The photophysics of $π$-conjugated polymers has been of considerable interest over the last three decades because of their organic semiconductor properties. Primary photoexcitations, Frenkel excitons, can be probed optically by means of numerous linear spectroscopies, providing a wealth of information on the the strength of excitonic coupling, the exciton coherence length, and on the nature of the disordered energy landscape. Nonetheless, there are intrinsic limitations in the information that can be obtained with linear spectroscopy compared to non-linear coherent techniques. Examples of this are the separation of homogeneous and inhomogeneous broadening contributions to the total exciton spectral lineshape, the detailed spectral structure of exciton-vibrational coupling, and correlations between optical excitations, including exciton-charge and exciton-exciton correlations. In the present work, we discuss the role of two-dimensional coherent excitation spectroscopy and review its applications towards unravelling the basic photophysics of $π$-conjugated polymers as well as polymer:fullerene blends, and we argue that these techniques are now valuable mainstream materials optical probes.
Optical devices fabricated using conjugated polymer systems give rise to singlet exciton yields which are high compared to the statistically predicted estimate of 25% obtained using simple recombination schemes. In this study we evaluate the singlet exciton yield in conjugated polymers systems by fitting to a model that incorporates the Pauli exclusion principle. The rate equations which describe the exciton dynamics include quantum dynamical components (both density and spin-dependent) which arise during the spin-allowed conversion of composite intra-molecular excitons into loosely bound char…
We report on high-dimensional quantum dynamical simulations of torsion-induced exciton migration in a single-chain oligothiophene segment comprising twenty repeat units, using a first-principles parametrized Frenkel J-aggregate Hamiltonian. Starting from an initial inter-ring torsional defect, these simulations provide evidence of an ultrafast two-time scale process at low temperatures, involving exciton-polaron formation within tens of femtoseconds, followed by torsional relaxation on a ~300 femtosecond time scale. The second step is the driving force for exciton migration, as initial conjuga…
Many optoelectronic devices based on organic materials require rapid and long-range singlet exciton transport. Key factors that control the transport of singlet excitons includes the electronic structure of the material, disorder and exciton-phonon coupling. An important parameter whose influence on exciton transport has not been explored is the symmetry of the singlet electronic state (S1). Here, we employ femtosecond transient absorption spectroscopy and microscopy to reveal the relationship between the symmetry of S1 and exciton transport in highly aligned, near-disorder free, one-dimension…
Attachment of chemical substituents (such as polar moieties) constitutes an efficient and convenient way to modify physical and chemical properties of conjugated polymers and oligomers. Associated modifications in the molecular electronic states can be comprehensively described by examining scattering of excitons in the polymer's backbone at the scattering center representing the chemical substituent. Here, we implement effective tight-binding models as a tool to examine the analytical properties of the exciton scattering matrices in semi-infinite polymer chains with substitutions. We demonstr…
This is a review of exciton dynamics in conjugated polymers. Exciton dynamics encompass multiple time and length scales. Ultrafast femtosecond processes are intrachain and involve a quantum mechanical correlation of the exciton and nuclear degrees of freedom. In contrast, post-picosecond processes involve the incoherent Forster transfer of excitons between polymer chains. Exciton dynamics is also strongly determined by the spatial and temporal disorder that is ubiquitous in conjugated polymers. Since excitons are delocalized over hundreds of atoms, a theoretical understanding of these processe…
Conjugated polymers offer potential for many diverse applications but we still lack a fundamental microscopic understanding of their electronic structure. Elementary photoexcitations - excitons - span only a few nanometres of a molecule, which itself can extend over microns, and how their behaviour is affected by molecular dimensions is not fully understood. For example, where is the exciton formed within a conjugated segment, is it always situated on the same repeat units? Here, we introduce structurally-rigid molecular spoked wheels, 6 nanometres in diameter, as a model of extended pi-conjug…
We report on large-scale simulations of intrachain exciton dynamics in poly(para-phenylene vinylene). Our coarse-grained 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 are 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…
A hot-exciton is usually the initial elementary excitation product of the solid phase, particularly in low dimensional photonic materials, which is a bottle-neck to all subsequent processes. Measurement of hot-exciton emission (HExEm) is a great challenge due to fast EK relaxation and thus very weak transient emission. Here we report the first unambiguous observation of femtosecond HExEm from thin films of a model quasi-one-dimensional π-conjugated organic rigid-rod quantum nanowire, MeLPPP (methyl-substituted ladder-type poly(para-phenylenes), by using femtosecond time-resolved fluorescence s…
