Prof. Jacques-E. Moser

http://photochemistry.epfl.ch/PC.html

Photochemistry I

CH-442

Content

PHOTOCHEMISTRY I

1. Basic principles1.1 Introduction1.2 Laws of light absorption1.3 Radiation and molecular orbitals1.4 Selection rules1.5 Light absorption by solids

2. Molecular photophysics2.1 Excited state's deactivation pathways2.2 Kinetics of photochemical processes2.3 Intermolecular energy transfer

3. Photochemical reactions3.1 Photodissociation3.2 Light-induced electron transfer

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Content (contd)

4. Synthetic organic reactions4.1 Reactions of ethenes and aromatic compounds4.2 Photochemistry of carbonyl chromophore4.3 Photo-oxygenation reactions

5. Polymer photochemistry5.1 Photo-polymerization and cross-linking5.2 Photodegradation and stabilization of polymers

6. Natural photochemical processes6.1 Atmospheric reactions6.2 Photochemistry of waters and soils6.3 Natural photosynthesis6.4 Mechanisms of vision

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1. Basic principles

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Photochemistry (light-induced chemistry)

Chemistry: forming or breaking of chemical bonds and charge transfer within or between molecules.

Photochemical reactions are processes during which the energy required for their activation (ΔU‡ ) or their development (ΔGr ) is provided by an electromagnetic radiation.

Activation energies of the order of ΔU‡ = 100 kJ·mol–1 and bond energies of the order of ΔG = 200-400 kJ·mol–1 imply absorption of photons that should individually carry an equivalent amount of energy.

100 200 300 400 500 600 700 800 900 1000

1000015000200003000050000100000

10.0 5.0 4.0 3.0 2.5 2.0 1.7 1.5 1.3

λ / nm

�ν / cm -1

E / eV

UV A B C bleu vert

jaun

e

roug

e

NIR

Ultra-violet Visible Infra-rouge

Ultraviolet Infrared

Blue

Blue

Gre

en

Yello

w

Red

E / kJ·mol–1800 400 100200300 150

1.1 Introduction

Bond ΔH [kJ mol–1] λ [nm] Bond ΔH [kJ mol–1] λ [nm]

H–H 436 274 N–N 160 748

C–H 413 290 N=N 631 190

N–H 393 304 N�N 941 127

P–H 297 403 N–O 201 595

C–C 347 345 N–P 297 403

C–O 358 334 O–H 464 258

C–N 305 392 O–S 265 451

C-Cl 397 301 O–Cl 269 445

C=C 607 197 O–O 204 586

C=O 805 149 C–F 552 216

O=O 498 240 C–S 259 461

Bond energies

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CO2 + H2O hνchloroplastes⎯ →⎯⎯⎯   1

6 C6H12O6 + O2 ΔG = 496 kJ ⋅mol–1

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a) ΔGr < 0 (exergonic reaction, spontaneous) Light enable for overcoming the activation barrier or to lower it by acting as a catalyst.

Such reactions are called "photocatalytic"

b) ΔGr > 0 (endergonic, non spontaneous)

Energy required by the reaction is brought by light. Light energy is (partially) converted into chemical energy.

Example: H2 + Cl 2 → 2 HCl

Example: Natural photosynthesis

∆∆

∆

Types of photochemical reactions

a) Light as a reactant- synthesis of B - reaction inhibition (photo-stabilization of A)

b) Light as an energy vector

- endergonic formation of B - energy storage

c) Light as information vector

- optical absorption profile (photography, information storage) - charge density profile (xerography) - 3D material profile (photolithography)

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Functions associated with light

A hν⎯ →⎯ B (± ΔG)

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Theodor von Grotthuss(1785-1822)

John W. Draper(1811-1882)

Grotthuss-Draper law (1812, 1842)

Light must be absorbed by a chemical substance in order for a photochemical reaction to take place.

Johannes Stark(1874-1957)

Albert Einstein(1879-1955)

Stark-Einstein law (1908-1913)

Also known as the "photo-equivalence law"For each photon of light absorbed by a chemical system, only one molecule is activated for a photochemical reaction.

