Mind the Gap

Intraband-gap states in conjugated polymers have captivated the chemistry community for the better part of five decades due to their position within the forbidden band gap, between the valence and conduction bands. In a large part, this fascination was (and still is) aided by the quest to find alternative materials that are easily processable compared to their solid-state semiconductor counterpart, which require considerable energy input. The outcome of the polymer story is well-known now, in 1977: “...the dream of combining the processing and mechanical properties of polymers with the electrical and optical properties of metals...” was first realized with the π-conjugated polymer, polyacetylene, or CHx. 2 There was an additional “surprise” that came out of these materialsthe transport properties measured were not consistent with electrons (or holes) being the charge carrier. Polarons, one of the quasiparticles that mediate the intraband-gap states, were implicated, and although being widely studied, there is still uncertainty in fundamental aspects of their nature. In this month’s ACS Central Science, Georg Heimel proposes a model that questions the view that photoexcited polarons lead to intragap states without a concomitant disruption in the localized valence and conduction orbitals. Taking into account the Coulomb interactions of the polaron with the surrounding electrons leads to a new band diagram via a re-evaluation of the accessible intragap polaron states. An important outcome of this viewpoint is a reversal in the ionization energy (or electron affinity) trend for the charged polymer, a trend having been observed in photoexcitation spectroscopic measurements. Using density functional theory (DFT), Heimel produces the full density of states (DOS) for a 30mer of the canonical conjugated polymer poly(para-phenylene) or PPP to inform this updated view. The confluence of polaronic quasiparticles and conjugated polymers has its own varied history and is rooted in concepts developed in the mid-20th century by the many-body electronic structure community to overcome the “band-gap problem”. The “band-gap problem” stemmed from the electronic structure models inability to predict the optical gap Eg for many crystalline semiconductors. 5 Quasiparticles, operating within the forbidden band gap, provided a suitable description for the missing physics in the “band-gap problem”. A few years later, in CHx polymers, it was observed that there was a degenerate ground state, and a defect radical, called a soliton, provided the pathway to navigate between the two states. Because the ground-state energy is identical left and right of the soliton, it is delocalized and noninteracting leading to high carrier mobilities. On the other hand, polymers like PPP do not have degenerate ground states, instead having bound defect pairs that lead to localized deformations or polarons. The Su−Schrieffer−Heeger (SSH) model was successfully used to describe solitons and polarons; being based on a tightbinding description it did not include Coulomb interactions. The band diagrams that came out of these models described polaron states as emanating out of the valence and conduction bands without a concomitant change in the local band structure. This is because they are based on one-