Transcript No Slide Title

SS902
ADVANCED
ELECTROCHEMISTRY
Murali Rangarajan
Department of Chemical Engineering
Amrita Vishwa Vidyapeetham
Ettimadai
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ELECTRODICS
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FARADAIC PROCESSES
• Two types of processes take place at electrode
– Faradaic Processes
– Non-Faradaic Processes
• Faradaic processes involve electrochemical redox
reactions, where charges (ex. electrons or ions) are
transferred across the electrode-electrolyte interface
• This charge transfer is governed by Faraday’s laws
• Faraday’s First Law: The amount of substance undergoing
an electrochemical reaction at the electrode-electrolyte
interface is directly proportional to the amount of electricity
(charge) that passes through the electrode and electrolyte
n  Q
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FARADAY’S FIRST LAW
• Every non-quantum process has a rate, a driving force
and a resistance to the process offered by the system
where the process takes place
Drivin gForce
Rate
• They are related to each other:
Re sistan ce
• Reaction rate is given by: r  dn  j
dt zF
• Here, j is current density, z is the number of electrons
transferred and F is Faraday’s constant = 96487 C/mol
• Problem: A 30cm  20cm aluminum sheet is anodized on both sides
in a sulfuric acid bath. (Thickness may be ignored for calculation of
area.) at 3 A/dm2 for 1 hour at 30% efficiency. Density of aluminum
is 2.7 g/cm3. Calculate the thickness of anodic film. The atomic
weight of aluminum is 27.
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NON-FARADAIC PROCESSES
• Non-Faradaic processes are those that occur at the
electrode-electrolyte interface but do not involve
transfer of electrons across the interface
– Adsorption/Desorption of ions and molecules on the
electrode surface
– These can be driven by change in potential or solution
composition
– They alter the structure of the electrode-electrolyte
interface, thus changing the interfacial resistance to
charge transfer
– Although charge transfer does not take place, external
currents can flow (at least transiently) when the potential,
electrode area, or solution composition changes
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NON-FARADAIC PROCESSES
– Both faradaic and non-faradaic processes occur at the
interface when electrochemical reactions occur
– Though only Faradaic processes may be of interest, the
non-Faradaic processes can affect the electrochemical
reactions significantly
– For instance, additives are used in electroplating which
adsorb on electrode surface, increases resistance to
deposition, resulting in smoother deposits
– So we first examine the structure of the electrodeelectrolyte interface and the non-faradaic processes that
happen there
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ELECTRICAL DOUBLE LAYER
• Electrode-electrochemical interface may be thought of
as a “capacitor” when voltage is applied to it
• A parallel-plate capacitor stores charges by polarization
of the two plates (due to applied voltage/other driving
forces & molecular structure of the medium in between)
q
C
V
Charging a capacitor with
a battery
The metal-solution
interface as a capacitor with a
charge on the metal, qM, (a)
negative and (b) positive
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ELECTRICAL DOUBLE LAYER
• The metal side of the double layer acquires either
positive or negative charge depending on whether the
electrode is an anode or a cathode
• The solution side of the double layer is thought to be
made up of several “layers”
• That closest to the electrode, the inner layer, contains
solvent molecules and sometimes other species (ions or
molecules) that are said to be specifically adsorbed
• This inner layer is called the Helmholtz or Stern layer
• The total charge density from specifically adsorbed ions
in this inner layer is  i
• The locus of the electrical centers of the specifically
adsorbed ions is called the inner Helmholtz plane (IHP)
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ELECTRICAL DOUBLE LAYER
• Solvated ions can approach the metal only till before the
IHP
• The locus of centers of these nearest solvated ions is
called the outer Helmholtz plane (OHP)
• The interaction of the solvated ions with the charged
metal involves only long-range electrostatic forces, so
that their interaction is essentially independent of the
chemical properties of the ions
• These ions are said to be nonspecifically adsorbed
• Because of thermal agitation in the solution, the
nonspecifically adsorbed ions are distributed in a 3-D
region called the diffuse layer, which extends from the
OHP into the bulk of the solution
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ELECTRICAL DOUBLE LAYER
• The excess charge density in the diffuse layer is d,
hence the total excess charge density on the solution
side of the double layer, s, is given by  S   i   d   M
The thickness of the diffuse layer depends
on the total ionic concentration in the
solution; for concentrations greater than
102 M, the thickness is less than ~100 A
Potential profile
across interface
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MEASURING DOUBLE LAYER PROPERTIES
• Use a cell consisting of an ideal polarizable electrode
(IPE) and an ideal reversible electrode (IRE)
Two-electrode cell with an
ideal polarized mercury drop
electrode and an SCE
This cell does not undergo any
Faradaic processes, so only doublelayer properties are measured
Resistances in the IPE-IRE cell
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ELECTROCHEMICAL CELLS
• Common cells are two-electrode and three-electrode
cells
• Refer to Bard and Faulkner pp. 24-28 for their
description
• Prepare short notes on both two-electrode and threeelectrode cells
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ELECTROCHEMICAL EXPERIMENTS
• A number of electrochemical experiments may be
performed with an electrochemical cell
• There are three main properties of electrochemical
systems that may be measured
– Voltage
– Current
– Impedance or Resistance
• Some of them are
–
–
–
–
Potential Step Experiments
Current Step Experiments
Potential Sweep (Voltage Ramp) Experiments
Electrochemical Impedance Spectroscopy
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ELECTROCHEMICAL EXPERIMENTS
• In each of these experiments, a predefined
perturbation of one of the properties is applied on the
system
• One of the other properties is measured as a response
• From these responses, both Faradaic and Non-Faradaic
processes, their rates and resistances may be studied
Experiment
Perturbed
Variable
Measured
Variable
Potential Step
Voltage
Current
Current Step
Current
Voltage
Potential Sweep
Voltage
Current
Impedance
Spectroscopy
Voltage
Impedance
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POTENTIAL STEP EXPERIMENTS
The current response for a potential step is:
E  t RsCd
i (t ) 
e
Rs
• There is an exponentially
decaying current having a
time constant  = RsCd.
• Peak Current = E/Rs.
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CURRENT STEP EXPERIMENTS
The voltage response for a current step is:

