Electrochemistry MAE-295
Dr. Marc Madou, UCI, Winter 2012
Class III Transport in Electrochemistry (I)
1
Table of Content
 Interface structure
 Two-electrode cells and three-electrode cells
 Cyclic voltammetry
 Diffusion
 Convection
 Migration
2
Interface structure
1-10 nm
The double-layer region is:
Electrode
surface
• Where the truncation of the metal’s
Electronic structure is compensated for
in the electrolyte.
↓
↓
•~1 volt is dropped across this region…
+
↓
l
↓ ↓ ↓
↓
↓
↓
↓
↓
↓
+
↓
l
↓
↓ ↓
↓
•1-10 nm in thickness
↓
↓
+
↓
↓
l
↓
↓
↓
l
↓ ↓ ↓
Solvated ions
Which means fields of order 107-8 V/m
↓
↓ ↓ ↓
+
↓
l
↓
l
3
IHL
OHL
“The effect of this enormous field at the electrode-electrolyte interface
is, in a sense, the essence of electrochemistry.”
Two-electrode and three-electrode cells
 Electrolytic cell (example):
 Au cathode (inert surface for e.g. Ni




4
deposition)
 Graphite anode (not attacked by Cl2)
Two electrode cells (anode, cathode, working
and reference or counter electrode) e.g. for
potentiometric measurements (voltage
measurements) (A)
Three electrode cells (working, reference and
counter electrode) e.g. for amperometric
measurements (current measurements)(B).
Non-polarizable electrodes: their potential
only slightly changes when a current passes
through them. Such as calomel and H2/Pt
electrodes
Polarizable electrodes: those with strongly
current-dependent potentials. A criterion for
low polarizability is high exchange current
density
Two-electrode and three-electrode cells
5
Two-electrode and three-electrode cells
Inert metals (Hg, Pt, Au)
•Polycrystalline
•Monocrystals
Carbon electrodes
•Glassy carbon
•reticulated
•Pyrrolytic graphite
•Highly oriented (edge plane, )
•Wax impregnated
•Carbon paste
•Carbon fiber
•Diamond (boron doped)
Semiconductor electrodes (ITO)
Modified electrodes
6
Potential window available for experiments is
determined by destruction of electrode material
or by decomposition of solvent (or dissolved
electrolyte)
Two-electrode and three-electrode cells:
activation control
 At equilibrium the exchange current
density is given by:
(1  )F
F
e
e




kT
kT
RT
i  i  k c zF e
 i  k a zF e RT
e
h
h
 The reaction polarization is then given by:

e
 
i i  i
 The measurable current density is then
given by:
i  ie (e
(1 )F
RT
 e
F
RT
)
(Butler-Volmer)
  For large enough negative overpotential:
7
  a( lnie )   log(i)
(Tafel law)
Two-electrode and three-electrode cells:
activation control
 With a symmetry coefficient  >0.5
the activation energy for the reduction
process is decreased while the
activation energy for the oxidation
process is increased.
 At =0.5 the curve is symmetrical in
that the anodic and cathodic portions
are equivalent.The dotted blue curve is
the result of the same equation but with
=0.6. The dashed green curve has
=0.7.
8
Two-electrode and three-electrode
cells: activation control
 Tafel plot: the plot of logarithm of the
current density against the over
potential.
 Example: The following data are the
cathodic current through a platinum
electrode of area 2.0 cm2 in contact
with an Fe 3+, Fe 2+ aqueous solution at
298K. Calculate the exchange current
density and the transfer coefficient for
the process. Slope is  and intercept is
a (=ln ie).
 In general exchange currents are large
when the redox process involves no
bond breaking or if only weak bonds
are broken.
 Exchange currents are generally small
when more than one electron needs to
be transferred, or multiple or strong
bonds are broken.
9
Transport in Electrochemistry
 The rate of redox reactions is
influenced by the cell potential
difference.
 However, the rate of transport to
the surface can also effect or even
dominate the overall reaction rate
and in this class we look at the
different forms of mass transport
that can influence electrolysis
reactions.
 There are three forms of mass
transport which can influence an
electrolysis reaction:
 Diffusion
 Convection
 Migration
10
Diffusion
11

In essence, any electrode reaction is a
heterogeneous redox reaction. If its rate depends
exclusively on the rate of mass transfer, then we
have a mass-transfer controlled electrode reaction.
If the only mechanism of mass transfer is diffusion
(i.e. the spontaneous transfer of the electroactive
species from regions of higher concentrations to
regions of lower concentrations), then we have a
diffusion controlled electrode reaction.

