lecture #17 of 18 - uci department of chemistryardo/echem/uci-chem248-2017w_lectur… · there is...

1237

Lecture #17 of 18

1238

Q: What’s in this set of lectures?

A: B&F Chapter 3 main concepts:

● Sections 3.1 & 3.6: Homogeneous Electron-Transfer

(ET) (Arrhenius, Eyring, TST (ACT),

Marcus Theory)

● Sections 3.2, 3.3, 3.4 & 3.6: Heterogeneous ET (Butler–Volmer

Eq, Tafel Eq, Volcano Plot,

Gerischer Theory, Quantum

Mechanical Tunneling)

● Section 3.5: Multistep ET Mechanisms

But wait! You told us that Marcus Theory led to an inverted region

… where is evidence for the inverted region by electrochemistry?

http://www.nobelprize.org/nobel_prizes/chemistry/laureates/1992/marcus-lecture.pdf

–ΔG0 < λ –ΔG0 > λ

–ΔG0 = λ

• Three regions of electron transfer• (I) Normal, (II) Barrierless, (III) Inverted

1239

… and you told us that this had a Gaussian shape…

http://www.nobelprize.org/nobel_prizes/chemistry/laureates/1992/marcus-lecture.pdf

There is no inverted region! Thank you, Fermi, Marcus & Gerischer! 1240

Ebias varies the probability function (0, 1)

… resulting in (D)istributions of occupied metal states

from Wiki andhttp://www.fhi-berlin.mpg.de/

pc/PChistory.html

Enrico Fermi(1901–1954)

Physicist

Heinz Gerischer(1919–1994)

Electrochemist



… resulting in (D)istributions of occupied metal states

ρ has units of

cm-2 eV-1

Enrico Fermi(1901–1954)

Physicist

Heinz Gerischer(1919–1994)

Electrochemist

from Wiki andhttp://www.fhi-berlin.mpg.de/

pc/PChistory.html



… resulting in (D)istributions of occupied metal states & molecule states

ρ has units of cm-2 eV-1

… and has units of cm-3 eV-1




ρ has units of cm-2 eV-1

… and has units of cm-3 eV-1

… it’s that Gaussian

term!

… the rate of electron transfer is dictated by the law of mass action 1244



constant(cm3 eV)

area(cm2)




constant(cm3 eV)

area(cm2)




≈ 0

… experimental validation of the theory and lack of inverted region 1247

Sikes, Smalley, Dudek, Cook, Newton, Chidsey & Feldberg, Science, 2001, 291, 1519Chidsey, Science, 1991, 251, 919


λ = 0.85 eV

λλ

Chidsey, Science, 1991, 251, 919

RC double layer charging 1st order electron-transfer kinetics


λ = 0.85 eV

λλ


… and there was no inverted region because at large driving forces there was

always a state in the metal that overlapped the most probable DO

Ebias


λ = 0.85 eV

λλ

Ebias




1252Well, that was disappointing… when is there an inverted region?

… at semiconductors!

… but how?

bandgapHamann, Gstrein, Brunschwig & Lewis,

JACS, 2005, 127, 7815 and JACS, 2005, 127, 13949



… but how?

Ebias


JACS, 2005, 127, 7815 and JACS, 2005, 127, 13949

inverted

1254

Ebias


JACS, 2005, 127, 7815 and JACS, 2005, 127, 13949

Well, that was disappointing… when is there an inverted region?


… but how?

… Vary the molecule, not the bias!

… but λ must be “the same” for each!

barrierless



Ebias


JACS, 2005, 127, 7815 and JACS, 2005, 127, 13949

normal



Ebias


JACS, 2005, 127, 7815 and JACS, 2005, 127, 13949

λ = 0.67 eV

… cm4 s-1… a second order rate

constant (… x concentration2)



Ebias


JACS, 2005, 127, 7815 and JACS, 2005, 127, 13949

λ = 0.67 eV

… cm4 s-1… a second order rate

constant (… x concentration2)

… but more work is still needed

in order to nail this!

1258

Q: What was in this set of lectures?

A: B&F Chapter 3 main concepts:

● Sections 3.1 & 3.6: Homogeneous Electron-Transfer

(ET) (Arrhenius, Eyring, TST (ACT),

Marcus Theory)

● Sections 3.2, 3.3, 3.4 & 3.6: Heterogeneous ET (Butler–Volmer

Eq, Tafel Eq, Volcano Plot,

Gerischer Theory, Quantum

Mechanical Tunneling)

● Section 3.5: Multistep ET Mechanisms

Electrode kinetics, … DONE!