Ring torsion effects on optical excitation properties in poly(para-phenylene) (PPP) and polyaniline (PAN) are investigated by extending the Shimoi-Abe model [Synth. Met. 78, 219 (1996)]. The model is solved by the intermediate exciton formalism. Long-range excitons are characterized, and the long-range component of the oscillator strengths is calculated. We find that ring torsions affect the long-range excitons in PAN more easily than in PPP, due to the larger torsion angle of PAN and the large number of bonds whose hopping integrals are modulated by torsions. Next, ring torsional disorder eff…
Copolymers such as PCDTBT (poly(N-9'-heptadecanyl-2,7-carbazole-alt-5,5-(4',7'-di-2-thienyl- 2',1',3'-benzothiadiazole))) are commonly employed as donor material in bulk heterojunction solar cells. Recently, chemical defects such as homocouplings have been shown to form at the material synthesis stage, strongly reducing the short circuit current in organic photovoltaics. Here we show that both, low molecular weight and homocoupling defects reduce the short circuit current of solar cells because of limited exciton diffusion. We propose a model that unites and explains the influence of both chem…
We employ five π-conjugated model materials of different molecular shape --- oligomers and cyclic structures --- to investigate the extent of exciton self-trapping and torsional motion of the molecular framework following optical excitation. Our studies combine steady-state and transient fluorescence spectroscopy in the ensemble with measurements of polarization anisotropy on single molecules, supported by Monte Carlo simulations. The dimer exhibits a significant spectral red-shift within $\sim$ 100 ps after photoexcitation which is attributed to torsional relaxation. This relaxation mechanism…
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 tec…
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…
Electronic structures and optical excitations in Moebius conjugated polymers are studied theoretically. Periodic and Moebius boundary conditions are applied to the tight binding model of poly(para-phenylene), taking exciton effects into account. We discuss that oligomers with a few structural units are more effective than polymers for observations of effects of discrete wave numbers that are shifted by the change in boundary condition. Next, calculations of optical absorption spectra are reported. Certain components of optical absorption for an electric field perpendicular to the polymer axis …
We present a hybrid quantum-classical simulation of charge-polaron transport in conjugated polymers. The charge, which couples to the angular rotations of the monomers, is modeled via the time-dependent Schrödinger equation, while the monomers are treated classically via the Ehrenfest equations of motion. In addition, the system is thermalized by assuming that the monomers are subject to Brownian fluctuations modeled by the Langevin equation. Charge coupling to the monomer rotations localizes the particle into a Landau polaron, while the thermal fluctuations of the monomers causes polaron dyna…
The scattering and recombination processes between two triplet excitons in conjugated polymers are investigated by using a nonadiabatic evolution method, based on an extended Su-Schrieffer-Heeger model including interchain interactions. Due to the interchain coupling, the electron and/or hole in the two triplet excitons can exchange. The results show that the recombination induces the formation of singlet excitons, excited polarons and biexcitons. Moreover, we also find the yields of these products, which can contribute to the emission, increase with the interchain coupling strength, in good a…
The electronic properties of macromolecular semiconductor thin films depend profoundly on their solid-state microstructure, which in turn is governed, among other things, by the processing conditions selected and the polymer chemical nature and molecular weight. Specifically, low-molecular-weight materials form crystalline domains of cofacially $π$-stacked molecules, while the usually entangled nature of higher molecular-weight polymers leads to microstructures comprised of molecularly ordered crystallites interconnected by amorphous regions. Here, we examine the interplay between extended exc…
Organic semiconductors have the remarkable property that their optical excitation not only generates charge-neutral electron-hole pairs (excitons) but also charge-separated polaron pairs with high yield. The microscopic mechanisms underlying this charge separation have been debated for many years. Here we use ultrafast two-dimensional electronic spectroscopy to study the dynamics of polaron pair formation in a prototypical polymer thin film on a sub-20-fs time scale. We observe multi-period peak oscillations persisting for up to about 1 ps as distinct signatures of vibronic quantum coherence a…
Inter- or intramolecular coupling processes between chromophores such as excimer formation or H- and J-aggregation are crucial to describing the photophysics of closely packed films of conjugated polymers. Such coupling is highly distance dependent, and should be sensitive to both fluctuations in the spacing between chromophores as well as the actual position on the chromophore where the exciton localizes. Single-molecule spectroscopy reveals these intrinsic fluctuations in well-defined bi-chromophoric model systems of cofacial oligomers. Signatures of interchromophoric interactions in the exc…
