Triplet Extinction Coefficients,Triplet Extinction Coefficients,Triplet Quantum Yields,Triplet Quantum Yields,

and (mainly)and (mainly)Laser Flash PhotolysisLaser Flash Photolysis

http://150.254.84.227/HUG

http://www.zfch.amu.edu.pl This weekend

Competitive Kinetics out of Singlet StateCompetitive Kinetics out of Singlet State

1M + h 1M*, kex

1M* products, kpc

1M* 3M* + heat, kisc

1M* 1M + heat, kic

1M* 1M + hf, kf

kS = kpc + kisc + kic + kf

T = kisc/kS

Competitive Kinetics out of Triplet StateCompetitive Kinetics out of Triplet State

3M* products, k’pc

3M* 1M + heat, k’isc

3M* 1M + hp, kp

kT = k’pc + k’isc + kp

Competitive KineticsCompetitive Kinetics

p

iscT

S0

Intramolecular decay channels

Intermolecular decay channels

T + Q S0 + Q’

]T][Q[]T[]T[]T[qpisc kkk

dtd

tkkk ]Q[exp]T[]T[ qpisc0

Transient AbsorptionTransient Absorption

S0

S1

S2

T1

Tn

A

TATA

PF

IC

IC

ISC

ISCIC

ISC

3M* + h’ 3M** k’ex

3M**

3M*

Creation of TripletsCreation of Triplets

3M1* + 1M 1M1 + 3M*

(1) Intramolecular radiationless transitions

(2) Intermolecular energy transfer

(3) Transfer from solvent triplets in radiolysis of benzene.

1M + h 1M* kex

1M* 3M* + heat kisc

Beer’s LawBeer’s LawConnection betweenConnection between

light absorption and concentrationlight absorption and concentration

OD = T* [3M*] l

OD = log10 (I0/I)

A = log100

IPMT

II0

time

A

t laser

0

time

Spatial Overlap ofSpatial Overlap ofLaser and Monitoring BeamLaser and Monitoring Beam

Laser

MonitoringLight Beam

Cell

Laser

MonitoringLight Beam

UnexcitedExcited

Proper alignment:Sample is excited along theentire optical pathlength

Improper alignment:Sample is not excited along theentire optical pathlength

Placement ofPlacement ofMonitoring BeamMonitoring Beam

Relative toRelative toIncident LaserIncident Laser

Laser

MonitoringLight Beam

Cell

[3M*] fromBeer’s Law

Cell WallLaserEntering

Cell WallLaserExiting

Extrapolated[3M*] for longcells

Triplet-Triplet Absorption Spectra of Organic Molecules

in Condensed Phases

Ian Carmichael and Gordon L. Hug

Journal of Physical and Chemical Reference Data 15, 1-150 (1986)

http://www.rcdc.nd.edu/compilations/Tta/tta.pdf

Methods of DeterminingMethods of DeterminingTriplet Extinction CoefficientsTriplet Extinction Coefficients

Energy Transfer MethodEnergy Transfer Method Singlet Depletion MethodSinglet Depletion Method Total Depletion MethodTotal Depletion Method Relative ActinometryRelative Actinometry Intensity Variation MethodIntensity Variation Method Kinetic MethodKinetic Method Partial Saturation MethodPartial Saturation Method

Energy Transfer (General)Energy Transfer (General)

Two compounds placed in a cell.Two compounds placed in a cell. Compound R has a known triplet extinction Compound R has a known triplet extinction

coefficient.coefficient. Compound T has a triplet extinction coefficient to Compound T has a triplet extinction coefficient to

be determined.be determined. Ideally, the triplet with the higher energy can be Ideally, the triplet with the higher energy can be

populated.populated. Thus triplet energy of one can be transferred to Thus triplet energy of one can be transferred to

the other.the other.

Energy Transfer (General)Energy Transfer (General)

If the lifetimes of both triplets are long in the If the lifetimes of both triplets are long in the absence of the other molecule, thenabsence of the other molecule, then

One donor triplet should yield one acceptor One donor triplet should yield one acceptor triplet.triplet.

In an ideal experimentIn an ideal experiment

T* = R* ( ODT / ODR )

Note it doesn’t matter whether T or R is the triplet energy donor.

