Energy relaxation dynamics and universal scaling laws in organic light emitting diodes

Electron-hole (e-h) capture in luminescent conjugated polymers (LCPs) is modeled by the dissipative dynamics of a multilevel electronic system coupled to a phonon bath. Electroinjected e-h pairs are simulated by a mixed quantum state, which relaxes via phonon-driven internal conversions to low-lying charge-transfer (CT) and excitonic (XT) states. The underlying two-band polymer model reflects PPV and spans monoexcited configuration interaction singlets (S) and triplets (T), coupled to Franck-Condon active C=C stretches and ring-torsions. Focusing entirely upon long PPV chains, we consider the recombination kinetics of an initially separated CT pair. Our model calculations indicated that S and T recombination proceeds according to a branched, two-step mechanism dictated by near e-h symmetry. The initial relaxation occurs rapidly with nearly half of the population going into excitons ($S_{XT}$ or $T_{XT}$), while the remaining portion remains locked in metastable CT states. While formation rates of $S_{CT}$ and $T_{CT}$ are nearly equal, $S_{XT}$ is formed about twice as fast $T_{XT}$ in concurrence with experimental observations of these systems. Furthermore, breaking e-h symmetry suppresses the XT to CT branching ratio for triplets and opens a slow CT$\to$ XT conversion channel exclusively for singlets due to dipole-dipole interactions between geminate and non-geminate configurations. Finally, our calculations yield a remarkable linear relation between chain length and singlet/triplet branching ratio which can be explained in terms of the binding energies of the respective final excitonic states and the scaling of singlet-triplet energy gap with chain length.Comment: For IJQC-Sanibel Quantum Chemistry Symposium, 200

Theory of the singlet exciton yield in light-emitting polymers

This paper presents a possible explanation for the enhanced singlet exciton yield in light emitting polymers. We propose a theory of electron-hole recombination via inter-molecular inter-conversion from inter-molecular weakly bound polaron pairs (or charge-transfer excitons) to intra-molecular excitons. This theory is applicable to parallel polymer chains. A crucial aspect of the theory is that both the intra-molecular and inter-molecular excitons are effective-particles, which are described by both a relative-particle wavefunction and a center-of-mass wavefunction. This implies two electronic selection rules. (1) The parity of the relative-particle wavefunction implies that inter-conversion occurs from the even parity inter-molecular charge-transfer excitons to the strongly bound intra-molecular excitons. (2) The orthonormality of the center-of-mass wavefunctions ensures that inter-conversion occurs from the charge-transfer excitons to the lowest branch of the strongly bound exciton families, and not to higher lying members of these families. The inter-conversion is then predominately a multi-phonon process, determined by the Franck-Condon factors. These factors are exponentially smaller for the triplet manifold than the singlet manifold because of the large exchange energy.Comment: To appear in Physical Review B, vol 70, 15 Oct 200

Multiphonon emission model of spin-dependent exciton formation in organic semiconductors

The maximum efficiency in organic light-emitting diodes (OLEDs) depends on the ratio, $r=k_S/k_T$, where $k_S$ ($k_T$) is the singlet (triplet) exciton formation rate. Several recent experiments found that r increases with increasing oligomer length from a value $r \approx 1$ in monomers and short oligomers. Here, we model exciton formation as a multi-phonon emission process. Our model is based on two assertions: (i) More phonons are emitted in triplet formation than in singlet formation. (ii) The Huang-Rhys parameter for this phonon emission is smaller in long oligomers than in short ones. We justify these assertions based on recent experimental and theoretical data.Comment: 8 pages, 7 figure

Spin-dependent electron-hole capture kinetics in conjugated polymers

The recombination of electron-hole pairs injected in extended conjugated systems is modeled as a multi-pathway vibron-driven relaxation in monoexcited state-space. The computed triplet-to-singlet ratio of exciton formation times $r = \tau_T/\tau_S$ increases from 0.9 for a model dimer to 2.5 for a 32-unit chain, in excellent agreement with experiments. Therewith we rationalize recombination efficiency in terms of spin-dependent interstate vibronic coupling and spin- and conjugation-length-dependent exciton binding energies.Our model calculations for various length polymers indicate that the ratio of the singlet to triplet formation ratios, $r = \sigma_S/\sigma_T$, is inversely related to the ratio of the singlet and triplet binding energies, $\epsilon^b_S/\epsilon^b_T$

