Theory and numerical study of exciton dynamics in a disordered linear chain

Effects of the environment on the electric conductivity of double-stranded DNA molecules

We present a theoretical analysis of the effects of the environment on charge transport in double-stranded synthetic poly(G)-poly(C) DNA molecules attached to two ideal leads. Coupling of the DNA to the environment results in two effects: (i) localization of carrier functions due to static disorder and (ii) phonon-induced scattering of the carriers between the localized states, resulting in hopping conductivity. A nonlinear Pauli master equation for populations of localized states is used to describe the hopping transport and calculate the electric current as a function of the applied bias. We demonstrate that, although the electronic gap in the density of states shrinks as the disorder increases, the voltage gap in the I-V characteristics becomes wider. A simple physical explanation of this effect is provided.

Scaling and universality in the optics of disordered exciton chains

The joint probability distribution of exciton energies and transition dipole moments determines a variety of optical observables in disordered exciton systems. We demonstrate numerically that this distribution obeys a one-parameter scaling, originating from the fact that both the energy and the dipole moment are determined by the number of coherently bound molecules. A universal underlying distribution is found, which is identical for uncorrelated Gaussian disorder in the molecular transition energies or in the intermolecular transfer interactions. The universality breaks down for disorder in the transfer interactions resulting from variations in the molecular positions. We suggest the possibility to probe the joint distribution by means of single-molecule spectroscopy.

Temperature-Dependent Relaxation of Excitons in Tubular Molecular Aggregates: Fluorescence Decay and Stokes Shift

We report temperature-dependent steady-state and time-resolved fluorescence studies to probe the exciton dynamics in double-wall tubular J-aggregates formed by self-assembly of the dye 3,3'-bis(3-sulfopropyl)-5,5',6,6'-tetrachloro-1,1'-dioctylbenzimidacarbocyanine. We focus on the lowest energy fluorescence band, originating from the inner cylindrical wall. At low temperatures, the experiments reveal a nonexponential decay of the fluorescence, with a typical time scale that depends on the emission wavelength. At these temperatures we also find a dynamic Stokes shift of the fluorescence spectrum and its nonmonotonic dependence on temperature under steady-state conditions. All these data indicate that below about 20 K the excitons in the lowest fluorescence band do not reach thermal equilibrium before emission occurs, while above about 60 K thermalization on this time scale is complete. By comparing the two lowest fluorescence bands, we also find indications for fast energy transfer from the outer to the inner wall. We show that the Frenkel exciton model with diagonal disorder, which previously has been proposed to explain the absorption and linear dichroism spectra of these aggregates, yields a quantitative explanation to the observed dynamics. To this end, we extend the model to account for weak phonon-induced scattering of the localized exciton states; the spectral dynamics are then described by solving a Pauli master equation for the exciton populations.

Controlled Formation of the Two-Dimensional TTBC J-Aggregates in an Aqueous Solution

Strong experimental and theoretical evidence was provided on the controlled formation of the two-dimensional J-aggregates that were assembled in the herringbone morphology. The exciton-band structure formation of 1,1',3,3'-tetraethyl-5,5',6,6'-tetrachlorobenzimidazolocarbocyanine (TTBC) J-aggregates was investigated in ionic (NaOH) aqueous solution at room temperature. The control was achieved by changing the [TTBC] at a given [NaOH], or vice versa, and was monitored through the changes in the absorption, fluorescence excitation, and emission spectra. Specific attention was paid to expose the excited-state structure and dynamics through simulations of the excitonic properties, which included diagonal energetic disorder and phonon-assisted exciton relaxation. Aggregates were characterized by an asymmetrically split Davydov pair, an H-band (approximately 500 nm, 1300 cm(-1) wide, Lorentzian-like) and a J-band (approximately 590 nm, 235 cm(-1) wide, with a band shape typical of a one-dimensional J-aggregate), whose relative intensities showed a strong dependence on the [TTBC]/[NaOH]. The H-band is favored by high [TTBC] or high [NaOH]. An explanation of the control on the aggregate formation was given by correlating the changes in the absorption with the structural modifications and the subsequent changes in the dynamics, which were induced by variations in the dye and NaOH concentrations. The J-band shape/width was attributed to disorder and disorder-induced intraband phonon-assisted exciton relaxation. The intraband processes in both bands were estimated to occur in the same time scale (about a picosecond). It has been suggested that the wide energetic gap between the Davydov split bands (3000 cm(-1)) could get bridged by the excitonic states of the loosely coupled chains, in addition to the monomeric species at low [TTBC]. Phonon-assisted interband relaxation, through the band gap states and/or directly from the H- to the J-band, are suggested for accounting the difference between the bandwidths and shapes of the two bands. Energy transfer between the H-band and the monomeric species is suggested as crucial for tuning the relative strengths of the two bands.