t
E ( t )  i  Rs 
Cd




• Potential increases linearly
with time
• The initial jump in the
potential is iRs.
• Slope is i/Cd.
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POTENTIAL SWEEP EXPERIMENTS
The current response for a linear
voltage ramp E = t is:
 t

Rs C d 
i ( t )  C d 1  e


• The time constant for
current is  = RsCd.
• The limiting current
(maximum current) is Cd.
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POTENTIAL SWEEP EXPERIMENTS
• A triangular wave is a ramp
whose sweep rate switches
from  to —  at some
potential, E.
• The steady-state current
changes from Cd during the
forward (increasing E) scan
to — Cd during the reverse
(decreasing E) scan
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FARADAIC PROCESSES
• When charger-transfer reactions (Faradaic processes)
take place in an electrochemical cell, the driving force
for the reactions is the departure in the voltage from
the equilibrium voltage of the cell
• This departure of voltage from the equilibrium voltage
of the cell is termed as overpotential   E  Eeq
• The rate of the reaction must be proportional to the
driving force
• Therefore there must be a relationship between the
overpotential and the Faradaic current
• Current-potential curves, particularly those measured
under steady-state, are termed polarization curves
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POLARIZABLE VS. NON-POLARIZABLE
• An ideal polarizable electrode is one that shows a very
large change in voltage for the passage of an
infinitesimal current
• An ideal non-polarizable electrode is one that shows a
very large change in current for an infinitesimal
overpotential
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WHAT AFFECTS POLARIZATION?
• Consider the overall electrochemical reaction O  ne  R
• A dissolved oxidized species, O, is converted to a reduced
form, R, also in solution
• There are a number of steps that are involved in the
overall electrochemical reaction
• The rate of electrochemical reaction is determined by the
slowest, i.e., rate-determining step
• Each step will contribute to the overpotential
(polarization)
• The overpotential needed for a certain reaction rate will
largely be determined by the rate-determining step
• Equally, the rate constants of the different steps will also
be dependent on the potential
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STEPS IN ELECTROCHEMICAL RXN
The following steps are involved in an electrochemical rxn:
• Mass transfer (e.g., of О from the bulk solution to the
electrode surface).
• Electron transfer at the electrode surface.
• Chemical reactions preceding or following the electron
transfer. These might be homogeneous processes (e.g.,
protonation or dimerization) or heterogeneous ones (e.g.,
catalytic decomposition) on the electrode surface.
• Other surface reactions, such as adsorption, desorption,
or crystallization (electrodeposition).
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STEPS IN ELECTROCHEMICAL RXN
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OVERPOTENTIAL
• The driving force for an electrochemical reaction is the
overpotential
• This driving force is used up by all the steps in the
electrochemical reaction
• Thus an applied overpotential may be broken into:
–
–
–
–
Mass transfer overpotential
Charge transfer overpotential
Reaction (Chemical) overpotential
Adsorption/Desorption overpotential
• Correspondingly, the resistance offered to the passage of
current may be viewed as sum of a series of resistances
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ELECTRODE KINETICS
• Consider the reversible charge transfer redox reaction
taking place at an electrode-electrolyte interface
O  ze  R
• Let the rate constants be kf and kr respectively for the
forward and the reverse reactions
• In the limit of thermodynamic equilibrium, the potential
established at the electrode-electrolyte interface is
given by the Nernst equation
RT C *O
E  E0 
ln
zF C * R
• Here C*O and C*R are bulk concentrations, z is the
number of electrons transferred, E0 is the formal
potential
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TAFEL EQUATION
• Without derivations, we present the rate equations
(relating current-overpotential)
• It is important to recall that a number of factors
(including interfacial electron transfer kinetics) that
determine the overall rate of an electrochemical reaction
• When the current is low and the system is well-stirred,
mass transfer of reactants to the interface is not the
rate-limiting step
• At such conditions, adsorption/desorption are also not
usually rate-limiting
• The reaction rate is determined mainly by chargetransfer kinetics : governed by Tafel Equation
  a  b lni
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TAFEL EQUATION
2.3 RT
2.3 RT
b
or
1   F
F
a
F
2.3 RT
ln i0

