Modelling of transient production and decay following laser excitation of opaque materials

Abstract

The generation and decay of transient species in light-scattering materials is examined theoretically. Two limiting cases of transient distribution can be identified for which straightforward mathematical solutions are available: (a) where an exponentially falling-off concentration of transients exists beneath the sample surface and (b) where a homogeneous transient concentration (a ‘plug’) exists beneath the sample surface. Between and including these limits, the concentration profile can be calculated by a numerical iterative thin-slice approach. This method also permits calculation of the experimentally available reflectances R of the sample at the analysing wavelength. The size of the transient absorption is governed by the extinction coefficients of the initial absorber and the transient. In the case of a transient species which shows both luminescence and absorption, it is found that the emission intensity and the transient absorption at the same wavelength are proportional to each other. For a transient decaying by a unimolecular pathway, the rate constant can be obtained in case (a) from the slope of a plot of ln (1 –R)vs. time, while for case (b) ln [F(R)] must be plotted against time, where F(R) is the Kubelka–Munk function. If the decay follows a bimolecular pathway, the rate constant can be evaluated from the slope of a 1/F(R) plot vs. time only for case (b). In all other cases no straightforward method is available. Experimental data are presented and discussed for benzil microcrystals, an example of case (a) where the predicted superimposition of transient decay and phosphorescence is also observed, and for acridine adsorbed on silica gel, an example of case (b).