Phase Angle Description of Perturbation Correlation Analysis and Its Application to Time-Resolved Infrared Spectra SHIGEAKI MORITA, MASARU TANAKA, ISAO NODA, and YUKIHIRO OZAKI* Department of Chemistry, School of Science and Technology, Kwansei-Gakuin University, Sanda 669-1337, Japan (S.M., Y.O.); Research Institute for Electronic Science, Hokkaido University, Sapporo 060-0812, Japan (M.T.); and The Procter & Gamble Company, 8611 Beckett Road, West Chester, Ohio 45069 (I.N.) A method of spectral analysis, phase angle description of perturbation correlation analysis, is proposed. This method is based on global phase angle description of generalized two-dimensional (2D) correlation spectroscopy, proposed by Shin-ichi Morita et al., and perturbation- correlation moving-window 2D (PCMW2D) correlation spectroscopy, proposed by Shigeaki Morita et al. For a spectral data set collected under an external perturbation, such as time-resolved infrared spectra, this method provides only one phase angle spectrum. A phase angle of the Fourier frequency domain correlation between a spectral intensity (e.g., absorbance) variation and a perturbation variation (e.g., scores of the first principle component) as a function of spectral variable (e.g., wavenumber) is plotted. Therefore, a degree of time lag of each band variation with respect to the perturbation variation is directly visualized in the phase angle spectrum. This method is applied to time-resolved infrared spectra in the O–H stretching region of the water sorption process into a poly(2- methoxyethyl acrylate) (PMEA) film. The time-resolved infrared (IR) spectra show three broad and overlapping bands in the region. Each band increases toward saturated water sorption with different relaxation times. In comparison to conventional methods of generalized 2D correlation spectroscopy and global phase angle mapping, the method proposed in the present study enables the easier visualization of the sequence as a degree of phase angle in the spectrum. Index Headings: Two-dimensional correlation spectroscopy; Perturbation- correlation moving-window 2D correlation spectroscopy; Global phase angle description; Time-resolved infrared spectra; Attenuated total reflection infrared spectroscopy; In situ ATR-IR spectroscopy; Poly(2- methoxyethyl acrylate); PMEA. INTRODUCTION Generalized two-dimensional (2D) correlation spectroscopy was proposed by Noda in 1993. 1–3 This method is character- ized by a pair of synchronous U(v 1 , v 2 ) and asynchronous W(v 1 , v 2 ) 2D correlation spectra spread on a plane between two spectral variables such as wavenumbers v 1 and v 2 . For a spectral data set of y(v, p) collected under an external perturbation with the associated variable p (p min  p  p max ), such as time, temperature, concentration, etc., the generalized 2D correlation function is given as Uðv 1 ; v 2 Þþ iWðv 1 ; v 2 Þ¼ 1 pðp max  p min Þ Z ‘ 0 ~ Y 1 ðxÞ ~ Y  2 ðxÞdx ð1Þ Here ~ Y 1 ðxÞ¼ Z ‘ ‘ ~ yðv 1 ; pÞexpðixpÞdp ð2Þ and ~ Y  2 ðxÞ¼ Z ‘ ‘ ~ yðv 2 ; pÞexpðþixpÞdp ð3Þ are, respectively, the forward Fourier transform from the perturbation p domain to the Fourier frequency x domain of the spectral intensity change observed at a given spectral variable v 1 and the conjugate of the Fourier transform observed at another spectral variable v 2 . Note that ˜ y(v, p) is a dynamic spectrum of y(v, p). 1 A sequential order of the observed spectral variation along p of two independent bands between v 1 and v 2 can be estimated from synchronous and asynchronous 2D correlation spectra with Noda’s rule. 4 The global phase angle mapping description of generalized 2D correlation spectroscopy was proposed by Shin-ichi Morita et al. in 2001. 3,5,6 Because synchronous and asynchronous 2D correlation spectra correspond, respectively, to the real and imaginary part of the Fourier (frequency) domain spectral correlation, i.e., in-phase and quadrature components of the spectral intensity changes between v 1 and v 2 , the phase angle of the Fourier frequency domain spectral correlation is given by Hðv 1 ; v 2 Þ¼ tan 1 Wðv 1 ; v 2 Þ Uðv 1 ; v 2 Þ ð4Þ Shin-ichi Morita et al. reported that the global phase angle description of Eq. 4 is useful for the determination of the sequential order of dynamic spectral changes having different amplitudes, including even weak signals, which are often difficult to assess in conventional generalized 2D correlation spectra. 5,6 Perturbation-correlation moving-window 2D (PCMW2D) correlation spectroscopy was proposed by Shigeaki Morita et al. in 2006. 7 This method is characterized by a pair of synchronous P U (v, p) and asynchronous P W (v, p) PCMW2D correlation spectra spread on a plane between spectral variable v and perturbation variable p. For a jth sub-divided data matrix comprising 2m þ 1 spectra, the so-called moving window, the jth synchronous and asynchronous PCMW2D correlation spectra are calculated as follows: P U; j ðv; p j Þ¼ 1 2m X jþm J¼jm ~ yðv; p J Þ ~ p J ð5Þ and P W; j ðv; p j Þ¼ 1 2m X jþm J¼jm ~ yðv; p J Þ X jþm K¼jm M JK  ~ p K ð6Þ Received 26 March 2007; accepted 17 May 2007. * Author to whom correspondence should be sent. E-mail: ozaki@ kwansei.ac.jp. Volume 61, Number 8, 2007 APPLIED SPECTROSCOPY 867 0003-7028/07/6108-0867$2.00/0 Ó 2007 Society for Applied Spectroscopy