photochemistry lecture 3 kinetics of electronically excited states
TRANSCRIPT
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Photochemistry
Lecture 3
Kinetics of electronically excited states
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Jablonski diagramS0 S1 T1
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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
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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
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Mirror image of absorption and fluorescence
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Fluorescence from v=0 following vibrational relaxation
absorption
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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
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Solvent relaxation leads to a shift of the 0-0 band
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Absorption and fluorescence in organic dyes
Population inversion between excited electronic state and higher vib levels of ground state.
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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
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Looking at single molecules using near field optical microscopy / fluorescence
Single molecules of pentacene in a p-terphenyl crystal
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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
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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)
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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).
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Absorption spectrum of chlorophyll in solution
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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
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Integrated absorption coefficient
band
d )(A ˜ ˜
varies with wavenumber
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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
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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).
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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
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Modern flash photolysis setup
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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
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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
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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
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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.
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Quantum Yield Definition:
absorptionphotonofrate
processspecifiedofrate
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Fluorescence quantum yields show strong dependence on type of compound excited
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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
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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.
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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.
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Chemical actinometer systems
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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
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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.
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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