Exciton migration in conjugated polymers; the
influence of positional and energetic disorder
Theodoros Papadopoulos
Department of Physics, University of Bath, U.K.
QuantSim09
Outline
• We present a platform which combines MD
simulations, quantum chemical calculations and MC
modelling to extract exciton diffusion dynamics.
• Our aim is to demonstrate how positional and
orientational disorder does not affect the ability of
excitons to diffuse.
• On the other hand, when energetic disorder becomes
dominant, a significant decrease on the exciton
diffusion length is observed.
The system studied
We use indenofluorene trimers (IF3)
• IF oligomers are blue emitters
• They are very well characterised experimentally
• Promising for optoelectronic device applications
Theoretical approach
• We use Molecular Dynamics to extract
realistic morphologies (NAMD, CHARMM)
• Exciton transfer rates are then extracted using
an improved Förster approach:
•The electronic coupling between chromophores is: Vij 
•The hopping rate between donor and acceptor is:
1
4 
 (m)  j (n)

rmn
m n
kij  a | Vij |2 J ij
where ri(m) is the transition density of each chromophore
(INDO/CCSD level), Jij the spectral overlap, m,n the atom sites and
i,j the chromophore sites.
Theoretical approach
• We use Monte Carlo modeling to follow the
time evolution of the energy transfer
1
ln( X )
– a waiting time is calculated for each possible event:
kij
Where X is a random number uniformly distributed between 0 and 1.
 ij 
• Finally diffusion dynamics are extracted
 x 2  y 2  z 2
– the diffusion length for each trial will be: Ltrial
d
– Finally we will have:
Ld   Ltrial
d 
where Dx, Dy, Dz is the spatial difference between the initial and final
point on the exciton trajectory.
The morphology used
300K
400K
z
500K
Electronic coupling
The electronic coupling is decreasing as a function of T
| Vij | as a function of q
2
Spectral overlap
The spectral overlap is found to be increasing as a
function of T.
Hopping rate & Diffusion length
Ld stays constant as T increases due to the cancelling
effect of the decrease in |Vij|2 and the increase in Jij as a
function of temperature.
Förster radius
Calculating the Förster radius as a function of temperature,
also seems to be independent of T, staying consistent with
our results on the diffusion length.
R
kij    0
R
 ij




6
1
 slope  6
R0  

  
Energetic disorder
Energetic disorder is introduced through a random rigid shift on the
chromophore spectra. Hence a randomly chosen spectral overlap is
taken for each hopping rate between donor and acceptor which
depend on the width s of a Gaussian distribution.
pli
plj
abni
2
i
kij  f [ Vij , J ( pli , abn j )]
j
k ji  f [ V ji , J ( pl j , abni )]
abnj
2
Influence on diffusion length
Each random shift is chosen for each chromophore from a
Gaussian distribution of width s centred on m=0.0eV.
Transport anisotropy
The direction of alignment of the trimers at 300K is
taken as the z-axis (parallel direction). The xy plane
is the perpendicular plane.
Diffusion length Ld
When the smectic phase on the morphology is still valid, we
observe that the diffusion length is greater along the z-axis.
As T is increased the morphology becomes isotropic.
Conclusions
• In this work we have studied the influence of morphology
on exciton dymanics.
• We have looked at the temperature dependence of exciton
diffusion and found that the diffusion length does not
depend on T.
• Positional disorder doesn’t seem to have an effect on the
diffusion length, showing that temperature is not a
limitation to exciton diffusion dynamics.
• The influence of energetic disorder on such polymer
systems plays a more crucial role than positional disorder in
the design of effective light emitting devices.
Acknowledgements
•
•
•
•
•
Luca Muccioli (Bologna)
Stavros Athanasopoulos (Mons)
Claudio Zannoni (Bologna)
David Beljonne (Mons)
Alison Walker (Bath)
Thank you!