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

Spatial Correlations Drive Long-Range Transport and Trapping of Excitons in Single H-Aggregates: Experiment and Theory

Describing long-range energy transport is a crucial step, both toward deepening our knowledge on natural light-harvesting systems and toward developing novel photoactive materials. Here, we combine experiment and theory to resolve and reproduce energy transport on pico- to nanosecond time scales in single H-type supramolecular nanofibers based on carbonyl-bridged triarylamines (CBT). Each nanofiber shows energy transport dynamics over long distances up to ∼1 μm, despite exciton trapping at specific positions along the nanofibers. Using a minimal Frenkel exciton model including disorder, we demonstrate that spatial correlations in the normally distributed site energies are crucial to reproduce the experimental data. In particular, we can observe the long-range and subdiffusive nature of the exciton dynamics as well as the trapping behavior of excitons in specific locations of the nanofiber. This trapping behavior introduces a net directionality or asymmetry in the exciton dynamics as observed experimentally.

Anderson Localization of Composite Particles

We investigate the effect of coupling between translational and internal degrees of freedom of composite quantum particles on their localization in a random potential. We show that entanglement between the two degrees of freedom weakens localization due to the upper bound imposed on the inverse participation ratio by purity of a quantum state. We perform numerical calculations for a two-particle system bound by a harmonic force in a 1D disordered lattice and a rigid rotor in a 2D disordered lattice. We illustrate that the coupling has a dramatic effect on localization properties, even with a small number of internal states participating in quantum dynamics.

Emergence of Collective Coherent States from Strong-Light Coupling of Disordered Systems

An empirical framework for studying the way vacuum fluctuations in a Fabry-Perot cavity produce collective light-matter hybrid states (polariton states) is reported. The reason that the Tavis-Cummings model, where a single mode of the radiation field couples to all the molecules, succeeds is discussed in terms of the strong phase correlation of the vacuum fluctuations in the cavity, which produces a single effective cavity mode (ECM). The model is used to study the onset of the collective state, or "superradiant phase", for ensembles of molecules with significant disorder in their transition energies, as a function of cavity strength factor, from low Q cavities to high Q cavities. A key result is the quantification of the coherence of the ensemble of the lowest energy eigenstate. This is assessed, primarily, using an entropy distance measure. The statistical model provides a physical intuition for the formation of coherence of polariton states when the collective coupling is strong enough that they dominate over the tail of the dark-state density-of-states.

Expanded Theory of H- and J-Molecular Aggregates: The Effects of Vibronic Coupling and Intermolecular Charge Transfer

The electronic excited states of molecular aggregates and their photophysical signatures have long fascinated spectroscopists and theoreticians alike since the advent of Frenkel exciton theory almost 90 years ago. The influence of molecular packing on basic optical probes like absorption and photoluminescence was originally worked out by Kasha for aggregates dominated by Coulombic intermolecular interactions, eventually leading to the classification of J- and H-aggregates. This review outlines advances made in understanding the relationship between aggregate structure and photophysics when vibronic coupling and intermolecular charge transfer are incorporated. An assortment of packing geometries is considered from the humble molecular dimer to more exotic structures including linear and bent aggregates, two-dimensional herringbone and "HJ" aggregates, and chiral aggregates. The interplay between long-range Coulomb coupling and short-range charge-transfer-mediated coupling strongly depends on the aggregate architecture leading to a wide array of photophysical behaviors.

Exciton dynamics in perturbed vibronic molecular aggregates

A site specific perturbation of a photo-excited molecular aggregate can lead to a localization of excitonic energy. We investigate this localization dynamics for laser-prepared excited states. Changing the parameters of the electric field significantly influences the exciton localization which offers the possibility for a selective control of this process. This is demonstrated for aggregates possessing a single vibrational degree of freedom per monomer unit. It is shown that the effects identified for the molecular dimer can be generalized to larger aggregates with a high density of vibronic states.

