Recent developments in two-dimensional infrared (2D IR) correlation spectroscopy are reviewed. Since the initial introduction of the basic concept seven years ...
Recent Developments in Two-Dimensional Infrared (2D IR) Correlation Spectroscopy I. N O D A , * A. E. D O W R E Y , and C. M A R C O T T The Procter and Gamble Company, Miami Valley Laboratories, P.O. Box 398707, Cincinnati, Ohio 45239-8707
Recent developments in two-dimensional infrared (2D IR) correlation spectroscopy are reviewed. Since the initial introduction of the basic concept seven years ago, the field of 2D IR spectroscopy has evolved considerably. The method for generating 2D IR spectra from perturbation-induced time-dependent fluctuations of IR intensities and the properties of such 2D spectra are summarized first. Applications of 2D IR spectroscopy are then surveyed, and improvements in the instrumentation are reviewed. Different types of external perturbation schemes capable of inducing dynamic fluctuations of IR spectra are listed. Finally, a new 2D correlation method for dynamic spectral data with arbitrary time-dependence is discussed. Index Headings: Correlation spectra; Fourier transform; Infrared; Review; Spectroscopic technique; Time-resolved spectroscopy; Two-dimensional spectroscopy; 2D IR spectroscopy.
levelY,3 Specific interactions often result in the appearance of characteristic correlation peaks in 2D IR spectra due to the synchronization of perturbation-induced responses of interacting functional groups. Enhanced spectral resolution is another major advantage of 2D IR spectroscopy. Many overlapped IR bands have been identified by spreading them along the second spectral dimension. 3 In the last seven years, 2D IR spectroscopy has evolved considerably. The utility of this technique has turned out to be much greater than originally envisioned. The purpose of this review is to bring together the recent developments in this field, including specific applications of 2D IR, improvements in instrumentation, and new types of 2D correlation methods.
INTRODUCTION
BACKGROUND
Since the initial introduction of the basic concept, 1 two-dimensional infrared (2D IR) correlation spect r o s c o p y 2,3 has gained considerable interest among scientists in various fields. ~ In 2D IR, a spectrum is obtained as a function of two independent IR wavenumbers. Peaks appearing on a 2D spectral plane provide useful information not readily accessible from a conventional one-dimensional spectrum. Most 2D IR spectra are currently generated from time-resolved IR spectra or fluctuations of IR intensity signals induced by an external perturbation applied to the system. A simple correlation analysis transforms these time-dependent spectral intensity variations to a set of 2D IR spectra. 3 The 2D IR technique was originally employed to analyze data obtained from infrared rheo-optical studies of polymers. These studies were designed to probe molecular-level responses of samples undergoing flow, deformation, and subsequent relaxations. 9-12 A small-amplitude oscillatory strain (i.e., mechanical perturbation) in the acoustic frequency range was applied to a thin polymeric film, and the resulting dynamic reorientations of dipole-transition moments associated with various chemical groups were monitored with polarized IR light. Two-dimensional infared spectroscopy based on such strain-induced dynamic IR measurements has been successfully used to probe the segmental dynamics of macromolecules. 9 In addition to investigations of molecular dynamics of polymeric materials, the 2D IR technique has been found to be surprisingly successful in general spectroscopic applications. For example, 2D IR is found to be useful in elucidating interactions of mixtures at the submolecular
Figure 1 describes the basic scheme for generating twodimensional correlation spectra from perturbation-induced fluctuations of spectral signals. In ordinary (i.e., one-dimensional) spectroscopy, electromagnetic radiation, such as UV, x-ray, or IR, is employed to obtain information from a system. A spectrum representing how such a probe interacts with various constituents of the system is acquired and interpreted. If an external physical perturbation is applied to the system, the spectrum may vary dynamically according to the characteristic time-dependent response of the system. There are, of course, many types of perturbations which could cause various dynamic spectral responses) The nature of the perturbation can be electrical, chemical, mechanical, magnetic, optical, thermal, etc. Mechanical perturbations, especially small-amplitude oscillatory strain in the acoustic frequency range, have been extensively used to study dynamic molecular reorientations. The time-dependent behavior of the externally applied stimulus is not fixed in 2D IR analysis. There are many possible types of perturbation waveforms (e.g., pulse, sinusoid, or even random noise) that could be considered for a 2D IR experiment. A sinusoidally varying smallamplitude perturbation has often been applied. The timedependent fluctuation of IR signals, referred to as the d y n a m i c I R s p e c t r u m , is transformed into a pair of 2D IR spectra by applying a simple correlation analysis. The s y n c h r o n o u s 2D I R correlation s p e c t r u m (Fig. 2) characterizes the coherence of dynamic fluctuations of IR signals measured at two different wavenumbers. The intensity of this correlation spectrum, therefore, becomes significant only if the time-dependent behavior patterns of the two IR signals are similar to each other. The asynchronous 2D I R correlation s p e c t r u m (Fig. 3), on the other hand, characterizes the independent or uncoordi-
Received 26 March 1993. * Author to whom correspondenceshould be sent. Volume 47, Number 9, 1993
