Lecture #17 of 17 - UCI Department of Chemistry › ~ardo › echem › UCI-CHEM248... · Lecture...

5/30/2019

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1230

Lecture #17 of 17

12311231

Q: What’s in this set of lectures?

A: B&F Chapters 9, 10, and 6 main concepts:

● Sections 9.1 – 9.4: Rotating (Ring-)Disk

Electrochemistry

● Sections 10.1 – 10.4: Electrochemical Impedance

Spectroscopy

● Sections 6.1 – 6.6, 11.7, 14.3: Linear Sweep Voltammetry

(LSV), Cyclic Voltammetry

(CV), Thin-Layer

Electrochemistry

… to really learn about your experimental systems…

… move beyond steady-state conditions!

1232

… since this goes through

(0, 0), it means that both R

and O are present…

… and recall that curvature

near (0, 0) implies activation

overpotential, and not

concentration overpotential

Sloooooooooooowwwww masssssss traaaaaannnnssssport

dooooooowwwwwwwwnnnnn, Dr. Butler and Dr. Volmer…

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1233Sloooooooooooowwwww masssssss traaaaaannnnssssport


1234

… wait a minute… all I need to do in

order to observe a CV/LSV peak is stop

stirring? … Seriously?… Why didn’t

anyone tell me this sooner?

… you already knew that, too!

Sloooooooooooowwwww masssssss traaaaaannnnssssport


stirring causes δ to become well-defined, time-invariant, and a short distance to conditions of the bulk

Bard & Faulkner, 2nd Ed., Figure 1.4.1

an “unstirred” solution will have δ ≈ 0.050 cm after ~1 sec (Bockris, Reddy,

and Gamboa-Aldeco, Modern EChem, Vol. 2A, 2002, pg. 1098)

1235… with (a little) stirring, the diffusion layer is fully formed (i.e.

time-independent) at each potential during the sweep

FLASHBACK

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stirring causes δ to become well-defined, time-invariant, and a short distance to conditions of the bulk

Bard & Faulkner, 2nd Ed., Figure 1.4.1

an “unstirred” solution will have δ ≈ 0.050 cm after ~1 sec (Bockris, Reddy,

and Gamboa-Aldeco, Modern EChem, Vol. 2A, 2002, pg. 1098)

1236… with (a little) stirring, the diffusion layer is fully formed (i.e. time-independent) at each potential during the sweep

FLASHBACK

1237

Eeq

> 200 mV

> 200 mV

FLASHBACK

C* = 1 x 10-6 M

D = 1 x 10-5 M

t = 1s

0.1s0.01s0.0001s

… without stirring, the diffusion layer grows over time and with a

big (enough) potential step (or even bigger, or a little smaller

again), the Cottrell equation results

1238

Eeq

> 200 mV

> 200 mV

FLASHBACK

hybrid catalysis and a little diffusion




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1239

FLASHBACK

mass-transfer limited

(Cottrellian)





1240

FLASHBACK


(Cottrellian)




peak occurs after E1/2


How are E1/2 and

Ep related?

1241who invented linear sweep voltammetry?

John E. B. Randles and A. Sevcik

… the Randles equivalent circuit

approximation of an electrochemical

cell… same as in EIS (but without

the Warburg diffusion portion)!

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1242

1243

Randles–Sevcik Equation (T = 298 K)

1244


What all LSV/CV’ers should know…

ip is proportional to the square root

of the scan rate when the molecules

are dissolved in solution and not

stuck to the surface…

… but when the molecules are

surface-adsorbed, ip is proportional

to the scan rate

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1245

1246… this is an analog oscilloscope… how did they capture these data?

1247

Tektronix C 59A Oscilloscope Camera

f2.8 .67MAG w/ Back Film Pack

… how did they capture these data? …

Answer: They photographed it! Click!