Quantum Diffusion on Molecular Tubes: Universal Scaling of the 1D to 2D Transition

The transport properties of disordered systems are known to depend critically on dimensionality. We study the diffusion coefficient of a quantum particle confined to a lattice on the surface of a tube, where it scales between the 1D and 2D limits. It is found that the scaling relation is universal and independent of the temperature, disorder, and noise parameters, and the essential order parameter is the ratio between the localization length in 2D and the circumference of the tube. Phenomenological and quantitative expressions for transport properties as functions of disorder and noise are obtained and applied to real systems: In the natural chlorosomes found in light-harvesting bacteria the exciton transfer dynamics is predicted to be in the 2D limit, whereas a family of synthetic molecular aggregates is found to be in the homogeneous limit and is independent of dimensionality.

Coherent quantum transport in disordered systems: A unified polaron treatment of hopping and band-like transport

Quantum transport in disordered systems is studied using a polaron-based master equation. The polaron approach is capable of bridging the results from the coherent band-like transport regime governed by the Redfield equation to incoherent hopping transport in the classical regime. A non-monotonic dependence of the diffusion coefficient is observed both as a function of temperature and system-phonon coupling strength. In the band-like transport regime, the diffusion coefficient is shown to be linearly proportional to the system-phonon coupling strength and vanishes at zero coupling due to Anderson localization. In the opposite classical hopping regime, we correctly recover the dynamics described by the Fermi's Golden Rule and establish that the scaling of the diffusion coefficient depends on the phonon bath relaxation time. In both the hopping and band-like transport regimes, it is demonstrated that at low temperature, the zero-point fluctuations of the bath lead to non-zero transport rates and hence a finite diffusion constant. Application to rubrene and other organic semiconductor materials shows a good agreement with experimental mobility data.

Insights into the excitonic states of individual chlorosomes from Chlorobaculum tepidum

Green-sulfur bacteria have evolved a unique light-harvesting apparatus, the chlorosome, by which it is perfectly adapted to thrive photosynthetically under extremely low light conditions. We have used single-particle, optical spectroscopy to study the structure-function relationship of chlorosomes each of which incorporates hundreds of thousands of self-assembled bacteriochlorophyll (BChl) molecules. The electronically excited states of these molecular assemblies are described as Frenkel excitons whose photophysical properties depend crucially on the mutual arrangement of the pigments. The signature of these Frenkel excitons and its relation to the supramolecular organization of the chlorosome becomes accessible by optical spectroscopy. Because subtle spectral features get obscured by ensemble averaging, we have studied individual chlorosomes from wild-type Chlorobaculum tepidum by polarization-resolved fluorescence-excitation spectroscopy. This approach minimizes the inherent sample heterogeneity and allows us to reveal properties of the exciton states without ensemble averaging. The results are compared with predictions from computer simulations of various models of the supramolecular organization of the BChl monomers. We find that the photophysical properties of individual chlorosomes from wild-type Chlorobaculum tepidum are consistent with a (multiwall) helical arrangement of syn-anti stacked BChl molecules in cylinders and/or spirals of different size.

Single Lévy states-disorder induced energy funnels in molecular aggregates

Using fluorescence super-resolution microscopy we studied simultaneous spectral, spatial localization, and blinking behavior of individual 1D J-aggregates. Excitons migrating 100 nm are funneled to a trap appearing as an additional red-shifted blinking fluorescence band. We propose that the trap is a Frenkel exciton state formed much below the main exciton band edge due to an environmentally induced heavy-tailed Lévy disorder. This points to disorder engineering as a new avenue in controlling light-harvesting in molecular ensembles.

Self-trapping of excitons, violation of Condon approximation, and efficient fluorescence in conjugated cycloparaphenylenes

Cycloparaphenylenes, the simplest structural unit of armchair carbon nanotubes, have unique optoelectronic properties counterintuitive in the class of conjugated organic materials. Our time-dependent density functional theory study and excited state dynamics simulations of cycloparaphenylene chromophores provide a simple and conceptually appealing physical picture explaining experimentally observed trends in optical properties in this family of molecules. Fully delocalized degenerate second and third excitonic states define linear absorption spectra. Self-trapping of the lowest excitonic state due to electron-phonon coupling leads to the formation of spatially localized excitation in large cycloparaphenylenes within 100 fs. This invalidates the commonly used Condon approximation and breaks optical selection rules, making these materials superior fluorophores. This process does not occur in the small molecules, which remain inefficient emitters. A complex interplay of symmetry, π-conjugation, conformational distortion and bending strain controls all photophysics of cycloparaphenylenes.

