Introduction to electrochemical
techniques
Valentin Mirčeski
Institute of Chemistry
Faculty of Natural Sciences and Mathematics
“Ss Cyril and Methodius” University, Skopje
Republic of Macedonia
Electrochemistry: basic terms

Electrochemistry is interdisciplinary science dealing with the interrelation between
the chemical and electrical phenomena.


Chemical (redox) transformations caused by a flow of electric current
Gaining electrical current due to spontaneous chemical transformation
Understanding electrochemistry means:
 Understanding electrode processes
 Understanding electrical properties of interfaces
The main phenomena: Charge transfer across an interfaces formed, most
frequently, between an electric conductor of a
 first kind (an electrode) (electron conductivity) and
 second kind (electrolyte solution, i.e., a solution of ions) (ion
conductivity)
Electrochemical cells
Galvanic cell:
Spontaneous redox (electrode) reactions
give raise to a current flow.
Electrolysis cell: nonspontaneous redox (electrode)
reactions are driven by the
power of an external electric
supply!
Electrochemical cells and electrochemical reactions


The simples electrochemical experiment involves charge transfer across at least
two interfaces
Electric potential
 difference between the electric potential of the two electrodes (the main
driving force as a measure for the energy available to drive electric charges
through the electrochemical cell)
Electric potential and current

Electrical potential (E (V – volt)) is a measure for the potential energy
of a charge in an electric field;

The difference in the potential (potential energy) causes a charged
species to move in the electric field (charge transfer)

Potential of 1 V (volt) is equivalent to the potential energy of 1J of a
charged species with a charge of 1 C (coulomb)

Charge transfer in time is called electric current (I (A – ampere)
Electrode reactions, half reactions…

electrode|solution Interface
O (oxidized species)
- e O + ne- ⇄ R
(electrode reaction)
R (reduced species)
Electrode/electrolyte interface
is characterized with a large
potential difference , thus a
strong electric filed exists at
the interface!
 Electrode reactions
 Half-reactions
 The overall reaction
 Working electrode
 Reference electrode
The main reference electrode: Standard (normal) hydrogen
electrode (SHE) (NHE)
Standard hydrogen electrode

Reference callomel electrode
Hg/Hg2Cl2/KCl (saturated in water)
0.242 V vs SHE

Reference silver-silver chloride
electrode
Ag/AgCl/KCl (saturated in water) 0.197
V vs SHE

In the course of the
electrochemical experiment the
chemical composition, hence the
electric potential, of the reference
electrode remains constant!
Controlling the potential difference between the working and reference electrode, one
controls actually the potential of the working electrode only!
Current sign convention, standard redox potential, Faraday law



Reduction
 Reduction current (“ – “)
Oxidation
 Oxidation current (“ + “)
Standard redox potential E, which is related to the standard Gibbs energy
DG  = -nFE 
Synonyms: standard electrode potential; standard reduction potential.
O + ne- = R
n – number of electrons
F – Faraday constant (96 485.3 C mol-1). Thus, the physical meaning of the
Faraday constant is that one mole of a single charged species has a charge of
96 485.3 C; e.g., one mole of electrons has a charge of - 96 485.3 C.

Faraday law: A charge of 96485.3 C corresponds to the transformation of 1 mol
reactant and 1 mol product in a one-electron electrohemical reaction O + e- = R
I – E curve: polarisation curve
(working electrode)
2H+ + 2e- = H2
(reference electrode)
Ag + Br- = AgBr + e2Br- = Br2 + 2eAgBr + e- = Ag + Br
The overall current flow must be
equal at both electrodes, and it is
dictated by the working electrode,
which has much smaller electrode
surface area.

Limiting potentials dictated by
electrochemical reactions of the
supporting electrolyte at particular
electrode.

Electrode reactions are
heterogeneous in their nature.

The rate depends on the electric
field, i.e., on the electrode potential.
Overpotential: additional energy required than
thermodynamically predicted due to the slow electrode kinetics
A large overpotential for
hydrogen reduction at
Hg electrode
Hg
Electroactive species in a supporting electrolyte
Polarization curve in the presence of traces of electroactive species (Cd2+)
Possible electrode reactions at different electrodes
Faradaic and nonfaradaic processes

Faradaic processes: charge transfer due to
redox reactions (electrode reaction)-current
flow

Nonfaradaic processes: no charge transfer
across the interface; adsorption, desorption,
changes in the structure of the layer of the
solution adjacent to the electrode formation of
an electic double layer etc.
 Important: although there is no charge
transfer, the nonfaradaic processes cause
the current to flow in the electrochemical
cell!

