Excitons and Polarons in Organic Materials

Excitons and polarons play a central role in the electronic and optical properties of organic semiconducting polymers and molecular aggregates and are of fundamental importance in understanding the operation of organic optoelectronic devices such as solar cells and light-emitting diodes. For many conjugated organic molecules and polymers, the creation of neutral electronic excitations or ionic radicals is associated with significant nuclear relaxation, the bulk of which occurs along the vinyl-stretching mode or the aromatic-quinoidal stretching mode when conjugated rings are present. Within a polymer chain or molecular aggregate, nuclear relaxation competes with energy- and charge-transfer, mediated by electronic interactions between the constituent units (repeat units for polymers and individual chromophores for a molecular aggregate); for neutral electronic excitations, such inter-unit interactions lead to extended excited states or excitons, while for positive (or negative) charges, interactions lead to delocalized hole (or electron) polarons. The electronic coupling as well as the local coupling between electronic and nuclear degrees of freedom in both excitons and polarons can be described with a Holstein Hamiltonian. However, although excitons and polarons derive from similarly structured Hamiltonians, their optical signatures are quite distinct, largely due to differing ground states and optical selection rules. In this Account, we explore the similarities and differences in the spectral response of excitons and polarons in organic polymers and molecular aggregates. We limit our analysis to the subspace of excitons and hole polarons containing at most one excitation; hence we omit the influence of bipolarons, biexcitons, and higher multiparticle excitations. Using a generic linear array of coupled units as a model host for both excitons and polarons, we compare and contrast the optical responses of both quasiparticles, with a particular emphasis on the spatial coherence length, the length over which an exciton or polaron possesses wave-like properties important for more efficient transport. For excitons, the UV-vis absorption spectrum is generally represented by a distorted vibronic progression with H-like or J-like signatures depending on the sign of the electronic coupling, J(ex). The spectrum broadens with increasing site disorder, with the spectral area preserved due to an oscillator strength sum rule. For (hole) polarons, the generally stronger electronic coupling results in a mid-IR spectrum consisting of a narrow, low-energy peak (A) with energy near a vibrational quantum of the vinyl stretching mode, and a broader, higher-energy feature (B). In contrast to the UV-vis spectrum, the mid-IR spectrum is invariant to the sign of the electronic coupling, t(h), and completely resistant to long-range disorder, where it remains entirely homogeneously broadened. Even in the presence of short-range disorder, the width of peak A remains surprisingly narrow as long as vertical bar t(h)vertical bar remains sufficiently large, a property that can be understood in terms of Herzberg-Teller coupling. Unlike for excitons, for polarons, the absorption spectral area decreases with increasing short-range disorder sigma (i.e., there is no oscillator sum rule) reflective of a decreasing polaron coherence length. The intensity of the low-energy peak A in relation to B is an important signature of polaron coherence. By contrast, for excitons, the absorption spectrum contains no unambiguous signs of exciton coherence. One must instead resort to the shape of the steady-state photoluminescence spectrum. The Holstein-based model has been highly successful in accounting for the spectral properties of molecular aggregates as well as conjugated polymers like poly(3-hexylthiophene) (P3HT) in the mid-IR and UV-vis spectral regions.