0003-7028/93/4709-131752.00/0 © 1993 Society for Applied Spectroscopy
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nated fluctuations of IR signals. Thus, the intensity of the asynchronous spectrum vanishes unless the dynamic IR signals vary at different rates. The interpretation of 2D IR correlation spectra is relatively straightforward. One can extract useful information which is often obscured in the original time-resolved IR spectrum by utilizing the basic properties of 2D IR correlation spectra summarized below. More detailed discussion of the properties of 2D IR spectra is found elsewhere? The peaks located at the diagonal position of a synchronous spectrum, called autopeaks, represent the extent of dynamic variations of IR signals for a given external perturbation. When the dynamic IR signals at two different wavenumbers are varying in phase (i.e., simultaneously) with each other, cross peaks appear at the off-diagonal positions of a synchronous spectrum. Coordinated local responses of system constituents may result in such synchronized behavior of IR signals. Highly coordinated responses, in turn, imply the possible existence of interactions or connectivity which restricts independent responses of individual constituents. The sign of synchronous cross peaks indicates the relative direction of change in dynamic spectral responses. A cross peak becomes positive if the spectral intensities
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are changing (either increasing or decreasing) in the same direction. It becomes negative if the changes are in opposite directions. If the spectral signal change is related to the reorientation direction of dipole-transition moments, as in the case of dynamic IR dichroism measurements, 1°-12the sign of a synchronous cross peak is directly related to the relative reorientation of two dipole-transition moments? In Fig. 2, signals at IR bands A and C are changing simultaneously but in opposite directions. Signals at bands B and D, on the other hand, are changing together in the same direction. If IR signals from two specific wavenumbers are not varying at the same rate, cross peaks appear at these wavenumber coordinates in the asynchronous 2D IR correlation spectrum. Such uncoordinated signal fluctuations suggest that submolecular structures contributing to the IR absorption at these wavenumbers do not strongly interact with each other. The appearance of asynchronous cross peaks for different functional groups becomes an attractive feature for differentiating IR bands which are often highly overlapped. It is possible to effectively enhance the spectral resolution by taking advantage of band-discriminating peaks in an asynchronous 2D IR spectrum. The sign of asynchronous peaks provides the temporal relationship between the responses of the system components to the external stimulus. The sign of an asynchronous cross peak is positive if an event attributed to the dynamic change of the IR intensity (e.g., the reorientation of the dipole-transition moment) observed at wavenumber vl occurs before the event observed at wavenumber ~2. If, on the other hand, the event at ~ occurs after the event at ~2, the sign of the cross peak becomes negative. The temporal relationship described above must be reversed if the corresponding synchronous correlation intensity is negative. In Fig. 3, the signal fluctuations at
IR bands A and C occur after the fluctuations at B and D. NEW DEVELOPMENTS
Applications. The first system studied in detail by 2D IR spectroscopy was solution-cast thin films of atactic polystyrene. 1,3,9,13-t5The IR band assignments of this glassy .polymer are well known. 164s This material forms a rigid single-phase plastic film without the complication of crystal formation. It was, therefore, selected as an excellent model system to gauge the potential utility of 2D IR spectroscopy. It was discovered that the behavior of perturbation-induced IR intensity fluctuations observed at different wavenumbers varies considerably for atactic polystyrene. 2,3By taking advantage of this band-selective behavior of time-dependent intensity fluctuations, it has become possible to enhance the resolution of mid-IR condensed-phase spectra. 3 In particular, it was shown that IR bands associated with the main chain of atactic polystyrene, such as backbone methylene stretching modes, exhibit time-dependent behavior substantially different from the behavior for side-group phenyls. 9,14,~5 When polarized light is used, the sign of cross peaks appearing in the synchronous 2D correlation spectrum provides the relative reorientational directions of various dipole transition moments. Thus, detailed information on local submolecular motions of polystyrene under a small-amplitude mechanical perturbation was elucidated. 9 It was found that such local submolecular motions are strongly influenced by the physical state of the polystyrene sample. ~5 Another excellent model system for 2D IR studies is atactic poly(methyl methacrylate). 19-2~For this polymer, there are three groups contributing to IR absorption in the CH-stretching region of the spectrum: ester methyl groups of the side chains; a-methyl groups attached to the main chain; and backbone methylene groups. While IR absorption bands arising from molecular vibrations of these groups are highly overlapped, the assignment for each group contribution has been well established by a systematic deuterium-substitution study reported previouslyY2 A 2D IR analysis of an atactic poly(methyl methacrylate) film shows that, even without the help of tedious deuterium substitution, IR bands assignable to separate groups can be readily differentiated. Strong synchronous cross peaks develop at spectral coordinates corresponding to ester methyl groups, while bands for other groups, such as a-methyl, can be clearly differentiated from ester methyl bands as a result of cross peaks appearing in the asynchronous 2D IR spectrum. Analysis based on the sign of cross peaks provides detailed information about submolecular-scale reorientation mechanisms of this polymer under a small strain. One of the major outcomes of these model studies is that the spectral coordinates of cross peaks in a 2D IR spectrum often correspond to the position of unique IR bands arising from a distinct molecular vibration. In other words, the 2D IR technique seems to provide true resolution enhancement for mid-IR spectra of condensed-phase materials. Another major advantage of 2D IR is the ability to detect possible submolecular-level interactions. This feature has been demonstrated by nu-
