Computational Design of Materials for
Organic Photovoltaics
Jarvist Moore Frost, Sam Foster, James Kirkpatrick,
Thomas Kirchartz, Jenny Nelson
Imperial College London
[email protected]
Originally: MRS Boston Fall 2012 – O8.08
Wednesday 28th November
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Tight Binding - The Hückel Method
[[ S J 0. 0. ]
[ J S J 0. ]
[ 0. J S J ]
[ 0. 0. J S ]]
H =
Hamiltonian very easy to solve
Parameters semi-empirical (can derive from DFT)
Can treat extremely large systems
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(Boon Kar, 2008)
High Mobility Polyfluorine
& the β-phase
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PF8 Proposed Structures
Grell et al. (Macromolecules 1999, 32, 5810-5817)
Chen et al. (Macromolecules 2004, 37, 6833-6838)
Planar Zig-Zag
[2,1 Helix]
Complex Unit Cell
[Longer Helix]
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Polyfluorene Copolymers
F5
F8
Sumitomo
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Transition Time for Backbone Movements
(extracted from MD oligomer simulation, PF8)
Transfer Integrals: PF8 vs. PF5:8
F8-F8-F8-F8
F8-F5-F8-F5
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Predicted Mobility in PF8 vs. PF5:8
cm2 / Vs
Simulated Hole Mobilities
Simulated Tetramer Densities
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Processing magic → di-octyl Polyfluorene can be persuaded to have high mobilities
Samples are glassy
Induction of the Beta-phase strongly reduces mobility
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β-Phase
α-Phase
HOMO Spin Density B3LYP/6-31g*
"Formation of the β-phase effectively
corresponds to crystallization in one
dimension, a remarkably uncommon
phenomenon in nature."
http://pubs.acs.org/doi/pdfplus/10.1021/nl071207u
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0
1
2
3
4
5
6
7
eV
In Vacuum, Beta Phase structures are strained
But at accessible energies
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Need larger systems for representative DoS
→ Python TightBinding
http://www.physics.rutgers.edu/pythtb/
Hybrid DFT on Octamers
(B3LYP/6-31g* & tuned BNL/6-31g*)
- get some trap formation (up to 140 meV)
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50meV Gaussian Site Energy Disorder
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Beta Phase Energetic Trap
(5 sites)
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Beta Phase Energetic Trap
(10 sites)
For Wide Enough trap ~10 sites (no confinement),
Trap depth = site Energy change
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P3HT–like polymer (normally flat)
A pproxim ate torsional distribution as norm al distribution
C onsider beta phase to be sm all pockets of flat regions
– (i.e. J is m axim ised is these regions to J0)
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Disordered (torsionally)
But FLAT (minima) polymer
70meV
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Polyfluorene–like polymer (Helix / twisted rod)
●
Approximate torsional distribution as normal distribution
(around 45 degree minima)
●
Consider beta phase to be small pockets of flat regions of
polymer
– (i.e. J is maximised is these regions to J0)
Conclusions
• In polymers, Torsion is important
– In P3HT, torsion suffcient to describe DoS
– In PFO, natural background twist makes
extended regions (Beta phase) deep traps
– Traps are not always what one imagines
(and be careful what you wish for)
Even (or especially?) 1930s electronic-structure
techniques can offer useful insights