First-principles calculation of the optical properties of an amphiphilic cyanine dye aggregate

Using a first-principles approach, we calculate electronic and optical properties of molecular aggregates of the dye amphi-pseudoisocyanine, whose structures we obtained from molecular dynamics (MD) simulations of the self-aggregation process. Using quantum chemistry methods, we translate the structural information into an effective time-dependent Frenkel exciton Hamiltonian for the dominant optical transitions in the aggregate. This Hamiltonian is used to calculate the absorption spectrum. Detailed analysis of the dynamic fluctuations in the molecular transition energies and intermolecular excitation transfer interactions in this Hamiltonian allows us to elucidate the origin of the relevant time scales; short time scales, on the order of up to a few hundreds of femtoseconds, result from internal motions of the dye molecules, while the longer (a few picosecond) time scales we ascribe to environmental motions. The absorption spectra of the aggregate structures obtained from MD feature a blue-shifted peak compared to that of the monomer; thus, our aggregates can be classified as H-aggregates, although considerable oscillator strength is carried by states along the entire exciton band. Comparison to the experimental absorption spectrum of amphi-PIC aggregates shows that the simulated line shape is too wide, pointing to too much disorder in the internal structure of the simulated aggregates.

Controlled aggregation and enhanced two-photon absorption of a water-soluble squaraine dye with a poly(acrylic acid) template

Controlling the aggregation behavior of organic dyes is important for understanding and exploring supramolecular assembly utilizing the specific characteristics of aggregation. Regulating J-aggregation by electrostatic interactions between anionic polyelectrolytes and cationic dyes has gained growing interest. Here, we report the formation of J-aggregates of a water-soluble cationic squaraine dye, 4-(pyridinium-1-yl)butylbenzothiazolium squaraine (SQ), using poly(acrylic acid) sodium salt (PAA-Na) as a template. Electrostatic interactions between the PAA-Na polyelectrolyte and the cationic SQ dye enhanced J-aggregation; the absorbance of the resulting J-band with the polyelectrolyte template was much sharper than the absorbance of the J-aggregate formed using a high concentration of NaCl. Significantly, removal of the polyelectrolyte PPA-Na template by the introduction of calcium ions, which can form stronger ionic binding with carboxylate groups, dissociated J-aggregates, freeing the SQ molecules back to unaggregated or lower aggregate forms. To demonstrate the reversibility of the J-aggregate formation cycle, an in situ experiment was conducted that showed 60% reversibility of the second cycle. In addition, an enhancement by ca. 23 times per repeat unit of the two-photon absorption (2PA) cross section was observed at 920 nm for the polyelectrolyte template-SQ J-aggregate compared to unaggregated or lower aggregate SQ. These results suggest a prominent role of polyelectrolyte templated SQ J-aggregation in the enhancement of 2PA efficiency and provide a means of modulating supramolecular assembly.

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.

Insights into excitons confined to nanoscale systems: electron-hole interaction, binding energy, and photodissociation

The characteristics of nanoscale excitons--the primary excited states of nanoscale systems like conjugated polymers, molecular aggregates, carbon nanotubes, and nanocrystalline quantum dots--are examined through exploration of model systems. On the basis of a valence bond-type model, an intuition is developed for understanding and comparing nanoscale systems. In particular, electron-hole interactions are examined in detail, showing how and why they affect spectroscopy and properties such as binding energy. The relationship between the bound exciton states and the nanoscale analogue of free carriers (charge-transfer exciton states) is developed. It is shown why the electron and hole act as independent particles in this manifold of states. The outlook for the field is discussed on the basis of the picture developed in the paper, with an emphasis on exciton binding and photodissociation.

