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Generalized Two-Dimensional Correlation Method Applicable to Infrared, Raman, and Other Types of Spectroscopy

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Abstract

A two-dimensional (2D) correlation method generally applicable to various types of spectroscopy, including IR and Raman spectroscopy, is introduced. In the proposed 2D correlation scheme, an external perturbation is applied to a system while being monitored by an electromagnetic probe. With the application of a correlation analysis to spectral intensity fluctuations induced by the perturbation, new types of spectra defined by two independent spectral variable axes are obtained. Such two-dimensional correlation spectra emphasize spectral features not readily observable in conventional one-dimensional spectra. While a similar 2D correlation formalism has already been developed in the past for analysis of simple sinusoidally varying IR signals, the newly proposed formalism is designed to handle signals fluctuating as an arbitrary function of time, or any other physical variable. This development makes the 2D correlation approach a universal spectroscopic tool, generally applicable to a very wide range of applications. The basic property of 2D correlation spectra obtained by the new method is described first, and several spectral data sets are analyzed by the proposed scheme to demonstrate the utility of generalized 2D correlation spectra. Potential applications of this 2D correlation approach are then explored.

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... Numerous methods can describe the structured variation of multiple components in convoluted spectral data sets [25,26]. Two complementary and widely used techniques are 2D correlation spectroscopy (2D-COS) and principal component analysis (PCA). ...
... 2D-COS is useful for the elucidation of convoluted peaks and for describing how peaks are related by interpreting characteristic patterns of correlation peaks in both the synchronous and asynchronous plots [26][27][28][29][30][31][32]. 2D-COS was applied to this system to identify convoluted peak positions. ...
... Cross peaks, located at off-diagonal positions, represent simultaneous changes of spectral intensities at two distinct spectral locations (i.e., peaks). Correlation squares joining pairs of cross peaks show coherent variation of spectral intensities at vertex locations [26]. The location of cross peaks, identified by the correlation squares, suggests that distinct peaks occur near 460, 477.5, 508, 513, 525, 543, 563, and 591.5 nm. ...
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... Spectroscopic data were analyzed by the generalized two-dimensional (2D) correlation method developed by Noda et al. [30,31]. A program used to perform the analysis was written by Szabó et al. [32] in the internal program language of GRAMS/AI (Array Basic). ...
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... The 2D-COS explores the very subtle spectral changes that are hardly detected by conventional 1D spectral analysis. In generalized 2D-COS, the perturbation can be concentration, pressure, temperature, etc. [36]. After that, the dynamic original data will be recast into two orthogonal representations in the 2D-COS analysis, i.e., the synchronous and asynchronous corrections. ...
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... The two-dimensional correlation spectroscopy improves the spectral resolution by increasing the dimensionality, and it can effectively extract the characteristic information of weak peaks, migrated peaks, and overlapping peaks [31]. The generalised two-dimensional correlation spectra are calculated using the discrete generalised 2DCOS algorithm. ...
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... However, signal peaks of the one-dimensional (1D) FT-NIR spectroscopy overlap seriously, making it difficult to extract feature information (Dong et al., 2021a). In 1993, Noda proposed Generalized two-dimensional correlation spectroscopy (2DCOS), which helps to highlight spectral features that are difficult to observe in 1D FT-NIR spectroscopy and enriches functional group information (Noda, 1993). 2DCOS can significantly improve the spectral resolution and reveal the correlation between frequencies, which is favorable to remedy the defects of conventional spectra (Karthikeyan et al., 2022). ...
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... Generalized 2DCOS is an effective method to improve the spectral resolution and solve spectral overlap problem by designing interference variables, which is obtained by discrete generalized two-dimensional correlation spectral algorithm. Its dynamic spectra are expressed as S, and the expression is provided in Equation (1), where v is the variable and t is the external disturbance (Noda, 1993). ...
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... Numerous studies have confirmed that infrared spectroscopy techniques like Mid-Infrared (MIR) and NIR combined with chemometrics were useful methods for adulteration detection [5][6][7]. Meanwhile, to meet the demand of extracting weak and overlapping spectral information, a method so-called two-dimensional correlation spectroscopy (2D-COS) was presented by Noda as an alternative approach to the traditional 1D spectroscopy method [8][9]. And 2T2D correlation spectroscopy using just two spectra rather than a series of spectra was recently reported as a simple method to 2D-COS [10]. ...
