Polaron–excitons and electron–vibrational band shapes in conjugated polymers

Ultrafast Fluorescence Depolarization in Conjugated Polymers

We report on large-scale simulations of intrachain exciton dynamics in poly(para-phenylenevinylene). Our theoretical model describes Frenkel exciton coupling to both fast, quantized C-C bond vibrations and slow, classical torsional modes. We also incorporate system-bath interactions. The dynamics is simulated using the time evolution block decimation method, which avoids the failures of the Ehrenfest approximation to describe decoherence processes and nonadiabatic interstate conversion. System-bath interactions are modeled using quantum trajectories and Lindblad quantum jump operators. We find that following photoexcitation, the quantum mechanical entanglement of the exciton and C-C bond phonons causes exciton-site decoherence. Next, system-bath interactions cause the stochastic collapse of high-energy delocalized excitons into chromophores. Finally, torsional relaxation causes additional exciton-density localization. We relate these dynamical processes to the predicted fluorescence depolarization, extract the time scales corresponding to them, and thus interpret the observed sub-ps fluorescence depolarization.

How charges separate: correlating disorder, free energy, and open-circuit voltage in organic photovoltaics

In order for a photovoltaic cell to function, charge carriers produced by photoexcitation must fully dissociate and overcome their mutual Coulomb attraction to form free polarons. This becomes problematic in organic systems in which the low dielectric constant of the material portends a long separation distance between independent polaron pairs. In this paper, we discuss our recent efforts to correlate the role of density of states, entropy, and configurational and energetic disorder to the open-circuit voltage, VOC, of model type-II organic polymer photovoltaics. By comparing the results of a fully interacting lattice model to those predicted by a Wigner-Weisskopf type model we find that energetic disorder does play a significant role in determining the VOC; however, mobility perpendicular to the interface plays the deciding role in the eventual fate of a charge-separated pair.

Spectroscopic Investigation of the Effect of Microstructure and Energetic Offset on the Nature of Interfacial Charge Transfer States in Polymer: Fullerene Blends

Despite performance improvements of organic photovoltaics, the mechanism of photoinduced electron–hole separation at organic donor–acceptor interfaces remains poorly understood. Inconclusive experimental and theoretical results have produced contradictory models for electron–hole separation in which the role of interfacial charge-transfer (CT) states is unclear, with one model identifying them as limiting separation and another as readily dissociating. Here, polymer–fullerene blends with contrasting photocurrent properties and enthalpic offsets driving separation were studied. By modifying composition, film structures were varied from consisting of molecularly mixed polymer–fullerene domains to consisting of both molecularly mixed and fullerene domains. Transient absorption spectroscopy revealed that CT state dissociation generating separated electron–hole pairs is only efficient in the high energy offset blend with fullerene domains. In all other blends (with low offset or predominantly molecularly mixed domains), nanosecond geminate electron–hole recombination is observed revealing the importance of spatially localized electron–hole pairs (bound CT states) in the electron–hole dynamics. A two-dimensional lattice exciton model was used to simulate the excited state spectrum of a model system as a function of microstructure and energy offset. The results could reproduce the main features of experimental electroluminescence spectra indicating that electron–hole pairs become less bound and more spatially separated upon increasing energy offset and fullerene domain density. Differences between electroluminescence and photoluminescence spectra could be explained by CT photoluminescence being dominated by more-bound states, reflecting geminate recombination processes, while CT electroluminescence preferentially probes less-bound CT states that escape geminate recombination. These results suggest that apparently contradictory studies on electron–hole separation can be explained by the presence of both bound and unbound CT states in the same film, as a result of a range of interface structures.

Assessing the nature of the charge-transfer electronic states in organic solar cells

The charge-transfer electronic states appearing at the donor-acceptor interfaces in organic solar cells mediate exciton dissociation, charge generation, and charge recombination. To date, the characterization of their nature has been carried out on the basis of models that only involve the charge-transfer state and the ground state. Here, we demonstrate that it is essential to go beyond such a two-state model and to consider explicitly as well the electronic and vibrational couplings with the local absorbing state on the donor and/or acceptor. We have thus developed a three-state vibronic model that allows us: to provide a reliable description of the optical absorption features related to the charge-transfer states; to underline the erroneous interpretations stemming from the application of the semi-classical two-state model; and to rationalize how the hybridization between the local-excitation state and charge-transfer state can lead to lower non-radiative voltage losses and higher power conversion efficiencies.

