of applications apart from organic semiconductors have been proposed [143], but
relatively few results have been reported for semiconducting polymers [147] even
though great success has been achieved in the study of charge transfer processes in
biophysical systems [148, 149], which provide a similar level of computational
challenge.
Finally, an obvious choice for calculation of the large-scale electronic structure
would be via semi-empirical methods. These have been the methods of choice for
many years for exploring charge [150] and exciton [151] dynamics in single-chain
polymers containing only carbon and hydrogen (e.g., PPV, polyethylene). However, there are very few systematic studies of their reliability for polymers
containing heteroatoms such as S, F, Se, and Ge, which are featured in a large
number of new polymers.
Although there seems to be no lack of options for the calculation of the
wavefunction of large models of polymeric systems, these calculations have been
attempted on a very limited number of systems. One of the main objectives of future
computational studies is to perform calibration of these methodologies, whereby
the results obtained with different approximate electronic structure methods on the
same structural models are compared.
5.3 Results from the Computation of the Wavefunction
for Large-Scale Polymer Models
The calculations performed on models of polymers, according to any of the
methodologies described in the previous section, provide in the first instance the
DOS and a measure of the localization length of the states relevant for transport,
i.e., those located at the edge of the valence (or conduction) band for holes
(or electrons). For all polymers considered (amorphous and semicrystalline), the
states deep in the tail of the DOS are more localized and the localization length
increases as states deeper in the band are considered (see Fig. 12), as predicted by
simplified generic polymer models [152]. The chemical description of these states
in the tail is potentially very useful because it may suggest possible routes for
increasing the charge mobility by reducing the number of trap states.
Calculations suggest that hole trap states (high-energy occupied orbitals) are
found in regions of P3HT where the conjugated backbone is more planar than on
average [108, 153]. The possibility of different degrees of planarity generates
regions where the HOMO–LUMO gap is smaller, coinciding with the more planar
segments of P3HT. Not surprisingly, when regioregularity defects are introduced,
the trap states become localized far away from the regioregularity defect and, for
this reason, the total number of trap states is not much affected by the
regioregularity. This has also been found experimentally [108].
By adopting fast methods for calculation of the electronic structure, it is possible
to monitor the lifetime of these trap states by repeating the electronic structure
Morphology and Charge Transport in P3HT: A Theorist’s Perspective
173
relatively few results have been reported for semiconducting polymers [147] even
though great success has been achieved in the study of charge transfer processes in
biophysical systems [148, 149], which provide a similar level of computational
challenge.
Finally, an obvious choice for calculation of the large-scale electronic structure
would be via semi-empirical methods. These have been the methods of choice for
many years for exploring charge [150] and exciton [151] dynamics in single-chain
polymers containing only carbon and hydrogen (e.g., PPV, polyethylene). However, there are very few systematic studies of their reliability for polymers
containing heteroatoms such as S, F, Se, and Ge, which are featured in a large
number of new polymers.
Although there seems to be no lack of options for the calculation of the
wavefunction of large models of polymeric systems, these calculations have been
attempted on a very limited number of systems. One of the main objectives of future
computational studies is to perform calibration of these methodologies, whereby
the results obtained with different approximate electronic structure methods on the
same structural models are compared.
5.3 Results from the Computation of the Wavefunction
for Large-Scale Polymer Models
The calculations performed on models of polymers, according to any of the
methodologies described in the previous section, provide in the first instance the
DOS and a measure of the localization length of the states relevant for transport,
i.e., those located at the edge of the valence (or conduction) band for holes
(or electrons). For all polymers considered (amorphous and semicrystalline), the
states deep in the tail of the DOS are more localized and the localization length
increases as states deeper in the band are considered (see Fig. 12), as predicted by
simplified generic polymer models [152]. The chemical description of these states
in the tail is potentially very useful because it may suggest possible routes for
increasing the charge mobility by reducing the number of trap states.
Calculations suggest that hole trap states (high-energy occupied orbitals) are
found in regions of P3HT where the conjugated backbone is more planar than on
average [108, 153]. The possibility of different degrees of planarity generates
regions where the HOMO–LUMO gap is smaller, coinciding with the more planar
segments of P3HT. Not surprisingly, when regioregularity defects are introduced,
the trap states become localized far away from the regioregularity defect and, for
this reason, the total number of trap states is not much affected by the
regioregularity. This has also been found experimentally [108].
By adopting fast methods for calculation of the electronic structure, it is possible
to monitor the lifetime of these trap states by repeating the electronic structure
Morphology and Charge Transport in P3HT: A Theorist’s Perspective
173