Exciton Dissociation Dynamics in Model Donor-Acceptor Polymer Heterojunctions: I. Energetics and Spectra

In this paper we consider the essential electronic excited states in parallel chains of semiconducting polymers that are currently being explored for photovoltaic and light-emitting diode applications. In particular, we focus upon various type II donor-acceptor heterojunctions and explore the relation between the exciton binding energy to the band off-set in determining the device characteristic of a particular type II heterojunction material. As a general rule, when the exciton binding energy is greater than the band off-set at the heterojunction, the exciton will remain the lowest energy excited state and the junction will make an efficient light-emitting diode. On the other hand, if the off-set is greater than the exciton binding energy, either the electron or hole can be transferred from one chain to the other. Here we use a two-band exciton to predict the vibronic absorption and emission spectra of model polymer heterojunctions. Our results underscore the role of vibrational relaxation and suggest that intersystem crossings may play some part in the formation of charge-transfer states following photoexcitation in certain cases

Isotopic Effect and Temperature Dependent Intramolecular Excitation Energy Transfer in a Model Donor-Acceptor Dyad

We consider here the non-adiabatic energy transfer dynamics for a model bi-chromophore system consisting of a perylenediimide unit linked to a ladder-type poly-(para-phenylene) oligomer. Starting from a semi-empirical parameterization of a model electron/phonon Hamiltonian, we compute the golden-rule rate for energy transfer from the LPPP5 donor to the PDI acceptor. Our results indicate that the non-adiabatic transfer is promoted by the out-of-plane wagging modes of the C-H bonds even though theses modes give little or no contribution to the Franck Condon factors in this system. We also predict a kinetic isotope effect of $k^{(H)}/k^{(D)} = 1.7 - 2.5$ depending upon the temperature

Photoswitching of Redox Potentials and Spectroscopic Properties in the UV/vis Region

The photoswitching of optical and electrochemical properties of di-donor, di-acceptor and donor-acceptor substituted photochromic tetrahydropyrene -[2,2]metacyclophanene and dihydropyrene -[2,2]metacyclophanediene systems has been studied theoretically. A switching of the halfwave oxidation and reduction potentials should be possible in the case of bis(pyridinium) and bis(hydroxyphenyl) substituted systems. Because of the relatively great perturbation of the planarity of the π-electron systems by large torsion of the substituents out of the π-electron structure of the photochromic system and the stair-like structure of the ring-opened isomer, relatively large excitation energies for CT transitions have been calculated with the AM1-CI procedure. The ring-closed structures should absorb in the visible spectral region, and the open-ring isomers should have a longestwavelength absorption in the UV region

Electronic and optical properties of families of polycyclic aromatic hydrocarbons: a systematic (time-dependent) density functional theory study

Homologous classes of Polycyclic Aromatic Hydrocarbons (PAHs) in their crystalline state are among the most promising materials for organic opto-electronics. Following previous works on oligoacenes we present a systematic comparative study of the electronic, optical, and transport properties of oligoacenes, phenacenes, circumacenes, and oligorylenes. Using density functional theory (DFT) and time-dependent DFT we computed: (i) electron affinities and first ionization energies; (ii) quasiparticle correction to the highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gap; (iii) molecular reorganization energies; (iv) electronic absorption spectra of neutral and $\pm1$ charged systems. The excitonic effects are estimated by comparing the optical gap and the quasiparticle corrected HOMO-LUMO energy gap. For each molecular property computed, general trends as a function of molecular size and charge state are discussed. Overall, we find that circumacenes have the best transport properties, displaying a steeper decrease of the molecular reorganization energy at increasing sizes, while oligorylenes are much more efficient in absorbing low-energy photons in comparison to the other classes.Comment: 26 pages, 9 figures, 4 tables, accepted for pubblication in Chemical Physics (14/04/2011