Hopping approach towards exciton dissociation in conjugated polymers

By employing random walk an analytic theory for the dissociation of singlet excitons in a random organic solid, for instance, a conjugated polymer, has been developed. At variance of conventional three-dimensional Onsager theory, it is assumed that an exciton with finite lifetime can first transfer endothermically an electron to an adjacent site, thereby generating a charge transfer state whose energy is above the energy of that of the initial exciton. In a second step the latter can fully dissociate in accordance with Onsager's concept Brownian motion. The results indicate that, depending of the energy required for the first jump, the first jump contributes significantly to the field dependence of the dissociation yield. Disorder weakens the temperature dependence of the yield dramatically and precludes extracting information on the exciton binding energy from it.     

Scattering process between polaron and exciton in conjugated polymers

Scattering process between a negative polaron and an exciton in a polymer chain is investigated by using the Su-Schrieffer-Heeger model modified to include electron-electron interactions, the Brazovskii-Kirova symmetry breaking term, and an external electric field. It is found that the scattering process is spin dependent. If the polaron and the exciton have parallel spins, the polaron can easily pass through the exciton as if it "do not see" the exciton. If the polaron and the exciton have antiparallel spins, there exist strong repulsion between them. The polaron may be bounced back, be dissociated or pass through the exciton depending on the strength of the external electric field. In any of these cases, the polaron cannot break the exciton.     

Structure—Property relationships for exciton transfer in conjugated polymers

The ability of conjugated polymers to function as electronic materials is dependent on the efficient transport of excitons along the polymer chain. Generally, the photophysics of the chromophore monomer dictate the excited state behavior of the corresponding conjugated polymers. Different molecular structures are examined to study the role of excited state lifetimes and molecular conformations on energy transfer. The incorporation of rigid, three‐dimensional scaffolds, such as iptycenes and cyclophanes, can encourage an oblique packing of the chromophore units of a conjugated polymer, thus allowing the formation of electronically‐coupled aggregates that retain high quantum yields of emission. Rigid iptycene scaffolds also act as excellent structural directors that encourage complete solvation of PPEs in a liquid crystal (LC) solvent. LC‐PPE mixtures display both an enhanced conformational alignment of polymer chains and extended effective conjugation lengths relative to isotropic solutions, which leads to enhanced energy transfer. Facile exciton migration in poly(p‐phenylene ethynylene)s (PPEs) allows energy absorbed over large areas to be funneled into traps created by the binding of analytes, resulting in signal amplification in sensory devices. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

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.     

Temperature dependence of radiation effects on polymers

Temperature dependence of radiation effect on various polymers including hydrocarbon and fluorocarbon polymers was investigated. Gas evolution and mechanical properties were measured in a wide range of temperatures. G-values of chain scission and crosslinking were estimated. It has been made clear from those experimental results that radiation effect be profoundly affected by temperature. Particularly, significant changes of radiation effect in the melting region were found out.     

Temperature dependence of nanoholes free volumes in amorphous polymers

Estimation of the free volume fraction in polymers from positron annihilation lifetime data is usually obtained by assuming spherical nanoholes. Although this guess is sometimes well verified, in other cases non-spherical geometries give better agreement with theoretical predictions. Furthermore, the assumption of isotropic expansion of nanoholes (implicit in these models) could be unrealistic owing to constrained movements of the molecules. Comparison of hole-lattice theory with experimental data for some oligomeric structures gives evidence of anisotropic nanoholes expansion versus temperature.     

Temperature dependence of the bulk crystallization rate of polymers

Data already existing in the literature for the overall crystallization kinetics of a variety of polymers have been analyzed according to different possible nucleation mechanisms. The conclusions reached are similar to those previously deduced from an examination of ata for spherulite growth rates. It is demonstrated that, if allowed a reasonable choice for the equilibrium melting temperature, no unbiased selection of a unique nucleation process can be made. Moreover, a set of universal parameters exists for each of the nucleation and growth processes considered which allows the data for all polymers to be represented by a single straight line. The only quantities that are unique to a given polymer are the equilibriun melting temperature and the activation energy for transport.     