merous examples. In particular, a number of polymerblend system were studied by 2D IR spectroscopy, and the existence or lack of specific interactions between the blend constituents was probed successfully. Some examples of 2D IR studies of polymer blends are discussed below. 2D IR spectra were obtained for an immiscible blend of atactic polystyrene and low-density polyethyleneY Synchronous peaks appear between IR bands arising from the same constituents, e.g., two phenyl bands assignable to polystyrene and two methylene bands for polyethylene. Little correlation intensity was observed between polyethylene and polystyrene bands. This result was interpreted as the consequence of individual polymer components of an immiscible blend responding to a given perturbation at very different rates. Phase-separated components cannot interact with each other at the molecular level to coordinate individual molecular motions. The appearance of asynchronous cross peaks between polystyrene and polyethylene bands also supports this interpretation. In addition to the asynchronicity observed between the different polymer constituents of this blend system, differentiation of functional groups within the same polymer molecule was also observed. Thus, asynchronous cross peaks appeared between overlapped polystyrene bands assignable to main-chain methylenebending and side-group semicircle-stretching vibrations. Several miscible blends of atactic polystyrene were studied with the hope that 2D IR analysis would provide information about specific chemical interactions occurring in these miscible polymers. 23-27 Miscible blends of atactic polystyrene and poly(vinyl methyl ether) have been studied extensively by polymer scientists as an important model system which shows lower critical solution temperature behaviorY s,29 Relatively little, however, is known about the origin of the apparent miscibility of these two very different polymers2 °-32 Polystyrene is a hard plastic resin, while poly(vinyl methyl ether) is a very soft, water-soluble polymer. The normal IR spectrum of poly(vinyl methyl ether) shows a single peak assignable to the CH-stretching vibrations of methoxyl groups. An asynchronous 2D IR spectrum of the blend reveals there are actually two separate bands under this peakY -25 Strong synchronous cross peaks develop between one of the two methoxyl bands and the phenyl bands of polystyrene, indicating the possible existence of a specific intermolecular interaction between the phenyl and methoxyl groups. Interestingly, no interaction was detected for the other methoxyl bands. In fact, this second methoxyl band develops strong asynchronous cross peaks with polystyrene phenyl bands. Thus, not all the methoxyl groups are apparently involved in this interaction with polystyrene phenyl groups. The result suggests that this system is not completely homogeneous, but there exists a certain degree of submolecular-level microheterogeneity. Similar observations have been made in N M R studiesY s-3° Another well-known miscible blend of poly(2,6-dimethyl 1,4-phenylene oxide) and polystyrene has also been studied by 2D IR spectroscopyY6 Again, some asynchronous cross peaks develop between the miscible constituents, indicating the possible existence of submolecular-level microheterogeneity. APPLIED SPECTROSCOPY
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The localized nature of molecular interactions was further demonstrated by a 2D IR analysis of atactic polystyrene plasticized with toluene. 27 Perturbation-induced dynamic reorientation of toluene molecules is virtually synchronized with that of polystyrene, suggesting the strong association of toluene and polystyrene. For polystyrene plasticized with dioctyl phthalate, 27synchronous cross peaks develop at the spectral coordinates corresponding to the aromatic rings of both components. Noticeable asynchronous peaks, however, appear between the absorption region of aliphatic ester chains of dioctyl phthalate and that of polystyrene phenyl groups. This observation suggests that the specific intermolecular interaction between polystyrene and dioctyl phthalate arises from highly localized association-like interactions of aromatic groups. Extensive work has been carried out on the 2D IR analysis of semicrystalline polymers, especially polyolefin films. 2,33-35This is partly due to the wealth of information accumulated previously in the form of dynamic IR linear dichroism (DIRLD) spectra obtained for the rheo-optical studies of such systems. 