and we apply an effective medium approximation (I.I. Fishchuk et al. PRB, 2003)

1. Triplet Exciton Diffusion in Conjugated Polymers II – The Effects of Geometric Relaxation and Energetic Disorder Ivan I. Fishchuk,1 Andrey. Kadashchuk,2,3Lekshmi Sudha Devi,4Paul Heremans,2 Heinz Bässler,5Anna Köhler 4 1Institute of Nuclear Research, National Academy of Sciences of Ukraine, Prospect Nauky 47, 03680 Kyiv, Ukraine 2IMEC v.z.w., SOLO-PME, Kapeldreef 75, B-3001 Leuven, Belgium 3 Institute of Physics, National Academy of Sciences of Ukraine, Prospect Nauky 46, 03680 Kyiv, Ukraine 4 Department of Physics, University of Bayreuth, D-95440 Bayreuth, Germany 5 Department of Chemistry, Philipps-Universität Marburg, Hans-Meerwein-Strasse, D-35032 Marburg, Germany Phys. Rev. B in press 1 Triplet diffusion Ep 2 Polaronic and disorder effects 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. l/2 = Polaron binding energy Ep Energy 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 l (ii) the energetic disorder, characterized by the variance of DOS, s. Polaronic transport, e.g. Marcus theory 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. s Energy s Disorder transport:Gaussian DOS andMiller-Abrahams hopping 3. Our theoretical approach to triplet transfer and we apply an effective medium approximation (I.I. Fishchuk et al. PRB, 2003) 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) . Emin‘s expression in the high temperature limit: Marcus – type expression EMA Emin‘s expression in the low temperature limit: Miller-Abrahams - type expression electronic coupling temperature activation Since we consider triplet motion, some parameters take on a different interpretation, such as L= effective triplet localization radius a= average neigbouring site distance Ea=l/4 activation energy for triplet transfer J0= coupling integral n0= average jump frequency 4. Results Increasing disorder A D Energy Hopping and tunneling in the non-adiabatic case Q The figure shows the the triplet transfer rate of the Pt-polymer along with fits from the two expressions The figure shows how the triplet transfer rate depends on the relative weight of energetic disorder s and geometric reorganization energy l. With increasing disorder, the tunneling regime acquires a temperature dependence and the Arrhenius-type hopping regime changes to a non-Arrhenius behaviour. Above TT, the transfer involves multi-phonon assisted hopping and can be described by the Marcus electron transfer theory Below TT, the transfer occurs by single phonon assisted hopping (tunneling) and can be described by the Miller-Abraham formalism. For s ≥ /13, the transition between the hopping and tunneling regime can no longer be distinguished