PFO Tight Binding / Beta Phase

Based on part of a talk as delivered to MRS Boston December 2012

Transcript

1. Computational Design of Materials for Organic Photovoltaics Jarvist Moore Frost, Sam Foster, James Kirkpatrick, Thomas Kirchartz, Jenny Nelson Imperial College London jarvist.frost@imperial.ac.uk Originally: MRS Boston Fall 2012 – O8.08 Wednesday 28th November
2. 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
3. (Boon Kar, 2008) High Mobility Polyfluorine & the β-phase
4. 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]
5. Polyfluorene Copolymers F5 F8 Sumitomo
7. Transition Time for Backbone Movements (extracted from MD oligomer simulation, PF8)
9. MD Representation → Stiff QM Representation (via Votca) Polyfluorene Tetramer Simulation 250 tetramers – 3.5ns
10. Transfer Integrals: PF8 vs. PF5:8 F8-F8-F8-F8 F8-F5-F8-F5
11. Predicted Mobility in PF8 vs. PF5:8 cm2 / Vs Simulated Hole Mobilities Simulated Tetramer Densities
12. Processing magic → di-octyl Polyfluorene can be persuaded to have high mobilities Samples are glassy Induction of the Beta-phase strongly reduces mobility
13. 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
14. 0 1 2 3 4 5 6 7 eV In Vacuum, Beta Phase structures are strained But at accessible energies
15. 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)
17. 50meV Gaussian Site Energy Disorder
18. Beta Phase Energetic Trap (5 sites)
19. Beta Phase Energetic Trap (10 sites) For Wide Enough trap ~10 sites (no confinement), Trap depth = site Energy change
20. 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)
21. Disordered (torsionally) But FLAT (minima) polymer 70meV
22. 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)
23. Disordered (torsionally) TWISTED (~PFO) polymer 596meV
24. 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