Ideally polarizable electrode: no charge
transfer, e.g. Hg in 1 M KCl in acetonitrile
over 2 V (from 0.25 to -2.1 V vs SHE.
Electrode/electrolyte interface: an electric capacitor
Structure of the electrical doubly layer
(IHP) - inner
Helmholtz
plane
(OHP) - Outer
Helmholtz
plane
Potential profile across the double-layer
Y = dE/dx
The intensity of the
electric field is very
high due to the
potential variation
over very small
(nanometer range)
distance!
Rate of an electrode reaction: the flux
electrode|solution Interface
O (oxidized species)
-e
O + ne- ⇄ R
(electrode reaction)
R (reduced species)
dq
I
dt
q  n(O)nF
dn(O)
v
A dt
dq 1
I
v

dt AnF AnF
I
v
nFA
Flux (the rate of the
heterogeneous electrode
reaction) is equal to the
amount of reacted
material per unit of time
per unit of electrode
surface area
(mol s -1 cm-2). This
chemical rate is equal to
the ratio of the electric
current, number of
exchanged electrons in a
unit reaction and
electrode surface area.
Electric current (I) measured at the
electrode is proportional to the rate (v)
of the electrode reaction!
(q – charge, t – time, F – Faraday constant; A –
electrode surface area; n – number of electrons, n(O)
– number of moles of the reactant O)
Factors affecting the rate of electrode processes
Modes of mass transfer:



Migration
Diffusion
Convection
Nernst-Plank equation
Electrode reaction controlled by the mass transport
If the mass transfer is the slowest step of the electrode reaction, then the electrode reaction is termed as being
“electrochemically reversible”. At each potential difference (DE) of the interface, the electrode reaction is
in redox equilibrium, which is described by the Nernst equation:
DE  E 0' 
O
O + ne ⇄ R
(electrode reaction)
R
electrolyte
solution
RT [O]x 0
ln
nF [R]x 0
The Nernst eq. reveals that variation of the potential
difference at the interface (DE) causes variation of the
equilibrium concentrations of the redox species ([O] and
[R]). In other words, it shifts the position of the redox
equilibrium, which is manifested as a flow of electric
current in the system.
DE = felecc. – fsol. (Potential difference (DE) across the interface
is externally controlled by controlling the inner potential (f) of the
electrode. In simple words, one controls the activity, i.e., concentration of
electrons participating in the electrode reaction, thus affecting both the
position of the redox equilibrium O/R and the kinetics of the redox
transformation. Note, frequently, the potential difference DE is designated
simply as electrode potential with a symbol E)
Semi-empirical treatment of a voltammetric experiment when the
diffusion layer has a constant thickness: a steady-state mass
transfer
In this experiment, the flux at the electrode (i.e., the rate of the electrode reaction, thus the current), depends on the
diffusion rate only (i.e., depends on the mass transfer only). According to the First Fick law, the rate of diffusion
depends on the diffusion coefficient (D) and the concentration gradient (dc/dx); (D – diffusion coefficient (it is the rate
constant of the diffusion (cm 2 s-1)). In addition, it is assumed that the diffusion layer has a constant thickness . The
flux of R species must be equal, but opposite in sign, with the flux of O species. R diffuses toward the electrode, while
O, formed by oxidation of R, diffuses away from the electrode (in the opposite direction)

R = O + ne-
cR
electrode
dc
v  DR ( R ) x 0
dx
*
R
c (bulk conc.)
cR ( x  0)
x
dc
v  ( R ) x 0
dx
I
cR*  cR ( x  0)
 DR
nFA


v  DR
cR*  cR ( x  0)

I
D 

 mR (cR*  cR ( x  0));  mR  R 
nFA
 

D 
I

 mO (cO*  cO ( x  0));  mO  O 
nFA
 

I
 mO cO ( x  0)
nFA
Il
 mR c R*
nFA
cO* (bulk conc.)  0
The maximal flux of R will be if cR(x = 0) = 0.
Thus, the corresponding current is termed
limiting current, Il
Il (limiting
current)
cR* 
Il
nFAmR
I /A
cR ( x  0) 
E1/2
Il  I
nFAmR
E  E0 
RT c O ( x  0)
ln
nF c R ( x  0)
E  E0 
RT mR RT
I
ln

ln
nF mO nF I l  I
I  Il / 2
E/V
Typical I-E curve (voltammogram) for
an electriochemical experiment with a
constant thickness of the diffusion layer
(steady state voltammetry)
E1/ 2  E  
E  E1/ 2 
RT mR
ln
nF mO
RT
I
ln
nF I l  I
Kinetics of a simple homogeneous chemical reaction
kf
A⇄
B
k
b
 f  k f cA
b  kb c B
net  k f cA  kbcB
kf
[ B]
K
kb
[ A]
The rate of a common chemical reaction
depends on the concentrations of
participants, and (through the rate
constant) on the temperature and
activation energy.
Symbols and abbreviations
f – forward
b – backward
net – overall reaction
K – equilibrium constant
[X] - equilibrium concentration of a
species X
Electrode kinetics
kf
R ⇄ O + nekb
 f  k f cR 
Ia
nFA
b  kb cO 
 net   f  b  k f cR  kb cO 
Ic
nFA
I
nFA
I  I a  I c  nFA[k f cR  kbcO ]
k f  k 0 exp[ 
nF
nF
( E  E 0 ' )]
( E  E 0 ' )] kb  k 0 exp[ (1   )
RT
RT
c – cathodic (reductive)
a – anodic (oxidative)
 – electron transfer
coefficient (dimensionless
number between 0 and 1;
most frequently the value is
0.5)
k (cm s-1)- standard
rate constant (rate
constant when the electrode
potential is equal to the
standard potential of the
redox couple, E’)
Rate constants depend on the potential! The unique feature of
electrochemical rate constants. Thus, the rate of the electrode
reaction can be controlled by the potential!
nF
nF

