Exciton Theory of the Electronic States of Dye–Polymer Complexes. I. Linear Polymers

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Abstract
A theory is developed for the excited electronic states of dye–polymer complexes in which dyes with many vibronic states are bound to infinite linear polymers with one excited state per monomer. Overlap of wavefunctions of monomers and dyes is neglected. Two aspects of the coupling of excited dye levels to the exciton states of the polymer are considered. First, dye transitions are assumed not to overlap the exciton band of the polymer. Problems considered include the perturbation of dye levels by the polymer (primary trap states), the formation of discrete states below the exciton band due to secondary interactions between dye and monomer, coupling of vibronic dye levels by the polymer, and the many‐dye problem, including the case where the dyes have a series of vibronic levels. In the latter it is shown how the degree of the secular equation reduces to the number of dyes present and how this is equivalent to a Frenkel exciton moving on a lattice with holes since the whole of the dye–polymer interaction can be incorporated into an effective dye–dye resonance interaction. The more subtle problems of exciton scattering by the dye molecule and the time development of prepared states, which arise when dye levels fall inside the exciton band, are considered using the techniques of second quantization.