Thermal broadening of the J-band in disordered linear molecular aggregates: A theoretical study

We theoretically study the temperature dependence of the J-band width in disordered linear molecular aggregates, caused by dephasing of the exciton states due to scattering on vibrations of the host matrix. In particular, we consider inelastic one- and two-phonon scatterings between different exciton states (energy-relaxation-induced dephasing), as well as the elastic two-phonon scattering of the excitons (pure dephasing). The exciton states follow from numerical diagonalization of a Frenkel exciton Hamiltonian with diagonal disorder; the scattering rates between them are obtained using the Fermi golden rule. A Debye-type model for the one- and two-phonon spectral densities is used in the calculations. We find that, owing to the disorder, the dephasing rates of the individual exciton states are distributed over a wide range of values. We also demonstrate that the dominant channel of two-phonon scattering is not the elastic one, as is often tacitly assumed, but rather comes from a similar two-phonon inelastic scattering process. In order to study the temperature dependence of the J-band width, we simulate the absorption spectrum, accounting for the dephasing-induced broadening of the exciton states. We find a power-law (T(p)) temperature scaling of the effective homogeneous width, with an exponent p that depends on the shape of the spectral density of the host vibrations. In particular, for a Debye model of vibrations, we find p approximately 4, which is in good agreement with the experimental data on J aggregates of pseudoisocyanine [I. Renge and U. P. Wild, J. Phys. Chem. A, 101, 7977 (1997)].

Low-temperature dynamics of weakly localized Frenkel excitons in disordered linear chains

We calculate the temperature dependence of the fluorescence Stokes shift and the fluorescence decay time in linear Frenkel exciton systems resulting from the thermal redistribution of exciton population over the band states. The following factors, relevant to common experimental conditions, are accounted for in our kinetic model: (weak) localization of the exciton states by static disorder, coupling of the localized excitons to vibrations in the host medium, a possible nonequilibrium of the subsystem of localized Frenkel excitons on the time scale of the emission process, and different excitation conditions (resonant or nonresonant). A Pauli master equation, with microscopically calculated transition rates, is used to describe the redistribution of the exciton population over the manifold of localized exciton states. We find a counterintuitive nonmonotonic temperature dependence of the Stokes shift. In addition, we show that depending on experimental conditions, the observed fluorescence decay time may be determined by vibration-induced intraband relaxation, rather than radiative relaxation to the ground state. The model considered has relevance to a wide variety of materials, such as linear molecular aggregates, conjugated polymers, and polysilanes.

Temperature dependent fluorescence in disordered Frenkel chains: interplay of equilibration and local band-edge level structure

We model the optical dynamics in linear Frenkel exciton systems governed by scattering on static disorder and lattice vibrations and calculate the temperature dependent fluorescence spectrum and lifetime. The fluorescence Stokes shift shows a nonmonotonic behavior with temperature, which derives from the interplay of the local band-edge level structure and thermal equilibration. The model yields excellent fits to experiments performed on linear dye aggregates.