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Rate of Reaction

• Since the current, i, which represents the number of coulombs of charge flowing per second, is stoichiometrically related to the number of mole of (say) Cd2+ reacting per second, it is a measure of the rate of the electrochemical reaction

v (mol s-1 cm-2) = i/nFA = j/nFwhere n is the number of electrons transferred, F is Faraday’s constant, A is the area of the electrode, and j = i/A is the current density (A m-2).

• Kinetics, rather than thermodynamics rule here!

Polarisation• Theoretically, an applied potential, Eappl, slightly in

excess of the cell emf would cause the reverse of the spontaneous cell reaction to occur.

• In practice, the applied potential may need to exceed the cell emf by anything up to a couple of tenths of a volt before this is achieved!

• The departure of the electrode potential from the equilibrium value on passage of a current is called polarisation.

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Ideal Polarised Electrodes• An ideal polarised electrode shows a very large change

in potential upon the passage of a small current, and is characterised by a horizontal i-E profile.

• An inert electrode (eg., Hg, Pt, Au) in a solution containing only electro-inactive species approaches this ideal.

• Ideal polarized (polarizable) electrode: An electrode is called "ideal polarizable" if no electrode reactions can occur within a fairly wide electrode potential range. Consequently, the electrode behaves like a capacitor and only capacitive current ( no faradaic current) is flowing upon a change of potential. Many electrodes can behave as an ideal polarized electrode but only within an electrode potential range called the "double-layer range." Also called "completely-polarizable electrode" and "totally-polarized electrode." Contrast with ideal non-polarizable electrode.

Ideal polarized (polarizable) electrode

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Ideal Nonpolarisable Electrode• The potential of an ideal nonpolarisable electrode does

not change on passage of current. It is an electrode of fixed potential.

• Nonpolarisable electrodes have a vertical i-E profile.• Reference electrodes (silver-silver chloride and SCE)

approach non-polarisability at low current densities.

Reference electrodesReference electrode is an electrode which has a stable and well-known electrode potential

The Standard Hydrogen Electrode (SHE) forms the basis of the thermodynamic scale of oxidation-reduction potentials

Based on2H+

(aq) + 2e- → H2(g)

Often impractical to use

Large area required : platinised platinum

Cumbersome, can be hazardous

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Reference electrodes

Ag/AgCl (3M NaCl) is one of the most commonly used

Based on

AgCl(s) + e- = Ag(s) + Cl-(aq)

Ideal non-polarizable electrode

E = 0.220 V vs SHEUnit activity at standard conditions

For Ag/AgCl (3M KCl)E = 0.196 V

Overpotential

• The extent of polarisation is measured by the overpotential,

= |E(i) - E(0)|,

the (absolute) difference between the cell potential when there is no current flow, E(0), and when there is current flow, i -E(i).

• The overpotential increases as the current flowing through the system increases.

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Overpotential

• Overpotential is always deleterious to performance - it decreases the potential available during discharge:

Edischarge = E(0) - and increases the potential required for charging:

Echarge = (Eappl) = E(0) +

Overpotential• An electrode reaction O + ne R can be thought of

as composing a series of steps:– mass transfer of O to and R away from the electrode– electron transfer at the electrode– chemical reactions before and after the electron transfer.– surface reactions - adsorption, desorption,

electrodeposition.

• Overpotentials can be associated with each of these steps. Overpotential serves as an activation energy required to drive the processes at the rate reflected by the current.

• Overpotential means must apply greater potential before redox chemistry occurs

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iR Drop

• With the passage of a current, i, through a cell of resistance R, there is a potential drop, iR (Ohm’s Law), that has the same effect as an overpotential - it decreases the potential available during discharge:

Edischarge = E(0) - - iR

and increases the potential required for charging:

Echarge = (Eappl) = E(0) + + iR

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The Capacitance Current• The charging or capacitance current, ic , is due to

the presence of the electrical double layer and it is always present. This current, of course, is not related to any movement of ions.

• Ic = Cdl x V

• Where:

• Cdl = the capacitance of the electrical double layer

• V = voltage scan rate

• The capacitance current makes its presence felt when measuring charge transfer (Faradaic) processes at concentrations of 10-5 M.

Butler-Volmer Equation

j = jc - ja = j0[e(1-)nF/RT - e-nF/RT]where– jc and ja are the cathodic and anodic current densities; – j0 is the exchange current density at equilibrium, where the

rates of the forward (cathodic reduction) and reverse (anodic oxidation) reactions are equal (but not zero);

– and is the transfer coefficient (usually ca. 0.5)– The charge transfer coefficient signifies the fraction of the interfacial

potential at an electrode-electrolyte interface that helps in lowering the free energy barrier for the electrochemical reaction. The electroactive ion present in the interfacial region experiences the interfacial potential and electrostatic work in done on the ion by a part of the interfacial electric field. It is charge transfer coefficient that signifies this part that is

utilized in activating the ion to the top of the free energy barrier.

• Remember is negative for reduction.

