, various forms of oligomers, polymers
• oligomers and polymers can spoil the electrode surface (!!!)
• WE has to be tested before an analyte is added
Pt, Au Ag (Rh, Pd, Ge, Ga, Pb)
graphene
Electrode materials
• Chemically modified electrodes
modified by:
- adsorption (quinhydron, trioctylphosphine oxide, PAA oxime on GC)
- chemical reaction (substituted silanes, metal porphyrins on CE)
- formation of polymer film ( Nafion containing dicyclohexyl-18crown-6ether,
polypyrrole-N-carbodithionate)
- preconcentration of analytes by complex-formation reactions
ion exchange or ion extraction
adsorptive accumulation (AdTS technique)
- electrocatalysis – attached the ET mediators which accelerate
electrode reactions. The catalyst is regenerated by the fast and
reversible electrode reaction, it is better to incorporate catalyst into a
polymer or copolymer film.
preliminary step or in situ
it is difficult to
give a definition
of ChME
Instrumentation, common techniques
Potential window
solution cathodic part anodic part
aqueous reduction of H+
(pH dependence)
oxidation of water
oxidation of the electrode material
(Hg = Hg2+ + 2e- )
non-aqueous reduction of cations of
electrolytes
(e.g., -R4N+, Li+)
oxidation of electrode material
oxidation of trace amont of water
oxidation of supporting electrolyte components
for different electrodes and supporting electrolyte
Potential window
Platinum – Pt
Carbon – C
Gold - Au
Diamond - BDDE
Direct Current (DC) polarography
Apply Linear Potential with Time Observed Current Changes with Applied Potential
Apply
Potential
E << Eo
scan rate – polarization rate
v = dE/dt
Diffusion
26
E2
E1
E1
E2
potential proud
v = different scan rate
E2
E1
E2E1
I(A)
dt
dE
v 
proud
time
Electron Transfer
(ET)
Oxidation
Linear sweep voltammetry (LSV)
Reduction
2 3 1 2 1 2
p bulkI const.z AD c v
LSV
Linear sweep (LSV) Cyclic (CV)
anodic
CV
anodic
cathodic
Epa
Epa
Epc
Ep
Ip
Randles-Sevcik equations
diffusion control
Voltammetry
2.303RT/zF
const. – according to the dimension of parameters, including also F, D – the diffusion coeficient, A - the electrode surface
 heterogenous kinetics (G activation in electron transfer 
Arrhenius  exp. function)
 I-E curves (exp. dependence)
 I-E curves under both overpotential
 fast ET Nernst equation J- flux of matter, D -diffusion coefficient
Cyclic and linear sweep voltammetry
 













 

RT
αzFη
exp
RT
zFηα1
expjj 0
Butler- Volmer equation for electrode process,
where rds is charge transfer
activation overpotential
 = Epolarization - Eequilibrium
j - current density , j0 - exchange current density,  - charge transfer coefficient
diffusion overpotential
dc
D
dx
electrode
J  
j
- +
-j
-jd,l
Polarization curves for diffusion controlled processes
- +
j
-j
jd,l,cat
jd,l,anod
o
mequilibriuonpolarizati E-E
Red
Red
Red
δ
DFz

Ox
Ox
Ox
δ
DFz
j
jj
ln
Fz
RT
ln
Fz
RT
EE d l
O x
R edo
c




without diffusion controll with diffusion controll
Direct Current (DC) polarography
the activation overvoltage (přepětí)
the concentration
overvoltage limit currents
jd,l
E1/2
ja
jc
- E + E
Diffusion overpotential – polarography/voltammetry
O x

