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ElectrochemistryLecture 2

Voltammetry

CHE 729

Dr. Wujian Miao

Reference Books

Electrochemical Cell Working electrode:

place where redox occurs, surface area few mm2 to limit current flow.

Reference electrode:constant potential reference

Counter (Auxiliary) electrode: inert material, plays no part in redox but completes circuit

•Supporting electrolyte:alkali metal salt does not react with electrodes but has conductivity

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Electrochemical Instrumentation

Voltammetry Electrochemistry techniques based on

current (i) measurement as function of voltage (Eappl)

Voltammetry — Usually when the working electrode is solid, e.g., Pt, Au, GC.

Polarograph — A special term used for the voltammetry carried out with a (liquid) MURCURY electrode.

Voltammogram — The plot of the electrode current as a function of potential.

Linear sweep voltammetryThe potential is varied linearly with time with

sweep rates v ranging from 10 mV/s to about1000 V/s with conventional electrodes and up to106 V/s with ultramicroelectrodes (UMEs).

It is customary to record the current as afunction of potential, which is equivalent torecording current versus time.

Linear sweep voltammetry, linear scanvoltammetry (LSV), or linear potential sweepchronoamperometry.

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X = 0

(Ox + ne Red) (reversible)

x = ∞ (“bulk”)

x = 0

Linear Sweep/Scan VoltammetryPeak-shaped i~E profile

For A + e = A- reversible reaction, E0(A/A-) = E0

(1) E >> E0, i ~ 0

(2) E = E0 + dE, i >> 0, increases

(3) E = E0, i >> 0, [A] = [A-] =[A*]/2

(4) E = E0 - 28.5 mV, i maximum, [A]x =0 ~ 0.25[A*]

(5) E << E0, i >> 0, decreases, as the depletion effect

DigiSim demonstration

0

00

A A

[A]ln

[A ]

where , [A] = [A ]x

e

RTE E

nF

E E

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Cyclic Voltammetry （CV）

DigiSim demonstration

Potential: E(t) = Ei - t (V), 0 < t

E(t) = Ei - 2 + t (V), t >

CV is not an ideal method for quantitative evaluation ofsystem properties. It is powerful in qualitative and semi-quantitative reaction behavior.

Cyclic Voltammetry- i vs time

DigiSim demonstration

NERNSTIAN (REVERSIBLE) SYSTEMS

Semi-infinite linear diffusion, only O exist initially

LSV: potential changes linearly at a sweep rate of v (\//s)

0'

0'

0'

(0, )( ) ln

(0, )

(0, )exp ( ) ( )

(0, )

( ) , =( / ) ; exp ( / )( )

O

R

Oi

R

ti

C tnFE t E

RT C t

C t nFE t E S t

C t RT

S t e nF RT v nF RT E E

Nernst equation

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Mass Transfer/Transport

-

rx

2

n mt

rxn

mt

m

-1

d

For a process:

/ flux ( )

: net rate of electrode reaction

: rate of mass transfer

: current; : area

unit : m

of electrod

ole cm

e

s

total c

Nernst

v v i nFA J

v

v

i A

i i i i

J

If use short times ( < 10 s) and don’t stir (quiescent),

then itotal = id + im

Nernst-Planck Equation(governing the mass transport to an electrode)

xx

x

RT

F

x

xx CCDzCDJ iii

iiii

Diffusion Migration Convection

Ji(x) = flux of species i at distance x from electrode (mole cm-2 s-1)Di = diffusion coefficient (cm2/s)Ci(x)/x = concentration gradient at distance x from electrode(x)/x = potential gradient at distance x from electrode(x) = velocity at which species i moves (cm/s)

“-”: flux direction opposites the concentration gradient change

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If We Use High Concentration of Good Electrolyte in Quiescent Solution...

Nernst-Planck Equation reduces to...

Fick’s First Law

• Flux of substance is proportional to its concentration gradient:

i.e., flux concentration gradient

0

,, o

o

x t ix t

x nFACJ D

LSV Reversible System

( ( / ) )nF RT

( ) is a pure number at any given point

and can be solved .numerica

where t

lly

After the Laplace transformation and a series of mathematical treatments of the diffusion equations:

𝜒 [“kai”]

Excel Calculation of t

0.446295

My Excelcalculation

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0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

-200-1000100200

t

)

n(E-E1/2) (mV)

Reversible system0

max{ ( )} 0.4463 when ( - ) 28.5t n E E mV

Peak current and potential

31/2 3/2 * 1/2 1/2

p

5 3/2 * 1/2 1/2

0.4463( )

= (2.69 10 ) at 25 C.

