An insight into the sequential order in 2D correlation spectroscopy using polymer transitions: Boltzmann Sigmoid, Gaussian Cumulative, Lorentz Cumulative, and Asymmetric Sigmoid. Findings in experiments and simulations

In this paper, we found the curves of infrared spectral intensity at specific wavenumbers of several polymer transitions can be accurately fitted by one of Boltzmann Sigmoid, Gaussian Cumulative, Lorentz Cumulative, or Asymmetric Sigmoid functions. These transitions include the melting of iPP, the Brill transition of PA66, the epoxy curing, the oxidation of SBS, and the melting of HDPE. These functions were obviously different from other important functions, which were earlier introduced into generalized 2D correlation spectroscopy, such as sinusoidal, exponential, and Lorentzian. The properties of the Boltzmann Sigmoid, Gaussian Cumulative, Lorentz Cumulative functions were studied using the simulated infrared spectra. The sequential order is only controlled by the parameter reflecting the center point location, while other parameter values have no relationship. The influences of the parameters in Asymmetric Sigmoid on the sequential order were also studied using the simulated IR spectra. Within the transition range, it was found the values of several waveform parameters co-determine the sequential order. We concluded that the MW2D or PCMW2D method should first be employed to determine a rational transition range before using 2D correlation infrared spectroscopy to study the mechanism of the polymer transitions. The clear physical meaning of the sequential order is the “earlier” or “later” of the transition points. As long as the experimental range (external perturbation) is wide enough and the data precision is good, the sequential order is absolutely reliable within the transition range. The results discussed throughout this paper have proven that the sequential order rules are absolutely correct. The content of the present study will solve the controversy on the sequential order rules to a large extent.