Global analysis of unmatched polarized fluorescence decay curves of systems exhibiting a residual anisotropy at long times

A previous study of the performance of the global, i.e., simultaneous, analysis of unmatched polarized decay traces [Crutzen, M.; et al. J. Phys. Chem. 1993, 97, 8133] is extended for the time-dependent anisotropy r(t), given by r(t) = beta exp(-t/Phi) + r infinity. The evaluation was done with computer-generated and experimentally collected data. Two different schemes of analysis of unmatched polarized decay traces were considered. In scheme A the decay curves measured with the analyzer set at 0 degrees, 54.7 degrees, and 90 degrees with respect to the polarization of the incident light were globally analyzed, while only the traces at 0 degrees and 90 degrees were taken into account in scheme B. Data were simulated for various Phi/tau ratios (0.1, 1, 3, and 10). The value obtained for the fluorescence lifetime tau was accurate and precise for all cases considered. For Phi/tau = 0.1, 1, and 3 (tau = 5 ns) the parameters beta and Phi, were well recovered. The accuracy and precision were very similar to the results obtained with matched decay traces. The recovery of r infinity was case dependent. Scheme A performed somewhat better than scheme B. When r(0) was fixed to the true value, the analysis with schemes A and B yielded the same accuracy and precision as the analysis of the matched curves. For Phi/tau = 10, the parameter estimates for the anisotropy parameters were inaccurate and suffered from very high uncertainty. No improvement was obtained when r(0) and the matching factors were kept fixed to the true value. This is in contrast with the results obtained for r(t) without an r infinity term, where Phi/tau can even be much higher when r(0) or the matching factors are kept fixed. There was some improvement when the signal to noise ratio was increased. When the decay of the total fluorescence was biexponential, scheme A performed much better than scheme B. The best results were obtained when G or r(0) was kept fixed. It was found that with respect to the normalization of the polarized decay traces the fundamental anisotropy r(0) and the matching factor G contain the same information. In general, the best accuracy and precision in the parameter recovery were obtained when a predetermined value for G or r(0) was used in the analysis. The performance of the analyses without the information on r(0) or G depended more on the Phi/tau ratio than for the analyses where this information was used. Fixing of both G and r(0) to the proper value might lead to an improved precision. It has to be emphasized that the use of incorrect values for G (with r(0) freely adjustable) or r(0) (with G freely adjustable) could lead to good data fits, although the parameter estimates are incorrect. A small change in r(0) can lead to a large change in Phi. Therefore, in general it can be recommended that either G or r(0) be fixed, but not both. Alternatively, the comparison of the results obtained with a freely adjustable G and a fixed G can provide a check for the data analysis.