1259Let’s summarize the steady-state behavior from the entire course…

… by looking at data on stirred (non-hysteretic) I–E (J–E) curves

… and at each location, let’s think about what resistance is limiting the

observed behavior…

Circuit representation of electrochemical cell

RuRET RMTRDL

1260RECALL: Let’s compare total capacitance (C) and differential

capacitance (Cd) as follows:

Ez = pzc




observed behavior

… so, we want to know what dictates at each E

Fe3+/2+ and H+

electrocatalysis

H+/H2electrocatalysis

𝑅 =𝜕𝐼

𝜕𝐸

−1




observed behavior

… so, we want to know what dictates at each E

… but this will be hard because we have several convoluting factors

… what are the limiting behaviors of each major resistance and can we

even begin to piece out which component is responsible, while recalling

that the total Eapp(I) = EET(I) + EDL(I) + EMT(I) + Eu(I) + …? …

𝑅 =𝜕𝐼

𝜕𝐸

−1

Circuit representation of electrochemical cell

RuRET RMTRDL

1263… what are the limiting behaviors of each major resistance and can

we even begin to piece out which component is responsible? …

electrocatalysis

masstransport

resistance(iR drop)

1264Let’s try some examples… EXAMPLE #1

electrocatalysis

masstransport

resistance(iR drop)


electrocatalysis

masstransport

resistance(iR drop)

1273Let’s try some examples… EXAMPLE #5… You get the idea! …

… and what does ELJ or EDonnan do to these plots? Shifts them left/right

electrocatalysis

masstransport

resistance(iR drop)

1274


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 laboratory systems

… move beyond steady-state conditions!

1275RDE is also a steady-state technique (slide 1 of 3)…

At high rotation rates, C(0,t) = C*

… and then series current limited by electron-transfer at electrode (iK)

B&F 9.3.1 B&F 9.3.4

Levich Equation (term)

1276RDE is also a steady-state technique (slide 2 of 3)…

By doing this as a function of

potential, one can determine k0

and α… kinetic parameters

without dealing with trying to

stir “perfectly” as required for

B–V kinetics

At high rotation rates, C(0,t) = C*

… and then series current limited by electron-transfer at electrode (iK)

Levich Equation (term)

1277… and RRDE is very useful, too! (slide 3 of 3)…

* Chemistry at disk can be confirmed at ring if ω is fast enough

1278How do we learn anything from complex systems?

Steady-state reactions and processes can be amazingly complex (e.g. see

everything we have covered thus far)… ideally, we need to piece out each

mechanistic component from interrelated processes… we do this by

performing studies over various time regimes… thus, we need to change

the temporal response of our measurements!

• R(R)DE: stirring removes mass-transport limits, which is nice… rotating

the electrode does the same thing… so precisely change the rotation

rate… we can also surround the disk/button by a second ring electrode

to observe products of electron transfer

• EIS: sweep/scan potentials over very small range… but then change the

region (DC)… and also change the scan rate (AC)?

• CV: change the scan rate… mechanisms by Saveant’s “Foot of the

Wave” (e.g. ECE, etc.)… modeling using BASi DigiSim, EC Lab, etc.

• UME: sweep/scan VERY fast forward and backward

1279

capacitor only:

capacitor &

resistor in series:

a few words about electrochemical impedance spectroscopy (EIS)

What is the “resistance”?

1280

capacitor only:

capacitor &

resistor in series:

a few words about electrochemical impedance spectroscopy (EIS)

What is the “resistance”?( )

( )

E tR

I t

1281we need a compact way to represent this impedance…

http://en.wikipedia.org/wiki/Electrical_impedance

Z = R + iX

1282a complex plane representation of the total electrical impedance…

… It’s called a Nyquist plot.

http://en.wikipedia.org/wiki/Electrical_impedance

the total impedance

the resistivecomponent of the impedance

the capacitivecomponent of the impedance(reactance)

Z = R + iX

Zim

(x 1

06)

1283let’s look at Nyquist plots for a few simple circuits:

Zim

(x 1

06)

1284first, a series RC circuit… like with double-layer charging

𝑋 = 𝑍im =1

ω𝐶=

1

0.01 10−5 F= 107 Ω = 10 MΩ

Zim

(x 1

06)

1285first, a series RC circuit… like with double-layer charging

for a capacitor, as

frequency increases

(max ~1 MHz), ZIm

decreases…

… until you hit the x-

axis, which is the

uncompensated

resistance in the cell

𝑋 = 𝑍im =1

ω𝐶=

1

0.01 10−5 F= 107 Ω = 10 MΩ

1286… what about a parallel RC circuit?

1287

at low frequency, Zim << ZRe

(= R), and the circuit

behaves like there is no

capacitor, and just a resistor

… a semi-circle… does this make sense?

1288

at high frequency, Zim = 0,

and the circuit behaves like

there is no capacitor and no

resistor… so here, Ru = 0


1289

in between these limits, the

circuit has both capacitive

and resistive behavior


maximum

phase angle

1290

… to an electrical engineer, an electrochemical cell looks like this:

Zf is the Faradaic impedance

… called the Randles equivalent circuit

1291

Here is the Nyquist plot for the “full” Randles equivalent circuit:

Angle is theoretically 45°

for a Warburg impedance, ZW

Finally, a simple way to measure Ru… assuming our potentiostat can do it

1292… that was a brief primer on EIS, where S is for spectroscopy?

For example, from Wiki,

one type of IS is dielectric

spectroscopy which

monitors the screening

(permittivity) of systems as

a function of the frequency

of light (which is an EM

wave and is related to

wavelength by the speed

(of light))… Our data was

based on EM AC signals as

a function of frequency

too… Also, “impedance is

the opposition to the flow of

alternating current (AC) in a

complex system” and so

EI"S" is appropriate (but

confusing).

FOR YOUR REFERENCE

1293


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 laboratory systems

… move beyond steady-state conditions!

lecture #17 of 18 - uci department of chemistryardo/echem/uci-chem248-2017w_lectur… · there is...

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