1°,1~,36-3sThe conversion of DIRLD spectra to 2D IR correlation spectra is quite straightforward. It was, therefore, natural to initiate the 2D IR analysis of polyolefins. Numerous DIRLD spectra have been collected for polyolefin films, including high-density polyethylene, 1°,36,37 isotactic polypropylene, ~1 low-density polyethylene, 37,38and their blends2 7 2D IR analysis was used to probe the morphology of linear low-density polyethylenes, which are copolymers of ethylene and a small amount of a-olefins. Linear lowdensity polyethylenes consist of a linear methylene backbone and sparsely distributed short side chains2 3 An asynchronous 2D IR spectrum can easily differentiate IR bands belonging to the crystalline regions from those arising from amorphous regions of this material. With the use of a deuterium-labeled sample, it was shown that short side chains are concentrated in the amorphous region, as expected. Blends of high-density and low-density polyethylenes were also studied2 4 2D IR spectra of polyethylene blend films reveal that high-density polyethylene forms separate crystalline domains from low-density polyethylene, resulting in a very complex superstructure of intertwined crystalline lamellae. The 2D IR analysis of isotactic polypropylene has been carried out by several groups. H,35Characteristic, distinct features of 2D IR spectra of polypropylene films were reproduced by different investigators. Due to the stability of this strong polymer film and the high level of dynamic IR signals induced by mechanical perturbation, isotactic polypropylene films have become a standard system for comparing the performance of spectrometers built for 2D IR spectroscopy studies. A large number of biopolymers have been looked at by 2D IR spectroscopy. Systems as complicated as human skin 3 and hair keratin 9,14,21,39,4°have been analyzed by this technique. Highly overlapped, conformationally sensitive amide bands of protein components can be discriminated by asynchronous 2D IR spectroscopy. Bands arising from the same protein conformations, such as fl sheet, random coil, or a helix, generate synchronous cross peaks among themselves. This feature is especially attractive since it offers the possibility of establishing 1320
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unique two-dimensional IR fingerprints for complex biological systems. Conformational changes of proteins occurring under various physical and chemical treatments are also readily monitored by 2D IR spectroscopy. By knowing the signature bands of each conformation, it is possible to deduce the origin of changes in macroscopic physical properties on the basis of molecular-level information29, 4o Poly(3-hydroxybutyrate) is a semicrystalline resin synthesized by certain species of bacteria. 41 The interest in this aliphatic polyester has increased considerably due to the biodegradability of this thermoplastic resin. It is considered a potential replacement for other conventional polymeric resins to reduce environmental problems associated with waste disposal of articles made of polymers. 2D IR spectroscopy has been used to show that miscible additives mixed with poly(3-hydroxybutyrate) tend to be rejected from the crystal lattice of this resin. They accumulate in the amorphous region located between crystalline lamellae. 23,42 Such localized accumulation of additives could have a profound effect on the mechanical properties of articles made from poly(3hydroxybutyrate). Composite materials, such as laminates consisting of several layers of polymer films, have been studied by photoacoustic 2D IR spectroscopy. 43 Phase differences due to the penetration depth of a photoacoustic probe can be readily analyzed by using the 2D correlation method. Ethylene vinyl acetate layered over an isotactic polypropylene film 43 and polyimide resin over polytetrafluoroethylene 44 have been successfully studied. Laminated samples are a popular way to examine materials, such as very thin films and viscous liquids, which do not stand up well under mechanical perturbations. With the use of a partially IR-transparent substrate, either polytetrafluoroethylene or polyethylene depending on the sample spectral region of interest, it is possible to study samples which do not form self-sustaining films.3,2,,23-25,27,39 Instrumentation. Earlier data used for the construction of 2D IR spectra were collected by using a dispersive instrument coupled with a dynamic mechanical stretcher as an excitation device. I°-12 The dispersive spectrometer was selected due to the perceived complexity of obtaining time-resolved spectra with an FT-IR instrument. If the time scale of dynamic IR signals falls within the range of interferometric modulation frequencies, decoupling of signals becomes very cumbersome. Unfortunately, the useful frequency range in the 2D IR study of solid-state samples often falls within this acoustic frequency range. Several strategies have been proposed to obtain acousticrange time-resolved IR spectra with the use of a conventional rapid-scan FT-IR spectrometer. 4~-52In so-called stroboscopic time-resolved measurements, a set of interferograms are collected while the spectrum is changing as a function of time. The signal sampling must be synchronized to the triggering mechanism of the time-resolved measurement so that each sampling point of the interferogram corresponds to some known time point of the measurement. Each interferogram is then sliced into short segments and combined with segments from other interferograms to produce a set of isochronal interferograms, each representing a fixed time-delay point. Such
