Four panels to illustrate the process to generate the randomly disordered polymers. Panel (a): initial starting structure. Panel (b): minimum energy structure after generation of 2000 conformers. Panel (c): starting structure for second round of conformational searching. Panel (d): minimum energy structure after generation of 2000 extended conformers.
Part of a typical strand of the P3HT structure. The torsion angle between thiophene units 15 and 16 is , and hence the -electron overlap is negligible between these units, causing a -conjugation break. The blue and red envelopes are schematic representations of the Coulombically coupled excitons [ and , respectively] that are localized either side of the conjugation break, as described in Sec. III. See also Fig. 5.
The bimodal distribution of the torsion angles between neighboring thiophene units.
The exciton center-of-mass wave functions, , as a function of the center-of-mass coordinate, (in units of the thiophene repeat unit). The state index is indicated in the box. Also shown is the relative magnitude of the interthiophene resonance integral, . The negligible values of between the 15th and 16th, and 29th and 30th thiophene units causes conjugation breaks and exciton localization. However, notice that exciton localization does not occur between the conjugation breaks at the 37th and 45th thiophene units. The spectroscopic segments 1, 2, and 3 are labeled.
The exciton states , , and showing that is the ground state exciton localized in segment 1, while and are formed from linear combinations of the first excited exciton localized in segment 1 and the ground state exciton localized in segment 2 (see Table I).
Low-lying excited states: excitation energies, , their components in terms of local exciton states, , and their transition dipole moments normalized relative to the lowest excitation. [ is the local excited exciton localized on segment .]
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