Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Advanced Spectral Analysis: Two-Dimensional Correlation Spectroscopy (2DCOS)


We have advanced a spectral analysis method to characterize overlapping spectral data based on two-dimensional correlation spectroscopy (2DCOS). Using advanced 2DCOS, we characterized spectral signatures associated with changes in the phase and configuration of polymers and other complex molecular systems.


A series of spectra are acquired from a sample of interest as a function of temperature, pressure, electric field strength, concentration, or any experimental parameters. Conventional spectral analysis is performed by monitoring the intensity change at a specific frequency as a function of the controlled variable. However, such a single frequency-based analysis becomes challenging if the spectral region is crowded with multiple overlapping peaks. To overcome the limitation of the univariate analysis, researchers have developed 2DCOS [1]. The 2DCOS method compares spectral intensity variations at a frequency pair with respect to a perturbation variable. 2DCOS provides positive and negative correlations between two spectral components. It also provides specific sequences of certain spectral intensity changes and is used to enhance the spectral resolution of highly overlapped spectra. 2DCOS has been applied extensively to analyze various types of spectral data from Raman and IR to X-ray, UV-Vis, and fluorescence.

We have applied 2DCOS analysis methods to unravel the phase transitions occurring in polymers and alkanes [2,3], the hydrogen bonding in dental resin mixtures [4], and the orientational difference between crystalline and amorphous chains [5]. For advanced spectral analysis, we have developed a moving-window approach to 2DCOS [6,7] and applied it to the polymeric melting [2,3].

Image 1
Figure 1. Moving-window two-dimensional correlation spectroscopic (MW-2DCOS) analysis of n-C21H44 phase transition [2]. Two narrow overlapping peaks are identified in the Raman CH2 twisting band in the orthorhombic phase. The two peaks become a single peak in the rotator phase, which then broadens and shifts to a higher frequency in the amorphous phase.
Figure 2
Figure 2. Least squares moving-window (LSMW) analysis [7] of the Raman spectra of high-density polyethylene (HDPE) [3]. This result is consistent with the multi-thickness lamellae model (the bottom scheme).
The asynchronous 2DCOS map of the (C=O) peak and the (COC) peak of a polycaprolactone (PCL) film with respect to polarization angle
Figure 3. The asynchronous 2DCOS map of the n(C=O) peak and the n(COC) peak of a polycaprolactone (PCL) film with respect to polarization angle [5]. The top and side views present the 3D orientations of the crystalline and amorphous chains in a shear-deformed PCL film.


[1] I. Noda, Y. Ozaki, TwoDimensional Correlation Spectroscopy Applications in Vibrational and Optical Spectroscopy, Wiley & Sons: Chichester, West Sussex, 2004.

[2] Y. Jin, A. P. Kotula, A. R. Hight Walker, K. B. Migler, and Y. J. Lee, Phase-Specific Raman Analysis of n-Alkane Melting by Moving-Window Two-Dimensional Correlation Spectroscopy, J. Raman Spectrosc. 47, 1375 (2016).

[3] Y. Jin, A. P. Kotula, A. R. Hight Walker, K. B. Migler, and Y. J. Lee, Raman Identification of Multiple Melting Peaks of Polyethylene, Macromolecules 50, 6174 (2017).

[4] I. S. Ryu, X. Liu, Y. Jin, J. Sun, and Y. J. Lee, Stoichiometric analysis of competing intermolecular hydrogen bonds using infrared spectroscopy, RSC Advances 8, 23481 (2018).

[5] S. Xu, C. R. Snyder, J. Rowlette, and Y. J. Lee, Three-dimensional molecular orientation imaging of a semicrystalline polymer film under shear deformation, Macromolecules 55, 2627 (2022).

[6] Y. J. Lee, Analytical and Numerical Characterization of Autocorrelation and Perturbation-Correlation Moving-Window Methods, Appl. Spectrosc. 71, 1321 (2017).

[7] Y. J. Lee, Least Squares Moving-Window Spectral Analysis, Appl. Spectrosc. 71, 1894 (2017).

Created May 15, 2019, Updated June 2, 2022