a stroboscopic technique is often difficult to carry out, since it requires exceptional system stability and reproducibility of each interferogram during the dynamic measurement. Under certain conditions, dynamic IR spectra can be measured with a conventional FT-IR spectrometer without the use of the stroboscopic method. As long as the time required to scan an interferogram is much shorter than the time scale of the measurement of dynamic IR spectra, a rapid-scan FT-IR spectrometer can provide adequate time resolution to monitor time-dependent changes in IR spectra. Likewise, it is relatively easy to detect high-frequency repetitive changes in an IR spectrum, such as those induced by ultrasonic perturbation of samples. If the frequency of dynamic fluctuation of IR signals is much higher than the highest frequency component of interferometric signals, the interferogram representing the dynamic intensity changes can be modulated by the high-frequency signals superposed on the interferogram. Demodulation of such signals can be readily accomplished, for example, by using a lock-in amplifier. The development of modern step-scan FT-IR instruments has essentially eliminated the difficulties in carrying out dynamic IR measurements, even when the experimental time scale falls within the acoustic frequency range. 53-~5 In step-scan interferometry, the relative position of the moving mirror of the interferometer (or more strictly speaking, the optical retardation of the IR beam) is kept at a constant value during the measurement of dynamic IR signals. The mirror is then stepped to the next position only after the completion of each dynamic measurement. Thus, the interferometric time scale is decoupled from the time scale of dynamic IR signal variations2 5 The introduction of step-scan FT-IR instrumentation is a major breakthrough in the field of 2D IR spectroscopy. 5~9 Step-scan 2D FT-IR measurements offer clear advantages over the dispersive approach when a broad range of the IR spectrum must be analyzed. The multiplexing advantage of FT-IR spectroscopy is especially attractive if one wishes to correlate different IR bands which are widely separated into the different spectral regions. The dispersive approach, on the other hand, may provide better efficiency for the investigation of narrower spectral regions, especially for the deconvolution of highly overlapped multiplet IR bands in a few composite peaks. Recently, a very promising approach to time-resolved IR measurements called asynchronous detection has been proposed2 °-63 This approach allows the use of a conventional continuous-scan FT-IR spectrometer for time-resolved measurements without synchronizing the signal detection with the excitation of the system. In an asynchronous time-resolved FT-IR measurement, a system is perturbed repeatedly with a rapid succession of excitation pulses. The interferogram signals measured during such a dynamic experiment, which are modulated by the responses of the system to the applied stimuli, are sent to a gate circuit with a trigger pulse delayed from the excitation pulse by a selected period of time. The key to this invention is the clever use of a low-pass filter which filters out high-frequency components of the signal to
convert the output from the gate circuit to an analog signal, which becomes equivalent to the isochronal interferogram at the selected delay time. Perturbation Methods. The 2D correlation approach to IR spectroscopy has been very successful in the area of dynamic IR rheo-optical studies of polymeric samples. However, this versatile spectroscopic technique certainly is not limited to the analysis of mechanically induced IR signals from polymer films. It is quite possible to generate many different types of 2D IR spectra depending on the waveforms and physical nature of the external perturbation, as well as the type of samples. Some potentially useful possibilities were previously discussed when the concept of 2D IR correlation spectroscopy was initially introduced. 3 Many new system perturbation methods have been explored since then. For example, 2D IR analysis has already been reported for electrically induced reorientation of liquid crystals. ~,5s,64It was shown that different components of the liquid-crystalline system respond separately to the applied electric field. Dynamic IR spectroscopy based on electrical perturbation is not a new idea. There are many examples of such electro-optical experiments2 ~-6s The transformation of time-dependent electro-optical data to a 2D IR correlation spectrum may make it easier to analyze the time-resolved IR data. 5s Spectral data obtained from depth-profiling photoacoustic FT-IR studies of laminated samples could also be analyzed via 2D correlation. 43 In this case, the orthogonal pair of photoacoustic spectra obtained by phasesensitive quadrature detection can be used to produce 2D correlation spectra. Photoacoustic IR signals originating from the same layer are synchronously correlated, while those arising from different depths are asynchronously correlated. Many other types of perturbation methods, including chemical and optical perturbations, 69 are now being explored. It is expected that even more different types of system perturbation methods will be considered in future, due partly to the new development in the 2D correlation method discussed in the following section. Signal Waveforms. Up to now, the waveform of perturbations selected to induce optical signal fluctuations used for 2D IR spectroscopy has been limited to a simple sinusoid with a fixed frequency. The resulting time-dependent spectral intensity signals also vary sinusoidally with the same periodicity, as long as the system responds linearly to the applied stimulus. Sinusoidal signals are, of course, easy to detect experimentally, and the correlation analysis of such signals is c o m p u t a t i o n a l l y straightforward. While the choice of a sinusoidal perturbation may be a logical starting point for 2D IR spectroscopy, the requirement for periodically varying spectral signals in order to construct 2D IR spectra has also restricted the applicability of this technique. In order to circumvent this limitation, a more generalized 2D correlation formalism has been proposedY ° By using this new formalism, it has now become possible to construct 2D spectra from dynamic IR signals having any arbitrary waveform. The basic strategy behind this generalized 2D correlation method is to treat a dynamic spectrum as a set of signals adaptable to classical timeseries analysis. 71,72By transforming dynamic spectral data APPLIED SPECTROSCOPY
