Excitation energy transport and reversible trapping in aromatic vinylpolymers: Transient long-time behavior of a dissociative monomer–excimer system. A deterministic kinetic treatment

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Abstract
A deterministic kinetic analysis has been presented in an attempt to model the δ-pulse dynamics of a monomer–excimer pair in presence of energy migration and detrapping. Because of the reversibility of the system and the formal treatment of excitation energy transport by means of a time-dependent rate function k(t), the linear first order equations of evolution are coupled and consist of nonautonomous coefficients. The formalism involves a linear, affine transform technique for decoupling the simultaneous rate equations. This procedure leads to nonlinear, but decoupled first-order Riccati equations which have been further transformed to yield a second-order differential equation with time-dependent coefficients. For k(t)=b+Ct−1/2, the present study develops approximate WKB solutions to the transient δ-pulse response behavior of the system under the condition of weak coupling. The limitation of this approach have been tested towards numerical computer results. The WKB solutions are well behaved at relatively long times and, thus, prove useful for providing the typical asymptotic behavior of a polychromophoric monomer–excimer system in which transport and trapping will proceed via a quasi-one-dimensional pathway. The physics of this treatment has been discussed on the basis of energy-dispersive hopping processes along the chromophor array of aromatic polymer with typical, diagonal disorder. The analytical solutions, however, might have more general significance, presumably, with respect to forthcoming, subnanosecond reconvolution procedures in the transient fluoresence analysis of dilute aromatic vinylpolymers.