33R* + R* + 11T T 11R + R + 33T*T*

ket = 1 × 109 M-1 s-1

[3R*]0 = 1 M[1T]0 = 1 mM

kobs = ket [1T]0[3R*] = [3R*]0 exp(kobs t)[3T*] = [3T*] {1 exp(kobs t)}

Initial Conditions

[3T*] = [3R*]0

Also a Also a iscisc Method Methodkobs = ket [1T]0[3R*] = [3R*]0 exp(kobs t)

[3T*] = [3T*] {1 exp(kobs t)} [3T*] = [3R*]0

If T* andabsorption of 3R* ismainly hidden underits ground-stateabsorption,

isc(R) =

[3T*] / # photons into R

= (OD l) / (T* photons)

Kinetic CorrectionsKinetic Corrections

(1) Need to account for unimolecular decay of the triplet donor:

3D* 1D kD

3D* + 1A 1D + 3A* ket

Ptr = ket[1A] / (ket[1A] + kD)

The probability of transfer (Ptr) is no longer one, but

A* = D* ( ODA / ODD ) / Ptr

33D* + D* + 11A A 11D + D + 33A*A*

kobs = kD + ket [1A]0[3D*] = [3D*]0 exp(kobs t)[3A*] = [3A*] {1 exp(kobs t)} [3A*] = [3R*]0 Ptr

kD = 0.5 × 106 s-1

ket = 1 × 109 M-1 s-1

[1A]0 = 1 mM

Unimolecular 3D* decay

Otherwise same initialconditions as before

Kinetic CorrectionsKinetic Corrections

(2) May need to account for the unimolecular decay

3A* 1A kA

if the rise time of 3A* is masked by its decay. Thenthe growth-and decay scheme can be solved as

[3A*] =W {exp(-kAt) - exp(-ket[1A]t-kDt)}

W =[3D*]0 ket[1A] / (kD + ket[1A] - kA)

the maximum of this concentration profile is at tmax

tmax = ln{kA/(ket[1A] + kD)} / (kA - ket[1A] - kD )

ODA = ODA(tmax) exp(kAtmax)

Kinetics involving decay of both tripletsKinetics involving decay of both triplets

kD = 0.5 × 106 s-1

ket = 1 × 109 M-1 s-1

[1A]0 = 1 mM

Unimolecular 3D* decay

kA = 0.5 × 106 s-1

Unimolecular 3A* decay

33D* + D* + 11A A 11D + D + 33A*A*

33D* D* 11DD

33A* A* 11AA

Energy Transfer

Uncertainty in Probability of TransferUncertainty in Probability of Transfer

If there is a dark reaction for bimolecular deactivation of

3D* + 1A 1D + 1A, kDA

then the true probability of transfer is

Ptr = ket[1A] / (kDA[1A] + ket[1A] + kD)

Energy TransferEnergy TransferAdvantages and DisadvantagesAdvantages and Disadvantages

The big advantage is over the next method which The big advantage is over the next method which depends on whether the triplet-triplet absorption depends on whether the triplet-triplet absorption overlaps the ground state absorption.overlaps the ground state absorption.

The big disadvantage is the uncertainty in the The big disadvantage is the uncertainty in the probability of transfer.probability of transfer.

Singlet DepletionSinglet Depletion

By Kasha’s Rule, after the excited singlets have By Kasha’s Rule, after the excited singlets have decayed, only the lowest triplet state and the decayed, only the lowest triplet state and the ground state should be present.ground state should be present.

Any ground state molecules that are missing Any ground state molecules that are missing should be in the lowest triplet state.should be in the lowest triplet state.

In other words, the missing concentration of In other words, the missing concentration of ground states should be the same as the triplet ground states should be the same as the triplet concentration.concentration.

At a wavelength where they both absorbAt a wavelength where they both absorbOD = (T* S) [3M*] l

Singlet DepletionSinglet Depletion

Assuming that there is a wavelength region (1) wherethe ground state absorbs and the triplet doesn’t

ODS(1) = S [3M*] l

A = log100

II0

time

A

t laser

0

time

“bleaching”

Step 1

Singlet DepletionSinglet DepletionStep 2

Go to a wavelength region (2) where the ground statedoesn’t absorb

ODT(2) = T* [3M*] l

A = log100

II0

time

A

t laser

0

time

Singlet DepletionSinglet DepletionAdvantages and DisadvantagesAdvantages and Disadvantages

The main problem is the assumption in Step 1: The main problem is the assumption in Step 1: that the chosen wavelength that the chosen wavelength 11 is in a region is in a region where the triplet does not absorb.where the triplet does not absorb.

There are methods for attempting to compensate There are methods for attempting to compensate for this, but they involve further assumptions.for this, but they involve further assumptions.

