kinetics of photochemical reaction

8/10/2019 Kinetics of Photochemical reaction....

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23.7 Kinetics of photochemical reactions

Primary photochemical process:products are formed directly from theexcited state of a reactant.

Secondary photochem ical process:intermediates are formed directly from theexcited state of a reactant.

Photophysical processes compete with theformation of photochemical products via

deactivating the excited state


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Times scales of photophysical processes

Within 10-16~ 10-15s for electronic transitions induced byradiation and thus the upper limit for the rate constant of afirst order photochemical reaction is about 1016s-1.

10-12~ 10-6s for fluorescence

10-12~ 10-4s for intersystem crossing (ISC)

10-6~ 10-1s for phosphorescence (large organic molecules)

A slowly decaying excited species can undergo a very largenumber of collisions with other reactants before deactivation.

The interplay between reaction rates and excited statelifetimes is a very important factor in the determination ofthe kinetic feasibility of a photochemical process.


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The primary quantum yield, , the number ofphotophysical or photochemical events that lead

to primary products divided by the number ofphotons absorbed by the molecules in the sameinterval, or the radiation-induced primary eventsdivided by the rate of photo absorption.

The sum of primary quantum yields for allphotophysical abd photochemical events mustbe equal to 1

)(

)(

absorbedlightofintensityI

processtheofratev

absorbedphotonsofnumber

eventsofnumber

abs

1i

i


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From the above relationship, the primary

quantum yield may be determined directly fromthe experimental rates of ALL photophysical

and photochemical processes that deactivate

the excited state.

i absi

i

iI

v

i

ii

v

v


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Decay mechanism of excited singlet state

Absorption: S +hv

i S*v

abs=Iabs

Fluorescence: S* S + hvi vf= kf[S*]

Internal conversion: S* S vIC= kIC[S*]

Intersystem crossing: S* T* vISC= kISC[S*]

S* is an excited singlet state, and T* is an excited triplet state.

The rate of decay = - kf[S*] -kIC[S*] - kISC[S*]

When the incident light is turn off, the excited state decays exponentially:

with

dt

Sd *][

0

0

/*][*][

tt eSS

I SCICf kkk

1

0


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If the incident light intensity is high and the absorbance

of the sample is low, we may invoke the steady-state

approximation for [S*]:Iabs - kf[S*] -kIC[S*] - kISC[S*] = 0

Consequently,

Iabs = kf[S*] -kIC[S*] - kISC[S*]

The expression for the quantum yield of fluorescence

becomes:

The above equation can be applied to calculate the

fluorescence rate constant.

I SCICf

f

abs

ff

kkk

k

I

v


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Quenching The presence of a quencher, Q, opens an additional channel for

deactivation of S*

S* + Q S + Q

vQ= kQ[Q][S*]

Now the steady-state approximation for [S*] gives:

Iabs

- kf

[S*] -kIC

[S*] - kISC

[S*] -kQ

[Q][S*] = 0

The fluorescence quantum yield in the presence of quencherbecomes

The ratio of / fis then given by

Therefore a plot of the left-hand side of the above equation against[Q] should produce a straight line with the slope

0k

Q. Such a plot is

calledStern-Volmerplot. (fluorescence intensity and life time)

][Qkkkk

k

QISCICf

f

][QkQof

1


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The fluorescence intensity and lifetime are both

proportional to the fluorescence quantum yield, plot of

If,0/I0and t0/t against [Q] should also be linear with thesame slope and intercept as

Self-test 23.4 The quenching of tryptophan

fluorescence by dissolved O2gas was monitored by

measuring emission lifetimes at 348 nm in aqueous

solutions. Determine the quenching rate constant for

this process[O2]/(10

-2M) 0 2.3 5.5 8 10.8

Tau/(10-9s) 2.6 1.5 0.92 0.71 0.57

][QkQof

1


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Three common mechanisms for

bimolecular quenching

Collisional deactivation:

S* + Q S + Q

is particularly efficient when Q is aheavy species such as iodide ion.

Resonance energy transfer:

S* + Q S + Q*

Electron transfer: S* + Q S+ + Q- or

S* + Q S- + Q+


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Energy Transfer Processes

(Forster theory,1952) Energy transfer is moreefficient when

1. The energy donor and acceptor are separatedby a short distance, in the nanometer scale

2. Photons emitted by the excited state of the

donor can be absorbed directly by the acceptor

The efficiency of energy transfer, ET, equals

Where R is the distance between the donorand the acceptor. R0is a parameter that ischaracteristic of each donor-acceptor pair.

Fluorescence resonance energy transfer (FRET)

66

0

6

0

0,

1

RR

REE T

f

f

T


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Electron transfer reactions

(Marcus theory) The distance between the donor and acceptor, with

electron transfer becoming more efficient as the distancebetween donor and acceptor decrease.

The reaction Gibbs energy, rG, with electron transferbecoming more efficient as the reaction becomes moreexergonic.

The reorganization energy, the energy cost incurred by

molecular rearrangements of donor, acceptor, andmedium during electron transfer.

The electron transfer rate is predicted to increaseas this reorganization energy is matched closely by thereaction Gibbs energy.


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23.8 Complex photochemical

processes

The overall quantum yield of a photochemical

reaction. (can be larger than 1)

Rate laws of complex photochemical reactions.

Photosensitization (no direct absorption).


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Quantum yield of a complex

photochemical reaction

Overall quantum yield: the number of reactant

molecules consumed per photon absorbed:

For example: HI + hv H. + I.

HI + H. H2 + I.

I. + I. + M I2 + M*

Here the overall quantum yield is two, because the

absorption of one photon destroys two reactant

molecules HI. Therefore, in a chain reaction the overall

quantum yield can be very large.


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Example:When a sample of 4-heptane was irradiatedfor 100s with 313 nm radiation with a power output of

50W under conditions of total absorption, it was foundthat 2.8 mmol C2H4was formed. What is the quantumyield for the formation of ethylene?

Solution: First calculate the number of photons generated in theinterval 100s.

Then divide the amount of ethylene molecules formed bythe amount of photons absorbed.

N(photons) = Pt/(hc/)

= n(C2H4)*NA/N

= 0.21

kinetics of photochemical reaction

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