Laurea specialistica in Scienza e Ingegneria dei Materiali

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1 Laurea specialistica in Scienza e Ingegneria dei Materiali
Curriculum Scienza dei Materiali Chimica Fisica dei Materiali Avanzati Part 7b – Photophysics and photochemistry of molecular materials (excitons, energy transfer and electron transfer) Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

2 Exciton 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). Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

3 Exciton 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 Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

4 Exciton model: excited state wavefunctions
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) Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

5 Exciton model: excited state energies
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6 Parallel transition dipoles
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7 In-line dipoles Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

8 Exciton in asymmetric dimer
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: and compete for the exciton delocalization: the first favors, the second opposes it. Corso CFMA. LS-SIMat

9 Main mechanisms of energy transfer
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10 Radiative electronic energy transfer
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11 Radiative energy transfer: distance dependence
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12 Radiative energy transfer: efficiency
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13 Förster mechanism from Fermi “Golden rule”
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14 Coulombic or dipole-dipole interaction (Förster energy transfer)
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15 Förster formulation of the dipole-dipole energy transfer
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16 Level diagrams for energy stransfer
Förster mechanism Dexter mechanism Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

17 Electronic exchange energy transfer: Dexter mechanism
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18 Applications of energy transfer
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19 Orientation factor Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

20 How to measure energy transfer
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21 Energetics of the electron transfer process
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22 Classical theory of electron transfer
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23 Marcus formulation Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

24 Normal and inverted regions
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25 Marcus rate plot Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

26 Reorganization energy
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27 Solvent reorganization energy (examples)
Quite a substantial energy! Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

28 Adiabatic and non-adiabatic processes
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29 Quantum mechanical theory
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30 Quantum theory - 2 Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

31 Comparison of quantum and classical theories
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32 Electronic coupling and maximum ET rate
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33 Distance dependence of the ET rate
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34 Effect of solvent dynamics
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35 Photoinduced charge separation and charge recombination
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