Photochemistry

Lecture 3

Kinetics of electronically excited states

Jablonski diagramS0 S1 T1

Main non-reactive decay routes following S1 excitation Non-radiative

IC to S0 followed by vibrational relaxation.

ISC to T1 then ISC’’ to S0 with vibrational relaxation after each step.

Collisional quenching (before or after ISC) Radiative

Fluorescence to S0

ISC to T1 then phosphorescence to S0

Delayed fluorescence

Fluorescence and phosphorescence in solution

Phosphorescence

Weak and slow – spin forbidden (ms – s)

Competing collisional processes may eliminate – unless frozen out e.g., in glass

Fluorescence

Rapid (10-8s) decay - spin allowed

Mirror image of absorption and fluorescence

Fluorescence from v=0 following vibrational relaxation

absorption

Mirror image depends on Molecule being fairly rigid (e.g., as in

polyaromatic systems) No dissociation or proton donation in

excited state

Good mirror image: anthracene, rhodamine, fluorescein

Poor mirror image: Biphenyl, phenol, heptane

Solvent relaxation leads to a shift of the 0-0 band

Absorption and fluorescence in organic dyes

Population inversion between excited electronic state and higher vib levels of ground state.

Fluorescence labelling and single molecule spectroscopy Attaching a fluorescent chromophore to

biological molecules etc

Near-field scanning optical microscopy – optical fibre delivers laser light to spot size 50-100 nm

Maintain sufficient dilution of sample so that single molecules are illuminated

Looking at single molecules using near field optical microscopy / fluorescence

Single molecules of pentacene in a p-terphenyl crystal

Rate of absorption; Beer Lambert Law

dcI

dI

cIddI

I0 It

clI

I t 0

ln

ℓ dℓ

c = concentration, ℓ = length

Intensity decreases as it passes through cell

Beer Lambert Law (cont)

clI

I t 0

ln

clabst IclIIII 10)exp( 000

clI

I t 0

logor

is known as the molar (decadic) absorption coefficient; it is often given units mol-1dm3 cm-1

Nb Intensity has units Js-1m-2 or Wm-2 and is the light energy per second per unit area

(2.3 log x= ln x)

Limit of very dilute concentrations

clII

clII

clIII

abs

abs

abs

0

0

00

434.0

)1(

Rate of absorption only proportional to concentration when above approximation is valid (cℓ « 1).

Absorption spectrum of chlorophyll in solution

Some values for max /(L mol-

1 cm-1) C=C (* ) 15000 at 163 nm (strong) C=0 (* n) 10-20 at 270- 290nm C6H5- (* ) 200 at 255 nm

[Cu(H2O)6]2+ 10 at 810 nm

max

Integrated absorption coefficient

band

d )(A ˜ ˜

varies with wavenumber

Integrated absorption coefficient proportional to square of electronic transition moment

2

03 c

RN ifAfi

A

dR ifif*

But from lecture 1, Einstein coefficient of absorption

fifi

fi

fififfifififidtdN

Bc

hA

ANEBNEBNi

3

38

)()(

20

2

6 if

if

RB

Determining spontaneous emission rates By measuring the area under the

absorption profile, we can determine the transition probability and hence the rate coefficients for stimulated absorption/emission (Bif), and also for spontaneous emission (Aif).

Flash Photolysis Use a short pulse of light to produce a large

population of S1 state.

Follow decay of S1 after excitation switched off Fluorescence in real time Delayed ‘probe’ pulse to detect ‘product’

absorption (e.g., T1 T2).

Choose light source according to timescale of process under study Conventional flashlamp ms - s Q switched laser ns

- s Mode locked laser ps – ns Colliding pulse mode locked laser fs - ps

Modern flash photolysis setup

Fluorescence lifetimes Following pulsed

excitation fluorescence would follow first order decay in absence of other processes.

kf is equivalent to the Einstein A coefficient of spontaneous emission

][ 1][ 1 Sk fdt

Sd

30

233

3

)(16

ch

RAk if

f

dR fif*

= frequency of transition

i and f are the initial and final states

typically kf 108 s-1

First order decay

)exp(][][ 011

1

1

tkSS

dtkS

Sd

ft

f

fff k

10 If there are no competing processes, then the fluorescence lifetime is equal to the true radiative lifetime

Define fluorescence lifetime f as time required, after switching off excitation source, for fluorescence to reduce to 1/e (=0.368) times original intensity.

f

Observed fluorescence lifetime But if there are

competing processes:

)'exp(

]['

]....[][][][

011

1

1111

tkSS

Sk

SkSkSkdt

Sd

t

iciscf

Decay is still first order but as the rate of fluorescence is proportional to [S1] the observed fluorescence lifetime is reduced to

....

1

iciscff kkk

01

11

01

10

SS

TS

hSS

ShS

ic

isc

f

abs

k

k

k

I

Branching ratio and quantum yield

]...)[(

][

1

1

Skkk

Sk

iciscf

ff

The fraction of molecules undergoing fluorescence (branching ratio into that decay channel), is equal to the rate of fluorescence divided by the rate of all processes.

In the present case the above quantity is equal to the quantum yield f – see below.

Quantum Yield Definition:

absorptionphotonofrate

processspecifiedofrate

Fluorescence quantum yields show strong dependence on type of compound excited

Fluorescence quenching and the Stern Volmer equation

QSQS

TS

hSS

ShS

01

11

01

10

Iabs

kf[S1]

kisc[S1]

kQ[S1][Q]

][1 Qkkk

IS

Qiscf

abs

Apply SSA

Continuous illumination

Fluorescence quantum yield

][

][ 1

Qkkk

k

I

Sk

Qiscf

f

abs

ff

f

isc

f

Q

f k

kQ

k

k ][1

1

Can determine ratios of kQ/kf and kisc/kf from suitable plot.

Chemical actinometer To determine a fluorescence quantum

yield need an accurate measure of photon intensity

A chemical actinometer uses a reaction with known quantum yield, and known absorption coefficient at a given wavelength to determine the light intensity.

Chemical actinometer systems

Fluorescence quantum yield

iscf

ff kk

k

0

Qkk

k

I

I

iscf

Q

f

f

f

f

10

0

Thus

Alternatively; define f0 as the fluorescence

quantum yield in the absence of quencher

][

][ 1

Qkkk

k

I

Sk

Qiscf

f

abs

ff

If assume diffusion limited rate constant for kQ ( 5 x 109 M-1s-1) then can determine kf + kisc.

Alternatively can recognise 1/(kf+kisc) as the observed fluorescence lifetime; if this is known can measure kQ.

The quantum yield represents a branching ratioFraction of molecules initially

excited to S1 that subsequently fluoresce; for the scheme on the right

Thus the fraction passing on to T1 state is 1- f

Fraction of T1 molecules undergoing phosphorescence

'01

01

11

01

10

'

hST

ST

TS

hSS

ShS

p

isc

isc

f

abs

k

k

k

k

I

f

iscf

fSkSk

Sk

f kkk

kiscf

f

11

1

'iscp

p

kk

k

')1( pfp kThus ’ is observed phosphorescence lifetime