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David H. Waldeck

Department of ChemistryUniversity of Pittsburgh

Basic Introduction to Electrochemical Cells and Methods

Chevron Annex

Eberly Hall

Chevron Science

Center

Ashe

Website: http://www.chem.pitt.edu/

The Electrochemical CellAn electrochemical cell is a device that transduces energy between chemical and electrical forms.

An electrochemical cell has at least two electrodes and an electrolyte, as such both ion and electron transport are important to consider.

The chemical reaction2 AgI (s) + Pb (s) → 2 Ag (s) + PbI2 (s)

consists of a reduction reaction and an oxidation reaction

The Electrochemical CellThe chemical reaction

2 AgI (s) + Pb (s) → 2 Ag (s) + PbI2 (s)consists of a reduction reaction and an oxidation reaction

A reduction, which occurs at the cathode

AgI (s) + e- → Ag (s) + I- (aq) = -0.1522 V

E Ag I / Ag =  E0   Ag I / Ag  − 𝑅𝑇1𝐹 ln(𝑎𝐴𝑔𝑎𝐼−

𝑎𝐴𝑔𝐼)

standard potential

# of electrons transferred in the reaction

Faraday’s constant

Absolute temperature

Molar gas constant

activity =1

activity =1

activity

The Electrochemical CellThe chemical reaction

2 AgI (s) + Pb (s) → 2 Ag (s) + PbI2 (s)consists of a reduction reaction and an oxidation reaction

… and an oxidation which occurs at the anode

Pb (s) + 2 I- (aq) → PbI2(s) + 2e- = 0.365 V

E Pb / PbI2= E 0   Pb / Pb I2  −  𝑅𝑇2𝐹 ln( 𝑎𝑃𝑏𝐼 2

𝑎𝑃𝑏𝑎𝐼 −❑2 )

standard potential

# of electrons transferred in the reaction

activity =1

activity =1

activity

The Electrochemical Cell

2AgI (s) + Pb (s) → 2Ag (s) + PbI2 (s) = 0.213V

Hence, we find that

Ag I (aq) + e- → Ag (s) + I- (aq) = -0.152 V

Pb (s) + 2 I- (aq) → PbI2(s) + 2 e- = 0.365 V

= = 0.213V

The Electrochemical Cell 0.213 V

A galvanic cell; i.e., chemical reaction does electrical work.

Electrolytic cell; i.e., electrical work drives chemical reaction.

Small changes in the applied potential allows us to reverse the direction of the chemical reaction.

E = 0.213 V The reversible work done by the system is

-wrev = E I∙ ∙t + PΔVand it is related to the Gibbs energy at constant T and P, namely

ΔG = wrev + PΔV = - E I∙ ∙t = - E Q∙ total = - E∙n F∙

or ΔrG = ΔG/n = - E F∙

The cell’s EMF is a direct measure of the Gibbs energy for the reaction.

The Electrochemical CellThe connection between the electrochemical potential and G.

0.213 VBecause ΔrG = - E F we can measure the temperature ∙dependence of the EMF and find the molar entropy

= ,

and thus we also have the molar enthalpy, via

ΔrH = ΔrG + T ΔrS = - E F + ∙

The Electrochemical Cell

DS ~14.5 J/(mol-K)

2 H+ (aq) + 2e- → H2 (g) and measure the potentials of other half cell reactions, such as

Cu2+ (aq) + 2 e- → Cu(s) with respect to it.

For the electrochemical cell reaction H2(g) + Cu2+ (aq) → Cu (s) + 2H+ (aq)

Under standard state conditions (all activities equal to one), we find that - = 0.345 V.

If we define = 0.0 V, then = 0.345 V

We can use a standard half cell reaction such as

Reference Electrodes &Electrode Potential

NHE is commonly used to define the zero of the electrochemical potential scale.

AgCl (s) + e- → Ag (s) + Cl- (aq)

EAgCl = -

For a saturated KCl solution EAgCl = 197 mV at 298 K

More common reference electrodes are

Hg22+ + 2e- → 2 Hg

Ecalomel = +

For a saturated KCl solution ESCE = 241.2 mV at 298 K

Reference Electrodes & Electrode Potential

Relate the half cell reaction: 2 H+ (aq) + 2e- → H2 (g) w to the vacuum potential, by using a thermodynamic cycle.

= -

so that depends on intrinsic properties of the redox couple and the electrode material.

The Absolute Electrode Potential

0

0

0

Using experiment, workers have related the half-cell potential to the vacuum potential (e.g., measure work function Pt in contact with solution (values range from 4.4 to 4.8 V --- IUPAC recommends 4.44 ± 0.02 V. Thus

Define (H2/H+)= =(H2/H+) -

Comments• about 1.21 V below W(Pt) measured in vacuum• use to find =-1102.4 kJ/mol (excellent agreement with -1104.5 kJ/mol as found

from cluster ion data)• For a half-cell reaction, M+ + e- M, we find that

(M+/M) =(M+/M) -

(H2/H+) =(H2/H+) -

The Absolute Electrode Potential

No current flows and system at equilibrium. Potential provides information on

• Gibbs energy, entropy, etc.• Nernst Equation• Activities of ions, such as pH, etc.• Concentration cells• Activity coefficients and solution thermodynamics• Equilibrium constants• Titrations• Solubility products• Fuel cell and battery energetics

Potentiometry: Equilibrium Measurements

Kinetics through Electrochemical Measurements

Apply perturbation and measure response:

Voltammetry example: Apply a potential jump and measure a current response.