Excitation energy transfer between closely spaced multichromophoric systems: effects of band mixing and intraband relaxation

We theoretically analyze the excitation energy transfer between two closely spaced linear molecular J-aggregates, whose excited states are Frenkel excitons. The aggregate with the higher (lower) exciton band edge energy is considered as the donor (acceptor). The celebrated theory of Förster resonance energy transfer (FRET), which relates the transfer rate to the overlap integral of optical spectra, fails in this situation. We point out that, in addition to the well-known fact that the point-dipole approximation breaks down (enabling energy transfer between optically forbidden states), also the perturbative treatment of the electronic interactions between donor and acceptor system, which underlies the Förster approach, in general loses its validity due to overlap of the exciton bands. We therefore propose a nonperturbative method, in which donor and acceptor bands are mixed and the energy transfer is described in terms of a phonon-assisted energy relaxation process between the two new (renormalized) bands. The validity of the conventional perturbative approach is investigated by comparing to the nonperturbative one; in general, this validity improves for lower temperature and larger distances (weaker interactions) between the aggregates. We also demonstrate that the interference between intraband relaxation and energy transfer renders the proper definition of the transfer rate and its evaluation from experiment a complicated issue that involves the initial excitation condition. Our results suggest that the best way of determining this transfer rate between two J-aggregates is to measure the fluorescence kinetics of the acceptor J-band after resonant excitation of the donor J-band.

Portable radiometer: a novel technique for in situ band gap measurements

Portable radiometers are commonly used in remote sensing applications for studying vegetation, soil, minerals, etc. However, we propose and demonstrate, for the first time, the applicability of this radiometer for high-resolution in situ band gap measurements of materials. The excitation source can be any white light source such as sun or tungsten halogen lamp. The flexibility in sample size and relative ease of varying temperature during measurements add to the advantages of using a portable radiometer for investigating new materials. Accurate measurements were made on standard samples of silicon, germanium, and gallium antimonide to demonstrate the feasibility of this technique.

Probing quantum-mechanical level repulsion in disordered systems by means of time-resolved selectively excited resonance fluorescence

We argue that the time-resolved spectrum of selectively-excited resonance fluorescence at low temperature provides a tool for probing the quantum-mechanical level repulsion in the Lifshits tail of the electronic density of states in a wide variety of disordered materials. The technique, based on detecting the fast growth of a fluorescence peak that is redshifted relative to the excitation frequency, is demonstrated explicitly by simulations on linear Frenkel exciton chains.

Effect of disorder on ultrafast exciton dynamics probed by single molecule spectroscopy

We present a single-molecule study unraveling the effect of static disorder on the vibrational-assisted ultrafast exciton dynamics in multichromophoric systems. For every single complex, we probe the initial exciton relaxation process by an ultrafast pump-probe approach and the coupling to vibrational modes by emission spectra, while fluorescence lifetime analysis measures the amount of static disorder. Exploiting the wide range of disorder found from complex to complex, we demonstrate that static disorder accelerates the dephasing and energy relaxation rate of the exciton.

Exciton-phonon coupling and disorder in the excited states of CdSe colloidal quantum dots

We study the origin of the spectral line shape in colloidal CdSe nanocrystal quantum dots. The three-pulse photon echo peak shift (3PEPS) data reveal a temperature-independent fast decay, obscuring the quantification of the homogeneous linewidth. The optical gap and Stokes shift are found to have an anomalous behavior with temperature, which is size, capping group, and surrounding polymer matrix independent. Using these results and combining them with simulations, we discuss the role of exciton-phonon coupling, static inhomogeneity, exciton fine structure, and exciton state disorder in the linewidth of the nanocrystal. In particular, our analysis shows that the disorder due to surface imperfections and finite temperature effects, as well as the relaxation within the fine structure, can have significant impact on the steady-state absorption spectrum, 3PEPS data, and dephasing processes.

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.

EXCITONS IN CONJUGATED OLIGOMER AGGREGATES, FILMS, AND CRYSTALS

Recent experimental and theoretical investigations of excitons in conjugated oligomer nanoaggregates, thin films, and crystals are reviewed. The review focuses on the technologically important unsubstituted oligo-phenylene vinylenes (OPVn) and oligo-thiophenes (OTn), which exhibit side-by-side herringbone crystal packing. Many of the salient photophysical properties displayed by OPVn and OTn solid phases, including the large Davydov splitting, the rich variety of peaks due to vibronic coupling in both absorption and emission, and the unusual behavior of the emission origin, are accounted for in a model including excitonic coupling between molecules, linear exciton-phonon coupling, and disorder.