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
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

4. 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
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 Faraday’s constant = 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 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
Potential Sweep
Impedance Spectroscopy
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 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).

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 C*O and C*R 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 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’ 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  10–9 and 1  10–3 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  > 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)

37. Transfer Coefficient