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BiFeO3 is one of the most attracting materials because it is the only known room-temperature multiferroic material. It has been studied by Raman spectroscopy extensively. We perform two-dimensional correlation spectroscopy (2D COS) and perturbation-correlation moving window two-dimensional correlation spectroscopy (PCMW2D) analysis on the temperature-dependent Raman spectra of a BiFeO3 single crystal. The two low temperature spin reorientation transitions around 135 K and 190 K are confirmed through the significant change in phonon peaks from PCMW2D correlation spectra. We also identify the origin of the mode at ~ 1255 cm⁻¹, which has been controversial until now. In our 2D COS analysis, the intensity of this mode has a strong correlation with the intensity of 145 and 176 cm⁻¹ phonons which correspond to the vibration modes of the Bi-O and Fe-O chemical bonds. We propose that the mode at ~ 1255 cm⁻¹ is the two-phonon scattering of the 551 cm⁻¹ mode assisted by the 145 –176 cm⁻¹ phonons.
Article
Introduction: Wolfiporia cocos, as a kind of medicine food homologous fungus, is well-known and widely used in the world. Therefore, quality and safety have received worldwide attention, and there is a trend to identify the geographic origin of herbs with artificial intelligence technology. Objective: This research aimed to identify the geographical traceability for different parts of W. cocos. Methods: The exploratory analysis is executed by two multivariate statistical analysis methods. The two-dimensional correlation spectroscopy (2DCOS) images combined with residual convolutional neural network (ResNet) and partial least square discriminant analysis (PLS-DA) models were established to identify the different parts and regions of W. cocos. We compared and analysed 2DCOS images with different fingerprint bands including full band, 8900-6850 cm-1 , 6300-5150 cm-1 and 4450-4050 cm-1 of original spectra and the second-order derivative (SD) spectra preprocessed. Results: From all results: the exploratory analysis results showed that t-distributed stochastic neighbour embedding was better than principal component analysis. The synchronous SD 2DCOS is more suitable for the identification and analysis of complex mixed systems for the small-band for Poria and Poriae cutis. Both models of PLS-DA and ResNet could successfully identify the geographical traceability of different parts based on different bands. The 10% external verification set of the ResNet model based on synchronous 2DCOS can be accurately identified. Conclusion: Therefore, the methods could be applied for the identification of geographical origins of this fungus, which may provide technical support for quality evaluation.
Article
Traditional spectral analysis is prone to integration and signals overlap. It makes the extracted information unavailable or inaccurate, limiting its application in the detection of complex components. Therefore, two-dimensional correlation spectroscopy (2D-COS) that was superior to traditional spectral analysis has been established, by extracting useful information under certain chemical or physical stimulus from a series of spectra to improve the spectral resolution. In this study, with the identification of the different origins and parts of Panax notoginseng as an example. First, as a comparison, the attenuated total reflection infrared spectroscopy (ATR-FTIR) of P. notoginseng samples combined with chemometric methods was applied to identify it. Then, we generated synchronous and asynchronous 2D-COS spectral images from the fingerprint regions in the spectrum, and established a Residual convolutional neural network (ResNet) to identify the different origins and parts. Finally, the externally verified was applied to evaluate the accuracy of the model. By comparison, the 2D-COS was more suitable for the identification of the origins and parts of P. notoginseng than traditional spectroscopy. The identification accuracy of these samples of synchronous 2D-COS spectral images in the training set and test set were both greater than 99%. And the results of the externally verified indicated that synchronous 2D-COS spectral images were significantly outperforming asynchronous 2D-COS spectral images, and the sensitivity, specificity, and accuracy of the samples are both better than 0.99. Furthermore, when the sample number was relatively small or large differences in sample number were large, the synchronous 2D-COS spectral images could also successfully distinguish the different origins and parts well of P. notoginseng. In general, the ResNet model could provide a better discriminant model, and perform high-resolution processing.
Article
Co-crystallization of different monomeric units fundamentally contributes to the versatile and tunable performance of random copolymers. At present, the crystallization manners of random binary copolymers have been divided into three categories: isomorphism, isodimorphism and comonomer exclusion. Each category, however, has its own advantages and disadvantages. Therefore, it is challenging to design and prepare random copolymer sharing the advantages of isomorphism and isodimorphism through a new co-crystallization manner beyond the ones already exist. On the basis of previous study on poly(alkylene succinate-ran-alkylene fumarate) whose co-crystallization can be extensively and finely regulated by simply varying the chemical structure of alkylene, random copolymers of poly(propylene succinate-ran-propylene fumarate) (PPSF) are synthesized using 1,3-propanediol as the diol source. The thermal properties and crystal structure of PPSF are investigated, and, intriguingly, it is proved that PPSF is an isodimorphism system while displays similar composition-dependent thermal properties and crystallinity as isomorphism. That is, PPSF exhibits a novel co-crystallization behavior that has rarely been discovered, which would combine the advantages of both isomorphism and isodimorphism. Consequently, PPSF could be termed as a new-type, special composition-dependent polymorphism. Besides, the altering of PPS-like to PPF-like crystal structure of PPSF when changing chain composition has been proved to originate from the shift of dominant inter-segment interaction from van der Waals forces to strong hydrogen-bonding interaction. This work enriches the co-crystallization manner of random copolymers, leading to more diverse performance design of polymer materials.
