Limits in the evaluation of closely spaced chemical relaxation processes

Earlier studies on fundamental errors in the evaluation of chemical relaxation parameters from curves of closely spaced relaxation processes are reinvestigated with rigorous mathematical tools. Very precise data referring to two neighboring relaxation processes are produced by non-linear equations and subsequently evaluated by non-linear least squares analysis, assuming two exponential terms. Previously, linear equations were used in the generation of precise data and then evaluated by graphical means. Relaxation processes are evaluated with ratios of two consecutive relaxation times of up to 2/3. The enzyme catalyzed isomerization is used as underlying chemical mechanism with most thermodynamic parameters fixed. The analyses showed that derived signal amplitudes should be used with great care, if relaxation times exceed ratios of around 1/10. If these amplitudes have the same sign, the relaxation times are generally quite precise, as long as the overall amplitudes are sufficiently large. If amplitudes become comparatively small in selected regions, evaluated amplitudes may deviate considerably from computed (theoretical) ones. The experimentalist has to be aware of this problem even if high signal-to-noise ratios are maintained (S/N ? 1000).