[147]. Considering that it was not possible to find a clear correlation between the
geometry of the chain and the existence of trap states, it was argued that the
excellent charge mobility in PBTTT could be due to the limited number of trap
states that are supported by the PBTTT morphology.
The attempt to correlate the local structure of the polymer with the localization
of the orbitals also yielded some interesting and counterintuitive results [133]. In
amorphous PPV, a significant number of high-energy occupied orbitals was found
in highly bent regions of the polymer spanning two fragments that, by considering
the shape of the polymer, ought to be considered belonging to two separate
conjugated units. Considering all the available studies together, it seems that simple
intuitive arguments are not sufficient to qualitatively predict the relation between
the local geometric structure of a polymer and the localization of its orbitals.
Once the one-electron states of a large system have been evaluated, it is very
challenging to derive a fully satisfactory master equation like Eq. (36) that
describes the hopping rate between these approximate states. Vukmirovic ´ and
Wang have proposed a perturbative expression assuming that these states are
coupled by nonadiabatic coupling terms that can be evaluated explicitly [107] or
can be approximated using the overlap between the absolute value of the
wavefunction [154]. Remarkably, the proposed expression does not contain the
effect of nuclear polarization in the presence of an additional charge (reorganization
energy) and so it is strictly valid in the limit of vanishing reorganization energy like
Miller–Abrahams rates [155]. Using this approach it was highlighted that the DOS
does not contain all the information needed to evaluate the mobility and that it is
possible to have reduced broadening of the DOS due to increased order, but still
have low mobility because the coupling between states is reduced [156]. Alternative
methods for combining nuclear polarization and disorder effects have been proposed but they have so far only been applied to highly simplified model systems
[157, 158].
Ideally, such large-scale calculations should be able to incorporate the effect of
nuclear and electronic polarization but, as outlined in Sect. 5.2, it is not clear how
such generalizations could be introduced within the available methodologies.
6 Outlook
To conclude, substantial method development is still required in order to achieve
parameter-free modeling of organic semiconductors. Imperative for predicting
large-scale morphologies are accurate polarizable force fields and computationally
efficient coarse-grained models. These models should be capable of describing
backbone crystallization and allow for reintroduction of atomistic details. Essential
for charge transport are extensions of large-scale, first-principles methods to
charged states. Challenges are the incorporation of polaronic effects and a unified
description of charge transfer along a single chain and between conjugated segments located on different chains. Last but not least, molecular charge transfer
Morphology and Charge Transport in P3HT: A Theorist’s Perspective
175
geometry of the chain and the existence of trap states, it was argued that the
excellent charge mobility in PBTTT could be due to the limited number of trap
states that are supported by the PBTTT morphology.
The attempt to correlate the local structure of the polymer with the localization
of the orbitals also yielded some interesting and counterintuitive results [133]. In
amorphous PPV, a significant number of high-energy occupied orbitals was found
in highly bent regions of the polymer spanning two fragments that, by considering
the shape of the polymer, ought to be considered belonging to two separate
conjugated units. Considering all the available studies together, it seems that simple
intuitive arguments are not sufficient to qualitatively predict the relation between
the local geometric structure of a polymer and the localization of its orbitals.
Once the one-electron states of a large system have been evaluated, it is very
challenging to derive a fully satisfactory master equation like Eq. (36) that
describes the hopping rate between these approximate states. Vukmirovic ´ and
Wang have proposed a perturbative expression assuming that these states are
coupled by nonadiabatic coupling terms that can be evaluated explicitly [107] or
can be approximated using the overlap between the absolute value of the
wavefunction [154]. Remarkably, the proposed expression does not contain the
effect of nuclear polarization in the presence of an additional charge (reorganization
energy) and so it is strictly valid in the limit of vanishing reorganization energy like
Miller–Abrahams rates [155]. Using this approach it was highlighted that the DOS
does not contain all the information needed to evaluate the mobility and that it is
possible to have reduced broadening of the DOS due to increased order, but still
have low mobility because the coupling between states is reduced [156]. Alternative
methods for combining nuclear polarization and disorder effects have been proposed but they have so far only been applied to highly simplified model systems
[157, 158].
Ideally, such large-scale calculations should be able to incorporate the effect of
nuclear and electronic polarization but, as outlined in Sect. 5.2, it is not clear how
such generalizations could be introduced within the available methodologies.
6 Outlook
To conclude, substantial method development is still required in order to achieve
parameter-free modeling of organic semiconductors. Imperative for predicting
large-scale morphologies are accurate polarizable force fields and computationally
efficient coarse-grained models. These models should be capable of describing
backbone crystallization and allow for reintroduction of atomistic details. Essential
for charge transport are extensions of large-scale, first-principles methods to
charged states. Challenges are the incorporation of polaronic effects and a unified
description of charge transfer along a single chain and between conjugated segments located on different chains. Last but not least, molecular charge transfer
Morphology and Charge Transport in P3HT: A Theorist’s Perspective
175