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1248… in the 1960s – 1980s, X–Y plotters were used to record all data

1249… and that plotter was connected to a voltammetric analyzer…

… the digital instruments of today do not actually sweep and so are “imperfect”

1250

Irving Shain

in the lab in 1956…

Rich Nicholson in 1963

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1251

… h

ere

are

th

e m

ech

anis

ms th

ey c

on

sid

ere

d…

1252

… h

ere

are

th

e m

ech

anis

ms th

ey c

on

sid

ere

d…

… and the critical time-dependent χ functions that they obtained

1253

http://upload.wikimedia.org/wikipedia/en/4/41/Cyclicvoltammetrywaveform.jpg

slope = v

units, V s-1

the “switching potential” or pos/neg limit

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1254the derivation of these equations is messy (involving the Laplace

transform and numerical approximations)… thus, we’ll omit it…

… but the key result from Nicholson and Shain is the following:

the dimensionless

“current function”

σ =𝑛𝐹

𝑅𝑇𝑣

1255

1256

NOTE: 0.4463 is the maximum value for

π1/2χ(σt)… and it’s not at E1/2…

… Why?

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1257

-28.5 mV

0.4463 is the maximum value for χ(σt),

… and it’s not at 0 V vs E1/2… Why?

χ(σt) = 0.4463

1258In this experiment, two things happen concurrently:

1) C(0, t) decreases, and 2) δ increases with t1/2

1259In this experiment, two things happen concurrently:

1) C(0, t) decreases, and 2) δ increases with t1/2

… δ is the diffusion layer thickness…

… and as an aside, don’t forget that

we’ve also learned about the

boundary layer thickness (where C* is

fixed from stirring) and the double

layer thickness (for charging the

compact/Helmholtz/Stern layer and

the diffuse layer)…

… that’s a lot of layers!

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… at least one thing about this I–E “trace” makes some sense…

… the behavior at large E – Eo’ is Cottrellian…

1260

1261… at least one thing about this I–E “trace” makes some sense…

… the behavior at large E – Eo’ is Cottrellian…

1262

Bockris, Reddy, and Gamboa-Aldeco, Modern EChem, Vol. 2A, 2002, pg. 1098

1) The reaction rate is

diffusion-controlled, and the

diffusion-layer thickness, δ, is

independent of time, and is

~0.5 mm thick after ~1 sec in

a solution that is not artificially

stirred

… but is there justification for

the pre-Cottrellian peak being

located at -28.5 mV?

Consider two limiting cases:

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1263


activation-controlled such

that there is no diffusion

layer… no diffusion limit!

… but is there justification for

the pre-Cottrellian peak being

located at -28.5 mV?

Consider two limiting cases:


diffusion-controlled, and the

diffusion-layer thickness, δ, is

independent of time, and is

~0.5 mm thick after ~1 sec in

a solution that is not artificially

stirred

12641) The reaction rate is diffusion-controlled, and the diffusion-

layer thickness, δ, is independent of time…

1265… now, according to Fick’s first law, the current will be proportional

to the concentration gradient at x = 0…

𝐽𝑖 𝑥 = −𝐷𝑖𝜕𝐶𝑖 𝑥

𝜕𝑥

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1266… now, according to Fick’s first law, the current will be proportional


the linearized version of which is…

first, consider a case where δO is independent of time… in this case,

J(0) will depend only on CO(0, t) and Jmax will correspond to CO(0, t) = 0.


𝜕𝑥

𝐽𝑖 𝑥 = −𝐷𝑖𝐶o∗ − 𝐶o 0, 𝑡

𝜕o

1267

Based on this we get a sigmoidal I–E curve (S-shaped), with a defined

limiting current, which we’ve seen many times in this course already

and is obviously not what we see for CV’s here. So the observed

peaked response must derive from the motion of δO with time,

convoluted with the potential dependence of CO(0, t)…

… now, according to Fick’s first law, the current will be proportional



𝜕𝑥

𝐽𝑖 𝑥 = −𝐷𝑖𝐶o∗ − 𝐶o 0, 𝑡

𝜕o

the linearized version of which is…

first, consider a case where δO is independent of time… in this case,

J(0) will depend only on CO(0, t) and Jmax will correspond to CO(0, t) = 0.

1268… we’ve already seen this. There is no “peak” in the current.Question: How far must one scan before obtaining il?

𝐸 = 𝐸1/2 +𝑅𝑇

𝑛𝐹ln

𝑖𝑙 − 𝑖

𝑖

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1269

i/il = 0.9…… at ≈ -55 mV

… at 0 V, you have just 50% of il…… so, to get 90% of il, you need to apply ~55 mV past Eeq…

1270… okay, so what about the other limiting case?

