Multiple Perturbation Two-Dimensional Correlation Analysis of Cellulose by Attenuated Total Reflection Infrared Spectroscopy HIDEYUKI SHINZAWA,* SHIN-ICHMORITA, KIMIE AWA, MARIKO OKADA, ISAO NODA, YUKIHIRO OZAKI, and HIDETOSHI SATO Optical Biopsy Development Research Unit, RIKEN, Saitama 351-0198, Japan (H.S., S.M., H.S.); Dainippon Sumitomo Pharma Co., Ltd. Osaka 554-0022, Japan (K.A.); Department of Chemistry and Research Center for Near Infrared Spectroscopy, School of Science and Technology, Kwansei-Gakuin University, Hyogo 669-1337, Japan (M.O., Y.O.); and The Procter & Gamble Company, 8611 Beckett Road, West Chester, Ohio 45069 (I.N.) An extension of the two-dimensional (2D) correlation analysis scheme for multi-dimensional perturbation is described. A simple computational form is provided to construct synchronous correlation and disrelation maps for the analysis of microscopic imaging data based on two independent perturbation variables. Sets of time-dependent attenuated total reflection infrared (ATR-IR) spectra of water and cellulose mixtures were collected during the evaporation of water from finely ground cellulose. The system exhibits complex behaviors in response to two independent perturbations, i.e., evaporation time and grinding time. Multiple perturbation 2D analysis reveals a specific difference in the rate of evaporation of water molecules when accompanied by crystallinity changes of cellulose. It identifies subtle differences in the volatility of water, which is related to the crystalline structure of cellulose. Index Headings: Two-dimensional correlation spectroscopy; 2D-COS; Perturbation; Cellulose; Infrared spectroscopy; IR spectroscopy; Phar- maceutical tablets. INTRODUCTION Generalized two-dimensional (2D) correlation spectroscopy, which was originally proposed by Noda in 1993, has been developed for the analysis of perturbation-induced spectral variation. 1–3 2D correlation is a powerful and versatile technique applicable to spectroscopy and many other analytical measure- ments. The basic concept of 2D correlation spectroscopy is the analysis of synchronicity and asynchronicity of dynamic spectra, which are induced by an applied external perturbation. 2D correlation spectra are derived from a set of analytical signals collected under a perturbation, and they provide rich and useful information about the presence of coordinated or independent changes among signals, as well as relative directions and the sequential order of signal intensity variations. Perturbations in 2D correlation spectroscopy can take various forms, as long as they induce systematic changes in analytical signals for the response of the system. There are numerous different types of external perturbations that could be used to stimulate a system of interest. For example, various molecular-level excitations may be induced by electrical, thermal, magnetic, chemical, mechanical, or even acoustic excitations. Each perturbation affects the system in a unique and selective way, governed by the specific interaction mechanisms relating the macroscopic stimulus to the micro- scopic or molecular level responses of individual system constituents. The type of physical information contained in dynamic signals, therefore, is determined by the selection of a specific perturbation method and analytical probe. In principle, any analytical experiment that leads to the generation of systematic dynamic signals becomes a good candidate for 2D correlation analysis. An extended form of 2D correlation and its application to handle dynamic signals stimulated by multiple physical stimuli are reported in this study. Dynamic spectra dealing with two simultaneous perturbation functions are defined with a simple expansion of the conventional 2D formula to derive synchro- nous correlation. Disrelation intensity for the case of multiple perturbation is newly defined as an approximation for the asynchronous spectrum by circumventing the need to transform spectral data into the Fourier domain. The introduction of the idea of disrelation as a substitute for asynchronous correlation makes the numerical computation for the so-called Hilbert– Noda transformation approach surprisingly simpler. Important- ly, it can take a combination of different physical stimuli, such as temperature and concentration, as long as they represent the systematic changes of analytical signals. This form of 2D correlation analysis is somewhat similar to the multi-way analysis used for handling data arranged in three or higher way arrays by using matrix algebra. The difference lies in the way of describing the underlying behavior of a system. 2D correlation analysis aims at describing the dynamics of spectral features found in multi-way data, while multi-way analysis mainly treats data to represent a linear combination of representative factors, such as latent variables. 4,5 In the present study, a useful demonstration example is provided to show how to handle multiple perturbation systems based on 2D correlation analysis. Sets of time-dependent attenuated total reflection (ATR) infrared (IR) spectra of microcrystalline cellulose (MCC) whose crystallinity is systematically controlled by the difference level of grinding are collected. This system exhibits the influence of two independent perturbation variables, i.e., evaporation time and crystallinity. It was found that 2D correlation analysis effectively sorts out subtle differences in the volatility of bound water and nonfreezing bound water. The result indicates that water absorption by cellulose is related to its amorphous structure. The degree of the prolonged retention of the bound water is related to the amount of the amorphous component. THEORY Generalized Two-Dimensional Correlation Spectroscopy. Assume a set of dynamic spectra at m evenly spaced points in time t between T min and T max represented as follows: ˜ y j ðmÞ¼ ˜ yðv; t j Þ; j ¼ 1; 2; ... ; m ð1Þ Received 15 December 2008; accepted 19 February 2009. * Author to whom correspondence should be sent. E-mail: hshinzawa@ riken.jp. Volume 63, Number 5, 2009 APPLIED SPECTROSCOPY 501 0003-7028/09/6305-0501$2.00/0 Ó 2009 Society for Applied Spectroscopy