Chromophores in Conjugated Polymers

For an ideal, perfectly stretched CP chain described with the H¨uckel model one would expect theπ electron system to be delocalised along the entire polymer backbone and the

overlap of theπ-electron wave functions would not be interrupted in the molecule. However, it has been shown that electron-electron and particularly electron-phonon interactions lead to a localisation of the wave functions on subunits of a chain [28, 76, 83]. Additionally, a CP chain is typically not perfectly aligned, but exhibits a disordered chain conformation due to structural defects [28, 30, 49] such as kinks, strong bending of the chain, and large torsional angles between adjacent phenylene-rings. Moreover, a polymer chain contains to some extend chemical defects, e. g. impurities or sp³-hybridised carbon atoms. Both the conformational and chemical defects interrupt the π-conjugation along the backbone.

According to a model put forward by B¨assler and co-workers [29,84,85] a CP may therefore be represented as a chain of short linear subunits each comprising several repeating units (typically 5 – 15 monomers). These linear segments are separated by chemical and/or conformational defects along the polymer backbone, which give rise to a scission of the π-electron system. The fully conjugated subunits of the chain are commonly referred to as chromophores, segments or sites and the length of such a segment (in terms of the number of repeating units) is calledconjugation length.

Conjugated polymer chains may be as long as several hundreds of repeating units and accordingly contain tens to hundreds of sites per chain [30, 49, 60]. Therefore, a CP consti-tutes an intrinsically multichromophoric system which is schematically shown in Fig. 2.3.

Due to the fact that the chemical/conformational defects, which break the π-conjugation, are statistically distributed, a distribution of conjugation lengths is present in a poly-mer sample. The average conjugation length is known as effective conjugation length. It has been found that both the effective conjugation length and the width of the distribu-tion of conjugadistribu-tion lengths depends on the chemical structure of the polymer (flexibility of the backbone) as well as on the sample processing and preparation, such as solvent polarity, temperature, polymer concentration, film deposition procedure, and thermal an-nealing [30, 49, 57, 60, 86, 87].

The effective conjugation length of CPs is typically determined from a comparison of the optical spectra of the polymer with those of the corresponding oligomers [85]. It has been found from measurements on short oligomers with increasing chain lengths, i. e. for an increasing degree of π electron delocalisation, that the energy separation between the HOMO and LUMO levels decreases, and consequently the optical spectra shift towards higher wavelengths [76, 83, 88]. Finally, a saturation of the shift is observed for longer oligomers (or short chain polymers). The length of the oligomer, where the onset of the saturation is found, defines the effective conjugation length for the polymer [83, 85].

Owing to the finding that the energy separation between the HOMO and LUMO levels depends on the π electron delocalisation the distribution of conjugation lengths present in

2.1 Introduction to π-Conjugated Polymers

conjugation breaking defect

chromophore

repeating unit

Figure 2.3: Schematic representation of aπ-conjugated polymer chain. Due to conformational and/or chemical defects theπ-conjugation along the polymer backbone is interrupted. This leads to the formation of several, fully conjugated subunits on a single chain, the so-called chromophores, each with a length of typically 5 – 15 repeating units.

a CP sample directly translates into a distribution of HOMO – LUMO transition energies.

This effect contributes to the inhomogeneous line broadening of the ensemble spectra of CPs, which will be discussed in section 2.2.4.

Recent theoretical work addressed the issue of the formation of chromophores in CPs by quantum chemical calculations on short chain oligo(thiophenes) and oligo(phenylene-vinylenes) with up to 30 repeating units. It was assumed that these systems contain two perfectly aligned branches that are connected by either a kink, ring torsion, or a sp³ -hybridised carbon [79, 80]. It was found that the ground state wave function is delocalised over the entire oligomer (i. e. across the ’defect’ over both branches) except in the presence of a sp³-hybridised carbon. In other words, only for a missing double bond between two carbon atoms along the backbone a segmentation of the chain into chromophores occurs, whereas kinks and ring torsions do not interrupt the π-conjugation (in contrast to the simple picture described above). Immediately after creating a photoexcitation the situation in the excited state is similar. However, within the first few tens of femtoseconds after the absorption process a dynamic localisation of the electronic excitations on the perfect chain segments (”exciton self-trapping”) is expected due to a structural relaxation of the backbone into its excited state equilibrium geometry caused by electron-phonon coupling [76, 79, 80].

Any further relaxation or deactivation process of electronic excitations (emission, energy transfer, see the following sections) occurs after full geometric relaxation [80].

To conclude this introductory part, it is worth noting that as yet all theoretical descrip-tions and concepts of e. g. chromophore formation in CPs suffer from several shortcomings.

The validity of these models relies on a precise knowledge of the fundamental electronic parameters of CPs, such as electron-electron interactions and electron-phonon coupling strengths. The calculations are performed for individual, isolated polymer chains, the

pa-rameters, however, are determined from ensemble data of CPs [20, 27, 76, 81]. Therefore a direct comparison between theory and experiment is very difficult due to the highly disordered sample morphologies of CPs. Moreover, the parameters found from ensemble data are restricted to averaged values. In contrast, single-molecule experiments allow to determine the entire distribution functions of the parameters, which will be demonstrated in chapter 6. Thus a direct verification of theoretical models comes within reach. In recent years it has been shown that single-molecule spectroscopy is indeed a valuable tool to over-come the intrinsic heterogeneity of bulk CP samples and to investigate the properties of the electronic states of individual conjugated polymer chains in great detail [52–56,89–94].

2.2 Electronic and Spectral Properties of