dynamics of excitons in thin-film aggregates of cyanine dyessaykin/presentations/jaggregates... ·...
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Dynamics of excitons in thin-film aggregates of cyanine dyes
Semion K. Saikin
Orlando, April 19, 2012
Department of Chemistry and Chemical Biology Harvard University
Molecular aggregates
Bulovic group, MIT
Thin-film J-aggregates
Bradley, M., et. al., Adv. Mat., 17, 1881 (2005)
• Few molecular layers • Self-assembly • Room temperature • Spatial order on the scale of 100 nm
Deposition generalizes to many sulfopropyl dyes Thin film cyanine dye J-aggregates
Brian Walker Bawendi group, MIT
• Spectra can be tuned by changing the dye
Molecular aggregates
Biomimicry:
Photosynthesis in green sulfur bacteria
Photonic devices: Photosensitization:
Strong exciton-photon coupling in organic cavities
Fluorescence enhancement from DCM molecules on a J-aggregate film
Intermolecular resonance coupling
ij ji rr
eH
2
0
Coulomb4
1
2
1
Förster interactions
monomer J-aggregates H-aggregates
E. E. Jelly, Nature 138, 1009 (1936) G. Scheibe, Angew. Chem. 49, 563 (1936)
molecule1 molecule2
Singlet excitons in aggregates
• Lattice structure is not well characterized • Transport properties are measured indirectly • Transport regime is hard to model quantum mechanically
• Frenkel excitons delocalized over tens of molecules • Large diffusion length (up to 100 nm at room T) • Signatures of wave-like exciton propagation
Existing claims:
Concerns:
• ab-initio computation of molecular and lattice properties • Phenomenological parameters fitted to experiments • Exciton dynamics is quantum • extraction of transport parameters
Our approach:
Dynamics model
~ 100 nm
• Monte-Carlo time propagation of exciton wave function on a lattice
• Haken-Reneker-Strobl model for coupling to the environment
• Phenomenological parameters: thermal noise, lattice imperfections
- static disorder, Gaussian distribution of transition frequencies
- dynamic disorder, white noise with the dephasing rate Г
2 3 4 5 6 70
50
100
150
200
TC
TDBC
U3
oscila
lto
r str
en
gth
de
nsity (
eV
-1)
energy (eV)
Intra-molecular excitations LUMO
HOMO
> 98% HOMO LUMO
• Hybrid functional PBE0 • Triple- basis set • Polarizable environment - COSMO
Förster coupling
X
Y
• 2D map of the Forster interaction computed ab-inito and fitted with an extended dipole model + -
+ - q l
V. Czikklely, H. D. Forsterling, H. Kuhn, Chem. Phys. Lett. 6 , 207, (1970)
Molecular monolayer
J-band shift
Ly
Lx
Brickstone model
• Ly is varied • Lx is fixed = length of the molecule + 2*VdW radii
Fitting lattice structure to J-band shift
D. Möbius and H. Kuhn, J. Appl. Phys. 64, 5138 (1988)
TDBC - DOS
Static disorder 70 meV
‘Diffusion band’ different from J-band
Different maximum in each direction
Exciton dynamics
Initial conditions
Exciton population dynamics
20 30 40 50 60 70 80 90 100 1100
1
2
3
4
5
TDBC Dxx
TDBC Dyy
TC Dxx
TC Dyy
diffu
sio
n c
oe
ffic
ien
t (A
2/p
s)
dephasing rate (meV)
Dephasing dependence
Static disorder 100 meV
Diffusion coefficient in 2D TDBC film from exciton-exciton annihilation Akselrod, et. al. PRB 82, 113106 (2010)
J-aggregate in cavity
A simple model
J-band Cavity mode
Site - cavity coupling ~0.1 meV
Cavity mode decay
-0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00
oscill
ato
r str
ength
(a.u
.)
frequency shift (eV)
J-aggregate in cavity
J-band polaritons
0 10 20 30 40 50 60 70 80 90 1000
1000
2000
3000
4000
5000
6000
7000
no cavity
cavity
second m
om
ent
MX
X
2 (
A2)
time (fs)
Diffusion
Change in the diffusion constant is about 3% only
Conclusions
• Ab-initio molecular properties
• Haken - Reineker – Strobl model for noise
• Monte Carlo wave function exciton transport
• Model can be extended to device structures
• Computed transport coefficients are comparable to experimental results
Concerns: • Need more data on lattice structure
• Need temperature dependences
• Need direct measurements of exciton diffusion
S. Valleau, S. K. Saikin, M.-H. Yung , A. Aspuru Guzik, arXiv:1202.5712
Acknowledgements
Alex Eisfeld MPI, Dresden; also @ Harvard
Gleb Akselrod Bulovič group
Dylan Arias Dorthe Eisele Nelson group
Stephanie Valleau Harvard
Man-Hong Yung Harvard
Alan Aspuru-Guzik Harvard
Brian Walker Bawendi group (now at Oxford)
MIT guys
System initialization • J-aggregate Hamiltonian • Initial state
)0(
Excitation dynamics
Monte Carlo propagation of the wave function A
vera
ge o
ver
an e
nse
mb
le
Unitary propagation
)()(~
tedtt dtHi
Random choice
Scattering
)()( tSt
Intermolecular resonance coupling
ij ji rr
eH
2
0
Coulomb4
1
2
1
k k’
m m’
M1 M2
M1 M2
molecule1 molecule2
Förster and Dexter interactions
molecule1 molecule2
k k’
m m’
M1
M2 M1
M2
More molecules Three 2-level molecules, site basis
X(1)
X(2)
X(3)
X(0) 000
100 010 001
110101
011
111
Coherent Forster coupling
Coherent interactions with optical fields
Optical relaxation is along the same paths
Coupling regimes
Weak: V << G
• Excitons jumps incoherently between molecules
• Environment thermalizes excitons on single molecules
g
e
absorption emission
g
e
V
G
vibrational relaxation
G
X
absorption emission
Strong: V >> G
• Molecular excitations form bands – coherent coupling between sites
• Coupling to the environment enters as thermalization between bands
Intermediate coupling, V G
g
e
g
e
V
G
• Molecules are coupled coherently • Coupling to the environment enters as frequency diffusion • Excitons are NOT thermalized
G
Coupling regimes
20 30 40 50 60 70 80 90 100 1100
1
2
3
4
TDBC Dxx
TDBC Dyy
TC Dxx
TC Dyy
diffu
sio
n c
oe
ffic
ien
t, 1
04 (
A2/p
s)
site disorder (meV)
Exciton population dynamics
Disorder dependence
Dynamic disorder 50 meV