Gas diffusion in partially crystalline polymers part I: Concentration dependence

In this work, a phenomenological model for the gas diffusion in partially crystalline polymers using differential effective medium theory is presented. By making an analogy with the power law known as Archie's law which relates the d.c. conductivity of a brine saturated porous rock to its porosity; we show that gas diffusion through semicrystalline polymers can be described in a similar way. It is assumed that the diffusion coefficient in the crystalline region is zero, while in the amorphous region it is given by a free volume model, and an effective diffusion coefficient D^eff, is obtained using the mentioned analogy. The variation of D^eff upon concentration is analyzed through its free volume dependence. The crystallinity dependence is considered through an average chain immobilization factor 〈β〉 which is explicitely derived. Finally, the results of this model are compared with experimental data given by Kreituss and Frisch, obtaining a good agreement. © 1996 John Wiley & Sons, Inc.     

Polaron effects and electric field dependence of the charge carrier mobility in conjugated polymers

Charge transport in conjugated polymers has been investigated using Monte Carlo simulations implemented on top of the Marcus theory for donor-acceptor transition rates. In particular, polaron effects and the dependency of the mobility on the temperature and the applied electric field have been studied. The conclusions are that while the qualitative temperature dependence is similar to that predicted by Miller-Abrahams theory in the Gaussian disorder model (GDM), the electric field dependence is characterized by a crossover into the Marcus inverted region, not present in the GDM. Furthermore, available analytical approximations to describe the electric field dependence of the mobility in Marcus theory fail to fit the simulation data and hence cannot be used to directly draw conclusions about the importance of polaron effects for charge transport in conjugated polymers.     

Metallocene-containing conjugated polymers

The paper gives a review of publications on polymers with conjugated matrices (PPy, PTh, PAni, hydrocarbon or mixed chains...) which incorporate metallocene complexes (Fe, Ru, Co; Ni, Ti, Zr, Ta) with two cyclopentadienyl ligands (Cp) and their derivatives, in particular with methylated cyclopentadienyl rings (Cp*), as well as hemi-metallocene complexes (Fe, Ru, Co, Mn), as pendant groups or inside the principal chain (part B). The information on related short-chain systems, monomers and oligomers, is also included. In part A, a brief overview of various conjugated polymer materials is presented, with their classification in accordance with the conductivity mechanism (ionic, electronic or mixed conductors) or with the structural type (linear-chain organic or mixed polymers, derivatization, metallopolymers, multi-dimensional structures, alternating and block copolymers with organic or mixed units, hybrid materials with a mixture of conjugated and inert polymers, polymers inside a solid matrix, conjugated polymers with incorporated nanoelements of transition metals, carbon, semiconductors etc.     

Temperature dependence of the dynamic mechanical properties of filled polymers

A theory has been developed to explain the jump in the relative modulus of filled polymers near the glass transition temperature T_g and the subsequent decrease in relative modulus at temperatures above the glass transition temperature. The theory is based upon the concept that there are some particle–particle contacts in doublets and in agglomerates containing a larger number of particles. Below T_g motion of particles at the contact points is possible because of the high modulus of the polymer. At T_g particle–particle motion mostly ceases because of the low modulus of the polymer. At higher temperatures, the mismatch in the coefficients of expansion allows some motion to occur at points of contact and slippage may occur at the polymer–particle interfaces, so the modulus decreases. It is shown theoretically and experimentally that both the elastic modulus and the mechanical damping depend upon the nature of the surface of the particles.     

