Analysis of heterogeneous fluorescence decays. Distribution of pyrene derivatives in an octadecylsilane layer in capillary electrochromatography

The distribution of solute molecules in the stationary phase in capillary electrochromatography (CEC) has been investigated with time-resolved fluorescence in the frequency domain. The analysis of fluorescence decay poses a challenging problem for the complex decay kinetics of heterogeneous systems such as the C18 stationary phase. The nonlinear least-squares (NLLS) method selects the decay model by minimizing the chi2 value. The chi2 criterion, in conjunction with the requirement that the residues should be randomly distributed around zero, frequently leads to a feasible set of multiple decay models that can all fit the data satisfactorily. The maximum entropy method (MEM) further chooses a unique model from the group of feasible ones by maximizing the Shannon-Jaynes entropy. The unique model, however, is not necessarily the most probable one. In this paper, the best model for the fluorescence decays of solute molecules is selected with NLLS using the chi2 statistics, the stability of the fit, and the consistency within replicate experiments. In addition, the recovered lifetime parameters of the true model should display the same trend as the fluorescence decay profiles when an experimental condition is varied. Using these criteria, a Gaussian distribution of fluorescence lifetimes satisfactorily fits the data under all experimental conditions. An additional minor component with a discrete lifetime is attributed to the systematic errors in the measurements. The distribution is a manifestation of an ensemble of heterogeneous microenvironments in the stationary phase of CEC. MEM is not suitable for the modeling of CEC data because of its inaccuracy in recovering broad fluorescence lifetime distributions and its lack of consistency in the replicate measurements in the studies of high-voltage effects.