Previous descriptions of the charge-transfer absorptions in organic solar cells only involve the charge transfer state and the ground state. Here Chen et al. underline that a third state, i.e., the local absorbing state on the donor and/or acceptor, needs to be considered.

Ultrafast decoherence dynamics govern photocarrier generation efficiencies in polymer solar cells

All-organic-based photovoltaic solar cells have attracted considerable attention because of their low-cost processing and short energy payback time. In such systems the primary dissociation of an optical excitation into a pair of photocarriers has been recently shown to be extremely rapid and efficient, but the physical reason for this remains unclear. Here, two-dimensional photocurrent excitation spectroscopy, a novel non-linear optical spectroscopy, is used to probe the ultrafast coherent decay of photoexcitations into charge-producing states in a polymer:fullerene based solar cell. The two-dimensional photocurrent spectra are interpreted by introducing a theoretical model for the description of the coupling of the electronic states of the system to an external environment and to the applied laser fields. The experimental data show no cross-peaks in the twodimensional photocurrent spectra, as predicted by the model for coherence times between the exciton and the photocurrent producing states of 20 fs or less.

Molecular Packing Determines Charge Separation in a Liquid Crystalline Bisthiophene-Perylene Diimide Donor-Acceptor Material

Combined electronic structure and quantum dynamical calculations are employed to investigate charge separation in a novel class of covalently bound bisthiophene-perylene diimide type donor-acceptor (DA) co-oligomer aggregates. In an earlier spectroscopic study of this DA system in a smectic liquid crystalline (LC) film, efficient and ultrafast (subpicosecond) initial charge separation was found to be followed by rapid recombination. By comparison, the same DA system in solution exhibits ultrafast resonant energy transfer followed by slower (picosecond scale) charge separation. The present first-principles study explains these contrasting observations, highlighting the role of an efficient intermolecular charge-transfer pathway that results from the molecular packing in the LC phase. Despite the efficiency of this primary charge-transfer step, long-range charge separation is impeded by a comparatively high Coulomb barrier in conjunction with small electron- and hole-transfer integrals. Quantum dynamical calculations are carried out for a fragment-based model Hamiltonian, parametrized by ab initio second-order Algebraic Diagrammatic Construction (ADC(2)) and Time-Dependent Density Functional Theory (TDDFT) electronic structure calculations. Simulations of coherent vibronic quantum dynamics for up to 156 electronic states and 48 modes are performed using the Multi-Layer Multi-Configuration Time-Dependent Hartree (ML-MCTDH) method. Excellent agreement with experimentally determined charge separation time scales is obtained, and the spatially coherent nature of the dynamics is analyzed.

Concurrent Effects of Delocalization and Internal Conversion Tune Charge Separation at Regioregular Polythiophene-Fullerene Heterojunctions

Quantum-dynamical simulations are used to investigate the interplay of exciton delocalization and vibronically induced internal conversion processes in the elementary charge separation steps at regioregular donor-acceptor heterojunctions. Ultrafast internal conversion leads to efficient deexcitation within the excitonic and charge transfer manifolds, thus modifying the charge separation dynamics. We address a model donor-acceptor junction representative of regioregular P3HT-PCBM, using high-dimensional quantum dynamics simulations by multiconfigurational methods. While partial trapping into an interfacial charge separated state occurs, long-range charge-separated states are accessed as previously demonstrated in the work of Tamura and Burghardt [J. Am. Chem. Soc. 2013, 135, 16364]. For an H-aggregate type, stacked donor species, the initial bright state undergoes ultrafast internal conversion within the excitonic manifold, creating multiple charge transfer pathways before reaching the lowest-energy dark exciton, which is uncoupled from the charge transfer manifold. This process profoundly affects the charge separation mechanism and efficiency. For small energetic offsets between the interfacial excitonic and charge transfer states, a delocalized initial bright state proves less prone to electron-hole capture by the interfacial trap than a localized, vibronic wavepacket close to the interface. For both delocalized and localized initial states, a comparable yield of free carriers is obtained, which is found to be optimal for energetic offsets of the order of the Coulomb barrier to charge separation. Interfacial trapping is significantly reduced as the barrier height decreases with fullerene aggregation. Despite the high-dimensional nature of the system, charge separation is an ultrafast coherent quantum process exhibiting oscillatory features as observed in recent experiments.

