Intraband relaxation and temperature dependence of the fluorescence decay time of one-dimensional Frenkel excitons: The Pauli master equation approach

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.

Orientational effects in the polarized absorption spectra of molecular aggregates

We present a detailed theoretical analysis of polarized absorption spectra and linear dichroism of cyanine dye aggregates whose unit cells contain two molecules. The studied threadlike ordered system with a molecular exciton delocalized along its axis can be treated as two chains of conventional molecular aggregates, rotated relative to each other at a certain angle around the aggregate axis. Our approach is based on the general formulas for the effective cross section of light absorption by a molecular aggregate and key points of the molecular exciton theory. We have developed a self-consistent theory for describing the orientational effects in the absorption and dichroic spectra of such supramolecular structures with nonplanar unit cell. It is shown that the spectral behavior of such systems exhibits considerable distinctions from that of conventional cyanine dye aggregates. They consist in the strong dependence of the relative intensities of the J- and H-type spectral bands of the aggregate with a nonplanar unit cell on the angles determining the mutual orientations of the transition dipole moments of constituting molecules and the aggregate axis as well as on the polarization direction of incident light. The derived formulas are reduced to the well-known analytical expressions in the particular case of aggregates with one molecule in the unit cell. The calculations performed within the framework of our excitonic theory combined with available vibronic theory allow us to quite reasonably explain the experimental data for the pseudoisocyanine bromide dye aggregate.

Scaling relations of exciton diffusion in linear aggregates with static and dynamic disorder

Exciton diffusion plays an important role in many opto-electronic processes and phenomena. Understanding the interplay of intermolecular coupling, static energetic disorder, and dephasing caused by environmental fluctuations (dynamic disorder) is crucial to optimize exciton diffusion under various physical conditions. We report on a systematic analysis of the exciton diffusion constant in linear aggregates using the Haken-Strobl-Reineker model to describe this interplay. We numerically investigate the static-disorder scaling of (i) the diffusion constant in the limit of small dephasing rate, (ii) the dephasing rate at which the diffusion is optimized, and (iii) the value of the diffusion constant at the optimal dephasing rate. Three scaling regimes are found, associated with, respectively, fully delocalized exciton states (finite-size effects), weakly localized states, and strongly localized states. The scaling powers agree well with analytically estimated ones. In particular, in the weakly localized regime, the numerical results corroborate the so-called quantum Goldilocks principle to find the optimal dephasing rate and maximum diffusion constant as a function of static disorder, while in the strong-localization regime, these quantities can be derived fully analytically.

Scanning Ultrafast Spectral Dynamics of Triphenylamine-Modified Vinylbenzothiazole Derivative: Role of Solvent Polarity and Temperature

The photophysical properties of a donor-acceptor compound based on triphenylamine-modified vinylbenzothiazole derivative (BTTM) are investigated by multispectral techniques. Based on the pump-probe and pump-dump/push-probe technique, it is found that the hybridized localized excited (LE) and charge transfer (CT) state (HLCT) participates in the relaxation process of excited BTTM. The excited state is the LE-dominated HLCT state in cyclohexane; then it evolves to the CT-dominated HLCT state in a high polarity solvent. Meanwhile, a new intermediate state named the HLCT' state also exists in a high polar solvent. When the temperature of BTTM film drops, the increasing photoluminescence (PL) lifetime and PL quantum yield are assigned to the nonradiative recombination inactivation. The pump-probe data show that exciton-exciton annihilation originating from exciton collision gradually increases owing to the weakening of phonon-exciton scattering at low temperature. Our results provide comprehensive insight into the optoelectronic properties of organic molecules.

Thermal Decoherence and Disorder Effects on Chiral-Induced Spin Selectivity

We use a nonlinear master equation formalism to account for thermal and disorder effects on spin-dependent electron transport in helical organic molecules coupled to two ideal leads. The inclusion of these two effects has important consequences in understanding the observed length and temperature dependence of spin polarization in experiments, which cannot be accounted for in a purely coherent tunneling model. Our approach considers a tight-binding helical Hamiltonian with disordered onsite energies to describe the resulting electronic states when low-frequency interacting modes break the electron coherence. The high-frequency fluctuating counterpart of these interactions, typical of intramolecular modes, is included by means of temperature-dependent thermally activated transfer probabilities in the master equation, which lead to hopping between localized states. We focus on the spin-dependent conductance and the spin-polarization in the linear regime (low voltage), which are analyzed as a function of the molecular length and the temperature of the system. Our results at room temperature agree well with experiments because our model predicts that the degree of spin-polarization increases for longer molecules. Also, this effect is temperature-dependent because thermal excitation competes with disorder-induced Anderson localization. We conclude that a transport mechanism based on thermally activated hopping in a disordered system can account for the unexpected behavior of the spin polarization.

