SS902 ADVANCED ELECTROCHEMISTRY

1
SS902 ADVANCED ELECTROCHEMISTRY

• Murali Rangarajan
• Department of Chemical Engineering
• Amrita Vishwa Vidyapeetham
• Ettimadai

2
ELECTRODICS
3
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 Faradays
  laws
• Faradays 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

4
Faradays 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
• They are related to each other
• Reaction rate is given by
• Here, j is current density, z is the number of
  electrons transferred and F is Faradays 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.

5
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

6
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
  electrode-electrolyte interface and the
  non-faradaic processes that happen there

7
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)

The metal-solution interface as a capacitor with
a charge on the metal, qM, (a) negative and (b)
positive
Charging a capacitor with a battery
8
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)

9
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

10
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

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
11
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 double-layer properties are
measured
Resistances in the IPE-IRE cell
12
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
  three-electrode cells

13
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

14
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
15
Potential Step Experiments
The current response for a potential step is

• There is an exponentially decaying current
  having a time constant ? RsCd.
• Peak Current E/Rs.

16
Current Step Experiments
The voltage response for a current step is

• Potential increases linearly with time
• The initial jump in the potential is iRs.
• Slope is i/Cd.

17
Potential Sweep Experiments
The current response for a linear voltage ramp E
?t is

• The time constant for current is ? RsCd.
• The limiting current (maximum current) is ?Cd.

18
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

19
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
• 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

20
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

21
What Affects Polarization?

• Consider the overall electrochemical reaction
• 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

22
Steps in Electrochemical Rxn

• The following steps are involved in an
  electrochemical rxn
• Mass transfer (e.g., of ? 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)
  .

23
Steps in Electrochemical Rxn
24
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

25
Electrode Kinetics

• Consider the reversible charge transfer redox
  reaction taking place at an electrode-electrolyte
  interface
• 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
• Here CO and CR are bulk concentrations, z is
  the number of electrons transferred, E0 is the
  formal potential

26
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
  charge-transfer kinetics governed by Tafel
  Equation

27
Tafel Equation
28
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
• Here i is current, A is area of the electrode, F
  is Faradays 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 is a reference potential

29
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

30
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
• CO is the concentration of species O at
  equilibrium
• The exchange current density values for two
  electrochemical reactions are 1 ? 109 and 1 ?
  103 A/cm2. How do they reflect on Tafel plot,
  all other parameters being constant?
• No effect on b only on a
• One with larger i0 needs lesser overpotential to
  achieve same current or rate of the reaction

31
Exchange Current
32
Butler-Volmer Equation

• In terms of exchange current and overpotential,
  Butler-Volmer equation is represented as
• 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

33
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

34
Butler-Volmer Equation
Note Butler-Volmer equation is not valid under
mass-transfer-limited 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.
35
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

36
Transfer Coefficient

• The second parameter in the Butler-Volmer
  equation is transfer coefficient ?
• Transfer coefficient determines the symmetry of
  the current-overpotential 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 ? gt 0.5, the system is likely to behave a
  better cathode (since more cathodic currents are
  achieved for smaller overpotentials)
• If ? lt 0.5, the system is likely to behave a
  better anode (since more anodic currents are
  achieved for smaller overpotentials)

37
Transfer Coefficient