( E E0' )
(1 )
( E E0' ) 

RT
I  FAk0 cR (0, t )e RT
 cO (0, t )e
 Butler-Volmer equation


Dependence of the current on the electrode potential
The current
increases
exponentially with
the potential as
predicted by the
dependence of the
rate constants on the
potential!
Limiting current
diffusion
O
(at the
electrode
surface)
O (in the
solution)
v = I/nFA
limiting current
Although the rate of the electrode reaction could be very fast due
to the large overpotential, the overall rate will by limited by the
supply of the electrode surface with the electroactive material by
the mass transport, i.e. diffusion!
R
Electrochemical techniques: chronoamperometry
R ⇄ O + ne
E2
E
I
E1
0
t
t
0
The dependence of the potential
and current on time in the course
of the chronoamperometric
experiment. The experiment is
conducted at a given fixed
potential (E2), which is
sufficiently height (E2 >> E) to
cause complete electrochemical
(redox) transformation of the
electroactive species at the
electrode surface. As a
consequence, the current is
flowing in the cell, and it is being
measured as a function of time.
Description of the mathematical model referring to a simple
chronoamperometric experiment - Cottrell equation
R ⇄ O + ne
Cottrell experiment: Chronoamperometric experiment
in a homogenous solution containing only R species, at a
potential E >> E , thus enabling complete transformation
of all R species at the electrode surface. Mass transfer is
occurring only by diffusion without any specific adsorption
phenomena on the electrode surface.
1
t =0
t = 0,1 s
t = 0,01 s
cR ( x, t )
c ( x, t )
 DR R 2
t
 x
cR / c*R
2
t=1s
lim x  cR ( x, t )  cR*
0,2
cR (0, t )  0
I (t )
 c (0, t ) 
 DR  R

nFA
 x  x 0
I (t )  I d (t )  nFAcR*
t = 0,001 s
DR
t
x
(Cottrell equation)
Concentration profiles. Variation of the
concentration of electroactive species with the
distance x measured from the electrode surface at
different times of the chronoamperometric
experiment. As shown above, the thickness of the
diffusion layer increases with time.
Chronoamperometry with a double potential step
For mechanistic purposes, i.e. to reveal the mechanism of the electrode reaction, the
chronoamperometric experiment can be conducted with a double potential step, as
shown in the figure below. At the potential E2, the initially present R species undergo
electrochemical oxidation at the electrode surface to produce species O, resulting in
the first branch of the current, presented in the right plot (i.e.. chronoamperogram).
In the second potential step, the potential is changed to a value E3, at which the
reduction of previously formed species O is taking place, producing the second
branch of the chronoamperogram presented on the right panel.
E2
E
I
E3
E1
0
t
t
0
t
t
Chronocoulometry
Chronocoulometry is equivalent method to chronoamperometry, the difference being
in measuring the charge consumed in the course of the electrode reaction instead of
the current. We recall, the definition of the current
I
dq
dt
Hence, the charge is simply calculated as an integral of the current-time function, i.e.
t
q   I (t )dt
0
In the course of the experiment, contrary to the chronoamerometry, the response of
the crhronocoulometry increases with time, as the amount of the material
transformed at the electrode increases with time. By integration of the current, the
noise effect is usually smoothed out and it is not so significant as in
chronoametrometry. The contribution of the double layer as well as from electrode
reaction of immobilized species can be easily separated from the contribution of
diffusing species. Thus, chronocoulometry is especially valuable for studying surface
processes, thus it is of particular importance in studying conducting polymers.
For a Cottrell experiment described on page 27, the chronocoulometric response is defined as:
Q
2nFAD1/ 2ct1/ 2
 1/ 2
The charge consumed during the experiment of species that diffuses toward the electrode is
proportional to the square-root of time and the plot vs. t1/2 is linear with a slop from which some of
the constants of the equation above can be obtained, given the knowledge of others.
The eq. above shows that at t = 0, the charge is 0.
However, in a real experiment the line Q vs t1/2
does not cross through the origin, as shown in the
plot. This is due to the charge consumed by the
double layer formation and by electrode
transformation of species immobilized on the
electrode surface. Thus the total charge can be
separated in three terms:
Q
2nFAD1/ 2ct1/ 2
 1/ 2
 Qdl  nFAΓ R
The first term is due to electrode reaction
controlled by the diffusion of the species,
homogeneously distributed in the solution, the
second term Qdl is due to formation of the double
layer and the third is due to electrode
transformation of adsorbed species.
29