Absorption and fluorescence spectra of poly(p-phenylenevinylene) (PPV) oligomers: an ab initio simulation

The absorption and fluorescence spectra of poly(p-phenylenevinylene) (PPV) oligomers with up to seven repeat units were theoretically investigated using the algebraic diagrammatic construction method to second order, ADC(2), combined with the resolution-of-the-identity (RI) approach. The ground and first excited state geometries of the oligomers were fully optimized. Vertical excitation energies and oscillator strengths of the first four transitions were computed. The vibrational broadening of the absorption and fluorescence spectra was studied using a semiclassical nuclear ensemble method. After correcting for basis set and solvent effects, we achieved a balanced description of the absorption and fluorescence spectra by means of the ADC(2) approach. This fact is documented by the computed Stokes shift along the PPV series, which is in good agreement with the experimental values. The experimentally observed band width of the UV absorption and fluorescence spectra is well reproduced by the present simulations showing that the nuclear ensemble generated should be well suitable for consecutive surface hopping dynamics simulations.

How disorder controls the kinetics of triplet charge recombination in semiconducting organic polymer photovoltaics

Theoretical models of polymer–fullerene interfaces indicate that inhomogeneous broadening of fullerene energy levels introduces strong coupling between the interfacial³CT and nearby fullerene triplet excitons that can enhance the decay of these states in systems with higher degrees of energetic disorder.

Electronically excited states in poly(p-phenylenevinylene): vertical excitations and torsional potentials from high-level ab initio calculations

Ab initio second-order algebraic diagrammatic construction (ADC(2)) calculations using the resolution of the identity (RI) method have been performed on poly-(p-phenylenevinylene) (PPV) oligomers with chain lengths up to eight phenyl rings. Vertical excitation energies for the four lowest π–π* excitations and geometry relaxation effects for the lowest excited state (S₁) are reported. Extrapolation to infinite chain length shows good agreement with analogous data derived from experiment. Analysis of the bond length alternation (BLA) based on the optimized S₁ geometry provides conclusive evidence for the localization of the defect in the center of the oligomer chain. Torsional potentials have been computed for the four excited states investigated and the transition densities divided into fragment contributions have been used to identify excitonic interactions. The present investigation provides benchmark results, which can be used (i) as reference for lower level methods and (ii) give the possibility to parametrize an effective Frenkel exciton Hamiltonian for quantum dynamical simulations of ultrafast exciton transfer dynamics in PPV type systems.

Thermodynamics of exciton/polaritons in one and two dimensional organic single-crystal microcavities

We consider here the thermodynamics and phase-diagram of exciton/polaritons formed in low-dimensional organic single-crystal microcavities. Using the Dicke model for a lattice of Frenkel excitons coupled to a common cavity mode, we explore the transition between normal and condensate regimes as depending upon the exciton band-width and temperature of the polariton gas. We show that for one-dimensional conjugated polymers, the coexistence curve at low temperatures shifts towards lower critical coupling strengths as the exciton band-width is increased. We also consider the effect of orientational disorder in a two-dimensional polyacene slab on the formation of the polariton BEC. Our results indicate that while a small degree of orientational disorder will not have a profound effect on the critical exciton/photon coupling strength needed to produce the transition from normal to BEC regimes, BEC will likely be suppressed in glassy or strongly disordered molecular films.

Exciton formation, relaxation, and decay in PCDTBT

The nature and time evolution of the primary excitations in the pristine conjugated polymer, PCDTBT, are investigated by femtosecond-resolved fluorescence up-conversion spectroscopy. The extensive study includes data from PCDTBT thin film and from PCDTBT in chlorobenzene solution, compares the fluorescence dynamics for several excitation and emission wavelengths, and is complemented by polarization-sensitive measurements. The results are consistent with the photogeneration of mobile electrons and holes by interband π-π* transitions, which then self-localize within about 100 fs and evolve to a bound singlet exciton state in less than 1 ps. The excitons subsequently undergo successive migrations to lower energy localized states, which exist as a result of disorder. In parallel, there is also slow conformational relaxation of the polymer backbone. While the initial self-localization occurs faster than the time resolution of our experiment, the exciton formation, exciton migration, and conformational changes lead to a progressive relaxation of the inhomogeneously broadened emission spectrum with time constants ranging from about 500 fs to tens of picoseconds. The time scales found here for the relaxation processes in pristine PCDTBT are compared to the time scale (<0.2 ps) previously reported for photoinduced charge transfer in phase-separated PCDTBT:fullerene blends (Phys. Rev. B 2010, 81, 125210). We point out that exciton formation and migration in PCDTBT occur at times much longer than the ultrafast photoinduced electron transfer time in PCDTBT:fullerene blends. This disparity in time scales is not consistent with the commonly proposed idea that photoinduced charge separation occurs after diffusion of the polymer exciton to a fullerene interface. We therefore discuss alternative mechanisms that are consistent with ultrafast charge separation before localization of the primary excitation to form a bound exciton.

