Novel kinetic model in amorphous polymers. Spiropyran-merocyanine system revisited

A kinetic model for the description of non-monoexponential decay of unimolecular reactions in amorphous polymers is developed. The thermal decay of the merocyanine (MC) form of 1,3′,3′-trimethyl-6-nitrospiro-[2H-1-benzopyran-2,2′-indoline] (spiropyran, SP) in poly(alkyl methacrylates) is taken as an example. The model assumes that the time dependent first-order rate constant describing the decay relaxes from an initial value k₀ to a completely relaxed value L_∞ with a relaxation time τ_m that depends on the matrix. A rate equation similar to the one provided by this model is found in fluorescence quenching either in micelles or in the picosecond range in solution. The fit of the temperature dependent decays of MC to SP with this model is as good as or better than the one obtained by other models such as the sum of exponential terms or the stretched exponential equation. The simple relaxation picture is unable to account for the decay at temperatures far below the glass transition temperature of the polymer. In this range, the average values of rates, represented by k₀, k_∞, and τ_m, poorly describe the real distribution of them. The values of k₀, k_∞, and τ_m for MC decay show an Arrhenius behavior in the polymers studied.