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into the Fourier domain first, it is possible to generate a set of 2D correlation spectra comparable to those produced from sinusoidally varying spectra. The basic properties of such 2D IR correlation spectra (e.g., identification of bands associated with the same species or functional groups, enhanced spectral resolution, and sorting of the temporal relationship) are similar to the properties originally proposed for 2D spectra2 The general applicability of the correlation technique, however, should be dramatically improved by the introduction of this new formalism. It can be applied to various transient spectral data collected at different time scales. Somewhat different types of 2D correlation spectra (strictly speaking, 2D covariance spectra) have been reported. 73 In this approach, a set of randomly ordered spectra are used instead of sequentially observed timeresolved spectra. A 2D plot of the correlation coefficient for statistical deviations from the mean value of IR intensity is constructed. The correlation-coefficient plot always has a constant value of unity at the diagonal position, which provides no useful spectral information. The spectral information content may be supplemented by multiplying the correlation coefficient by variances of spectral intensity measured at two wavenumbers. This operation produces a 2D plot of the covariance of spectral intensities. 24 Such a plot may be considered as a continuous form of the variance-covariance matrix of spectral intensities plotted over the entire spectral range. The idea of plotting the covariance of spectral signals as a function of two independent spectral variables has been known. For example, such plots have been reported in mass spectrometryTM and astronomy. 75 In this type of analysis, however, no attention is paid to the specific order of the time-dependent spectral changes taking place during the measurement. Thus, a 2D plot containing temporal information equivalent to an asynchronous 2D correlation spectrum cannot be generated. Other Areas of Spectroscopy. The basic 2D correlation formalism initially developed for IR spectroscopy may be readily applied to areas other than IR. It has been shown, for example, that intensity fluctuations of an x-ray beam scattered by a multi-phase sample undergoing a dynamic deformation may be analyzed by the same 2D correlation technique. 9 The intensity profile of x-ray scattering at different angles corresponds to the spatial distribution of various microscopic constituents of the system. The time-dependent fluctuation of x-ray scattering intensities, therefore, is related to the dynamic rearrangement of such structural units. 2D x-ray scattering spectra produced by the correlation analysis of dynamic x-ray data provide information on the coordinated and independent dynamic reorganizations of system constituents. More recently, the time-resolved resonance Raman spectrum of a benzil anion radical has been successfully transformed into 2D Raman spectra. 76 This was accomplished by using the generalized 2D correlation formalism capable of analyzing spectral signals varying as a function of time in a nonsinusoidal manner. TM Likewise, time-dependent variations of IR spectra observed during a chemical reaction may be converted to a set of 2D correlation spectra. 77 Such 2D IR spectra should reveal detailed reaction steps of complex chemical reaction pro1322
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cesses. Similar work for 2D UV spectroscopy is underway.78 The use of the generalized 2D correlation forrealism should make it possible to apply this unique and versatile technique to various fields of spectroscopy. A very interesting possibility exists when intensity fluctuation signals originating from two different types of spectroscopy are analyzed simultaneously by the 2D correlation technique. As long as a common perturbation is used in both experiments, dynamic fluctuations of IR signals, for example, may be correlated with x-ray scattering intensities, generating 2D correlation spectra consisting of wavenumber and scattering axes. Such heterocorrelation analysis3,9may yield valuable information not readily obtainable by either technique alone. With the use of the integrated information at different spatial scales (ranging from submolecular, supermolecular, and macroscopic dimensions), this technique should provide useful insight into the complex dynamics of interacting systems. CONCLUSION 2D IR correlation spectroscopy has evolved considerably since it was introduced seven years ago. Many successful applications of this powerful and versatile technique have been reported. Important features of 2D IR spectra have been demonstrated. Numerous examples support the validity of the enhancement of spectral resolution observed in 2D IR spectra. Correlations among IR bands which belong to the same chemical group, or groups interacting strongly, have also been observed. Detailed spatial and temporal information provided by 2D IR spectra has led to new insights into complex molecular-scale mechanisms of dynamic systems. The introduction of a new correlation formalism, improvements in the instrumentation, and successful implementation of different perturbation methods should make the 2D correlation approach a universal spectroscopic tool generally applicable to a very wide range of applications. ACKNOWLEDGMENTS The authors wouldlike to thank R. A. Palmer, K. Masutani,and T. Nakano for providingvaluable reprints. 1. 2. 3. 4.