Diffusion occurs in all solutions and arises from
local uneven concentrations of reagents. Entropic
forces act to smooth out these uneven distributions
of concentration and are therefore the main driving
force for this process.

For a large enough sample statistics can be used to
predict how far material will move in a certain time
- and this is often referred to as a random walk
model where the mean square displacement in
terms of the time elapsed and the diffusivity:
Diffusion
 The rate of movement of material by diffusion
can be predicted mathematically and Fick
proposed two laws to quantify the processes.
The first law:
this relates the diffusional flux Jo (ie the rate of
movement of material by diffusion) to the
concentration gradient and the diffusion
coefficient Do. The negative sign simply signifies
that material moves down a concentration
gradient ie from regions of high to low
concentration. However, in many measurements
we need to know how the concentration of
material varies as a function of time and this can
be predicted from the first law.
 The result is Fick's second law:
12
in this case we consider diffusion normal to
an electrode surface (x direction). The rate of
change of the concentration ([O]) as a
function of time (t) can be seen to be related
to the change in the concentration gradient.
 Fick's second law is an important relationship
since it permits the prediction of the
variation of concentration of different species
as a function of time within the
electrochemical cell. In order to solve these
expressions analytical or computational
models are usually employed.
Diffusion
 The thickness of the Nernst diffusion layer
varies within the range 0.1-0.001 mm
depending on the intensity of convection caused
by agitation of the electrodes or electrolyte.
 According to the definition of the Nernst
diffusion layer the concentration gradient may
be determined as follows:
Where: C0 - bulk concentration;Cc concentration of the ions at the cathode
surface;c - thickness of the Nernst diffusion
layer.
 Therefore the flux of ions toward the cathode
surface:
13
 Each ion possesses an electric charge.
The density of the electric current
formed by the moving ions:
Where: F - Faraday’s constant, F =
96485 Coulombs; z - number of
elementary charges transferred by each
ion.
 The maximum flux of the ions may be
achieved when Cc=0 therefore the
electric current density is limited by the
value:
Diffusion
 From activation control to diffusion
•
Homework II: derive the identity:
control:

 Concentration difference leads to another
overpotential i.e. concentration
polarization:
c 
RT
C
ln c
nF
C0
 Using Faraday’s law we may write also:

j  nFAD 0
C0  Cs

 At a certain potential C s=0 and then:

j l  nFAD 0
14

C0

j  jl (1  e
nF c
RT
)
Cyclic Voltammetry
•In voltammetry the potential is
continuously changed as a linear
function of time. The rate of change
of the potential with time is referred
to as the scan rate (v).
• In Cyclic voltammetry, the
direction of the potential is reversed
at the end of the first scan. Thus, the
waveform is usually of the form of
an isosceles triangle.
15
 Cyclic voltammetry is a powerful
tool for the determination of
formal redox potentials, detection
of chemical reactions that precede
or follow the electrochemical
reaction and evaluation of electron
transfer kinetics.
 An advantage is that the product of
the electron transfer reaction that
occurred in the forward scan can
be probed again in the reverse
scan.
Diffusion: Cyclic voltammetry
 Scan the voltage at a given speed (e.g. from




+ 1 V vs SCE to -0.1 V vs SCE and back at
100 mV/s) and register the current .
At low current density, the conversion of
the electroactive species is negligible.
At high current density the consumption of
electroactive species close to the electrode
results in a concentration gradient.
Concentration polarization: The
consumption of electroactive species close
to the electrode results in a concentration
gradient and diffusion of the species
towards the electrode from the bulk may
become rate-determining. Therefore, a
large overpotential is needed to produce a
given current.
Polarization overpotential: ηc
Ferricyanide
Diffusion: Cyclic voltammetry
 The thickness of the Nernst
diffusion layer (illustrated
in previous slide) is
typically 0.1 mm, and
depends strongly on the
condition of hydrodynamic
flow due to such as stirring
or convective effects.
 The Nernst diffusion layer
is different from the
electric double layer, which
is typically less than 1 nm.
17
Diffusion: Cyclic voltammetry (also polarography)
Diffusion: Microelectrodes
Microelectrode: at least one dimension must be comparable to diffusion layer thickness
(sub μm upto ca. 25 μm). Produce steady state voltammograms.
Converging diffusional flux
Electrode
Metal contact
Conductive joint
1 1 
I  nFADc 0   
 r 
Electrode body
Fiber
A)
Insulator
B)
C)
  2Dt

