Electrochemistry P2

8/3/2019 Electrochemistry P2

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SS902ADVANCED

ELECTROCHEMISTRYMurali Rangarajan

Department 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 redoxreactions, where charges (ex. electrons or ions) aretransferred across the electrode-electrolyte interface

This charge transfer is governed by Faradays laws

Faradays First Law: The amount of substance undergoingan electrochemical reaction at the electrode-electrolyteinterface is directly proportional to the amount of electricity(charge) that passes through the electrode and electrolyte

Qn


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FARADAYS FIRST LAW

Every non-quantum process has a rate, a driving forceand a resistance to the process offered by the systemwhere 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 electronstransferred and Fis Faradays constant = 96487 C/mol

Problem: A 30cm 20cm aluminum sheet is anodized on both sidesin a sulfuric acid bath. (Thickness may be ignored for calculation ofarea.) at 3 A/dm2 for 1 hour at 30% efficiency. Density of aluminumis 2.7 g/cm3. Calculate the thickness of anodic film. The atomicweight 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 theelectrode-electrolyte interface but do not involvetransfer 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 tocharge transfer

Although charge transfer does not take place, externalcurrents 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 theinterface when electrochemical reactions occur

Though only Faradaic processes may be of interest, thenon-Faradaic processes can affect the electrochemical

reactions significantly For instance, additives are used in electroplating which

adsorb on electrode surface, increases resistance todeposition, resulting in smoother deposits

So we first examine the structure of the electrode-electrolyte interface and the non-faradaic processes thathappen there


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ELECTRICAL DOUBLE LAYER

Electrode-electrochemical interface may be thought ofas a capacitor when voltage is applied to it

A parallel-plate capacitor stores charges by polarizationof 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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The metal side of the double layer acquires eitherpositive or negative charge depending on whether theelectrode 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 ormolecules) that are said to be specifically adsorbed

This inner layer is called theHelmholtz 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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Solvated ions can approach the metal only till before theIHP

The locus of centers of these nearest solvated ions iscalled the outer Helmholtz plane (OHP)

The interaction of the solvated ions with the chargedmetal involves only long-range electrostatic forces, sothat their interaction is essentially independent of thechemical 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-Dregion called the diffuse layer, which extends from the

OHP into the bulk ofthe solution


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The excess charge density in the diffuse layer is d,hence the total excess charge density on the solutionside of the double layer, s, is given by MdiS

The thickness of the diffuse layer depends

on the total ionic concentration in thesolution; for concentrations greater than102 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 anideal polarized mercury drop

electrode and an SCE

Resistances in the IPE-IRE cell

This cell does not undergo anyFaradaic processes, so only double-

layer properties are measured


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ELECTROCHEMICAL CELLS

Common cells are two-electrode and three-electrodecells

Refer to Bard and Faulkner pp. 24-28 for theirdescription

Prepare short notes on both two-electrode and three-electrode cells


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ELECTROCHEMICAL EXPERIMENTS

A number of electrochemical experiments may beperformed with an electrochemical cell

There are three main properties of electrochemicalsystems 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 predefinedperturbation of one of the properties is applied on thesystem

One of the other properties is measured as a response

From these responses, both Faradaic and Non-Faradaicprocesses, their rates and resistances may be studied

Experiment PerturbedVariable

MeasuredVariable

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:

dsCR

t

s

eREti

)(

There is an exponentiallydecaying 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:

d

sCtRitE )(

Potential increases linearlywith time

The initial jump in thepotential is iRs.

Slope is i/Cd.


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POTENTIAL SWEEP EXPERIMENTS

The current response for a linearvoltage ramp E = t is:

dsCRt

d eCti 1)(

The time constant forcurrent is = RsCd. The limiting current(maximum current) is Cd.


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POTENTIAL SWEEP EXPERIMENTS

A triangular wave is a rampwhose sweep rate switchesfrom to at somepotential, E.