Theory for polariton-assisted remote energy transfer

Strong-coupling between light and matter produces hybridized states (polaritons) whose delocalization and electromagnetic character allow for novel modifications in spectroscopy and chemical reactivity of molecular systems. Recent experiments have demonstrated remarkable distance-independent long-range energy transfer between molecules strongly coupled to optical microcavity modes. To shed light on the mechanism of this phenomenon, we present the first comprehensive theory of polariton-assisted remote energy transfer (PARET) based on strong-coupling of donor and/or acceptor chromophores to surface plasmons. Application of our theory demonstrates that PARET up to a micron is indeed possible. In particular, we report two regimes for PARET: in one case, strong-coupling to a single type of chromophore leads to transfer mediated largely by surface plasmons while in the other case, strong-coupling to both types of chromophores creates energy transfer pathways mediated by vibrational relaxation. Importantly, we highlight conditions under which coherence enhances or deteriorates these processes. For instance, while exclusive strong-coupling to donors can enhance transfer to acceptors, the reverse turns out not to be true. However, strong-coupling to acceptors can shift energy levels in a way that transfer from acceptors to donors can occur, thus yielding a chromophore role-reversal or "carnival effect". This theoretical study demonstrates the potential for confined electromagnetic fields to control and mediate PARET, thus opening doors to the design of remote mesoscale interactions between molecular systems.

Insight into the mechanism of the photoluminescence of carbon nanoparticles derived from cryogenic studies

The unexpected discovery of the photoluminescence of carbon nanoparticles attracted the attention of many researchers and resulted in their use in a variety of applications. However, the origin of their emission is still obscure, and the majority of the discussions on the subject focus on their molecular and/or excitonic emissive states. We performed cryogenic studies down to 10 K and did not observe any signatures of suppressed molecular relaxation - the spectra remained broad, showing large unaltered Stokes shifts and temperature-independent emission intensities and lifetimes below 80 K with a weak dependence above this value. We demonstrated that the most general features of carbon nanoparticles, the very large Stokes shifts and considerable differences between the absorption and excitation spectra, are the result of the formation of a dynamic defect, the self-trapped Frenkel exciton. It looks like the distorted domain of the H-aggregate due to the exciton-lattice interaction and the local overheating caused by the exciton relaxation. In addition, at low temperatures the long-lifetime spectral component was found and was attributed to phosphorescence. The obtained results strongly support the excitonic nature of the fluorescence of nanocarbon materials.

Beyond Förster resonance energy transfer in biological and nanoscale systems

After photoexcitation, energy absorbed by a molecule can be transferred efficiently over a distance of up to several tens of angstroms to another molecule by the process of resonance energy transfer, RET (also commonly known as electronic energy transfer, EET). Examples of where RET is observed include natural and artificial antennae for the capture and energy conversion of light, amplification of fluorescence-based sensors, optimization of organic light-emitting diodes, and the measurement of structure in biological systems (FRET). Forster theory has proven to be very successful at estimating the rate of RET in many donor-acceptor systems, but it has also been of interest to discover when this theory does not work. By identifying these cases, researchers have been able to obtain, sometimes surprising, insights into excited-state dynamics in complex systems. In this article, we consider various ways that electronic energy transfer is promoted by mechanisms beyond those explicitly considered in Forster RET theory. First, we recount the important situations when the electronic coupling is not accurately calculated by the dipole-dipole approximation. Second, we examine the related problem of how to describe solvent screening when the dipole approximation fails. Third, there are situations where we need to be careful about the separability of electronic coupling and spectral overlap factors. For example, when the donors and/or acceptors are molecular aggregates rather than individual molecules, then RET occurs between molecular exciton states and we must invoke generalized Forster theory (GFT). In even more complicated cases, involving the intermediate regime of electronic energy transfer, we should consider carefully nonequilibrium processes and coherences and how bath modes can be shared. Lastly, we discuss how information is obscured by various forms of energetic disorder in ensemble measurements and we outline how single molecule experiments continue to be important in these instances.