Issues affecting Meaningful Measurements

Current can affect Reference Electrode PotentialFor example, at high currents the Cl- concentration of Ag/AgCl reference electrode could change and affect E

EAgCl = -

iR drop: The current flow through the solution causes a voltage drop so that the applied potential between the working and reference electrode is not the true potential drop …

The 2 electrode cell:

Ohmic losses (iR drop)The resistive loss in the solution causes a change in the potential and can affect the measurement.

Issues Affecting Meaningful Measurements

Electron current, Ie, is flowing in themetal wires, while ion current, Iion, is flowing in the cell.

In total Iion=Ie

current source

A Potentiostatic Cell Can Resolve these Issues

Use a 3-electrode cellThe reference electrode measures potential and has little current flow. Most of the current goes between working and auxiliary electrode

iRs Drop becomes an iRu dropIn this way the potential drop is minimizes if the reference is placed close to working.

A Potentiostatic Cell Can Resolve these Issues

Potential and Current Flow: non-Faradaic

Ideal Polarized Electrode -- An electrode in which no charge transfer occurs as the potential is changed.

Some electrodes approximate over limited ranges:• Hg electrode over 2V range in KCl solution

• Hg oxidation at +0.25 V versus NHE• K+ reduction at -2.1 V versus NHE• Note that H2O reduction is kinetically slow and does not

interfere• Gold• Pt• Gold SAMs

hexanethiolon gold

Kolb and coworkers, Langmuir (2001)

Potential and Current Flow: non-Faradaic

Ideal Polarized Electrode Applying a potential causes charge rearrangement: excess charge on electrode surface and ion charge near electrode (electrode double layer)

Negative potential Potential of Zero Charge Positive potential

----

+

+++

--

--

--

++

+--

+

++++

+

+++

--

---

-+

+

-++

-

+

+++

--

--

--

+

+

C = Q/E

and Q = σM x area

Potential and Current Flow: non-Faradaic

Ideal Polarized Electrode Applying a potential causes charge rearrangement: excess charge on electrode surface and ion charge near electrode (electrode double layer)

Q = C E

i = dQ/dti = C (dE/dt)

No direct charge transfer across capacitor, but current flows whenever the potential changes.

Q = σM * area

Potential and Current Flow: non-Faradaic

Electrode Double Layer Typically it is divided into an inner layer (also called compact, Helmholtz, Stern) and an outer layer (also called diffuse layer, ….)

Define IHP and OHP as centers of charge. Diffuse layer is > OHP and Stern layer is < OHP.

σS = σi + σd = -σM

IHP

+

-

-

-

-

V

–

–

V VV

V

V

V

V

VV

VV

V

V

V

VV V

VV

V

+

+

+

VV

V

VV

V

V

VV V

VV

V

V

V

VV

V

V

VV

OHP

V

V

V

V

+

V

VVV

σi σd

Double Layer Potential Profile

h𝑡𝑎𝑛 (𝑧𝑒 𝜙/ 4𝑘𝑇 )h𝑡𝑎𝑛 (𝑧𝑒𝜙2/4 𝑘𝑇 )

=𝑒𝑥𝑝 (−𝜅 (𝑥−𝑥2 ))

Solve the Poisson-Boltzmann Eqn:

and solve for the potential via

so that the capacitance is

Model the electrochemical cell by a combination of circuit elements.

Potential and Current Flow: non-Faradaic

Imagine a potential step experimentWe begin with the system at equilibrium and E=0, then we ‘rapidly’ jump the potential to E.

i = E/Rs exp(-t/(RsC∙ d))

and

q = Ecd [1- exp(-t/RsCd))]

Potential and Current Flow: non-Faradaic

Q = Cd x EC and E = ER + EC

so thatE = i Rs + Q/Cd

or

which gives the result

Imagine a potential step experimentWe begin with the system at equilibrium and E=0, then we ‘rapidly’ jump the potential to E.

i = E/Rs * exp(-t/(RsCd))

and

q = Ecd [1- exp(-t/RsCd))]

Potential and Current Flow: non-Faradaic

Imagine a potential sweep experimentLet us vary the potential in a triangle waveform and measure the current.

Potential and Current Flow: non-Faradaic

Potential and Current Flow: FaradaicOrigin of Faradaic CurrentChanges in the charge state of atoms and molecules

Ideal Polarizable Electrode versus Ideal Nonpolarizable electrode

Potential and Current Flow: Faradaic

Factors affecting Faradaic Current (rxn rate)

Potential and Current Flow: Faradaic

Potential and Current Flow: FaradaicNernst Diffusion LayerWhen the electrode reaction is fast compared to the diffusion of species to the surface, a depletion layer is formed.