Advantages of microelectrodes:
• fast mass flux - short response time (e.g. faster CV)
• significantly enhanced S/N (IF / IC) ratio
• high temporal and spatial resolution
• measurements in extremely small environments
• measurements in highly resistive media
19
Diffusion: Microelectrodes
• Microelectrodes have at least one dimension of the order of microns
• In a strict sense, a microelectrode can be defined as an electrode that has a characteristic
surface dimension smaller than the thickness of the diffusion layer on the timescale of the
electrochemical experiment
• Small size facilitates their use in very small sample volumes. - opened up the possibility of
in vivo electrochemistry. This has been a major driving force in the development of
microelectrodes and has received considerable attention..
20
Diffusion: Microelectrodes
•At short times size of the diffusion layer is smaller than that of the
electrode, and planar diffusion dominates--even at microelectrodes.
•At very short time scale experiments (e.g., fast-scan cyclic voltammetry)
a microelectrode will exhibit macroelectrode (planar diffusion) behavior.
•At longer times, the dimensions of the diffusion layer exceed those of the
microelectrode, and the diffusion becomes hemispherical. The molecules
diffusing to the electrode surface then come from the hemispherical
volume (of the reactant-depleted region) that increases with time; this is
not the case at macroelectrodes, where planar diffusion dominates
21
Convection
 Convection results from the action of a
force on the solution. This can be a
pump, a flow of gas or even gravity.
There are two forms of convection the
first is termed natural convection and
is present in any solution. This natural
convection is generated by small thermal
or density differences and acts to mix the
solution in a random and therefore
unpredictable manner. In the case of
electrochemical measurements these
effects tend to cuase problems if the
measurement time for the experiment
exceeds 20 seconds.
22
 It is possible to drown out the natural
convection effects from an
electrochemical experiment by
deliberately introducing convection
into the cell. This form of convection is
termed forced convection. It is
typically several orders of magnitude
greater than any natural convection
effects and therefore effectively
removes the random aspect from the
experimental measurements. This of
course is only true if the convection is
introduced in a well defined and
quantitative manner.
Convection
 If the flow is controlled, after a small
lead in length, the profile will become
stable with no mixing in the lateral
direction, this is termed laminar flow.
 For laminar flow conditions the mass
transport equation for (1 dimensional)
convection is predicted by:
where vx is the velocity of the solution
which can be calculated in many
situations be solving the appropriate
form of the Navier-Stokes equations. An
analogous form exists for the three
dimensional convective transport.
23
 When an electrochemical cell
possesses forced convection we
must be able to solve the electrode
kinetics, diffusion and convection
steps, to be able to predict the
current flowing. This can be a
difficult problem to solve even for
modern computers.
Migration
 The final form of mass transport
we need to consider is
migration. This is essentially an
electrostatic effect which arises
due the application of a voltage
on the electrodes. This
effectively creates a charged
interface (the electrodes). Any
charged species near that
interface will either be attracted
or repelled from it by
electrostatic forces. The
migratory flux induced can be
described mathematically (in 1
dimension) as:
24
 The contribution of migration is
typically avoided by adding a lot
of indifferent electrolyte.
 See example: Nanogen DNA
chip.
Homework
1.
2.
3.
4.
25
Calculate the potential of a battery with a Zn bar in a 0.5 M Zn 2+ solution
and Cu bar in a 2 M Cu 2+ solution.
Show in a cyclic voltammogram the transition from kinetic control to
diffusion control and why does it really happen ?
Derive how the capacitive charging of a metal electrode depends on potential
sweep rate.
What do you expect will be the influence of miniaturization on a
potentiometric sensor and on an amperometric sensor?