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/lambda(2), where N is the number of chromophores comprising the aggregate and lambda(2) 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 S-R equivalent to 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/lambda(2). In the presence of disorder and for T > 0 K, lambda S-2(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/lambda(2), where the thermal coherence size is given by N-T = 1 + [4 pi omega(c)/k(b)T](d/2) for an aggregate of dimension d, where omega(c) is the exciton band curvature at k = 0.