approaches, on the contrary, derive the coarse-grained model from macroscopic
observables (e.g., the phase behavior). These are often based on experimental
measurements [51, 52, 58] but can also incorporate elements of bottom-up
coarse-graining. In the following sections, we review the results obtained using
structure-based coarse-grained models and also introduce a coarse-graining technique based on soft interaction potentials.
3.1 Structure-Based Coarse-Graining
The idea of structure-based coarse-graining is to match structural properties, such
as radial distribution functions, of the fine- and coarse-grained systems. Structurebased coarse-grained models have been developed for melts [45, 46], hightemperature (liquid) mixtures of P3HT/PCBM [45, 50, 59], and solutions of
P3HT [60]. The P3HT monomers are normally coarse-grained into three interaction
sites placed at the center of mass of the thiophene rings, then on the first and last
three methyl groups of the hexyl side-chain, as shown in Fig. 4. The bonded and
nonbonded interaction parameters are optimized using the iterative Boltzmann
inversion method [54, 61], although phenomenological refinement is also used [59].
The three-site models allow for self-assembling polymer backbones into lamellar arrangements [59, 60]. They have also been used to study the morphology of
phase-separated P3HT/PCBM blends, where explicit incorporation of side chains
helped to understand penetration of acceptor molecules into side chains as a
function of their grafting density along the backbone. No intercalation was found
for P3HT, in contrast to poly(bithiophene-alt-thienothiophene) (PBTTT), which
has a lower grafting density of side chains [59]. A further advantage of coarsegraining is that solvent-mediated interactions can be incorporated into coarsegrained interactions, leading to a dramatic decrease in the number of degrees of
freedom. Simulations of P3HT aggregation in solutions with anisole could reproduce the experimentally observed aggregation of P3HT as a function of temperature
with the back-folded hairpins of stacked P3HT molecules [60]. The spacing
between P3HT lamellae was found to be 1.7 nm, which is comparable to experimental observations [9].
Three-site coarse-grained models normally employ orientationally isotropic
nonbonded interactions and are parametrized either on high-temperature P3HT
melts or solutions. Thus, by construction, they cannot capture the directionality of
π–π interactions between thiophenes. The backbones of the P3HT chains within the
same lamella are also less correlated, leading to smectic-like ordering [59, 60]. In
fact, this type of ordering has been reported experimentally, although in a narrow
temperature window, prior to melting [10].
Morphology and Charge Transport in P3HT: A Theorist’s Perspective
147
observables (e.g., the phase behavior). These are often based on experimental
measurements [51, 52, 58] but can also incorporate elements of bottom-up
coarse-graining. In the following sections, we review the results obtained using
structure-based coarse-grained models and also introduce a coarse-graining technique based on soft interaction potentials.
3.1 Structure-Based Coarse-Graining
The idea of structure-based coarse-graining is to match structural properties, such
as radial distribution functions, of the fine- and coarse-grained systems. Structurebased coarse-grained models have been developed for melts [45, 46], hightemperature (liquid) mixtures of P3HT/PCBM [45, 50, 59], and solutions of
P3HT [60]. The P3HT monomers are normally coarse-grained into three interaction
sites placed at the center of mass of the thiophene rings, then on the first and last
three methyl groups of the hexyl side-chain, as shown in Fig. 4. The bonded and
nonbonded interaction parameters are optimized using the iterative Boltzmann
inversion method [54, 61], although phenomenological refinement is also used [59].
The three-site models allow for self-assembling polymer backbones into lamellar arrangements [59, 60]. They have also been used to study the morphology of
phase-separated P3HT/PCBM blends, where explicit incorporation of side chains
helped to understand penetration of acceptor molecules into side chains as a
function of their grafting density along the backbone. No intercalation was found
for P3HT, in contrast to poly(bithiophene-alt-thienothiophene) (PBTTT), which
has a lower grafting density of side chains [59]. A further advantage of coarsegraining is that solvent-mediated interactions can be incorporated into coarsegrained interactions, leading to a dramatic decrease in the number of degrees of
freedom. Simulations of P3HT aggregation in solutions with anisole could reproduce the experimentally observed aggregation of P3HT as a function of temperature
with the back-folded hairpins of stacked P3HT molecules [60]. The spacing
between P3HT lamellae was found to be 1.7 nm, which is comparable to experimental observations [9].
Three-site coarse-grained models normally employ orientationally isotropic
nonbonded interactions and are parametrized either on high-temperature P3HT
melts or solutions. Thus, by construction, they cannot capture the directionality of
π–π interactions between thiophenes. The backbones of the P3HT chains within the
same lamella are also less correlated, leading to smectic-like ordering [59, 60]. In
fact, this type of ordering has been reported experimentally, although in a narrow
temperature window, prior to melting [10].
Morphology and Charge Transport in P3HT: A Theorist’s Perspective
147