Vibronic Coupling in J-Aggregates and Beyond: A Direct Means of Determining the Exciton Coherence Length from the Photoluminescence Spectrum

Exciton coherence in a J-aggregate with exciton−phonon coupling involving a single intramolecular vibration is studied. For linear aggregates with no disorder and periodic boundary conditions, the 0−0 to 0−1 line strength ratio, SR, corresponding to the low-temperature photoluminescence spectrum is rigorously equal to N/λ2, where Nis the number of chromophores comprising the aggregate and λ2is the Huang−Rhys factor of the coupled vibrational mode. The result is independent of exciton bandwidth and therefore remains exact from the weak to strong exciton−phonon coupling regimes. The simple relation between SRand Nalso holds for more complex morphologies, as long as the transition from the lowest exciton state to the vibrationless ground state is symmetry-allowed. For example, in herringbone aggregates with monoclinic unit cells, the line strength ratio, defined as SR≡ Ib0−0/Ib0−1(where Ib0−0and  Ib0−1correspond to the b-polarized 0−0 and 0−1 line strengths, respectively) is rigorously equal to N/λ2. In the presence of disorder and for T> 0 K, λ2SRis closely approximated by the exciton coherence number Ncoh, thereby providing a simple and direct way of extracting Ncohfrom the photoluminescence spectrum. Increasing temperature in linear J-aggregates (and herringbone aggregates) generally leads to a demise in SRand therefore also the exciton coherence size. When no disorder is present, and under the fast scattering and thermodynamic limits, SRis equal to NT/λ2, where the thermal coherence size is given by NT= 1 + [4πωc/kbT]d/2for an aggregate of dimension d, where ωcis the exciton band curvature at k= 0.