… This one we have not seen before…

1) The reaction rate is diffusion-controlled, and the

diffusion-layer thickness, δ, is independent of time.

2) The reaction rate is activation-controlled such

that there is no diffusion layer… no diffusion limit!

1271… let’s imagine electrochemical systems for which diffusion does not control the rate of faradaic reactions…

example: redox chemistry of an adsorbed monolayer:

2H+ + 2e– ⇌ 2Pt–H

Clavilier’s papillon(butterfly pattern)

UPDhydrogen

UPDoxygen

HER

OER

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example: redox + chemistry at a conjugated M–molecule:graphite=molecule–Cl – 1e– – Cl– ⇌ graphite=molecule

Jackson, …, Surendranath, J. Am. Chem. Soc., 2018, 140, 1004

(GCC)

(moleculein solution)

(graphite=molecule)

1273… let’s imagine electrochemical systems for which diffusion

does not control the rate of faradaic reactions…

example: redox + chemistry at a conjugated M–molecule:graphite=molecule–Cl – 1e– – Cl– ⇌ graphite=molecule

(moleculein solution)

(graphite=molecule)

(substrate binds/releases Cl–, like EC mechanism) (simple “E” mechanism)



example: redox + chemistry at a conjugated M–molecule:

graphite=molecule–Cl – 1e– – Cl– ⇌ graphite=molecule

… they showed that the applied potential bias is only useable within/outside of the double layer…

… some screening must occur to generate

some usable capacitive potential drop!

––

––

–

++

++

+

–––––––

++

++

++

+

––

––

–

++

++

+

–––––––

++

++

++

+

Zaban, Ferrere & Gregg, J. Phys. Chem. B, 1998, 102, 452


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1275

electrode Nafion

[RuII(bpy)3]2+

⇌[RuIII(bpy)3]

3+

d << (2Dt)1/2

… let’s imagine electrochemical systems for which diffusion does not control the rate of faradaic reactions…

example: redox chemistry with an ultra-thin Nafion film

1276

electrode Nafion

[RuII(bpy)3]2+

⇌[RuIII(bpy)3]

3+

d << (2Dt)1/2

… let’s imagine electrochemical systems for which diffusion

does not control the rate of faradaic reactions…

example: redox chemistry with an ultra-thin Nafion film

… noticeable small peak splitting may be due to iRu drop… keep currents small

1277… this is called thin-layer (zero-gap) electrochemistry… we already discussed this in the context of single-molecule EChem

… capillary action of water

will get you ~10 µm

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1278

Question: what is a “thin-layer cell”?

Answer: Any “cell” with a thickness:

… this is called thin-layer (zero-gap) electrochemistry…

ℓ ≪ 𝐷𝑡

1279

OR

… |dConc/dE| has

a maximum at Eo’

… this capacitance

times v, is current

… the voltammetric response will therefore be proportional

to the derivative of these curves… more on this in a second…

1280… what does B&F tell us about it? … in Section 11.7!

𝑖𝑝 =𝑛2𝐹2𝑣𝑉𝐶O

∗

4𝑅𝑇

𝑖 =𝑛2𝐹2𝑣𝑉𝐶O

∗

𝑅𝑇

exp𝑛𝐹𝑅𝑇 𝐸 − 𝐸𝑜′

1 + exp𝑛𝐹𝑅𝑇

𝐸 − 𝐸𝑜′2

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1281… so, thin-layer voltammetry has the following properties:

● ip ∝ V (the total volume of the thin-layer cell) and

● ip ∝ Co*… taken together, this really means that....

● ip ∝ Γ (the “coverage”/capacity of the surface by

electroactive molecules in units of moles cm-2)…

● ip ∝ v1 important… this is how one recognizes & diagnoses

thin-layer behavior experimentally… more on this later…

● NOTE: No diffusion, so no D!