Conformational disorder and ultrafast exciton relaxation in PPV-family conjugated polymers

We report combined experimental and theoretical studies of excitation relaxation in poly[2-methoxy,5-(2'-ethyl-hexoxy)-1,4-phenylenevinylene] (MEH-PPV), oligophenylenevinylene (OPV) molecules of varying length, and model PPV chains. We build on the paradigm that the basic characteristics of conjugated polymers are decided by conformational subunits defined by conjugation breaks caused by torsional disorder along the chain. The calculations reported here indicate that for conjugated polymers like those in the PPV family, these conformational subunits electronically couple to neighboring subunits, forming subtly delocalized collective states of nanoscale excitons that determine the polymer optical properties. We find that relaxation among these exciton states can lead to a decay of anisotropy on ultrafast time scales. Unlike in Forster energy transfer, the exciton does not necessarily translate over a large distance. Nonetheless, the disorder in the polymer chain means that even small changes in the exciton size or location has a significant effect on the relaxation pathway and therefore the anisotropy decay.

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.

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.

A Multistate Model for the Fluorescence Response of R-Phycoerythrin

Although strong fluorescence makes the R-phycoerythrin (R-PE) proteins increasingly useful in biological and clinical assays, they are subject to nonlinear effects including transitions to collective dark states and photodegradation, which complicate quantitative applications. We report measurements of R-PE fluorescence intensity as a function of incident power, duration of illumination and temperature. Emission intensity in the band at 570 nm is proportional to incident power for low power levels. At higher incident power, the emission at 570 nm is smaller than expected from a linear dependence on power. We propose that R-PE undergoes both reversible emission cessation on a millisecond time scale attributed to transitions to a collective dark state, and irreversible photodegradation on a time scale of minutes. Singlet oxygen scavengers such as dithiothreitol and n-propyl gallate have protective effects against the latter effect but not the former. Electrophoretic analysis of irradiated solutions of R-PE indicates that significant noncovalent aggregation is correlated with photodegradation. A multistate model based on fluorescence measurements and geometric analysis is proposed for the fluorophores in R-PE. The phycobilin fluorophores are partitioned into three groups: the phycourobilins (PUB) absorbing at 490 nm, one group of phycoerythobilins (PEB) absorbing at 530 nm (PEB-530) and another group of PEB absorbing at 560 nm (PEB-560). The two processes that result in the loss of fluorescence intensity are most likely associated with the PEB-560 group.

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)].

Temperature dependent exciton emission from herringbone aggregates of conjugated oligomers

In this work, the effect of temperature, exciton bandwidth, and size on the photoluminescence spectra of defect-free two-dimensional herringbone aggregates of pi-conjugated oligomers such as oligophenylene vinylene and oligothiophene is investigated theoretically. The model is based on exciton-phonon coupling in two-dimensional herringbone lattices with the exciton deriving from the lowest optical (1Ag-->1Bu) transition and the phonon from the most strongly coupled intramolecular vibrational mode with frequency omega0. Simple analytical expressions are obtained for the line strengths of the emission origin (0-0) and first replica (0-1) as a function of the number of molecules comprising the aggregate, N, the free exciton bandwidth, WD, and the temperature, T. At a given temperature, the 0-0 emission intensity initially scales as N/Nth, where Nth is the superradiant threshold number, but eventually converges to NT/Nth, where NT is the size independent thermal coherence number. NT is inversely proportional to temperature and proportional to the exciton band curvature (omegac) near the band bottom; NT=1+4piomegac/kbT. In striking contrast, the 0-1 line strength is relatively insensitive to temperature and size, but scales as the inverse square of WD+omega0. The insensitivity of the first replica to the exciton coherence number makes the ratio of the 0-0 to 0-1 line strengths a measure of the exciton coherence number. The ratio can be used to test for crystal purity. Comparison to experiments on thin films of quaterthiophene shows that the thermal coherence size is given by NT approximately 1+450/T (K) and that superradiance, which requires NT>Nth, can only be observed at temperatures less than 1 K.

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.