The main advantage of singlet depletion is that it The main advantage of singlet depletion is that it is free from kinetic considerations.is free from kinetic considerations.

Total Depletion MethodTotal Depletion Method

Assumes that increasing the intensity of the pulse Assumes that increasing the intensity of the pulse complete conversion of a small ground state complete conversion of a small ground state conversion to the triplet state is possible if the conversion to the triplet state is possible if the intersystem crossing is not negligibly small.intersystem crossing is not negligibly small.

Then the concentration of triplet is equal to the Then the concentration of triplet is equal to the initial ground state concentration.initial ground state concentration.

[3M*] = [1M]

Total DepletionTotal DepletionKinetic DerivationKinetic Derivation

d[1M]/dt = -2303SIp(t)T[1M]

d[3M*]/dt = +2303SIp(t)T[1M]

kex = 2303 S Ip(t)where the excitation rate constant is

note its intensity dependence

[3M*] = [1M]0(1 - exp{-2303SIpTt})

Total DepletionTotal Depletion

When a three-state model is used, namely When a three-state model is used, namely including the excited singlet state, then it was including the excited singlet state, then it was found that 95% conversion could occur only iffound that 95% conversion could occur only if

S Tp/2 where p is the laser pulse width This is difficult to satisfy for most lasersThis is difficult to satisfy for most lasers

Total DepletionTotal DepletionAdvantages and DisadvantagesAdvantages and Disadvantages

Principal advantage is that it offers a simple Principal advantage is that it offers a simple direct estimate of the triplet concentrationdirect estimate of the triplet concentration

However, even though the approach to total However, even though the approach to total depletion is inferred from a saturation in the depletion is inferred from a saturation in the OD, OD, the curve can saturate for other reasonsthe curve can saturate for other reasons

Multiphotonic processes, e.g. biphotonic Multiphotonic processes, e.g. biphotonic ionization can come into play at high laser ionization can come into play at high laser intensitiesintensities

Excited state absorption can also invalidate the Excited state absorption can also invalidate the simple kinetic equationssimple kinetic equations

Relative ActinometryRelative Actinometry

This is a two cell experiment.This is a two cell experiment. In one cell there is a compound of unknown In one cell there is a compound of unknown

TT*(*(11), but with a known intersystem crossing ), but with a known intersystem crossing yield yield TT(T)(T)

In the other cell there is a compound of known In the other cell there is a compound of known RR*(*(22), and also with a known intersystem ), and also with a known intersystem crossing yield of crossing yield of TT(R)(R)

Relative ActinometryRelative Actinometry

If the optical densities at the respective If the optical densities at the respective wavelengths are the same, then the number of wavelengths are the same, then the number of photons absorbed by each cell is exactly the photons absorbed by each cell is exactly the same andsame and

This is a consequence of Beer’s LawThis is a consequence of Beer’s Law The monitor beam must also be fixed relative to The monitor beam must also be fixed relative to

the cell and the laserthe cell and the laser

T*(1) = { ODT T(R) / ODR T(T) }R*(2)

Relative ActinometryRelative ActinometryAdvantages and DisadvantagesAdvantages and Disadvantages

Disadvantage is that both triplet quantum yields Disadvantage is that both triplet quantum yields must be knownmust be known

However, it is more often used to measure However, it is more often used to measure intersystem crossing quantum yields once both intersystem crossing quantum yields once both triplet extinction coefficients are knowntriplet extinction coefficients are known

Relative Actinometry and Relative Actinometry and iscisc

T() = T(R)ODT (1) R*(2)

ODR (2) T*(1)

Rearranging formula from one of the preceding slides

This is one of the most popular ways to measure triplet yields

Need two extinction coefficients and the reference triplet yield

Partial Saturation MethodPartial Saturation Method

OD = a(1 exp{bIp})

a = (T* S)[1M]0l

b = 2303StT

t is length of pulse

Partial Saturation MethodPartial Saturation MethodAdvantages and DisadvantagesAdvantages and Disadvantages

This has the same conceptual foundation as the This has the same conceptual foundation as the Total Depletion MethodTotal Depletion Method

However, the fitting parameters a and b can be However, the fitting parameters a and b can be obtained without total saturation being reachedobtained without total saturation being reached

It has this advantage over the Total Depletion It has this advantage over the Total Depletion MethodMethod

The disadvantage is that high laser intensities The disadvantage is that high laser intensities must be used to reach the region where the plots must be used to reach the region where the plots of of OD vs OD vs IIpp becomes nonlinear. becomes nonlinear.