∗

4𝑅𝑇

1282… so, to sum up our observations about these two limiting cases:

● diffusion-controlled, static δ. Ep – Eo’ > 55 mV

● activation-controlled, No δ! Ep – Eo’ = 0 mV

● expanding δ using LSV/CV. Ep – Eo’ = 28.5 mV

-28.5 mV

1283

2 electrodes, E1 = E2

1 electrode, E1

2 electrodes, E1 ≠ E2

… now let’s take a closer look at thin-layer behavior, notably becauseit is highly relevant to molecular homogeneous electrocatalysis…… anyway, there are three types of thin-layer cells:

1 nm to 50 µm

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1284

http://upload.wikimedia.org/wikipedia/en/4/41/Cyclicvoltammetrywaveform.jpg

E1 = E2

E0’

1285

1 electrode, E1.


3 cases of interest:

1286

1 electrode, E1.


… what’s the current?

… assuming the concentration everywhere in the cell follows C(x, t)

= C(0, t), which means it is uniform (NOT as shown above):

consider the generic reaction:

𝑖 = 𝑛𝐹𝑉𝑑𝐶O 𝑡

𝑑𝑡= 𝑛𝐹 ℓ𝐴

𝑑𝐶O 𝑡

𝑑𝑡

O + ne– ⇋ Rn–

5/30/2019

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1287

Note: i and j∝ ℓ = the cell thickness… small ℓ small V small j



𝑑𝐶O 𝑡

𝑑𝑡

𝑗 = 𝑛𝐹ℓ𝑑𝐶O 𝑡

𝑑𝑡

1288


Now, according to the Nernst Equation (written as a fraction)…

this equation makes sense: if E = E0’, CO(t) = 0.5CO*

E << E0’, CO(t) = 0 … you’re reducing as fast as possible

E >> E0’, CO(t) = CO* … you’re doing nothing

𝐶O 𝑡 = 𝐶O∗ 1 − 1 + exp

𝑛𝐹

𝑅𝑇𝐸 − 𝐸𝑜′

−1



𝑑𝐶O 𝑡

𝑑𝑡


𝑑𝑡

1289

𝐶O 𝑡 = 𝐶O∗ 1 − 1 + exp

𝑛𝐹


−1



𝑑𝐶O 𝑡

𝑑𝑡


𝑑𝑡

… there is no explicit time dependence in this equation, but E is time

dependent if we scan: E(t) = Ei + vt. Substituting and differentiating…



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1290

Note: i and j∝ ℓ = the cell thickness… small ℓ small V small j.

Now, according to the Nernst Eq…

𝐶O 𝑡 = 𝐶O∗ 1 − 1 + exp

𝑛𝐹


−1



𝑑𝐶O 𝑡

𝑑𝑡


𝑑𝑡



1291

𝐶O 𝑡 = 𝐶O∗ 1 − 1 + exp

𝑛𝐹


−1




∗

𝑅𝑇

exp𝑛𝐹𝑅𝑇

𝐸 − 𝐸𝑜′


𝐸 − 𝐸𝑜′2


∗

4𝑅𝑇


1292


∗

𝑅𝑇

exp𝑛𝐹𝑅𝑇

𝐸 − 𝐸𝑜′


𝐸 − 𝐸𝑜′2

… as the volume of the cell is decreased, for example, by

reducing the cell thickness, ip falls…

… also, ip depends on scan rate and is proportional to v1!

(Recall that for an LSV/CV, ip is proportional to v1/2)


∗

4𝑅𝑇

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1293… again, here is the resulting i vs E thin-layer-cell voltammogram:


∗

4𝑅𝑇


∗

𝑅𝑇

exp𝑛𝐹𝑅𝑇 𝐸 − 𝐸𝑜′


𝐸 − 𝐸𝑜′2

1294

current

potential

… schematically what is happening is the following:

imagine doing the experiment in many small potential steps…

OR

1295

current

potential


OR


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1296

current

potential


OR


𝑄 = 𝑛𝐹𝑉Δ𝐶

𝑖 = 𝑛𝐹𝑉Δ𝐶

Δ𝑡

1297

current


OR

potential


1298

current


OR



Δ𝑡potential


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1299

current


OR



Δ𝑡

potential


1300

OR


current

potential


1301

OR

… |dConc/dE| has

a maximum at Eo’

… this capacitance

times v, is current

Now this makes more sense…

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1302


1 nm to 50 µm

Okay, so the two-electrode thin-layer cell (with E1 = E2) gives the

peaked I–E curve that we just calculated…

1303


1 nm to 50 µm

Now, what happens if you get rid of one electrode?