1   F
or 
ln i
2.3 RT
0
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BUTLER-VOLMER EQUATION
• The exponential relationship between current density and
overpotential, observed experimentally by Tafel, is an
important result and is true for more general cases as
well
• For a one-step (only charge transfer resistance in a
single step), one-electron process, the general rate
equation is O  e  R

i
1  f E  E 0 ' 
 f E  E 0 ' 
 k0 CO 0, t e
 C R 0, t e
AF

• Here i is current, A is area of the electrode, F is Faraday’s
constant, k0 is the standard rate constant (at eqbm), CO(0,t) &
CR(0,t) are instantaneous concentrations of O & R at the
electrode surface,  is the transfer coefficient, f is F/RT, E0’
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is a reference potential
STANDARD RATE CONSTANT
• The standard rate constant k0: It is the measure of the
kinetic facility of a redox couple. A system with a large k0 will
achieve equilibrium on a short time scale, but a system with
small k0 will be sluggish
• Values of k0 reported in the literature for electrochemical
reactions vary from about 10 cm/s for redox of aromatic
hydrocarbons such as anthracene to about 109 cm/s for
reduction of proton to molecular hydrogen
• So electrochemistry deals with a range of more than 10 orders
of magnitude in kinetic reactivity
• Another way to approach equilibrium is by applying a large
potential E relative to E0’.
• Both of these together are represented by the term exchange
current
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EXCHANGE CURRENT
• Exchange current is the current transferred between
the forward and the reverse reactions at equilibrium –
they are equal at equilibrium and the net current is zero
i0
 f E eq  E 0 ' 
 k 0C O * e
AF
• CO* is the concentration of species O at equilibrium
• The exchange current density values for two
electrochemical reactions are 1  10–9 and 1  10–3 A/cm2.
How do they reflect on Tafel plot, all other parameters
being constant?
  a  b lni
– No effect on b only on a;
– One with larger i0 needs lesser overpotential to achieve same
current or rate of the reaction
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EXCHANGE CURRENT
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BUTLER-VOLMER EQUATION
• In terms of exchange current and overpotential, ButlerVolmer equation is represented as
 CO 0, t   f C R 0, t  1  f 
i  i0 
e

e

C
*
C
*
R
 O

• First term denotes cathodic contribution and the second
denotes anodic contribution
• Ratio of concentrations is a measure of effects of mass
transfer – they govern how much reactants are supplied to the
electrode
• In the absence of mass transfer effects (CO(0) = CO* always),
the current-overpotential relationship is given by

i  i0 e  f  e 1  f

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LIMITING CURRENT
• Now let us look at the other extreme where the electron
transfer is extremely fast compared to mass transfer
• Therefore the current (rate of charge transfer) is entirely
governed by the rate at which the reacting species (say, O) is
brought to the electrode surface
• This rate of mass transfer is proportional to the
concentration difference of O between the bulk and the
interface, i.e., CO*  CO(0)
• The proportionality constant is termed as mass transfer
coefficient k
• This is equal to the electrochemical reaction rate il/nF
• Here il is called the limiting current – the maximum current
when the process is mass-transfer-limited il
*
nF

 m 0 C O  C O ( 0)

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BUTLER-VOLMER EQUATION
Note: Butler-Volmer
equation is not valid
under mass-transferlimited conditions
Note: For small , i
increases linearly with ;
For medium , Tafel
behavior is seen; For
large , i is independent
of : limiting current
 = 0.5, T = 298 K, il,c =  il,a = il, and i0/il = 0.2. Dashed
lines show the component currents ic and ia.
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EXCHANGE CURRENT & OVERPOTENTIAL
• Therefore the regime where Butler-Volmer equation is valid is
the charge-transfer-limiting regime
• Here, most of the driving force is spent in overcoming the
activation energy barrier of the charge transfer process
• Therefore, the overpotential in this regime is termed activation
overpotential
• We have already seen that for sluggish redox kinetics, the
exchange current must be small : Small i0   : Activation
overpotential
• On the other hand, when the exchange current is very large,
even for very small overpotentials, the current approaches the
limiting current, i.e., since charge transfer is very fast, mass
transfer to the electrode becomes rate-limiting
• In such conditions, Large i0   : Concentration overpotential
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TRANSFER COEFFICIENT
• The second parameter in the Butler-Volmer equation is transfer
coefficient 
• Transfer coefficient determines the symmetry of the currentoverpotential curves
• For the cathodic term, the exponential term is multiplied by 
while for the anodic term the multiplying factor is (1  )
• If  = 0.5, both cathodic and anodic behavior of the electrode
will be symmetric
• If  > 0.5, the system is likely to behave a better cathode (since
more cathodic currents are achieved for smaller overpotentials)
• If  < 0.5, the system is likely to behave a better anode (since
more anodic currents are achieved for smaller overpotentials)
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TRANSFER COEFFICIENT
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