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, S(R), corresponding to the low-temperature photoluminescence spectrum is rigorously equal to N/λ2, where N is the number of chromophores comprising the aggregate and λ2 is 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 S(R) and N also 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 ≡ I(b)(0−0)/I(b)(0−1) (where I(b)(0−0) and I(b)(0−1) correspond 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, λ2S(R) is closely approximated by the exciton coherence number N(coh), thereby providing a simple and direct way of extracting N(coh) from the photoluminescence spectrum. Increasing temperature in linear J-aggregates (and herringbone aggregates) generally leads to a demise in S(R) and therefore also the exciton coherence size. When no disorder is present, and under the fast scattering and thermodynamic limits, S(R) is equal to N(T)/λ2, where the thermal coherence size is given by N(T) = 1 + 4πω(c)/k(b)T(d/2) for an aggregate of dimension d, where ω(c) is the exciton band curvature at k = 0.