1304Answer: Nothing! … The I–E curve is the same as the two-

electrode case…

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– –

–

1305… both electrodes are doing the same thing… and the rate of

diffusion is, by definition, negligible

1306

● ip ∝ V (the total volume of the thin-layer cell) and

● ip ∝ Co*… taken together, this really means that....

● ip ∝ Γ (the “coverage”/capacity of the surface by

electroactive molecules in units of moles cm-2)…

● ip ∝ v1 important… this is how one recognizes & diagnoses

thin-layer behavior experimentally… more on this later…

● NOTE: No diffusion, so no D!


∗

4𝑅𝑇

… so, this equation, and the conclusions below, apply both to

one-electrode and two-electrode thin-layer cells, with E1 = E2…

1307


1 nm to 50 µm

Now what about the two-electrode E1 ≠ E2 case?

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1308Now what about the two-electrode E1 ≠ E2 case? Huh?

– –

–

– –

1309… in this instance, when “O” is consumed, it is simultaneously

regenerated at the other electrode

Much larger…

Observed for

homogeneous

electrocatalysis!

1310

and then linearize this as in Chapter 1…

The numerator here will be bounded by CO*, so the limiting current is

What’s the current? … Just Fick’s first law of diffusion…

𝐽 0 = −𝐷𝜕𝐶 𝑥

𝜕𝑥𝑥 = 0

𝐽 0 = −𝐷Δ𝐶

Δ𝑥= −𝐷

𝐶 ℓ − 𝐶 0

ℓ

𝑖𝑙 = −𝑛𝐹𝐴𝐷𝐶O∗

ℓ

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1311

NOTE: We’ve got D in this equation… that’s

because the current depends on the transport

rate of molecules across the cell.

𝑖𝑙 = −𝑛𝐹𝐴𝐷𝐶O∗

ℓ

… what’s the current?

1312… one can also calculate the “gain” imparted by the

positive feedback produced by the second electrode…

gain =𝑖𝑙𝑖𝑝=

𝑛𝐹𝐴𝐷𝐶O∗

ℓ

𝑛2𝐹2𝑣 ℓ𝐴 𝐶O∗

4𝑅𝑇

=4𝐷𝑅𝑇

𝑛𝐹𝑣ℓ2

1313

example: for v = 100 mV s-1, and ℓ = 10 µm we have:



ℓ


4𝑅𝑇

=4𝐷𝑅𝑇

𝑛𝐹𝑣ℓ2

gain =4 10−5 8.314 298.15

𝑛 96485 0.1 ℓ2=1.0 x 10−5

𝑛ℓ2

=1.0 x 10−5

1 10 x 10−4 cm 2= 10

… one can also calculate the “gain” imparted by the


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1314

For l = 1 µm, we get 1000; for l = 100 nm we get 105… Wow! “Amplified”!

gain =4 10−5 8.314 298.15

𝑛 96485 0.1 ℓ2=1.0 x 10−5

𝑛ℓ2

=1.0 x 10−5

1 10 x 10−4 cm 2= 10



ℓ


4𝑅𝑇

=4𝐷𝑅𝑇

𝑛𝐹𝑣ℓ2


… one can also calculate the “gain” imparted by the


1315

{effectively a thin-layer region

For l = 1 µm, we get 1000; for l = 100 nm we get 105… Wow! “Amplified”!


gain =4 10−5 8.314 298.15

𝑛 96485 0.1 ℓ2=1.0 x 10−5

𝑛ℓ2

=1.0 x 10−5

1 10 x 10−4 cm 2= 10

1316

… this also makes Warburg (Fickian) diffusion in EIS look capacitive (due to thecapacitance of the second electrode)… it is now represented by a parallel Rmt + Cdl-2

http://www.consultrsr.net/resources/eis/diff-o.htm

https://www.bio-logic.net/wp-content/uploads/Zdiffusion.pdf



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1317

… this also makes Warburg (Fickian) diffusion in EIS look capacitive (due to thecapacitance of the second electrode)… it is now represented by a parallel Rmt + Cdl-2



… for the non-feedback cases (first two examples)this also changes Warburg (Fickian) diffusion

… it is now represented by a series Rmt + Cdl-2

1318Anyway… in cyclic voltammetry you scan back and forth…

1319for a Nernstian, reversible reaction, ΔEp ≈ 57 – 60 mV… for n = 1



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1320How do you measure ip?

