dynamics of excitons in thin-film aggregates of cyanine dyessaykin/presentations/jaggregates... ·...

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

TDBC

U3

TC

Molecules

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)

J-band Initial site

Exciton dynamics

Initial conditions

Exciton population dynamics

Exciton dynamics

Coherences

• Coherence = two-sites one-time correlation functions

Static disorder 70 meV

Dynamic disorder 30 meV

Exciton coherence dynamics


Ballistic and diffusive transport

ballistic (≈ t2)

diffusive (≈ t)

TDBC - DOS


‘Diffusion band’ different from J-band

Different maximum in each direction

Exciton dynamics

Initial conditions


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


Diffusion coefficient in 2D TDBC film from exciton-exciton annihilation Akselrod, et. al. PRB 82, 113106 (2010)


2D maps of diffusion constants

• Dxx TDBC

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

http://arxiv.org/abs/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

Thank you for your attention!

Defense Threat Reduction Agency

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

Molecular monolayer

J-band shift

Convergence

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

Molecular monolayer

Coupling strength

Dexter contribution is small

-20 meV

-70 meV

+55 meV

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

Exciton dynamics

Static disorder 70 meV Dynamic disorder 30 meV

Population transfer between dyes

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)


Disorder dependence

Dynamic disorder 50 meV

0 20 40 60 80 100

0.8

1.2

1.6

jump

HRS

se

co

nd

mo

me

nt

M2 1

04 (

A2)

static disorder (meV)

HRS vs jump model

dynamics of excitons in thin-film aggregates of cyanine dyessaykin/presentations/jaggregates... ·...

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