Nematic ordering and charge mobility in semiconducting copolymers
Organic semiconducting polymers are rather stiff compared to traditional polymers, because the monomers are aromatic rings, and the deflection angle between successive rings is small. This leads to significant nematic interactions between chains in an isotropic melt from steric considerations alone. Working against this tendency are solubilizing sidechains, which dilute the stiff backbones with flexible “grease”.
In recent work, we have used atomistic simulations to predict the nematic coupling constant alpha for semiconducting polymers such as P3HT, and predicted the isotropic-nematic (IN) transition temperature. Our method does not rely on observing nematic ordering with its slow kinetics, but instead infers alpha from its amplifying effect on elongation of chains in a melt in response to applied external tension.
Even when alpha is not large enough to give a nematic phase, nematic interactions can amplify the aligning effect of an impenetrable surface, at which semiflexible chains tend to lie parallel. We have investigated this effect with coarse-grained MD simulations of melts near a wall, in which we observe how far nematic order extends from the wall into the bulk, as a function of chain stiffness. These results compare well to our predictions from self-consistent field calculations adapted to semiflexible chains.
We have exploited this surface alignment effect to locate the IN transition, by observing how surface alignment propagates into a slab of polymer chains confined between walls, as the chain stiffness increases. Below the IN transition, surface-induced alignment grows into the bulk with a velocity proportional to the undercooling. By observing how the front propagates as we cool (or increase chain stiffness), we can accurately locate the transition.
Nematic order is important in semiconducting polymers because electronic transport in semiconducting polymers is inherently anisotropic. Carriers move readily along straight chains, can hop with relative ease between parallel chains in a crystal, and hop only with difficulty between obliquely oriented chains in an isotropic melt. Crystallization from a nematic phase may give better-organized crystalline domains with fewer amorphous regions, and may induce chain alignment even in the amorphous regions.
In a separate research thrust, we have developed coarse-grained electronic models to describe carrier states and motion in crystalline and amorphous semiconducting polymers such as P3HT. We use tight-binding models, in which each ring moiety is a site, with hopping between adjacent sites. Parameters are fit to state-of-the-art DFT calculations for small systems in well-defined geometries. Hopping matrix elements along chains are large for trans dihedrals, but fall off and vanish as dihedrals rotate to 90 degrees, breaking conjugation.
Carriers in P3HT form polarons, in which the surrounding material reorganizes (“polarizes”) in response to the presence of the charge. The polaron size is set by a competition between electronic kinetic energy (which seeks to delocalize the charge) and the reorganization energy (which stabilizes a localized charge more effectively). The most important contribution to reorganization energy in these materials is dielectric polarization of nearby material, leading to polarons a few rings long.
These polarons can move between chains a crystal, by hops described by Marcus theory. In the hopping barrier state, the polaron is midway between two degenerate locations, in a symmetric superposition of states. We use our tight-binding model to compute barriers for hopping between chains, in a crystal and an amorphous melt. The melt barrier is larger, because obliquely oriented chains do not share very effectively the same polarization field, which increases the reorganization energy.