An appealing definition of the term "molecule" arises from consideration of the nature of fluorescence, with discrete molecular entities emitting a stream of single photons. We address the question of how large a molecular object may become by growing deterministic aggregates from single conjugated polymer chains. Even particles containing dozens of individual chains still behave as single quantum emitters due to efficient excitation energy transfer, while the brightness is raised due to the increased absorption cross-section of the suprastructure. Excitation energy can delocalize between indi…
Charges in conjugated polymer materials have a strong impact on the photophysics and their interaction with the primary excited state species has to be taken into account in understanding device properties. Here, we employ single-molecule spectroscopy to unravel the influence of charges on several photoluminescence (PL) observables. The charges are injected either stochastically by a photochemical process, or deterministically in a hole-injection sandwich device configuration. We find that upon charge injection, besides a blue-shift of the PL emission and a shortening of the PL lifetime due to…
Understanding of degradation mechanisms in polymer:fullerene bulk-heterojunctions on the microscopic level aimed at improving their intrinsic stability is crucial for the breakthrough of organic photovoltaics. These materials are vulnerable to exposure to light and/or oxygen, hence they involve electronic excitations. To unambiguously probe the excited states of various multiplicities and their reactions with oxygen, we applied combined magneto-optical methods based on multifrequency (9 and 275 GHz) electron paramagnetic resonance (EPR), photoluminescence (PL), and PL-detected magnetic resonan…
Component of photoexcited states with large spatial extent is investigated for optical absorption spectra of the electroluminescent conjugated polymers by using the intermediate exciton theory. We calculate the ratio of oscillator strengths due to long-range excitons with respect to sum of all the oscillator strengths of the absorption as a function of the monomer number. The oscillator strengths of the long-range excitons in poly(para-phenylene) are smaller than those in poly(para-phenylenevinylene), and those of poly(para-phenylenedivinylene) are larger than those in poly(para-phenylenevinyl…
In the last two decades, the three-beams pump-push-probe (PPP) technique has become a well-established tool for investigating the multidimensional configurational space of a molecule, as it permits to disclose precious information about the multiple and often complex deactivation pathways of the excited molecule. From the spectroscopic point of view, such a tool has revealed details about the efficiency of charge pairs generation and conformational relaxation in p-conjugated molecules and macromolecules. In addition, PPP has been effectively utilised for modulating the gain signal in conjugate…
We develop a stochastic theory that treats time-dependent exciton-exciton s-wave scattering and that accounts for dynamic Coulomb screening, which we describe within a mean-field limit. With this theory, we model excitation-induced dephasing effects on time-resolved two-dimensional coherent optical lineshapes and we identify a number of features that can be attributed to the many-body dynamics occurring in the background of the exciton, including dynamic line narrowing, mixing of real and imaginary spectral components, and multi-quantum states. We test the model by means of multidimensional co…
By employing the Dirac-Frenkel time-dependent variational principle, we study the dynamical properties of the Holstein molecular crystal model with diagonal and off-diagonal exciton-phonon coupling. A linear combination of the Davydov D$_1$ (D$_2$) Anstaz, referred to as the multi-D$_1$ Ansatz (multi-D$_2$ Ansatz), is used as the trial state with enhanced accuracy but without sacrificing efficiency. The time evolution of the exciton probability is found to be in perfect agreement with that of the hierarchy equations of motion, demonstrating the promise the multiple Davydov trial states hold as…
Singlet fission is a spin-allowed exciton multiplication process in organic semiconductors that converts one spin-singlet exciton to two triplet excitons. It offers the potential to enhance solar energy conversion by circumventing the Shockley-Queisser limit on efficiency. Recently, the mechanism of the primary singlet fission process in pentacene and its derivatives have been extensively investigated, however, the nature of the primary ultrafast process in singlet fission is still a matter of debate. Here, we study the singlet fission process in a pentacene film by employing a combination of …
We propose a two-dimensional spectroscopic protocol for measuring the time-dependent coherences between the stationary states of a system induced by a time-dependent system-bath interaction. We also investigate the role of temporally-correlated noise on coherence dephasing. This protocol enables dynamical information about the system and its coupling to the environment to be determined. Our results are based on the quantum-trajectory method, and are obtained from both approximate, analytical and exact, numerical solutions of the time-dependent Schroedinger equation. As an example, we show how …
