Charge mobility of discotic mesophases: a multiscale quantum/

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1 Charge mobility of discotic mesophases: a multiscale quantum/classical study Max Planck Institute for Polymer esearch LEA meeting Fundamental and Applied Macromolecular Science: Toward ext Generation Materials January 2007, Strasbourg, France The pdf file of this presentation is available here

2 Organic electronics Function-adjasted material properties Field-effect transistors high electron/hole mobilities (ordered morphology) Light-emmiting diodes high charge mobilities efficient photon absorption large recombination area (disordered morphology) Solar cells high electron/hole mobilities small recombination efficient percolation of charges (ordered morphology) Structure Morphology Properties

3 Existing problems How can theory/simulations be useful? Morphology: coarse-grained MD, MC, SCF Self-organization: MC, MD, SCF Charge transport: Markus-Hush formalism, Green functions, KMC, DFT Excited states: TDDFT, CI Can we predict material properties prior to synthesis of compounds?

4 Discotic liquid crystals Triphenylenes, hexabenzocoronenes, phthalocyanines... Properties Easy to process Self-organize into columnar structures One-dimensional transport of charges along columns (µ 0.5cm 2 /V sec) Self-healing upon heating Actively studied for use in solar cells and OFETs H H A. M. van de Graats et al, Advanced Materials 1999 L. Schmidt-Mende et al, Science 2001 H. J. äder et. al. at. Mat M. Van der Auweraer, F. C. De Schryver at. Mat. 2006

5 Studied systems Derivatives of hexabenzocoronenes C12 PhC12 h d a C10-6 b c Experimental data S d, nm h, nm C C C PhC I. Fischbach et al J. Phys. Chem. B (2002) A. Fechtenkotter et al Angew. Chem. (1999) S. P. Brown, I. Schnell et al J. Am. Chem. Soc. (1999) P. Herwig et al Adv. Mater. (1996)

6 Atomistic molecular dynamics Development of the force-field Quantum chemistry calculations. Matching calorimetric, X-ray scattering, and M data. Potential energy Atom types U = X 1 2 K b (r r 0 ) 2 + bonds X 1 2 K θ (θ θ 0 ) 2 + angles X 3X» Vn dihedrals n= ( 1) n+1 cos nφ + X K d (ψ ψ 0 ) 2 + impropers " (! X X 12 1 q i q j σ ij + 4ǫ ij σ! 6 )# ij 4πǫǫ i j>i 0 r ij r ij r ij C1 C2 CA CP CH H CB C3 A. von Lilienfeld and D. Andrienko J. Chem. Phys (2005) D. Andrienko et al J. Chem. Phys. (2006)

7 Atomistic molecular dynamics MD simulations of HBC derivatives C10 C12 C14 C16 C10-6 Ph-C12 system S d, nm h, nm C C C C C PhC g xy g xy 20 D Andrienko, V Marcon, K Kremer 10 J Chem Phys (2006) r (nm) r (nm)

8 Charge mobility Master equation approach Master equation P i t = j [ω ij P j (1 P i ) ω ji P i (1 P j )] Mobility r i ω ji ω ij i v = ij ω ji P i (1 P j )(r j r i ) r j j v = µe P i - probability of a charge to be on a site i ω ij - hopping rate from site j to site i Yu et al Phys. ev. Lett. (2000) B. Derrida J. Stat. Phys. (1983)

9 Charge mobility KMC simulations of time-of-flight experiments TOF KMC simulation geometry 10V + injection E MD snapshot 1 µm inject a charge pick a neighboring site j at random, weighting by its rate ω ij advance waiting time by t i = P log ξ, where ξ is a random j=0 ω ij number. J elson and Chandler Coord. Chem. eviews (2004)

10 Marcus-Hush formalism Marcus rates Marcus expression for charge transfer rates ] ω ij = J 2 π [ λkt exp ( G λ)2 4λkT J - transfer integral G = E r - free energy difference between initial and final states λ - reorganization energy Kirkpatrick et al in preparation (2006) K. F. Freed and J. Jortner J. Chem Phys. (1970) Geometry optimization UB3LYP, 6-31g** basis set. HOMO splitting or a monomer electron density - ZIDOS

11 Histograms of the transport integral Histograms of the transport integral 150 C 12 counts Ph-C 12 C log 10 (J / ev) 2 Hystograms of log 10 ( J 2 /ev 2) MD snapshots of C 12 and C 10 6 derivatives.

12 Histograms of the transport integral Time of Flight simulations 1 Photocurrent C 12 Ph-C 12 C e-10 1e-09 1e-08 1e-07 1e-06 time (sec) Photocurrent transients (holes only) t tr U = 10 Volt d = 1 µm average over 200 MD snapshots average over 1000 transients per snapshot

13 Mobility KMC, ME, and experimental (P-TMC) mobilities mobility (cm 2 / V sec) P-TMC TOF ME Electron (e) and hole (h) mobilities. compound µ exp µ e ToF µ h ToF µ e ME µ h ME C C C C C e PhC C 10 C 12 C 14 C 16 C 10-6 PhC 12 J. Kirkpatrick, V. Marcon, J. elson, K. Kremer, D. Andrienko cond-mat/

14 Conclusions Molecular disorder decreases charge mobility Presence of [static] defects kills 1D charge transport Temperature dependence of the mobility agrees well with the experiments Message to take home It is possible to predict not only trends, but also values of mobilities. This can be done without fitting parameters, starting only from molecular structures.

15 Collaborations and financial support Collaborators Valentina Marcon, Thorsten Vehoff, Kurt Kremer (MPIP Mainz) James Kirkpatrick and Jenny elson (Imperial College London) Anatole von Lilienfeld-Toal and Mark Tuckerman (ew York University) umerous discussions with the members the group of Prof. Müllen. Financial support DFG (German-Korean ITG program) Alexander von Humboldt foundation MMM initiative