… well, for the first forward scan, you just measure it…



How can you convert

the x axis from E to t?



/v = t (s)

How can you convert

the x axis from E to t?... Divide by v!

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/v = t (s)

… and now, what

is this function?



/v = t (s)

… and now, what

is this function?… A Cottrellian

current transient

1325… so ip for the reverse scan must be measured from the decaying,

Cottrellian current of the forward scan!

i ∝ t –1/2

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1326… a similar problem exists if you have two processes in close

proximity, in terms of potential… here is a solution…

ip

1327

-28.5 mV

χ(σ,t) =

0.4463

… and how is this “reversible CV” affected by slow electron transfer

kinetics (small

k0, α)?

1328Answer: ΔEp increases from ~60 mV to larger values…

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1329

Peaks can be:

(a) Electrochemically reversible,

Answer: ΔEp increases from ~60 mV to larger values…

Evans, …, Kelly, J. Chem. Educ. 1983, 60, 290

Peaks can be:


1330

Peaks can be:


(b) Quasi-reversible (|Epa – Epc| > 58/n mV

at room temperature, after iRu and/or

other potential corrections), or

(c) Irreversible (ipc ≠ ipa, and they are not

even close)

… Slow kinetics and iRu are

indistinguishable by CV

(thus, turn a knob, or keep iRu small)

Answer: ΔEp increases from ~60 mV to larger values…

1331

iRu

Eapplied

Eattenuated

... iRu drop looks a lot

like slow catalysis…

minimize i and/or Ru,

or just correct for iRu

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1332… peak current increases with v1/2… but, is faster always better?

… what about signal-to-noise ratio?

signal:


noise: Double-layer charging𝑖𝑐 = 𝐶𝑑𝐴𝑣

1333

… Therefore, for better S:N, slow scan rates are best!

… peak current increases with v1/2… but, is faster always better?

… what about signal-to-noise ratio?

ratio:

signal:



S: N =2.69 x 105 𝑛3/2𝐴𝐷1/2𝐶∗𝑣1/2

𝐶𝑑𝐴𝑣

=2.69 x 105 𝑛3/2𝐷1/2𝐶∗

𝐶𝑑𝑣1/2

1334peak current increases with v1/2… but, is faster always better?… what about signal-to-noise ratio?

ratio:

signal:


… Therefore, for better S:N, slow scan rates are best!


S: N =2.69 x 105 𝑛3/2𝐴𝐷1/2𝐶∗𝑣1/2

𝐶𝑑𝐴𝑣

=2.69 x 105 𝑛3/2𝐷1/2𝐶∗

𝐶𝑑𝑣1/2

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1335… but UMEs can help measure things… like fast kinetics!

◆ measuring processes that occur in small spaces

e.g. single cells, SECM, etc. (i is “small”; j is large)

◆ measuring in highly resistive media (Ru is “small”)

e.g. solvent glasses, no supporting electrolyte,

nonpolar solvents, gas phase reactions

◆ observing & measuring the kinetics of fast reactions

(Cd is small; Ru is “small”)

𝒊 =𝑬

𝑹𝒆𝒙𝒑

−𝒕

𝑹𝑪

1336

… but wait… Recall that for better S:N slow scan rates are best… Uh oh!

… but UMEs can help measure things… like fast kinetics!