 R edo
c21 ln
Fn
RT
EE
2d ljj 
Direct Current (DC) polarography
General Uses of Voltammetric Techniques
 Determination of org.and inorg.compounds in aqueous and nonaq.solutions
 Study of structures of organic and inorganic compounds
 Determination adsorption processes on surfaces
 Determination electron transfer and reaction mechanisms
 Measurement of kinetic rates and constants
 Determination of thermodynamic properties of solvated species
 Fundamental studies of oxidation and reduction processes in various media
 Determination of complexation and coordination values
 Determination of equilibrium protonation constants
 Electrochemical sensors
Voltammetry
Common Applications
 Quantitative determination of pharmaceutical compounds
 Determination of metal ion concentrations in water to sub–parts-per-billion levels
 Determination of redox potentials
 Detection of eluted analytes in HPLC and flow injection analysis
 Determination of number of electrons in redox reactions
 Kinetic and mechanistic studies of reactions
Analytical applications
cathodic
anodic
Voltammetry
FOX-7
geminální diamin
nitroglycerin
propan-1,2,3-triyl-trinitrát
Reduction of nitro- compounds
trinitrotoluen
RDX
1,3,5-trinitroperhydro-1,3,5-triazine
TNT Research Department Formula X
Mechanistic study (example)
2,2-dinitroethen-l,l-diamin
J Phys Org Chem. 2020;e4046.
https://doi.org/10.1002/poc.4046
Mechanistic study - reduction of FOX-7
Voltammetric and spectral experiment
UV-vis-NIR ESR
Polarography
R1, R2, R3
R3
MS
electrochemistry electroactive
groups)
electronics(push-pull)
structure (mesomeric
forms, protonation/
deprotonation forms,
tautomerism, changing
geometry, and planarity)
Polarographic "Brdicka reaction" of blood sera of different patients with following
diagnoses: 1) status febrilis 2) tumor hepatis susp 3) ca. ventriculi susp 4) normal
serum 5) cirrhosis hepatic 6) atherosclerosis.
Brdička reaction
Heyrovsks's second assistant, Dr. Rudolf Brdicka, discovered a sensitive catalytic
hydrogen-evolution reaction of proteins: in buffer solutions of pH about 9,
containing ions of cobalt, proteins yield a prominent catalytic "double-wave"; this
polarographic reaction was used in many countries over several decades as a
diagnostic tool in treatment of cancer
Voltammetry
Rudolf Brdička 1906 - 1970
Cyclic Voltammetry
-0,9
-0,7
-0,5
-0,3
-0,1
0,1
-1500 -1000 -500 0E /mV
I/μA
-1
-0,8
-0,6
-0,4
-0,2
0
-1500 -1400 -1300 -1200 -1100 -1000
E /mV
I/μA
-0,05
-0,03
-0,01
0,01
0,03
0,05
0,07
0,09
-500 -400 -300 -200 -100 0
E /mV
I/μA
A + C
G
Anodická část
Katodická část
-0,9
-0,7
-0,5
-0,3
-0,1
0,1
-1500 -1000 -500 0E /mV
I/μA
-1
-0,8
-0,6
-0,4
-0,2
0
-1500 -1400 -1300 -1200 -1100 -1000
E /mV
I/μA
-0,05
-0,03
-0,01
0,01
0,03
0,05
0,07
0,09
-500 -400 -300 -200 -100 0
E /mV
I/μA
A + C
G
Anodická část
Katodická část
Anodic part - oxidation
Cathodic part -
reduction
Applications –mechanism of the electrode process
Microelectrodes
0
0
2
 d
zFADc
I zFr Dc
r
How do currents flow through
electrodes?
Neural Electrode Arrays
Steady state of spherical
diffusion.
2
0r2A 
Biogenic amine levels are detected by rapidly cycling a voltage across an implanted carbon
fiber sensor and measuring the resultant current. Our systems can measure spontaneous subsecond
neurotransmitter release events while conducting detailed behavioral studies. Both
the wireless and tethered systems sweep from 250 to 400 V/s in a user-selectable range
spanning -1.1 to +1.3 V. All systems have built-in support for controlling an external stimulus.
Fast Cyclic Voltammetry (FCV)
microelectrodes
3,4-dihydroxyphenethylamine
Important roles in the brain and body
Neurotransmiter
Brain dopamine pathways
(neuromodulatory) are involved in motor
control and controlling the release of
various hormones.
Voltammetry
Cd2+ + 2e-  Cd k0 = 1 cm/s
Pb2+ + 2e-  Pb k0 ~ 2 cm/s
Tl+ + e-  Tl k0 ~ 2 cm/s
Zn2+ + 2e-  Zn k0 ~ 10-2 – 10-3 cm/s
Heterogeneous rate constant kh and kh
o
Dependence on parameters (E, solvent,electrode,pH, I, adsorption…)
Applications – kinetics
ET
Direct Current (DC) Voltammetry
Randles-Ševčík equation
diffusion control
5 3 2 1 2 1 2
2 686 10p *I . z AD v c
p p
p p
I I
i or j
A A
 
