and we apply an effective medium approximation (I.I. Fishchuk et al. PRB, 2003) EpEp Triplet Exciton Diffusion in Conjugated Polymers II – The Effects of Geometric Relaxation and Energetic Disorder Ivan I. Fishchuk, 1 Andrey. Kadashchuk, 2,3 Lekshmi Sudha Devi, 4 Paul Heremans, 2 Heinz Bässler, 5 Anna Köhler 4 1 Institute of Nuclear Research, National Academy of Sciences of Ukraine, Prospect Nauky 47, Kyiv, Ukraine 2 IMEC v.z.w., SOLO-PME, Kapeldreef 75, B-3001 Leuven, Belgium 3 Institute of Physics, National Academy of Sciences of Ukraine, Prospect Nauky 46, Kyiv, Ukraine 4 Department of Physics, University of Bayreuth, D Bayreuth, Germany 5 Department of Chemistry, Philipps-Universität Marburg, Hans-Meerwein-Strasse, D Marburg, Germany 1 Triplet diffusion 2 Polaronic and disorder effects 3. Our theoretical approach to triplet transfer Above T T, the transfer involves multi-phonon assisted hopping and can be described by the Marcus electron transfer theory Below T T, the transfer occurs by single phonon assisted hopping (tunneling) and can be described by the Miller- Abraham formalism. We use Holstein small polaron theory, modified by Emin for non-adiabatic transport of charges (D. Emin, Adv. Phys., 1975) and apply it to triplets. We then employ an effective medium approach (EMA), to allow for comparison with experimental data (I.I. Fishchuk et al. PRB, 2003). Marcus – type expression Miller-Abrahams - type expression There are also differences between charge and triplet transport. The density of states (DOS) of charges is wide while the DOS of triplets is narrow. This is because triplet excitons are neutral and small, so their energy is affected little by variations in the surrounding polarization or in the molecular conformation. Triplet diffusion allows us to experimentally probe charge transfer in the low-disorder regime. Here, the relative contributions of polaronic and disorder effects on Dexter transfer are studied theoretically. With increasing disorder, the tunneling regime acquires a temperature dependence and the Arrhenius-type hopping regime changes to a non- Arrhenius behaviour. A * + B → A + B * The migration of a triplet exciton is governed by the transfer of two charges. Therefore, triplet transfer can be described using charge transport models. Charge transport, and therefore also triplet transfer, is determined by two parameters, (i) the lattice relaxation associated with the charge transfer, i.e. the reorganization energy (ii) the energetic disorder, characterized by the variance of DOS,   Polaron binding energy E p   Polaronic transport, e.g. Marcus theory Disorder transport: Gaussian DOS and Miller-Abrahams hopping 4. Results Energy Emin‘s expression in the high temperature limit: Emin‘s expression in the low temperature limit: E a = /4 activation energy for triplet transfer J 0 = coupling integral L= effective triplet localization radius a= average neigbouring site distance Since we consider triplet motion, some parameters take on a different interpretation, such as electronic coupling EMA  = average jump frequency temperature activation The figure shows how the triplet transfer rate depends on the relative weight of energetic disorder  and geometric reorganization energy. The figure shows the the triplet transfer rate of the Pt-polymer along with fits from the two expressions Energy Q Increasing disorder For  ≥ /13, the transition between the hopping and tunneling regime can no longer be distinguished D A Hopping and tunneling in the non-adiabatic case Phys. Rev. B in press