◆ measuring processes that occur in small spaces

e.g. single cells, SECM, etc. (i is “small”; j is large)

◆ measuring in highly resistive media (Ru is “small”)

e.g. solvent glasses, no supporting electrolyte,

nonpolar solvents, gas phase reactions

◆ observing & measuring the kinetics of fast reactions

(Cd is small; Ru is “small”)

𝒊 =𝑬

𝑹𝒆𝒙𝒑

−𝒕

𝑹𝑪

1337Experimentally, we also observe an overpotential that is intrinsic

to the electron transfer process…

as examples, these are two of the fastest known heterogeneous electron-transfer rxns

anthracene anthracene•–

+ 1e– ⇌

• –

[RuII(bpy)3]2+[RuIII(bpy)3]

3+

+ 1e– ⇌

2+3+

5/30/2019

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1338

6.8 pA

1.9 pA

Science 1990, 250, 1118

r0 = 1.1 µm

r0 = 1.1 nm

r0 = 2.3 nm

r0 = 4.7 µm

1339

… smaller electrodes are better!

1340

Wightman, Anal. Chem., 1981, 53, 1125A

… scanning is “often” steady-state at a UME

… steady-state occurs when v << RTD/(nFr02)

… v (mV s-1) << 26 mV x (D/r02)… for a BASi UME with r0 = 5 𝜇m…

… (1 x 10-5 cm2 s-1) / (0.5 x 10-3 cm)2 = 26 x 40 mV s-1s

… v << 1 V s-1… Wow!

Recall…

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38

1341

1342

scan rate is inmegavolts s-1!That is MV s-1

… wow!anthracene anthracene•–

+ 1e– ⇌

• –

1343Anthracene and [RuII(bpy)3]2+ are not that similar, chemically…

… so what do these two ultrafast reactions have in common?

anthracene anthracene•–

+ 1e– ⇌

• –

[RuII(bpy)3]2+[RuIII(bpy)3]

3+

+ 1e– ⇌

2+3+

5/30/2019

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1344

means Ru(II)means Ru(III)

1345

1346

Anthracene and [RuII(bpy)3]2+ are not that similar, chemically…

So what do these two ultrafast reactions have in common?

1) reactant and product are almost structurally identical

2) electron transfer involves no bond-making or bond-breaking

3) in polar solvents, bigger is faster…

… thus, exchange current (density) is large

due to “small” reorganization energy!

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40

1347

FLASHBACK

hybrid catalysis and diffusion


(Cottrellian)

RECALL… without stirring, the diffusion layer grows over time and with a

big (enough) potential step (or even bigger, or a little smaller again), the

Cottrell equation results…

1348

• CVs are not pure Butler–Volmer behavior “ever,” unless you do what?

Why are "normal" CVs useful, when Tafel Plots seem ideal?…

1349


• Why are Tafel Plots (and/or with RDE) better than CVs? … Stir!

Not limited by mass transfer and so one can measure interfacial

faradaic charge-transfer kinetic parameters with ease (α, j0, k0)


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1350





• Why is CV better than Tafel?

Can tell if species is adsorbed to the surface by performing a facile

scan-rate dependence (linear ip vs. v1/2 = homogeneous reaction…

… linear ip vs v1 = heterogeneous reaction)

Easy to compare 1ET and 2ET steps, as ip contains n.



1351










… determine kinetics based on the shape… if you are a computer.


1352Why are "normal" CVs useful, when Tafel Plots seem ideal?…










… determine kinetics based on the shape… if you are a computer.

• And lastly… what is the midpoint potential for Tafel plots versus CV

plots? … Eeq

… E0’, if DO = DR

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42

1353

Q: Explain cyclic voltammetry.

RECALL: Course goal, i.e. best 2-hour-long final-exam question ever!

From syllabus

Evans, …, Kelly, J. Chem. Educ. 1983, 60, 290

Course philosophy

Theory/Experiments versus Technologies (me vs you)

I will teach the theory, history, and experimental specifics, and you will

teach the technologies, and real-world and academic state-of-the-art

WE DID IT!

1354

Q: What was in this set of lectures?

A: B&F Chapters 9, 10, and 6 main concepts:

● Sections 9.1 – 9.4: Rotating (Ring-)Disk

Electrochemistry

● Sections 10.1 – 10.4: Electrochemical Impedance

Spectroscopy

● Sections 6.1 – 6.6, 11.7, 14.3: Linear Sweep Voltammetry

(LSV), Cyclic Voltammetry

(CV), Thin-Layer

Electrochemistry

… to really learn about your experimental systems…

… move beyond steady-state conditions!

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