Exciton dissociation in conjugated polymers

In conjugated polymers, a majority of photogenerated charges form metastable geminate pairs (GPs), of which only some fraction can dissociate completely. Both the yield of GP photogeneration and the probability of further dissociation of GPs into free charges depend upon an external electric field. In the present article we discuss several experimental methods to detect the existence of geminate pairs such as delayed field collection of charges, field quenching of fluorescence, and field-assisted photoinduced optical absorption. It is shown that the field dependences of the exciton dissociation into GPs and of the free carrier photogeneration yield are rather similar. This is in contrast with the traditional Onsager theory, which assumes field-independent yield of primary photoionization and disregards the field dependence of the initial separations between carriers in GPs.     

Bipolaron recombination in conjugated polymers

By using the Su-Schrieffer-Heeger model modified to include electron-electron interactions, the Brazovskii-Kirova symmetry breaking term and an external electric field, we investigate the scattering process between a negative and a positive bipolaron in a system composed of two coupled polymer chains. Our results show that the Coulomb interactions do not favor the bipolaron recombination. In the region of weak Coulomb interactions, the two bipolarons recombine into a localized excited state, while in the region of strong Coulomb interactions they can not recombine. Our calculations show that there are mainly four channels for the bipolaron recombination reaction: (1) forming a biexciton, (2) forming an excited negative polaron and a free hole, (3) forming an excited positive polaron and a free electron, (4) forming an exciton, a free electron, and a free hole. The yields for the four channels are also calculated.     

Triplet-polaron quenching in conjugated polymers

We studied the triplet-polaron quenching in a platinum(II) porphyrin- (PtOEP-) doped polyspirobifluorene (PSF-TAD) copolymer. The copolymer contains a hole-transporting phenylenediamine unit (TAD) as a comonomer. Triplet-polaron quenching was probed by the change in PtOEP phosphorescence lifetime under an applied voltage in a unipolar device. The charge-induced reduction of the optically excited lifetime of PtOEP is one-third for the highest applied bias. The charge density can be obtained from current-voltage characteristics in the space-charge-limited (SCL) regime. The obtained hole mobility under SCL conditions is (7 +/- 2) x 10(-5) cm(2)/(V s). This result is in accord with recent mobility measurements of the time-of-flight mobility in our polymer. The triplet-polaron recombination constant was evaluated to be (4 +/- 1) x 10(-13) cm(3)/s, implying a triplet-polaron interaction radius of 2 x 10(-10) m. The results show that triplet-polaron annihilation cannot be neglected in device models for phosphorescent light-emitting diodes.     

Embedded units in conjugated polymers

The problem of embedding of several monomeric units (benzene, thiophene, isothianaphthene) into linear oligoenes or into a polymer built up by the same units is discussed. Using a simple model Hamiltonian, we evaluate the geometry (bond lengths) and electronic structure (energy gaps) of conjugated oligomers containing up to 200 atoms. Special attention is paid to end effects. The quinoid-aromatic transition and the conjugation interruption due to embedded defects is studied in some detail.     

Two-photon dispersion in conjugated polymers

The frequency dependence of the dispersive and absorptive parts of a strongly allowed two-photon transition is determined in a series of conjugated polymer solutions. The data analysis yields the energy and width of the two-photon transition, symmetry assignment for the two-photon transition (A_g → A_g), and oscillator strengths for both the one-photon and two-photon transitions.     

Temperature dependence of ESR spectra of nitroxide spin probe in glassy polymers

Temperature dependencies of ESR spectra of nitroxide spin probes in glassy polymers near and below glass transition temperature were examined in detail. Three temperature ranges, each characterized by specific changes in spectral shape, were defined. (i) In the low temperature range, ESR spectra of nitroxide radical in glassy polymer matrix weakly depend on temperature and remain qualitatively the same. (ii) In the intermediate temperature range, significant changes in the shape of spectra are observed. (iii) A new phenomenon was revealed near and below glass transition temperature: narrowing of linewidths occurs while the ratio of amplitudes of different components varies insignificantly. Analysis of molecular rotational mobility was carried out by means of commonly used empirical approaches. It was shown that widely used formulas and empirical approaches are not applicable for characterization of molecular mobility in glassy polymers. Mechanisms of rotational molecular movements in glassy polymers are discussed. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 563–575, 2009