ΔGmolecule = NA ⋅hν = NA ⋅hcλ

1 Einstein = 1 mol of photons = NA photons

Fundamental laws of photochemistry

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Johann H. Lambert(1728-1777)

Lambert's law

Phenomenological (macroscopic) law of absorption

α = absorption constant [cm–1]

x0

I0 IT

IR

xl

l

IT = I0 − IA − IR

I(x) = I0 ⋅ exp(−αx)

ln I(x)I0

= −αx ln ITI0

= lnT = –αl

T =ITI0

transmittance IAI0

absorptanceIRI0

reflectance

A = − log ( ITI0

) = – logT absorbance

Link with the medium's complex refractive index:

⌢n = n − iκ   [−]

α =4π ⋅κλ0

κ = absorption coefficient [-]

(imaginary part of the refractive index)

1.2 Laws of light absorption

Example: c = 10–3 M, = 104 mol–1 · L · cm–1

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molar decadic extinction coefficient

I0 IT

l

c A = − log ITI0

= − logT = ε ⋅ c ⋅ l [-]

ε

c molar concentration [mol l–1]l optical pathlength [cm]

Superimposition of absorbing systems

Beer-Lambert Law

Transmittance is multiplicative:

Absorbance is additive:

ε

⇒ T = 0.01,  A = 2 ⇒ 99% of the light is absorbed within the first 2 mm of the solution

Ttot = Tii∏

Atot = Aii∑

August Beer(1825-1863)

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Justification of Beer-Lambert law

Initial assumptions

- individual molecules totally block light within a characteristic cross-section σ- monochromatic light

- molecules do not cast any shadow on each other (only conceivable if the concentration c is very low)

dx

σS

I(x+dx)

I(x)

Absorptance of a solution volume S·dx containing n molecules :

−dII(x)

 =  I(x + dx) − I(x)I(x)

 = n ⋅σS =  c ⋅S ⋅NA ⋅dx ⋅σ

S = c ⋅σ ⋅NA ⋅dx

−1I(x)

 dI  = c ⋅σ ⋅NA ⋅dx

By defining : ε  = σ ⋅NA ⋅ log(e) = σ ⋅NA

2.303⇒

0

l

∫⎯ →⎯  − ln I

I0 = c ⋅σ ⋅ l ⋅NA

− log II0 = A = ε ⋅ c ⋅ l

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Absorption by non-continuous media

n0 = 1

n ≠ 1

I0 = IR + IA + IT

Rs = IR / I0 specular reflectance

Absorption and reflexion by a specular (mirror-like) surface

Fresnel law

Augustin Fresnel(1788-1827)

Rs =IRI0

=(n −1)2 + n2 ⋅κ 2

(n +1)2 + n2 ⋅κ 2ϕ = 0at

0 2 4 6 8 10 12 14 160

0.2

0.4

0.6

0.8

1.0

κ  [−]

n = 1.414

R s

ϕI0 IR

IT

ϕ

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Absorption by a scattering medium

I0 = IRd + IA + ITDiffuse reflectance

Schuster-Kubelka-Munk theory

IT

I0

IT

IRd

I0

IT

IRd

dx

x

l

0

I(x)

I(x+dx) J

I0

Phenomenological extinction constants:

k  [cm−1]   absorption     ks→0 = −1dx

⋅ ln dII0     { }−dI = −kI ⋅2dx − sI ⋅2dx + sJ ⋅2dx

dJ = −kJ ⋅2dx − sJ ⋅2dx + sI ⋅2dx

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Kubelka and Kubelka-Munk equations

Kubelka's hyperbolic solutions

Kubelka-Munk simplified solution

IT

a = 1+ ks

b = a2 −1

Rg = background reflectancewith:

l→∞   ⇒ F(R∞ ) = ks =  (1− R∞ )

2

2R∞

Absorber homogeneously dispersed in a scattering medium (powder)

F(R∞ ) = (1− R∞ )

2

2R∞

= ε ⋅ c ⋅ ln(10)s

T =b

a ⋅ sinh (b ⋅2s ⋅ l) + b ⋅ cosh (b ⋅2s ⋅ l)

R =1− Rg (a − b ⋅ coth (b ⋅2s ⋅ l))a + b ⋅ coth (b ⋅2s ⋅ l) − Rg

k [cm–1] = ln(10) ⋅ε [mol–1 L cm–1]⋅c [mol L–1]

Integrating sphere for diffuse reflectance spectroscopy

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B. Total reflectance

Specular white plate

A. Diffuse reflectance

Specular light trap