I. Noda, Bull. Am. Phys. Soc. 31, 520 (1986). I. Noda, J. Am. Chem. Soc. 111, 8116 (1989). I. Noda, Appl. Spectrosc. 44, 550 (1990). J. L. Koenig,Spectroscopy of Polymers (American Chemical Society, Washington,D.C., 1992), pp. 101-104. 5. N. Reynolds,Adv. Mater. 3, 614 (1991). 6. S. Stinson, Chem. Eng. News 68(1), 21 (1990). 7. N. Nemoto, Kobunshi [Highpolymers,Japan] 4, 540 {1991). 8. S. Ghosh, Current Sci. 59, 344 (1990). 9. I. Noda, Chemtracts-Macromol.Ed. l, 89 (1990). 10. I. Noda, A. E. Dowrey,and C. Marcott,J. Polym.Sci., Polym.Lett. Ed. 21, 99 (1983). 11. I. Noda, A. E. Dowrey, and C. Marcott, in Fourier Transform Infrared Characterization of Polymers, H. Ishida, Ed. (Plenum, New York, 1987), pp. 33-59. 12. I. Noda, A. E. Dowrey,and C. Marcott, Appl. Spectrosc. 42, 203 (1988). 13. I. Noda, A. E. Dowrey,and C. Marcott, Mikrochim. Acta [Wien] I, 101 (1988). 14. I. Noda, Kobunshi [Highpolymers,Japan] 39, 214 (1990). 15. I. Noda, A. E. Dowrey,and C. Marcott, Polym. Prepr. 33(1), 70 (1992).
16. N. B. Colthup, L. H. Daly, and S. E. Wilberley, Introduction to Infrared and Raman Spectroscopy (Academic Press, New York, 1975). 17. P. C. Painter, M. M. Coleman, and J. L. Koenig, The Theory of Vibrational Spectroscopy and Its Application to Polymeric Materials (Wiley, New York, 1982). 18. R. W. Snyder and P. C. Painter, Polymer 22, 1633 (1981). 19. I. Noda, Polym. Prepr. Japan, Engl. Ed. 39(2), 1620 (1990). 20. I. Noda, A. E. Dowrey, and C. Marcott, Polym. Prepr. 31(1), 576-7 (1990). 21. I. Noda, A. E. Dowrey, and C. Marcott, in Time-Resolved Vibrational Spectroscopy V (Springer-Verlag, 1992), pp. 331-334. 22. S. K. Dirlikov and J. L. Koenig, Appl. Spectrosc. 33, 555 (1979). 23. I. Noda, A. E. Dowrey, and C. Marcott, Oyo Buturi 60(10), 1039 (1991). 24. C. Marcott, I. Noda, and A. E. Dowrey, Anal. Chim. Acta 250, 131 (1991). 25. M. M. Satkowski, J. T. Grothaus, S. D. Smith, A. Ashraf, C. Marcott, A. E. Dowrey, and I. Noda, in Polymer Solutions, Blends, and Interfaces, I. Noda and D. N. Rubingh, Eds. (Elsevier, Amsterdam, 1992), pp. 89-108. 26. R.A. Palmer, V. G. Gregoriou, and J. L. Chao, Polym. Prepr. 33(1), 1222 (1992). 27. I. Noda, '92 Bio-Rad Seminar on 2D/Time-Resolved FT-IR (Nippon Bio-Rad Laboratories, Tokyo, 1992), pp. 53-73. 28. T. K. Kwei, T. Nishi, and R. G. Roberts, Macromolecules 7, 667 (1974). 29. T. Nishi, T. Wang, and T. K. Kwei, Macromolecules 8, 227 (1975). 30. P. Mirau, H. Tanaka, and F. Bovey, Macromolecules 21, 2929 (1988). 31. F. J. Lu, E. Benedetti, and S. L. Hsu, Macromolecules 16, 1525 (1983). 32. D. Garcia, J. Polym. Sci., Polym. Phys. Ed. 22, 107 (1984). 33. R. S. Stein, M. Satkowski, and I. Noda, in Polymer Blends, Solutions, and Interfaces, I. Noda and D. N. Rubingh, Eds. (Elsevier, New York, 1992), pp. 109-131. 34. V. G. Gregoriou, J. L. Chao, H. Toriumi, C. Marcott, I. Noda, and R. A. Palmer, SPIE 1575, 209 (1991). 35. R. A. Palmer, C. J. Manning, J. A. Rzepicla, J. M. Widder, P. J. Thomas, J. L. Chao, C. Marcott, and I. Noda, SPIE 1145, 277-279 (1989). 36. I. Noda, A. E. Dowrey, and C. Marcott, Polym. Prepr. 24(1), 122 (1983). 37. I. Noda, A. E. Dowrey, and C. Marcott, J. Molec. Struct. 224, 265 (1990). 38. S. Nomura, Sen-i to Kogyou 41,450 (1985). 39. A. E. Dowrey, G. G. Hillebrand, I. Noda, and C. Marcott, SPIE 1145, 156 (1989). 40. I. Noda, A. E. Dowrey, and C. Marcott, Polym. Prepr. 32(3), 671 (1991). 41. Y. Doi, Microbial Polyesters (VCH, New York, 1990). 42. I. Noda, Polym. Prepr. Japan 40(1), 34 (1991). 43. R. M. Dittmar, J. L. Chao, and A. Palmer, in Photoacoustic and Photothermal Phenomena III, 0. Bicanic, Ed. (Springer-Verlag, Berlin, 1992), pp. 492-496. 44. R. A. Palmer, R. M. Dittmar, V. G. Gregoriou, and J. L. Chao, Polym. Prepr., 32(3), 673 (1991). 45. R. E. Murphy, F. H. Cook, and H. Sakai, J. Opt. Soc. Am. 65, 600 (1975).
