2 Morphology
The theoretical and computational toolbox used to study self-assembling properties
of conjugated polymers is very versatile: On the highest level of resolution, it
includes accurate quantum chemical calculations capable of predicting the properties of isolated oligomers and dimers, normally without side chains. Less computationally demanding density functional methods can deal with much longer
oligomers (10–20 repeat units), including side chains, and are often used to
compare ground state energies of experimentally proposed arrangements of atoms
in a unit cell. To assess crystalline packing modes at ambient conditions and during
annealing, as well as to study amorphous melts and longer chain lengths, classical
force fields have been parametrized. To access even longer length and time scales
(micrometers, microseconds), coarse-grained models have been developed to study
amorphous melts and liquid-crystalline phases of P3HT.
The ultimate goal of these simulations is to self-assemble the polymer in silico,
i.e., to predict its polymorphs as well as the degree of disorder in the kinetically
trapped molecular arrangements. The honest assessment is that we are fairly far
from achieving this goal. The main obstacles are insufficient accuracy of methods at
a specific level of resolution, long simulation times required to study self-assembly,
and uncontrolled error propagation from one level to another, e.g., when parameterizing force fields based on quantum chemical calculations, or developing coarsegrained models using force-field-generated reference data.
We will provide a summary of simulation results, starting with single-molecule
properties and then expanding to molecular arrangements of P3HT in crystals,
melts, and finally binary mixtures with PCBM, a typical acceptor used in organic
solar cells.
2.1 Single Molecules
Ab initio methods have been extensively used to analyze conformations of the
conjugated backbone and side-chain orientations with respect to the plane of
conjugation [25]. Here, the extended π-conjugated system flattens the backbone,
whereas nonbonded interactions between consecutive repeat units (i.e., steric
repulsions between hydrogen atoms, Coulomb interactions, and van der Waals
interactions) often tend to distort its planarity. For P3HT, both planar [26] and
nonplanar stable geometries have been reported, depending on the side-chain
orientation [27]. At the B3LYP/6-31+G level of density functional theory (DFT),
the nonplanar backbone has an energy of ~0.03 eV lower (per monomer) than the
planar backbone (evaluated in a 10-mer) [28]. This indicates that chain conformations in the bulk are predominantly determined by interchain van der Waals and
Coulomb interactions, a conclusion also drawn from calculations of molecular
dimers [29].
Morphology and Charge Transport in P3HT: A Theorist’s Perspective
143
The theoretical and computational toolbox used to study self-assembling properties
of conjugated polymers is very versatile: On the highest level of resolution, it
includes accurate quantum chemical calculations capable of predicting the properties of isolated oligomers and dimers, normally without side chains. Less computationally demanding density functional methods can deal with much longer
oligomers (10–20 repeat units), including side chains, and are often used to
compare ground state energies of experimentally proposed arrangements of atoms
in a unit cell. To assess crystalline packing modes at ambient conditions and during
annealing, as well as to study amorphous melts and longer chain lengths, classical
force fields have been parametrized. To access even longer length and time scales
(micrometers, microseconds), coarse-grained models have been developed to study
amorphous melts and liquid-crystalline phases of P3HT.
The ultimate goal of these simulations is to self-assemble the polymer in silico,
i.e., to predict its polymorphs as well as the degree of disorder in the kinetically
trapped molecular arrangements. The honest assessment is that we are fairly far
from achieving this goal. The main obstacles are insufficient accuracy of methods at
a specific level of resolution, long simulation times required to study self-assembly,
and uncontrolled error propagation from one level to another, e.g., when parameterizing force fields based on quantum chemical calculations, or developing coarsegrained models using force-field-generated reference data.
We will provide a summary of simulation results, starting with single-molecule
properties and then expanding to molecular arrangements of P3HT in crystals,
melts, and finally binary mixtures with PCBM, a typical acceptor used in organic
solar cells.
2.1 Single Molecules
Ab initio methods have been extensively used to analyze conformations of the
conjugated backbone and side-chain orientations with respect to the plane of
conjugation [25]. Here, the extended π-conjugated system flattens the backbone,
whereas nonbonded interactions between consecutive repeat units (i.e., steric
repulsions between hydrogen atoms, Coulomb interactions, and van der Waals
interactions) often tend to distort its planarity. For P3HT, both planar [26] and
nonplanar stable geometries have been reported, depending on the side-chain
orientation [27]. At the B3LYP/6-31+G level of density functional theory (DFT),
the nonplanar backbone has an energy of ~0.03 eV lower (per monomer) than the
planar backbone (evaluated in a 10-mer) [28]. This indicates that chain conformations in the bulk are predominantly determined by interchain van der Waals and
Coulomb interactions, a conclusion also drawn from calculations of molecular
dimers [29].
Morphology and Charge Transport in P3HT: A Theorist’s Perspective
143