O O

O O

Fi n AC D

RT

n AC D

p 1/2 28.5 / (mV) 25E E n at C

Peak current ip

Peak potential Ep

0' 1/ 21/ 2 ( / ) ln( / )R OE E RT nF D D

Ep is independent of scan rate.

Units: Amperes, cm^2, cm^2/s, mol/cm^3, V/s

1/2pi v

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E0’

Cur

rent

i (A

)

E (mV, vs. ref electrode)

p 1/2

p/2 1/2 1/2

0' 1/2 0'R1/2

o

1.109 / 28.5/ mV @ 25 C

1.109 / 28.5/ mV @ 25 C

ln( )

E E RT nF n

E E RT nF E n

DRTE E E

nF D

p p/2

1/2p p

| | 2.22 / 57.0/ mV@ 25 C

( ) ( )

E E RT nF n

E f v i f v

o Rne

Cyclic Voltammetry

Cyclic Voltammograms for a Reversible Reaction

pc pa

pa pc

o

0'pa pc

3/2 1/2 * 1/2p

o 5

/ 1.0

( ) 2(1.109 )

57 mV/n at 25 C

(independent of the scan rate)

= ( ) / 2

= constant

(at 25 C, constant = 2.69 10 )

o o

i i

RTE E

nF

E E E

i n AD c v

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Diffusion Controlled Reversible Process

p

For electrode adsorption process

i v

Peak separation potentials, although close to 57 mV, are slightly a function of switching potentials.

Reversibility of Electrochemical System Can be Changed via the Change of Scan Rate

At small v (or long times),systems may yield reversiblewaves, while at large v (orshort times), irreversiblebehavior is observed.

/ lamda

f = nF/RT

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0

0

Electron Transfer Rate

, ,p p

k

k E i

Totally Irreversible System

(NO Reversal Peak)

CV Applications in Diagnosing Chemical Reaction Mechanisms

EC Reaction (Electron Transfer followed by A Chemical Reaction

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EC Reaction: Scan Rate Dependent

(a) At Fast Scan Rate (b) At Slow scan Rate

ECE Process

(a) S is more difficult to reduce than O (i.e., E0’S < E0’O)

(b) S is easier to reduce than O (i.e., E0’S > E0’O)

OR ST

TS

OR

(ST)

TS

(2nd ST)

Multi-step Systems

O + n1e R1 (E10)

R1 + n2e R2 (E20)

E0 = E20 - E1

0

E0: (a) -180 mV; (b) -90 mV; (c) 0 mV; (d) 180 mV.

0 (2 / ) ln 2 36E RT F mV

The CV looks the same as one electron-transfer process.

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Ohmic Potential, IR Drop

• Potential change (drop) due to electrochemical solution resistance

• Eir = IRI—current of the electrochemical cell,R—resistance of the electrolyte solution.

• Ecell = Ecathode-Eanode- IR

• Question: In electrochemical study, an inert electrolyte is always added to the analyte solution. Why?

A A + e = B

R = 0R = 10 Ohm

Ep = 58 mVEp = 100 mV

cA =1 mM50 mV/sArea = 1 cm2

Faradaic and Nonfaradaic Processes

Faradaic• Charges or electrons are transferred

across the electrode|electrolyte interface as a result of electrochemical reactions

• Governed by Faraday’s law

A

A

A

where = # of e transfered

= Faraday constant (96, 485 C/mol)

= # of moles of electroactive species

Q nFN n

F

N

dNdQi nF

dt dt

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Nonfaradaic Process• Charges associated with movement of

electrolyte ions, reorientation of solvent dipoles, adsorption/desorption of species, etc. at the electrode|electrolyteinterface.

• Changes with changing potential and solution composition

• Charges do not cross the interface but external currents can still flow

• Regarded as “background current”

Nonfaradaic Processes and the nature of electrode|electrolyte interface; the Double layer

• Electrons transferred at electrode surface by redox reactions occur at liquid/solid interface (heterogeneous)

• (1) A compact inner layer (d0 d1)• (2) a diffuse layer (d1 –d2)

com

pact

inne

r la

yer

diff

use

laye

r

Charging current ic

10-40 F/cm2

Potential dependent

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Equivalent Circuits of Electrochemical Cell

CSCE >> Cd

RC Circuit-Voltage Ramp (Potential Sweep)

S d

s d

d s d

( / ) /

if 0 at 0

[1 exp( / )]

