2D correlation analysis: sequential order judging

Using a two-dimensional (2D) correlation analysis technique to determine the sequential order of physical or chemical events has received keen interests in the past ten years. However, our continuous work demonstrates that the sequential order of events determined by the "sequential order" rules of this technique may lead to ambiguous or even wrong conclusions, because the physical significance of the sequential order in generalized 2D correlation analysis is neither well-defined nor meaningful in general situations, and the word "occur" used in the "sequential order" rules may easily give rise to ambiguity. In contrast to the integrated sequential order derived from periodic changes as in mechanical perturbation based 2D correlation infrared spectroscopy, there is a local/chronological sequential order for nonperiodic changes in general situations. The current work shows that the integrated sequential order in 2D correlation analysis is a reflection of the sequential order of the phases, i.e., phase sequence/difference. The integrated sequential order may indicate the relative state of two events (one event occurs/exists before or after the other one) according to a specific reference, only if both are obtained under the same frequency for periodic changes or even speeds for nonperiodic changes in general situations. The integrated sequential order may not always be able to reveal whether one event occurs/happens before or after another one for nonperiodic changes in terms of timings of happenings. For nonperiodic changes, the integrated sequential order is not so meaningful and must be replaced by the local/chronological sequential order. To judge whether one event occurs/happens before or after another one for two nonperiodic changes in general situations, the original spectral intensity changes must be verified to determine if a chronological/local sequential order exists between two events.