Because typical energy differences between planar and nonplanar conformations
are in the order of tens of millielectronvolts, which is the accuracy threshold of
density functional methods, one is forced to use more accurate (and computationally demanding) quantum-chemical methods. However, the ground-state twist
angle between repeat units has been found to depend on the oligomer length,
saturating at about ten repeat units. Furthermore, torsional potentials are correlated
up to the second-nearest-neighbor rings [30], thus making geometry predictions a
formidable task even for isolated oligomers [31].
2.2 Crystalline Oligothiophenes
Both density functional and force-field calculations have been used to study
crystalline P3HT mesophases. Density functional calculations have been primarily
used to establish whether experimentally reported crystal structures correspond to
well-defined energy minima [32–35]. Using a van-der-Waals-corrected generalized
gradient approximation (GGA) functional, Dag and Wang concluded that the
crystal with shifted backbones (i.e., with one of the thiophene layers shifted along
the chain direction by the thiophene–thiophene distance) and side chains rotated
around the torsion angle is the most stable of three studied structures [36]. Xie
et al. reached the conclusion that a structural motif without this registry shift and
without rotation of the side chains, but instead with a small backbone tilt, has the
lowest potential energy [34]. Similar to the situation with a single isolated chain,
typical energy differences between different packing motives are in the order of
10 meV per unit cell and, hence, theoretical methods are at their accuracy limits,
making it difficult to rank different molecular arrangements. Also, unit-cell optimizations are performed at zero Kelvin, meaning that entropic effects, notably the
chain excluded volume, are ignored.
To study larger systems and longer timescales, various flavors of P3HT force
fields were developed. In the majority of cases, parameters of an existing force field
were refined in order to reproduce the torsional potential between thiophene units
and electrostatic potential around an isolated oligomer [13, 37]. The parametrization has been subsequently refined to account for the change in the backbone
potential with oligomer length [13, 26, 28, 38–40]. To this end, atomistic simulations have been used to analyze proposed packing arrangements of three P3HT
polymorphs (phases I, I
0 , and II; see Fig. 2), and to scrutinize the effect of
regioregularity on paracrystalline, dynamic, and static nematic order parameters
[13]. Molecular dynamics simulations suggest that the most stable P3HT polymorph has planar thiophene backbones shifted by one thiophene ring with respect to
each other. Hexyl side chains are twisted away from the backbone in a trans
fashion, resulting in a non-interdigitated packing structure, although stable structures with interdigitated side chains were also reported [41]. Force-field-based
estimates of the mass density (1.05 g cm
À3 ), melting temperature (490 K), and
surface tension (32 mN/m) all agree with the reported experimental values
144
C. Poelking et al.
are in the order of tens of millielectronvolts, which is the accuracy threshold of
density functional methods, one is forced to use more accurate (and computationally demanding) quantum-chemical methods. However, the ground-state twist
angle between repeat units has been found to depend on the oligomer length,
saturating at about ten repeat units. Furthermore, torsional potentials are correlated
up to the second-nearest-neighbor rings [30], thus making geometry predictions a
formidable task even for isolated oligomers [31].
2.2 Crystalline Oligothiophenes
Both density functional and force-field calculations have been used to study
crystalline P3HT mesophases. Density functional calculations have been primarily
used to establish whether experimentally reported crystal structures correspond to
well-defined energy minima [32–35]. Using a van-der-Waals-corrected generalized
gradient approximation (GGA) functional, Dag and Wang concluded that the
crystal with shifted backbones (i.e., with one of the thiophene layers shifted along
the chain direction by the thiophene–thiophene distance) and side chains rotated
around the torsion angle is the most stable of three studied structures [36]. Xie
et al. reached the conclusion that a structural motif without this registry shift and
without rotation of the side chains, but instead with a small backbone tilt, has the
lowest potential energy [34]. Similar to the situation with a single isolated chain,
typical energy differences between different packing motives are in the order of
10 meV per unit cell and, hence, theoretical methods are at their accuracy limits,
making it difficult to rank different molecular arrangements. Also, unit-cell optimizations are performed at zero Kelvin, meaning that entropic effects, notably the
chain excluded volume, are ignored.
To study larger systems and longer timescales, various flavors of P3HT force
fields were developed. In the majority of cases, parameters of an existing force field
were refined in order to reproduce the torsional potential between thiophene units
and electrostatic potential around an isolated oligomer [13, 37]. The parametrization has been subsequently refined to account for the change in the backbone
potential with oligomer length [13, 26, 28, 38–40]. To this end, atomistic simulations have been used to analyze proposed packing arrangements of three P3HT
polymorphs (phases I, I
0 , and II; see Fig. 2), and to scrutinize the effect of
regioregularity on paracrystalline, dynamic, and static nematic order parameters
[13]. Molecular dynamics simulations suggest that the most stable P3HT polymorph has planar thiophene backbones shifted by one thiophene ring with respect to
each other. Hexyl side chains are twisted away from the backbone in a trans
fashion, resulting in a non-interdigitated packing structure, although stable structures with interdigitated side chains were also reported [41]. Force-field-based
estimates of the mass density (1.05 g cm
À3 ), melting temperature (490 K), and
surface tension (32 mN/m) all agree with the reported experimental values
144
C. Poelking et al.