A. E. Mantz, Appl. Spectrosc. 30, 459 (1976). H. Sakai and R. E. Murphy, Appl. Opt. 17, 1342 (1978). A. E. Mantz. Appl. Opt. 17, 1347 (1978). W. G. Fateley and J. J. Koenig, J. Polym. Sci., Polym. Lett. Ed. 20, 445 (1982). 50. J. A. Graham, W. G. Gim, and W. G. Fateley, J. Molec. Struct. 113, 311 (1984). 51. D. J. Burchell, J. E. Lasch, E. Dobrovolny, N. Page, J. Domian, R. J. Farris, and S. L. Hsu, Appl. Spectrosc. 38, 343 (1984). 52. J. E. Lasch, D. J. Burchell, T. Masaoka, and S. L. Hsu, Appl. Spectrosc. 38, 351 (1984). 53. C. J. Manning, J. L. Chao, and R. A. Palmer, Rev. Sci. Instrum. 62, 1219 (1991). 54. R. A. Palmer, R. M. Dittmar, V. G. Gregoriou, and J. L. Chao, Polym. Prepr. 32(3), 673 (1991). 55. R. A. Palmer, Spectroscopy 8, 26 (1993). 56. R. A. Palmer, C. J. Manning, J. A. Rzepicla, J. M. Widder, P. J. Thomas, J. L. Chao, C. Marcott, and I. Noda, SPIE 1145, 277 (1989). 57. R. A. Palmer, C. J. Manning, J. L. Chao, I. Noda, A. E. Dowrey, and C. Marcott, Appl. Spectrosc. 45, 12 (1991). 58. V. G. Gregoriou, J. L. Chao, H. Toriumi, C. Marcott, I. Noda, and R. A. Palmer, SPIE 1575, 209 (1991). 59. R. A. Palmer, V. G. Gregoriou, and J. L. Chao, Polym. Prepr. 33(1), 1222 (1992). 60. K. Masutani, U.S. Patent 5,021,661 (1991). 61. K. Masutani, H. Sugisawa, A. Yokota, Y. Furukawa, and M. Tasumi, Appl. Spectrosc. 46, 560 (1992). 62. K. Masutani, A. Yokota, Y. Furukawa, and M. Tasumi, in TimeResolved Vibrational Spectroscopy V (Springer-Verlag, Berlin, 1992), pp. 335-336. 63. K. Masutani, Kogaku 21,386 (1992). 64. V. G. Gregoriou, J. L. Chao, H. Toriumi, and R. A. Palmer, Chem. Phys. Lett. 179, 491 (1991). 65. D. Naegele and D. Y. Yoon, Appl. Phys. Lett. 33, 132 (1978). 66. T. Takahashi, M. Date, and H. Fukuda, Appl. Phys. Lett. 37, 791 (1980). 67. F. J. Lu and S. L. Hsu, Polymer 25, 1247 (1984). 68. D. Porschke, Ann. Rev. Phys. Chem. 36, 159 (1985). 69. See other papers in this issue of Appl. Spectrosc. 70. I. Noda, Appl. Spectrosc. 47, 1329 (1993). 71. E. J. Hannan, Multiple Time Series (Wiley, New York, 1970). 72. D. R. Brillinger, Time Series Data Analysis and Theory (Holt, Rinehart and Winston, New York, 1975). 73. F. B. Barton II, D. S. Himmelsbach, J. H. Duckworth, and M. J. Smith, Appl. Spectrosc. 46, 420, (1992). 74. L. J. Frasinski, K. Codling, and P. A. Hatherly, Science 246, 1029 (1989). 75. R. Hanbury Brown, The Intensity Interferrometry (Taylor and Francis, London, 1974). 76. K. Ebihara, H. Takahashi, and I. Noda, Appl. Spectrosc. 47, 1343 (1993). 77. T. Nakano, S. Shimada, R. Saitoh, and I. Noda, Appl. Spectrosc. 47, 1337 (1993). 78. A. Shchegolikhin, private communication.
46. 47. 48. 49.
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