Exciton Transfer Integrals Between Polymer Chains

The line-dipole approximation for the evaluation of the exciton transfer integral, $J$, between conjugated polymer chains is rigorously justified. Using this approximation, as well as the plane-wave approximation for the exciton center-of-mass wavefunction, it is shown analytically that $J \sim L$ when the chain lengths are smaller than the separation between them, or $J\sim L^{-1}$ when the chain lengths are larger than their separation, where $L$ is the polymer length. Scaling relations are also obtained numerically for the more realistic standing-wave approximation for the exciton center-of-mass wavefunction, where it is found that for chain lengths larger than their separation $J \sim L^{-1.8}$ or $J \sim L^{-2}$, for parallel or collinear chains, respectively. These results have important implications for the photo-physics of conjugated polymers and self-assembled molecular systems, as the Davydov splitting in aggregates and the F\"orster transfer rate for exciton migration decreases with chain lengths larger than their separation. This latter result has obvious deleterious consequences for the performance of polymer photovoltaic devices

Computational Investigations of the Primary Excited States of Poly(para-phenylene vinylene)

The Pariser-Parr-Pople model of pi-conjugated electrons is solved by the density matrix renormalization group method for the light emitting polymer, poly(para-phenylene vinylene). The energies of the primary excited states are calculated. When solid state screening is incorporated into the model parameters there is excellent agreement between theory and experiment, enabling an identification of the origin of the key spectroscopic features.Comment: 6 pages, 3 figure

Localization of Large Polarons in the Disordered Holstein Model

We solve the disordered Holstein model via the DMRG method to investigate the combined roles of electron-phonon coupling and disorder on the localization of a single charge or exciton. The parameter regimes chosen, namely the adiabatic regime, $\hbar\omega/4t_0 = \omega' < 1$, and the `large' polaron regime, $\lambda < 1$, are applicable to most conjugated polymers. We show that as a consequence of the polaron effective mass diverging in the adiabatic limit (defined as $\omega' \to 0$ subject to fixed $\lambda$) self-localized, symmetry breaking solutions are predicted by the quantum Holstein model for infinitesimal disorder -- in complete agreement with the predictions of the Born-Oppenheimer Holstein model. For other parts of the ($\omega'$, $\lambda$) parameter space, however, self-localized Born-Oppenheimer solutions are not expected. If $\omega'$ is not small enough and $\lambda$ is not large enough, then the polaron is predominately localized by Anderson disorder, albeit more than for a free particle, because of the enhanced effective mass. Alternatively, for very small electron-nuclear coupling ($\lambda \ll 1$) the disorder-induced localization length is always smaller than the classical polaron size, $2/\lambda$, so that disorder always dominates. We comment on the implication of our results on the electronic properties of conjugated polymers

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

Role of Quantum Coherence and Energetic Disorder on Exciton Transport in Polymer Films

The cross-over from coherent to incoherent exciton transport in disordered polymer films is studied by computationally solving a modified form of the Redfield equation for the exciton density matrix. This theory models quantum mechanical (ballistic) and incoherent (diffusive) transport as limiting cases. It also reproduces Forster transport for certain parameter regimes. Using model parameters appropriate to polymer thin films it is shown that short-time quantum mechanical coherence increases the exciton diffusion length. It also causes rapid initial energy relaxation and larger line widths. The route to equilibrium is, however, more questionable, as the equilibrium populations of the model do not satisfy the Boltzmann distributions over the site energies. The Redfield equation for the dimer is solved exactly to provide insight into the numerical results.Comment: Accepted for publication in Phys. Rev. B. (July 2006). 19 pages and 8 figure

Dynamical model of the dielectric screening of conjugated polymers

A dynamical model of the dielectric screening of conjugated polymers is introduced and solved using the density matrix renormalization group method. The model consists of a line of quantized dipoles interacting with a polymer chain. The polymer is modelled by the Pariser-Parr-Pople (P-P-P) model. It is found that: (1) Compared to isolated, unscreened single chains, the screened 1Bu- exciton binding energy is typically reduced by ca. 1 eV to just over 1 eV; (2) Covalent (magnon and bi-magnon) states are very weakly screened compared to ionic (exciton) states; (3) Screening of the 1Bu- exciton is closer to the dispersion than solvation limit.Comment: 12 pages, 2 figure

Ultra-Fast Relaxation, Decoherence and Localization of Photoexcited States in π\pi-Conjugated Polymers: A TEBD Study

The exciton relaxation dynamics of photoexcited electronic states in poly($p$-phenylenevinylene) (PPV) are theoretically investigated within a coarse-grained model, in which both the exciton and nuclear degrees of freedom are treated quantum mechanically. The Frenkel-Holstein Hamiltonian is used to describe the strong exciton-phonon coupling present in the system, while external damping of the internal nuclear degrees of freedom are accounted for by a Lindblad master equation. Numerically, the dynamics are computed using the time evolving block decimation (TEBD) and quantum jump trajectory techniques. The values of the model parameters physically relevant to polymer systems naturally lead to a separation of time scales, with the ultra-fast dynamics corresponding to energy transfer from the exciton to the internal phonon modes (i.e., the C-C bond oscillations), while the longer time dynamics correspond to damping of these phonon modes by the external dissipation. Associated with these time scales, we investigate the following processes that are indicative of the system relaxing onto the emissive chromophores of the polymer: 1) Exciton-polaron formation occurs on an ultra-fast time scale, with the associated exciton-phonon correlations present within half a vibrational time period of the C-C bond oscillations. 2) Exciton decoherence is driven by the decay in the vibrational overlaps associated with exciton-polaron formation, occurring on the same time scale. 3) Exciton density localization is driven by the external dissipation, arising from `wavefunction collapse' occurring as a result of the system-environment interactions. Finally, we show how fluorescence anisotropy measurements can be used to investigate the exciton decoherence process during the relaxation dynamics.Comment: 16 pages, 15 figure