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SS902 ADVANCED

ELECTROCHEMISTRYMurali RangarajanDepartment of Chemical

EngineeringAmrita 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

Qn

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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

• 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 = 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.

Resistance

ForceDrivingRate

zF

j

dt

dnr

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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 electrode-electrolyte 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)

Charging a capacitor with a battery

V

qC

The metal-solutioninterface 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 MdiS

The thickness of the diffuse layer depends on the total ionic concentration in the solution; for concentrations greater than 102 M, the thickness is less than ~100 A

Potential profileacross 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

Resistances in the IPE-IRE cell

This cell does not undergo any Faradaic processes, so only double-layer properties are

measured

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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 three-electrode 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:

dsCRt

s

eR

Eti

)(

• 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:

ds C

tRitE )(

• 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:

dsCR

t

d eCti 1)(

• 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 theforward (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

• 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

eqEE

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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• 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

RneO

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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

• 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

RzeO

R

O

C

C

zF

RTEE

*

*ln0

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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 charge-transfer kinetics : governed by Tafel Equationiba ln

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TAFEL EQUATION

FRT

orF

RTb

1

3.23.2 00 ln

3.2

1ln

3.2i

RT

Fori

RT

Fa

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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

• 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

'0'0 10 ,0,0 EEf

REEf

O etCetCkAF

i

ReO

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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 109 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

• 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

'0*0

0 EEf

OeqeCk

AF

i

iba ln

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EXCHANGE CURRENT

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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

ff eeii 10

f

R

Rf

O

O eC

tCe

C

tCii 10 *

,0

*

,0

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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 )0(*

0 OOl CCmnF

i

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BUTLER-VOLMER EQUATION

= 0.5, T = 298 K, il,c = il,a = il, and i0/il = 0.2. Dashed lines show the component currents ic and ia.

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

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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 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)

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TRANSFER COEFFICIENT