U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat1 Chimica Fisica dei Materiali Avanzati Part...

UUNIVERSITA’ DEGLI NIVERSITA’ DEGLI SSTUDI DI TUDI DI PPADOVAADOVAUUNIVERSITA’ DEGLI NIVERSITA’ DEGLI SSTUDI DI TUDI DI PPADOVAADOVA

Corso CFMA. LS-SIMat 1

Chimica Fisica dei Materiali AvanzatiChimica Fisica dei Materiali Avanzati

Part 7b – Photophysics and photochemistry of Part 7b – Photophysics and photochemistry of molecular materials molecular materials

(excitons, energy transfer and electron transfer)(excitons, energy transfer and electron transfer)

Laurea specialistica in Scienza e Ingegneria dei MaterialiCurriculum Scienza dei Materiali



ExcitonExciton

Exciton: In some applications it is useful to consider an electronic excitation as a quasi-particles capable of migrating. This is termed an exciton. In organic materials two models are used: the band or wave model (low temperature, high crystalline order) and the hopping model (higher temperature, low crystalline order or amorphous state). Energy transfer in the hopping limit is identical with energy migration.

The following consideration follows M. Kasha et al [Pure Appl. Chem. 11 (1965) 371] model of dimer exciton interaction (the band or wave model).



Exciton model: ground stateExciton model: ground state

We consider a weak interaction between 2 molecules (chromophores),

so that perturbation theory can be used.

The ground state wave-function is

and are ground state wave-functions of molecules u and v.

The Hamiltonian operator is

Hu and Hv are the Hamiltonians of the isolated molecules,

Vuv is the intermolecular perturbation potential approximated by (point)

dipole-dipole interaction term.

The energy of the ground state is

vuG

u v

uvvu VHHH

vuuvvuvug VEEE



If molecules u and v are the same and have identical environments and the excited state wave-functions of the molecules are denoted and , the excited dimer wavefunctions and are degenerate.

Thus, the excited state wave-function of the dimer must be written

with r and s coefficients to be determined.

The Schrödinger equation is

Solution for wave-functions (with Hamiltonian matrix elements Huu = Hvv and Hvu = Hvu)

Exciton model: excited state Exciton model: excited state wavefunctionswavefunctions

**vuvuE sr

*u *

v

****vuvuEvuvu srEsrH

**

**

2

12

1

vuvuE

vuvuE

vu * *vu



Exciton model: excited state energiesExciton model: excited state energies



Parallel transition dipolesParallel transition dipoles



In-line dipolesIn-line dipoles


Exciton in asymmetric dimerExciton in asymmetric dimer

Corso CFMA. LS-SIMat

If the molecules in the dimer are not equivalent because of, say, local perturbations, disorder, etc., the diagonal elements of the Hamiltonian are different. The excitation energies then become:

and the wavefunctions:

*2

*1

*

2

1

2**

*2

*1

**

42

1

DDD

LD

DDE

*

*

2211

12

*212

*1

*

*212

*1

*

2arctan

2

12arctan

2

1

cossin

sincos

D

L

HH

H

and compete for the exciton delocalization: the first favors, the second opposes it.

*D*L



Main mechanisms of energy Main mechanisms of energy transfertransfer



Radiative electronic energy transferRadiative electronic energy transfer



Radiative energy transfer: distance Radiative energy transfer: distance dependencedependence



Radiative energy transfer: efficiencyRadiative energy transfer: efficiency



FFörster mechanism from Fermi “Golden örster mechanism from Fermi “Golden rule”rule”



Coulombic or dipole-dipole interaction Coulombic or dipole-dipole interaction (F(Föörster energy transfer)rster energy transfer)



FFörster formulation of the dipole-dipole örster formulation of the dipole-dipole energy transferenergy transfer



Level diagrams for energy stransferLevel diagrams for energy stransfer Förster mechanism

Dexter mechanism



Electronic exchange energy transfer: Electronic exchange energy transfer: Dexter mechanismDexter mechanism



Applications of energy transfer Applications of energy transfer



Orientation factorOrientation factor



How to measure energy transferHow to measure energy transfer



Energetics of the electron transfer Energetics of the electron transfer processprocess



Classical theory of electron transferClassical theory of electron transfer



Marcus formulationMarcus formulation



Normal and inverted regionsNormal and inverted regions



Marcus rate plotMarcus rate plot



Reorganization energyReorganization energy



Solvent reorganization energy Solvent reorganization energy (examples)(examples)

Quite a substantial energy!



Adiabatic and non-adiabatic Adiabatic and non-adiabatic processesprocesses



Quantum mechanical theoryQuantum mechanical theory



Quantum theory - 2Quantum theory - 2



Comparison of quantum and classical Comparison of quantum and classical theoriestheories



Electronic coupling and maximum ET Electronic coupling and maximum ET raterate



Distance dependence of the ET rateDistance dependence of the ET rate



Effect of solvent dynamicsEffect of solvent dynamics



Photoinduced charge separation and Photoinduced charge separation and charge recombinationcharge recombination

U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat1 Chimica Fisica dei Materiali Avanzati Part...

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