The steady-state currentchanges from Cdduring theforward (increasing E)scanto 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 forcefor the reactions is the departure in the voltage fromthe equilibrium voltage of the cell

This departure of voltage from the equilibrium voltageof the cell is termed as overpotential

The rate of the reaction must be proportional to thedriving force

Therefore there must be a relationship between theoverpotential and the Faradaic current

Current-potential curves, particularly those measuredunder steady-state, are termed polarization curves

eqEE


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POLARIZABLE VS. NON-POLARIZABLE

An ideal polarizable electrode is one that shows a verylarge change in voltage for the passage of aninfinitesimal current

An ideal non-polarizable electrode is one that shows a

very large change in current for an infinitesimaloverpotential


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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 from the bulk solution to the

electrode surface).

Electron transfer at the electrode surface.

Chemical reactions preceding or following the electrontransfer. 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 theoverpotential

This driving force is used up by all the steps in theelectrochemical 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 reactiontaking 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 isgiven by the Nernst equation

Here C*O and C*R are bulk concentrations, z is thenumber of electrons transferred, E0 is the formal

potential

RzeO

R

O

CC

zFRTEE

**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 therate-limiting step

At such conditions, adsorption/desorption are also notusually rate-limiting

The reaction rate is determined mainly by charge-transfer kinetics : governed by Tafel Equation

iba ln


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TAFEL EQUATION

FRTorFRTb 1 3.23.2

00 ln3.2

1ln

3.2i

RT

Fori

RT

Fa


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BUTLER-VOLMER EQUATION

The exponential relationship between current density andoverpotential, observed experimentally by Tafel, is animportant result and is true for more general cases aswell

For a one-step (only charge transfer resistance in asingle step), one-electron process, the general rateequation is

Here iis current, A is area of the electrode, F is Faradaysconstant, k0 is the standard rate constant (at eqbm), CO(0,t) &CR(0,t) are instantaneous concentrations of O & R at theelectrode surface, is the transfer coefficient, fis F/RT, E0is a reference potential

'0'0 10 ,0,0

EEf

R

EEf

O etCetCk

AF

i ReO


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STANDARD RATE CONSTANT

The standard rate constant k0: It is the measure of thekinetic facility of a redox couple. A system with a large k0willachieve equilibrium on a short time scale, but a system withsmall k0 will be sluggish

Values of k0

reported in the literature for electrochemicalreactions vary from about 10 cm/s for redox of aromatichydrocarbons such as anthracene to about 109 cm/s forreduction 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 exchangecurrent


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EXCHANGE CURRENT

Exchange current is the current transferred betweenthe 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 twoelectrochemical reactions are 1 109 and 1 103 A/cm2.

How do they reflect on Tafel plot, all other parametersbeing constant? No effect on b only on a;

One with larger i0 needs lesser overpotential to achieve samecurrent or rate of the reaction

'0*0

0 EEf

O

eqeCk

AF

i

iba ln


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EXCHANGE CURRENT


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

First term denotes cathodic contribution and the seconddenotes anodic contribution

Ratio of concentrations is a measure of effects of masstransfer they govern how much reactants are supplied to theelectrode

In the absence of mass transfer effects (CO(0) = CO* always),the current-overpotential relationship is given by

ff eeii 10

fR

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 electrontransfer is extremely fast compared to mass transfer

Therefore the current (rate of charge transfer) is entirelygoverned by the rate at which the reacting species (say, O) isbrought to the electrode surface

This rate of mass transfer is proportional to theconcentration difference of O between the bulk and theinterface, 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 currentwhen the process is mass-transfer-limited

)0(*0 OOl CCmnFi


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

Note: Butler-Volmerequation is not valid

under mass-transfer-limited conditions

Note: For small , iincreases linearly with ;

For medium , Tafelbehavior is seen; For

large , i is independentof : limiting current


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EXCHANGE CURRENT& OVERPOTENTIAL

Therefore the regime where Butler-Volmer equation is valid isthe charge-transfer-limiting regime

Here, most of the driving force is spent in overcoming theactivation energy barrier of the charge transfer process

Therefore, the overpotential in this regime is termed activationoverpotential

We have already seen that for sluggish redox kinetics, theexchange current must be small : Smalli0 : Activationoverpotential

On the other hand, when the exchange current is very large,even for very small overpotentials, the current approaches thelimiting current, i.e., since charge transfer is very fast, masstransfer 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 transfercoefficient

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 electrodewill 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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Electrochemistry P2