Kinetic Model of the Thermally Stimulated Luminescence of Poly(diphenylene phthalide) Films

Abstract

The thermally stimulated luminescence (TSL) of poly(diphenylene phthalide) (PDP) films with terminal acid and diphenyl groups was studied using mathematical modeling methods. An adequate description (relative mean deviation, 6%) of the kinetic curves of TSL was obtained and the activation parameters of individual steps were determined by solving an inverse kinetic problem within the framework of a three-center four-step reaction scheme. The kinetics of TSL indicated the existence of two independent channels leading to the generation of an electronically excited diphenylene fragment of the polymer chain. The photoexcitation of PDP leads to the formation of a system of separated ion–radical states and, as a result, to the activation of individual polymer fragments. The subsequent recombination processes with the participation of the most active states occur through successive stages, and they are characterized by relatively low activation energies (E_a2 = 23 kJ/mol and E_a3 = 42 kJ/mol), which are traditionally interpreted in terms of the theory of mechanical relaxation as the vibrations of the smallest structural elements of the polymer (supposedly, the triarylmethyl-type side fragments of PDP). The high-temperature TSL (>370 K) is described in terms of the Randall–Wilkins model, and it is probably caused by the segmental mobility of the polymer (E_a1 = 70.5 kJ/mol). The data obtained indicate that the mid-chain units of the polymer mainly participate in the generation of electronically excited states: an analysis of activation parameters estimated from the kinetics of TSL of PDP films with different terminal units showed no significant differences in the described recombination processes.