R CE vt E E

vt R dq dt q C

q t

i vC t R C

ic = f(v)

General Equivalent Circuit

c f

f

c

Overall current

Signal-to-noise ratio (SNR) =

SNR , limit of detection (LOD)

I i i

ii

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Cyclic Voltammetry

v = dE/t

c d s d

c c

[1 exp( / )]

( ; , )

v

v

i C t R C

i t i

f

f

pc 5 3/2 1/2 1/2Ox

1/2

Ox

pc

2.69 10

( )

i n AD C

i

v

v

f1/2

c

-5 -6

1SNR

small at fast and low

LOD of CV ~ 10 -10 M

ii v

v C

Itotal

How do we eliminate the charging current so that

electrochemical techniques could be used in quantifying low

concentrations of redox species?

(Pulse Voltammetry)

RC Circuit-Potential Step

RsCd time constantin s

I = 5% (E/Rs) at t = 3

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A is reduced to A- at potential E2

(A)

(A-)

This kind of experiment is called chronoamperometry, because current

is recorded as a function of time.

0 0

* * *

* 1/ 2 *

1/ 2 1/ 2

Cottrell Equation

( ) ( ) , δδ

0 0 ( ) ( )

δ

o oo x o x

o o o oo o

o o o o

c ciD D Dt

nFA x

c c D cD

D c nFAD ci nFA

tD

DDt

t

Curves 1, 2, 3, Co(0, t) not 0-not diffusion controlled(electrode reaction-controlled)

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Sampled Current Voltammetry(Normal Pulse Voltammetry)

Eliminating ic: Potential Step/Pulse Voltammetry

(LOD~10-8 M)

if

Po

ten

tial E

Time

E

t

sample point

ic

c s d cs

*1/2Ox Ox

f f

c

When applying :

exp( / )

( )

at , 0, so SNR

t

E

Ei t R C i e

R

nFAD Ci t i t

t

i

Staircase Voltammetry

Normal Pulse VoltammetryDifferential Pulse Voltammetry

Additive Cyclic Square Wave Voltammetry (ACSWV)

faci

fcci

fac c

fcc c

rac c

rcc c

: forward

: forward

: reverse

: reverse

i anodic i

i cathodic i

i anodic i

i cathodic i

Fci

Rci

fa fcc c

r

Fc

Rc

F Rc

a rcc c

c

c c

additive

0

i i

i i

To

i

i

i i

tal I

I

j j'

2H+1

4H+1

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Pulse Voltammetric Techniques

• All pulse techniques are based on the difference in the rate of the decay of the charging and the faradaic currents following a potential step (or "pulse").

• The rate of decay: ich much faster than if.-- ich is negligible at a time of 5RsCd (time constant, ~µs to ms) after the potential step.

• The sampled i consists solely of the faradaic current.

*

ch fexp( ); ( .)o

s s d

nFA DCE ti i Cottrell Eq

R R C t

Important parameters

Pulse amplitude: the height of the potential pulse. This may or may not be constant depending upon the technique.

Pulse width: the duration of the potential pulse.

Sample period: the time at the end of the pulse during which the current is measured.

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Staircase Polarography/Voltammetry

Digital potentiostats use a staircase wave form as an approximation to a linear wave form. This approximation is only valid when E is small (< =0.26 mV) and analog current integration filtering is used.

Normal Pulse Polarography/Voltammetry

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Differential Pulse Voltammetry (DPV)

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Square Wave Voltammetry (SWV)

Peak Current:

=1 for large pulse amplitudes

Charging current (smaller more than an order of magnitude than that of NPV) with LOD 10 nM.

C60 reductions

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Square Wave Voltammetry (SWV)

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SWV Response

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Comparison between SWV and CV

• Low electrochemical background.

• Much low detection limit.

• Much less distortion of voltammogram-easy to fit theoretical data.

• Better for evaluating quantitative parameters.

• More intuitively in chemical terms for most practitioners.

• Reversal of CV covers a large span of E—more readily highlights linkages b/w processes occurring at widely separated potentials.

• Wider range of time scales.

SWV Strengths CV Strengths

Applications of Voltammetry

• Dopamine detection in mice brains

• ……

• Au or Si NPs redox behavior

• ……

Anodic Striping Voltammetry (ASV)

Principle of anodic stripping. (a) Preelectrolysis at Ed; stirred solution, (b) Rest period; stirrer off. (c) Anodic scan.

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ASV-Electrode Dependence

HMDE

Pyrolytic graphite

Unpolished GC

Polished GC

Sensitivity and Limit Detection

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