peak height Ip (A ) A (cm2), D (cm2.s-1), v (V.s-1),
c (in solution) ( mol.cm-3)
or Delahay equation
 
3 25 1 2 1 2
2 686 10p *I . z AD v c current
current
density
Calibration redox couples: [Fe(CN)6]3-/4- dopamine
D (cm2.s-1) (1oC, i.e., 1.7%) [Ru(NH3)6]2+/3+ ferrocene
Capacity (charging) current Ic
 the electric double layer charging (as a capacitance)
 Icapacity (Ic) - the connection with surface tension (important
Epzc - zero charge potential: the charges are balanced at the interface (electrode/electrolyte)
 each Hg drop is recharged
 Ic = f(E) is not linear and its time dependence:
Voltammetry
c
s s dl
E t
I exp
R R C
 
  
 Elimination of Ic
1) SMDE – electronically controlled mercury drop; sampled
technique (tast methods - vzorkovací)
2) Application of pulse methods (non – stationary methods)
3) AC voltammetry (phase shift between Ic and If
4) Elimination methods (software approaches)
Pozn.: tast - vzorkovací
the measured quantity is a function of time
Staircase technique, pulse techniques
Voltammetry
E
I
time
E1
E2
time
I
E
E1
E2
1 2
1 2faradaic
zFAD c
I (t )
( t )


Cottrell
charging
s s dl
E t
I exp
R R C
 
  
 
Parameters:
Pulse amplitude (mV)
Pulse width (ms)
Sample period (ms)
Pulse period (s)
sampling
window
time
time
amplitude
E
 perturbation
 measurement during
short time (sampling)
pulse
width
In the pulse a capacity current
decays faster then a faradaic
current (electron transfer)
Barker
Osteryoung
s dlR C time constant (5RC ~ 30ms ~ 0.68% drop of Ic]
Pulse Polarography (Voltammetry)
Normal pulse (NPP, NPV) Differential pulse (DPP, DPV)
1 2
NPP
m
zFAD c
I
t
 Cottrell equation
or Cottrell factor
tm time after application of the
pulse where the current is sampled
1 2
1
1
DPP
m
zFAD c
I
t


 
  
 
  2exp zf RT E /    
E...pulse amplitude
f ...frequency

E
tt EE
E
I1
I2
I2-I1
I
I
I
pulse period
(drop time)
pulse period
(drop time)
-1.3-1.2-1.1-1.0-0.9-0.8-0.7
0
10
20
30
E, V vs SCE
0
10
20
30
40
SW
DP
0
50
100
150
i,A
0.0
2.5
5.0
7.5
10.0
NP
DC
c
(a) Potential sequences (E-t curves).
(b) Potential sequence on one drop ( tast).
(c) Current-potential curves for 1 mM Zn2+ in 1 M KNO3.
DC:  = 2 s; NP:  = 2 s, tp = 5 ms; DP:  = 2 s, tp = 5 ms; Ep = 20 mV; SW: Ep = 20 mV, f = 100 Hz.
a b c
time (s)time (s)
E (mV) E (mV) I (μA)
E (mV)
Pulse and square wave voltammetry
Perturbation by pulses
DPV with stripping
Improving by
stripping mode
z
M M ze 
 