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a + b = 1

Small

• For x<<1, ex = 1 + x, and the Butler-Volmer equation becomes

j = j0(nF/RT) or = RTj/nFj0• There is a linear relationship between j and at

small overpotentials (< 10 mV).

• This linear region is called "polarization resistance" due to its formal similarity to Ohm’s law

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Problem - Small

• The exchange current density of a Pt|H2(g)|H+

electrode at 298 K is 0.79 mA cm-2. What current flows through a standard electrode of area 5.0 cm2 when the overpotential is 5.0 mV?

• j = j0(nF/RT)

= (0.79)(1)(96485)(0.005)/(8.314)(298)

= 0.15 mA cm-2

• i = 0.15 mA cm-2 x 5.0 cm2 = 0.75 mA.

Large Oxidation• For large either negative or positive, one of

the exponential terms in the Butler -Volmer equation becomes negligible.

• At large positive potentials (corresponding to oxidation), the first term predominates and

j = j0e(1-nF/RT

or lnj = lnj0 + (1- )nF/RT

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Large - Reduction

• At large negative potentials (for reduction),

j = -j0e-nF/RT

or ln(-j) = lnj0 - nF/RT

• Remember is negative for reduction

• Same form as the Tafel equation

= a + b logi

Large • The Tafel form holds when ja/jc < 0.01 (or vice-versa) –

i.e., for ||>118/n mV.

• If the electrode kinetics are fast (large j0), the current will be limited by mass transfer by the time such a large overpotential is applied, and the Tafel relationship will not be observed.

• When electrode kinetics are slow (small j0) and activation potentials are required, the Tafel equation holds.

• Tafel behaviour is thus an indicator of totally irreversible kinetics.

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Problem - Oxidation

• A solution of 1 M KOH is electrolysed at 250C with a Pt electrode to produce O2 at the anode. At an overpotential of 0.40 V, the current density is 1.0 x 10-3 A cm-2. What does j become when = 0.6 V? Assume = 0.5 and n = 1.

Solution

• Since >>RT/F, the Tafel equation applies.• lnj0 = lnj - (1-)nF/RT

= ln(1x10-3)- (0.5)(1)(96485)(0.4)/(8.314)(298)= -6.91 - 7.79 = -14.7

j0 = 4.1 x 10-7 A cm-2. • lnj = lnj0 + (1-)nF/RT

= -14.7 + (0.5)(1)(96485)(0.6)/(8.314)(298)= -14.7 + 11.7 = -3.0

j = 0.05 A cm-2

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Problem - Reduction• The exchange current density and transfer

coefficient for the reduction of H+ to H2 on Ni are 6.3 A cm-2 and 0.58. What is the current density at an overpotential of 200 mV?

• ln(-j) = lnj0 - nF/RT

= ln(6.3) - (0.58)(1)(96485)(-0.2)/(8.314)(298)

= 1.84 + 4.52

= 6.36

• (-j) = 578 A cm-2 or j = - 578 A cm-2

Tafel Equation

• The overpotential, , increases as the current flowing through the system increases.

• Tafel (1905) found that the overpotential is related to the logarithm of the current:

= a + b logi

where a and b are empirical constants.

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Tafel Plots

• lnj = lnj0 + (1- )nF/RT from Butler Volmer

• ln(-j) = lnj0 - nF/RT from Butler Volmer

• A plot of lnj versus has an anodic branch with slope (1-)nF/RT and a cathodic branch with slope - nF/RT. Both linear segments extrapolate to an intercept of lnj0.

• The transfer coefficient, , and the exchange current density, j0, can thus be obtained.

• Tafel plot: the plot of logarithm of the current density against the over potential.

• Example: The following data are the cathodic current through a platinum electrode of area 2.0 cm2 in contact with an Fe 3+, Fe 2+ aqueous solution at 298K. Calculate the exchange current density and the transfer coefficient for the process. Slope is and intercept is a (=ln i0).

• In general exchange currents are large when the redox process involves no bond breaking or if only weak bonds are broken.

• Exchange currents are generally small when more than one electron needs to be transferred, or multiple or strong bonds are broken.

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Migration or Transport• Is the fraction of current carried by the ions.• For example in a solution of copper sulphate the

transport number of Cu2+ is 0.4 and that of SO42- = 0.6.

• t+ + t- = 0.4 + 0.6 = 1• Since the migration current depends on the ionic

strength of the solution it is usually eliminated by addition of excess of an inert supporting electrolyte (100 – 1000 fold excess in concentration)

• The current is carried by the inert supporting electrolyte (e.g. NaCl , KNO3 etc) – because the ions produced do not undergo any electrochemical reaction the transport current is effectively removed.

• In excess inert supporting electrolyte, the current measured due to the electro-active species of interest is due only to diffusion which can be related to mass transfer.

Half-wave Potential, E1/2

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Half-wave Potential, E1/2

• A plot of E versus ln{(iL - i)/i} – is a straight line of slope RT/nF, and an intercept of E1/2 on the

vertical axis.

• A plot of E versus log10{(iL - i)/i} – is a straight line of slope 2.303RT/nF = 59.1/n mV at 250C, and an

intercept of E1/2 on the vertical axis

• When DO = DR, E1/2 = E0.

