Structure and sources of disorder in poly(3-hexylthiophene) crystals investigated by density functional calculations with van der Waals interactions

The crystal structure of poly(3-hexylthiophene) (P3HT) has been studied by first-principles calculations based on density functional theory. The generalized gradient approximation is employed and van der Waals interactions are treated accurately by the recently proposed local atomic potential approach. A variety of different models were tested, and the model having the lowest energy is a noninterdigitated structure having an orthorhombic cell with $a$ $=$ 17.2 Å, $b$ $=$ 7.7 Å, and $c$ $=$ 7.8 Å, where $a$, $b$, and $c$ are the lengths of the lattice vectors perpendicular to the lamellae, in the π-π stacking direction, and along the thiophene backbone, respectively. These values are in reasonably good agreement with experiment. The P3HT polymer is not invariant under inversion and therefore exhibits directionality. Our calculations suggest that a likely structural defect occurring in P3HT is one in which one of the polymer backbones within a lamella runs in the direction opposite to the majority. Such defects may form in the process of self-assembly of the noninterdigitated lamellae and may be an important source of π-π stacking disorder. A possible explanation for a recently observed structural phase transition in polythiophene is proposed.

Figure 1

Regioregular head-to-tail alkyl-substituted polythiophene. (a) and (b) are schematic representations of structures defining the L (a) and R (b) backbone chains. L can be converted into R by a 180° rotation around the $T$ axis. (c) This depicts a stacking fault, where an R chain has been inserted into a lamella consisting of L chains. Such defects could form in the process of self-assembly out of solution and could be an important source of structural disorder.

Figure 2

CCSD(T) and DFT$+$LAP calculations for benchmark systems (a) parallel thiophene dimer, and (b) parallel ethane dimer. The insets show the structures of the dimers, where C, H, and S are represented by black (medium), blue (small), and yellow (large) balls, respectively.

Figure 3

Definitions of (a) $a$, $b$, ${\theta }_1$, ${\theta }_2$, and γ; (b) $c$ and ${\theta }_4$; (c) ${\theta }_3$, δ${}_{\mathit{c}}$, and stacking sequence LL; (d) stacking sequence LR.

Figure 4

(a) Model I(LL) at δ${}_{\mathit{c}}$ $=$ 0, (b) model I(LR) at δ${}_{\mathit{c}}$ $=$ 0, (c) model II(LL) at δ${}_{\mathit{c}}$ $=$ 0.5$c$, and (d) model II(LR) at δ${}_{\mathit{c}}$ $=$ 0.5$c$.

Figure 5

Depiction of model III prior to relaxation: (a) projection along c vector; (b) projection along b vector. Depiction of model III after relaxation: (c) projection along c vector; (d) projection along b vector.

Figure 6

Models I–III (a) energy as function of δ${}_{\mathit{c}}$, and corresponding (b) $a$, (c) $b$, and (d) angle γ.