Improving DPV by
the stripping
mode:
Anodic stripping
(ASV)
Cathodic stripping
(CSV)
Adsorptive stripping
(AdSV)
dissolution of metals
Anodic stripping voltammetry
(ASV)
Zn
Cd
Pb
Cu
the accumulation
of metals (here is cathodic)
Square Wave Voltammetry (SWV)
A B
ΔI = If – I b
potential wave form for SWV measured SWV currents
time
ΔI = If - Ib
Ramaley&Krause and Osteryoung&O´Dea
1 2
DPP
m
nFAD c
I
t
  

I differential current peak value 
dimensionless parameter which gauges the peak height in SWV
relative to the limiting response in normal pulse voltammetry
 
one cycle
Cottrell factor
1
1
 
 
  
 2exp ( zf / RT )( E /  
rev
vs.
irrev.!
 the application of a sinusodially oscillating voltage; alternating potential usually has a
frequency of 50-200 Hz and 5-50 mV amplitude
 the AC signal causes a perturbation in the surface concentration
 an electrochemical process, mass transport, chemical and adsorption steps and electron
transfer
 electric double layer EDL
 adsorption (nucleation) studies, study of surface active compounds (PAL)
Alternating Current (AC) Voltammetry
E~
t
Eramp
I~
Ep
the suppression of a capacity current
1) phase sensitive AC current regulation (the faradaic current component is phase shifted by
/4 compared to the input potential, the capacity current component by /2
2) using the second harmonic current component (the frequency 2f)
reversible system
Alternating Current (AC) Voltammetry
potential area
of adsorption
1 – supporting electrolyte
2-5 – surface active compound
Tensammetry
Adsorption/desorption
of biomacromolecules
involved in catalytic
hydrogen evolution
(Emil Paleček)
Adsorption of Nucleosides
on Mercury Surface
(Vladimír Vetterl)
pits – stacking interactions of adsorbed molecules
adsorption/desorption peaks
supporting
electrolyte
„phase transition“
non-stacked molecules
Electrochemical impedance spectroscopy
EIScorrosion
electrodeposition,
electrodissolution, passivity
SAM
diffusion of ions across
membranes semiconductor
interfaces
The fundamental approach of all
impedance methods is to apply a
small amplitude
sinusoidal excitation signal
49
Electrochemical impedance spectroscopy EIS
Taylor series expansion for the current is given by
....
,,












 2
E
2
2
E
E
dE
Id
2
1
E
dE
dI
I
0I00I0

If the magnitude of the perturbing signal ΔE is small, then the higher
order terms can be assumed to be negligible. The impedance of the
system can then be calculated using Ohm’s law:
)(
)(
)(



I
E
Z  )(fimpedanceis)(  Z
frequency range of 100kHz – 0.1Hz
50
Principles of EIS measurements
Electrode system - model
51
ctdl
ct
RCj
R
Z


1
dl
ctdlct
Cj
RCj/RZ



1
1
111
Rct
ctdl
ct
e
RCj
R
RZ


1
222
1 ctdl
ct
ereal
RC
R
RZ


222
2
1 ctdl
dlct
im
RC
CR
Z




Electrochemical impedance spectroscopy EIS
2 2
Z R X 
Z impedance
R rezistance
X reak tance
induktance L capacitance C
j
EIS plots
In cartesian co-ordinates (w)jZ(w)ZZ(w) jr 
In polar co-ordinates

 eZZ )()( 
magnitude of the
impedance
phase shift
The plot of the imaginary part against the real part of impedance - Nyquist plot.
The shape of the curve is important in making qualitative interpretations of the data.
The disadvantage of the Nyquist representation is that one loses the frequency
dimension of the data. One way of overcoming this problem is by labelling
the frequencies on the curve. The absolute value of impedance and the phase shifts
are plotted as a function of frequency in two different plots giving a Bode plot. The
relationship between the two ways of representing the data is as follows:
52
0
0
0
cos( )( ) cos( )
( )
( ) cos( ) cos( )
E tE t t
Z t Z
I t I t t
 