The two cases (1 and 2) correspond to two potentials

Steady-State Voltammogram for Nernstian Reaction

E = E1/2 +(RT/nF) ln((il-i)/i) and the limiting current is il = n F A (DO/d0) C*O

At the half-wave potential (il = il/2), thenE = E1/2 =E0’ - (RT/nF) ln(mO / mR )

Potential and Current Flow: Faradaic

The case of only the oxidant being present initially.For the case of both reductant and oxidant present initially in the solution, one finds that

Cyclic Voltammograms and Kinetics

Potential and Current Flow: Faradaic

We will discuss this topic next time.

A Case Study with Steady-State Photocurrent & a Slow RxnGoal: Determine the distance dependence of the electron tunneling.

Method: A) Prepare monolayer films of alkanethiols.

B) Measure the photocurrent for differentalkane chain lengths.

InP

Electrochemical Characterization

- Mott-Schottky analysis gives flatband of -0.7 V (vs. SCE)

- Photocurrent onset is -0.65 V (vs. SCE)

-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4

Volts (vs SCE)

0

1

2

3

4

5

j = kHT CD ps

C8

C12

C16 InP SAM redox couple

Pt

A

Concentration Dependence of Photocurrent

0.0 0.1 0.2 0.3 0.4 0.5

Concentration (M)

0

1

2

3

4

5

6

7

8

phot

ocur

rent

(mA)

0.003 0.008 0.0130

1

2

3

4

5

6

Bare ElectrodeFe(CN)6

3-/Fe(CN)64- in 0.5 M K2SO4

Intensity Dependence of Photocurrent

Bias Voltage 0.0 V vs SCE0.5 M Fe(CN)6

3-/Fe(CN)64-

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Intensity (mW)

0

10

20

30

40

photocurrent

(×50)

(×250)C16

C10

bare

bare

C10 (x50)

C16 (x250)phot

ocur

rent

/ nA

Chain Length Dependence of Current Density

8 10 12 14 16

0

1

2

3

4

5

ln (j

/A)

Number of Methylene

= - 0.54

InP/SAM/Fe(CN)63-/4- Contact

InP SAM redox couple

Pt

A

Thickness and Tilt Angle of Chains on InP

cosd

IIlnc

: escape depth of photoelectron through alkanethiol, 26.7 Å for In 3d5/2 peak.

d (Å) Tilt ()C8 6.4 0.7 62 4

C12 11.1 0.6 53 3C16 14.9 1.2 51 4

Avg = 55 ± 6

Measured film thicknesses for InP/SAMs

d

InP

e--Photoelectron

-3

-2.5

-2

-1.5

-1

-0.5

00.50 1.00 1.50 2.00 2.50

1/cos()

ln(I/

Io)

Tilt Angle and Correlate

System (per CH2) ln(It/I0) Tilt angle /

Hg 1.14 ± 0.09 [1] -13.68 1.08 16 2

Au(111) 1.02 ± 0.20 [2] -12.24 2.40 32 2

Au(111) 0.90 ± 0.30 [3] -11.70 3.60 27 6

InP(100) 0.54 ± 0.07 -5.88 0.84 55 6

1. Slowinski, K.; Chamberlain, R. V.; Miller, C. J.; Majda, M, JACS 1997, 119, 11910. 2. Xu, J.; Li, H-L.; Zhang, Y.; JPC 1993, 97, 11497. 3. Miller, C.; Cuendet, P.; Grätzel, M.; J.PC 1991, 95, 877.  

Hg studies are particularly important because tilt angle can be systematically changed.

Slowinski used model with single interchain tunneling ‘hop’ allowed and found

tb = 0.91 per A ; ts = 1.31 per A

Yamamoto etal. JPC B 2002, 106, 7469

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

0 20 40 60 80

Tilt angle / °

In (I

t/I0) βtb

βts

Hg /CnCH3

Au/SCnOH Au/SCnCH3

InP/SCnCH3

1 interchain hop

2 interchain hops

0 interchain hop

Tunneling Current versus Tilt Angle

Summary

Electrochemical Cells – Definitions etc.

Equilibrium properties of Echem cells – potentiometry etc.

Some features of kinetic and transient measurements (more to come ….)

CitationsMany of the figures used in the talk are taken from two textbooks.

Electrochemical Methods by Bard and FaulknerPrinciples of Physical Chemistry by Kuhn, Waldeck, and Foersterling

Homework Assignment1. Find an example of a potentiometric measurement and explain how the electrochemical cell operates.

2. Show that the charging current that results froma sweep in the potential of an ideally polarizable electrode at a rate of v, is given by

3. Consider the data given in the table for the alkali ions. Write out a thermodynamic cycle and extract the Gibbs solvation energy for each of the ions. Examine the relationship between the solvation energy and the ionic radius, and compare it to the predictions of the Born model of solvation. Note that the sublimation energies are given in kJ/mol.