Effect of exciton self-trapping and molecular conformation on photophysical properties of oligofluorenes

Electronic absorption and fluorescence transitions in fluorene oligomers of differing lengths are studied experimentally and using density functional theory (DFT) and time-dependent DFT. Experimental values are determined in two ways: from the measured molar absorption coefficient and from the radiative rate deduced from a combination of fluorescence quantum yield and lifetime measurements. Good agreement between the calculated and measured transition dipoles is achieved. In both theory and experiment a gradual increase in transition dipoles with increasing oligomer length is found. In absorption the transition dipole follows an approximately n(0.5) dependence on the number of fluorene units n for the range of 2 < or = n < or = 12, whereas a clear saturation of the transition dipole with oligomer length is found in fluorescence. This behavior is attributed to structural relaxation of the molecules in the excited state leading to localization of the excitation (exciton self-trapping) in the middle of the oligomer for both twisted and planar backbone conformations. Twisted oligofluorene chains were found to adopt straight or bent geometries depending on alternation of the dihedral angle between adjacent fluorene units. These different molecular conformations show the same values for the transition energies and the magnitude of the transition dipole.

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.

Lattice theory of ultrafast excitonic and charge-transfer dynamics in DNA

We propose a lattice fermion model suitable for studying the ultrafast photoexcitation dynamics of ordered chains of deoxyribonucleic acid (DNA) polymers. The model includes both parallel (intrachain) and perpendicular (cross-chain) terms as well as diagonal cross-chain terms coupling neighboring bases. The general form of our Hamiltonian is borrowed from lattice fermion models of quantum chromodynamics. The band structure for this model can be determined analytically, and we use this as a basis for computing the singly excited states of the poly(dA)poly(dT) DNA duplex using configuration interaction singles. Parameters for the model are taken from various literature sources and our own ab initio calculations. Results indicate that the excited states consist of a low energy band of dark charge-separated states followed by separate bands of delocalized excitonic states which have weak mixing between the thymidine and adenosine sides of the DNA chain. We then propose a lattice exciton model based upon the transition dipole-dipole couplings between bases and compare the analytical results for the survival probability of an initially localized exciton to exact numerical results. The results herein underscore the competing role of excitonic and charge-transfer dynamics in these systems.

Exciton dissociation at donor-acceptor polymer heterojunctions: Quantum nonadiabatic dynamics and effective-mode analysis

The quantum-dynamical mechanism of photoinduced subpicosecond exciton dissociation and the concomitant formation of a charge-separated state at a semiconducting polymer heterojunction is elucidated. The analysis is based upon a two-state vibronic coupling Hamiltonian including an explicit 24-mode representation of a phonon bath comprising high-frequency (C==C stretch) and low-frequency (torsional) modes. The initial relaxation behavior is characterized by coherent oscillations, along with the decay through an extended nonadiabatic coupling region. This region is located in the vicinity of a conical intersection hypersurface. A central ingredient of the analysis is a novel effective mode representation, which highlights the role of the low-frequency modes in the nonadiabatic dynamics. Quantum dynamical simulations were carried out using the multiconfiguration time-dependent Hartree method.