Irreversible Processes

• Voltammetric waves for irreversible processes are more drawn out than reversible ones and their half-wave potentials, E1/2, are more extreme than E0.

• A quick test for reversibility is the Tomes criteria:

|E3/4 - E1/4| = 56.4/n mV at 250C,

where the potentials E3/4 and E1/4 are those for which i = 3iL/4 and iL/4, respectively.

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Practical details

Nearly every experiment requires the presence of a supporting electrolyte –minimises solution resistance

For CV experiments we use a 3 electrode setup

WE : working electrode : process of interest occursTypically Pt, Au, carbon, ITO, boron doped diamond

CE : counter electrode : Pt wire/coil/mesh, graphite rod

REF : Reference electrode Dependent on solvent system

A potential is applied between WE and REF Current is recorded between WE and CE.

Therefore a stable REF electrode is essential (eg Ag/AgCl, Calomel…..)

Dropping Mercury Electrode

• Clean, reproducible surface.

• Large overpotential for 2H+ + e H2(g) (Eo = 0 V) means Hg electrode can operate at more negative potentials than other electrodes. Good for studying reduction reactions: Mn+ + ne = M(Hg).

• Oxidation of Hg (~0.25 V vs SCE) means Hg electrodes not suitable for studying oxidation.

• Other ‘working’ electrodes - C, Pt, Au

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The Voltammogram

• At E < -0.6 V, only small residual currents flow.

• At E ~ - 0.6 V, reduction of Cd2+ occurs: Cd2+ + 2e Cd(Hg) and Faradaic current flows. Cd dissolves in Hg to form an amalgam.

• The current plateaus as the rate of reaction (and hence the current) is limited by the rate at which Cd2+ diffuses from the bulk solution to the surface of the electrode to replace those that have been reduced.

• At E > -1.2 V, reduction of H+ occurs.

Oscillations are due to growth and fall of Hg drops. As drop grows, area increases, more Cd2+ ions reach surface, and current increases.Current quickly decreases as drop falls off

Typical values

E1/2 (V) Ion

-0.38 Pb2+

-0.46 Tl+

-0.58 Cd2+

-0.99 Zn2+

-2.12 Na+

-2.14 K+

Original “polarographic spectrum” developed 1920-30 by Heyrovsky –

Note shift wrt table due to different RE, and E convention

reversed

Note problem detecting Na, K.

Modern instrumentation and further development of technique allows analysis with excellent limit of detection

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Edc = Einitial + t

Initial potential

Switching potential

Switching potentialA = B + e-

Sweep rate

What does this actually represent?

Take the oxidation of species R to O

Point A: Only R is present in solution : still below the redox potential of solution species

Increase the electrode potential towards the redox potential : R is converted to O.

As R is converted to O a concentration gradient is setup at the electrode

Point B: R is instantaneously converted to O

After point B the current is dependent on the rate of mass transfer to the electrode surface

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-1.2 -0.9 -0.6 -0.3 0.0 0.3 0.6 0.9

-60

-40

-20

0

20

40

I [A

]

E [V] vs Ag ref

0.0 0.1 0.2 0.3 0.4 0.5 0.60.000000

0.000005

0.000010

0.000015

0.000020

0.000025

0.000030

i p [A

]

sweep rate [V s-1]1/2

ferrocene Data1B

ip = 2.69 x 105 n3/2 A D1/2 v1/2 C

Randles Sevcik Equation

n : no of electrons D : diffusion coefficient C : concentrationA : electrode area v : sweep rate

Develop a protocol

Find a suitable solvent for your analyte

Find a suitable supporting electrolyte (SE)

Run a background - SE + whatever (e.g., buffer, ligand, acid, base…..) with no analyte present

Run a simple CV with the analyte

Chosen a value of – typically 50 or 100 mVs-1

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Many mechanisms• Identify some “basic” mechanisms

E A + e = B

EE A + e = B; B + e = C;

EC A1 + e = B1; B1 = B2

EC’ A + e = B; B + P = A + Q

EC2 A + e = B; 2B = B2

CE Y = A; A + e = B

ECE A1 + e = B1; B1 = B2; B2 + e = C2;

• Use DigiSim or a simulator of choice to explore the behavior of selected basic mechanisms.

Chronoamperometry

• Stationary electrode

• Solution must be stationary and unstirred = mass transport by diffusion

• Constant potential

• Measure current vs time (t)

Theory

Assume A = B + e-

- Both A and B are soluble

- Reversible reaction (electrochemically)

- Potential (E) set so oxidation or reduction goes to completion at the electrode surface

E

t (time)0

E1

E2

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Can analyse i–t profile to elucidate mechanism

Hills and Scharifker model

• Regarded as a model system

-2 adsAu H O Au OH H e

place exchange reaction - +adsAu OH OH Au

- + 2- 2+ + -OH Au O Au H e

+ -2 2 32AuO H O Au O 2H 2e

Double layer region Oxide formation

Oxide reduction

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