Analytical solution for time-resolved photoacoustic calorimetry data and applications to two typical photoreactions

Time-resolved photoacoustic calorimetry (PAC) allows the measurement of lifetimes and energy fractions of molecular nonradiative deactivation processes, as well as structural volume changes associated with such processes. The photoinduced acoustic wave generated by a given photochemical sample, E(t), is the result of the convolution between the heat function H(t), describing the kinetics of the photochemical processes in the sample, and the instrument response given by a calorimetric reference wave, T(t). A relatively simple mathematical description of the T(t) wave parametrized by the rise time, frequencies and damping time of the transducer is presented for transducers of distinct frequencies. This description allows for a non-restrictive analytical solution of the convolution of the T(t) wave with the heat function. Comparison of the analytical solution with the experimental wave E(t) allows the determination of the fractions of excitation energy and lifetimes of the intermediate species. Published photochemical systems with two and three sequential decaying processes were analyzed to validate the efficacy of this method. This new method of analysis, and a software application that simulates E(t), allows a better understanding of the underlying physics through their phenomenological description.