Exciton Regeneration Dynamics in Model Donor−Acceptor Polymer Heterojunctions

We present a theoretical investigation on various semiconducting materials that exhibit photovoltaic and photoluminecent properties. Our focus is on the relaxation dynamics that occur upon photoexcitation of a couple of type II donor-acceptor heterojunction systems. In addition to the diabatic approach our two-band exciton model employs to study the phonon-assisted relaxations, we adopt the Marcus-Hush semiclassical method to incorporate lattice reorganization. This enables us to look at the state-to-state interconversions from the relaxed excited-state configurations in model polymer blends of poly(9,9-dioctylfluorene-co-N-(4-butylphenyl)diphenylamine) (TFB) with poly(9,9-dioctylfluorene-co-benzothiadiazole) (F8BT) and poly(9,9-dioctylfluorene-co-bis-N,N-(4-butylphenyl)-bis-N,N-phenyl-1,4-phenylenediamine) (PFB) with F8BT. Our results stress the significance of vibrational relaxation in the state-to-state relaxation. Furthermore, while a tightly bound charge-transfer state (exciplex) remains the lowest excited state, we show that the regeneration of the optically active lowest excitonic state in TFB:F8BT is possible via the existence of a steady state.

Time-convolutionless master equation for mesoscopic electron-phonon systems

The time-convolutionless master equation for the electronic populations is derived for a generic electron-phonon Hamiltonian. The equation can be used in the regimes where the golden rule approach is not applicable. The equation is applied to study the electronic relaxation in several models with the finite number of normal modes. For such mesoscopic systems the relaxation behavior differs substantially from the simple exponential relaxation. In particular, the equation shows the appearance of the recurrence phenomena on a time scale determined by the slowest mode of the system. The formal results are quite general and can be used for a wide range of physical systems. Numerical results are presented for a two level system coupled to Ohmic and super-Ohmic baths, as well as for a model of charge-transfer dynamics between semiconducting organic polymers.

Effect of Temperature and Chain Length on the Bimodal Emission Properties of Single Polyfluorene Copolymer Molecules

Fluorescence emission spectra were recorded for isolated polymer chains of the polyfluorene copolymer, F8BT [poly(9,9-di-n-octylfluorene-alt-benzothiadiazole)], at 298 and 20 K for two molecular weights (chain lengths). For long-chain F8BT at 298 K, the observed distribution of single-molecule emission maxima G(Emax) is bimodal, with peaks at approximately 2.35 eV ("blue") and approximately 2.25 eV ("red"). Previously, the red forms have been assigned to polymer chains that possess intrachain contacts, which lowers the local singlet exciton energy. At approximately 20 K, G(Emax) collapses into a single broad distribution centered at approximately 2.3 eV for long-chain F8BT. However, this distribution can be further divided into a high-energy edge that is dominated by the "blue" form, while the remainder of the distribution is composed of the "red" form. Low-molecular-weight F8BT samples emit exclusively from the blue form, and no shift in peak maxima with low temperature was observed. A Franck-Condon analysis reveals a decrease in emitting state displacements between spectra measured at 298 and 20 K, suggesting that temperature-induced structural displacements are responsible for the change in the bimodal emission.

Spectral broadening and diffusion by torsional motion in biphenyl

We have studied biphenyl by time-dependent density-functional theory. In particular, we have analyzed the dependence of singlet excitation energies and transition dipoles on the torsional angle between the phenyl groups. The torsional spectrum has been computed quantum mechanically as well as semiclassically in order to understand how this influences the broadening of absorption and luminescence spectra. Our results are in best agreement with supersonic jet spectroscopy data, but also fit astonishingly well to spectra of biphenyl in condensed phase. Furthermore, we compare the torsional and vibrational relaxation and discuss qualitatively the general consequences for poly-para-phenylenes and related conjugated polymers as poly-thiophenes, considering, in particular, how side chains and solvents may affect the optical spectra.

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 offset 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 offset 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 offset 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.

Photoconductivity and current producing states in molecular semiconductors

We present a methodology for computing photocurrent production in molecular semiconducting molecules. Our model combines a single-configuration interaction picture with the nonequilibrium Green's function approach to compute the current response of a molecular semiconducting wire following excitation. We give detailed analysis of the essential excitonic, charge transfer, and dipole states for poly-(phenylenevinylene) chains of length 32 and 48 repeat units under an electric field bias and use this to develop a reduced dimensional tunneling model which accounts for chain-length and field-dependent behavior. In this paper, we consider the decay of an excited electron/hole state on a molecular wire under bias attached to semiconducting leads at either end. We find that the current produced by the decay of an excitation depends not only upon the lifetime of the state, as given by the imaginary part of its complex eigenvalue, but also upon the net charge on terminal ends of the molecule. We also find that weakly bound electron/hole charge-transfer pairs can decay into the continuum via field induced tunneling and produce a net current whereas excitonic states decay via tunneling but give no net current contribution.