   
  
 
Electrochemical impedance spectroscopy EIS
53

Z
´
Z”
The impedance data are the red points.
Their projection onto the Z“-Z‘ plane is called the Nyquist plot
The projection onto the Z“- plane is called the Cole Cole diagram
The different views on impedance data
The absolute value of Z and the phase shifts are plotted as a function of
frequency in two different plots giving a Bode plot
Electrochemical impedance spectroscopy EIS
Nyquist and Bode plot
   222
ZZZ ImRe 
Z
Z
tg
Re
Im

  cosRe ZZ 
  sinIm ZZ 
54
Electrochemical impedance spectroscopy EIS
EIS: experiment parameters
FRA parameters or settings
1. AC mode (single sine or multi sine)
2. perturbation (sine wave) amplitude (10 mV)
3. Open Circuit Potential (OCP)
4. three electrode set
5. frequency range (1MHz – 0.1Hz)
6. frequency distribution (linearly, logarithmically or with a square root distribution)
55
Cdl capacitance of double layer
Rct resistance of electron transfer
Rs or R resistance of solution
Output parameters from circuit models
RZ R
C
j
Z
C


LZ j L 
Randles circuit
equivalent circuit models
56
Electrochemical impedance spectroscopy EIS
57
Electrochemical impedance spectroscopy EIS
equivalent circuit models
e.g., porous electrodes
Complementary or Related Techniques in-situ
 Spectroelectrochemistry SE: Simultaneous use of
spectroscopic methods can identify species undergoing
reaction, in-situ study.
 EQCMB (EQCNB) with CV in situ the study of
layers on electrode surfaces together with cyclic
voltammetry
 HPLC - ED Liquid chromatography is often used to
separate individual analytes before analysis.
 EC - AFM in situ the study of layers on electrode
surfaces by means of microscopy.
Other electroanalytical techniques may provide additional or preliminary information
Hyphenated methods (HEM)
Spectroelectrochemistry
an experimental method that combines an electrochemical measurement coupled to an:
 in situ spectroscopical measurement (UV-Vis, IR, ESR, NMR)
 ex situ spectroscopical measurement (LEED, AES, XPS, AFM)
Optically Transparent Thin Layer
Electrochemical (OTTLE) Cell
CV
UV-Vis
UV-Vis
1 2 1 2
1 2
2 / /
Ox Red Ox
Red /
c D t
A



ferri
ferro
ferri
Applications
 mechanism
 kinetics
 E0´, z: log (AOx/Ared) = f(E)
 dA/dt = f(E)
 selectivity in complex reactions
Spectroelectrochemistry
UV-Vis 1 2 1 2
1 2
2 / /
Ox Red Ox
Red /
c D t
A



 formal redox potentials: E0´, z: log (AOx/Ared) = f(E)
 evaluation as the derivative function: dA/dt = f(E) (greater accuracy)
 selectivity in complex reactions
1 2 1 2
1 2
2 / /
Red Ox Red
Ox /
c D t
A



diffusion of Ox to the electrode the
absorbance Ared as a function
of time can be observed
diffusion of Red to the electrode the
absorbance AOx as a function of
time can be observed
 1 2/
A f t
kinetics and mechanism of electrode processes
Applications
(not affected by capacity)
Electrochemical Quartz Crystal Microbalance
 A mass variation (m) per unit area (A) by measuring the change in frequency
(f) of a quartz crystal resonator
 The resonance is disturbed by the addition or removal of a small mass due to
oxide growth/decay or film deposition at the surface of the acoustic resonator.
 sensitivity – 0.1-1 ng/cm2
 the calibration is necessary (Cf)
f on E
I on E
http://www.maxtekinc.com/
http://chinstruments.com
Quartz crystal the heart of the QCM
Piezoelectric effect (brothers Curie – 1880)
Some crystal could produce electricity when pressure
is applied in certain crystalographic directions.
(EQCM)
QCM or QCN
 Surface film mass
 Thickness
 Viscoelasticity
 Surface roughness
 Kinetics time dependence
Applications
Quartz crystal microbalance
and nanobalance (QCM, QCN)
Sauerbrey equation
2
02
q q
f
f m
A
   
 
where f0 is the resonant frequency (Hz), Δf is
frequency change (Hz), Δm is mass change (g),
A is piezoelectrically active crystal area (Area
between electrodes in cm2), ρq is density of quartz
(2.643 g/cm3) and μq is the shear modulus of quartz
for AT-cut crystal (2.947x1011 g·cm−1·s−2).
A mass variation (m) per unit area (A) by measuring the change in frequency
(f) of a quartz crystal resonator Gűnter Sauerbrey (1959)
M M
m Q I t
zF zF
  
Faraday:
ff C m  
 thin and rigid film
 sensitivity – 0.1-1 ng/cm2
 for vacuum or for gas phase (correction)
(in water - decrease in f ~ 750Hz)
 the calibration is necessary (Cf)
polyvinyferrocene
HPLC with Electrochemical Detection (ECD)
 An extremely selective and sensitive detection technique that is applied in a
number of analyses such as the neurotransmitters (dopamine, serotonin and
noradrenalin – neurotransmiter analyzer). In combination with the proper
electronics, ECD has an enormous linear dynamic range of more then 6
orders of magnitude (50 pmol/L - 100 µmol/L).
 Amperometric electrochemical detection (hydrodynamic mode)
 Interest: electrochemical detectors; electrochemical flow cells; electrodes
(carbon); electroactive compounds
HPLC with Electrochemical Detection (ECD)
 DC or pulse mode; S/N ratio; optimal E, (low E – no signals, high E – interference
and noise)
 Difference between UV-Vis detection and ECD
Lambert-Beer equation vs. Cottrell equation
 Aplications: 1) neurotransmitter (in blood and brain)
2) vitamins, carbohydrates (in food)
3) phenols (in enviromental samples)
Hydrodynamic
voltammogram
Electroactive groups
Applications
absorbance d c zFAc D
current
t
Electrochemical Atomic Field Microscopy
EC-AFM
 combines atomic force microscopy (AFM) together with electrochemical
measurements
 allows to perform in-situ AFM measurements in an electrochemical cell, in order to
investigate the actual changes in the electrode surface morphology during
electrochemical reactions (increasing interest, „gnome“)
 AFM apparatus is integrated with a three electrode electrochemical cell
 The AFM probe is monitored: surface changes as a function of time, when a
potential is applied to the sample.
 Several electrochemical experiments (CV, DPV); E is applied to the tip, with
respect to a suitable RE, to drive the process of interest at the tip and the current
that flows is typically amplified by a current-to-voltage converter
 During the potential sweeping, the current flows through the sample and the
morphology is monitored.
Electrochemical Atomic Field Microscopy
Scanning electrochemical microscopy: principles and applications to biophysical
systems: Martin A Edwards et al 2006 Physiol. Meas. 27 R63 doi:10.1088/0967-
3334/27/12/R01
EC-AFM
transport-limited current for the one-electron
oxidation of ferrocyanide as a function of tip
position under pressure); dentin - substrate
Slyšel jsem a zapomněl jsem.
Viděl jsem a pamatuji si.
Dělal jsem a pochopil jsem.
(Confucius)
I hear and I forget.
I see and I remember.
I do and I understand.
(Confucius)
"Co slyším, to zapomenu. Co
vidím, si pamatuji. Co si
vyzkouším, tomu rozumím."
551 BC – 479 BC
Moral philosophy
Social philosophy
Ethics
Confucius