Article
Raman spectroscopy provides an extremely high chemical selectivity. Raman difference spectroscopy is a technique to reveal even the smallest differences that occur due to weak interactions between substances and changes in the molecular structure. To enable parallelized and highly sensitive Raman difference spectroscopy in a microtiter-array, a diffractive optical element, a lens array, and a fiber bundle were integrated into a Raman spectroscopy setup in a unique fashion. The setup was evaluated with a microtiter-array containing pyridine-water complexes, and subwavenumber changes below the spectrometer's resolution could be resolved. The spectral changes were emphasized with two-dimensional correlation analysis. Density functional theory calculation and "atoms in molecule" analysis were performed to simulate the intermolecular long-range interactions between water and pyridine molecules and to get insight into the involved noncovalent interactions, respectively. It was found that by the addition of pyridine, the energy portion of hydrogen bonds to the total complexation energy between pyridine and water reduces. These results demonstrate the unique abilities of the new setup to investigate subtle changes due to biochemically important molecular interactions and opens new avenues to perform drug binding assays and to monitor highly parallelized chemical reactions.
Article
In the growth of hydrogenated amorphous carbon (a-C:H) films by plasma enhanced chemical vapor deposition (PECVD) with H2, CH4 and C3H6 plasma, the gas phase reaction of active species and their contribution to properties of deposited a-C:H film were quantitatively investigated using appearance quadrupole mass spectrometry (QMS) and machine learning. The QMS measurement indicated that two-types of neutral radicals were generated by the dissociation and polymerization of the raw material gasses. A random forest regression model was employed as a prediction model to analyze the correlation between the neutral species and etching rates by molecular oxygen (O2) plasma without any stage bias, which were measured by in-situ ellipsometry. The coefficient of determination (R²), an indicator of the degree of prediction accuracy, was 0.906 and 0.584 for the training and test data, respectively. SHapley Additive exPlanations (SHAP), interpreting the random forest model, were used to quantitatively indicate the contribution of radicals to the etching rate, including their synergistic and secondary effects. They indicated that carbon-rich radicals, such as C3H3 and C5H5, contributed to a decrease in the etching rate, whereas hydrogen-rich radicals, such as CHx (x=1,2,3,4), C2H5, C4H9, and C5H9,11 induced an increase in the etching rate by the O2 plasma. (200 words)
Article
This comprehensive survey review, as the first of three parts, compiles past developments and early concepts of two-dimensional correlation spectroscopy (2D-COS) and subsequent evolution, as well as its early applications in various fields for the last 35 years. It covers past review articles, books, proceedings, and numerous research papers published on 2D-COS. 2D-COS continues to evolve and grow with new significant developments and versatile applications in diverse scientific fields. The healthy, vigorous, and diverse progress of 2D-COS studies in many fields confirms that it is well accepted as a powerful analytical technique to provide the in-depth understanding of systems of interest.
Article
Yunnan is known for its rich biodiversity and is known as the Wild Mushroom Kingdom. Boletes are a world‐renowned wild edible mushroom, with unique sensory characteristics, nutritional value and medicinal value extraordinary. However, the species and geographical origin of boletes influence their price and quality. In this study, a method was developed to identify species and geographical origin simultaneously. Therefore, Fourier transform near‐infrared (FT‐NIR) data sets of boletes were collected and converted to two‐dimensional correlation spectroscopy (2D‐COS). On this basis, the species and geographic origins of boletes were identified using Residual neural network (ResNet) image analysis model. The results showed that FT‐NIR could identify boletes species and geographical origins, 7000‐4000 cm‐1 band was more suitable for species identification, 7000‐5300 cm‐1 band was more suitable for geographical origins identification. In addition, the environmental factors with high contribution to the distribution of boletes were screened based on the maximum entropy (MaxEnt) model. To characterize the potential geographic distribution of boletes. The results showed that precipitation factors played a vital role in its distribution, and might even be responsible for the difference in chemical composition.
Article
Two novel vanadoborates were synthesized under hydrothermal conditions with different conformations (eclipsed and staggered) Li5[V6B20O39(OH)11]·8H2O 1 and (enH)2(enH2)2Cs2[V6B20O42(OH)8(H2O)0.5]·3H2O 2 (en = ethylenediamine) and analyzed by single crystal X-ray diffraction, powder X-ray diffraction (PXRD) analysis, two-dimensional infrared correlation spectroscopy (2D-IR COS) Characterization and density functional theory calculations. The cluster anion of both compounds is [V6B20O50]¹⁶⁻, which is a sandwich structure composed of a V6 ring and two [B10O16] triangles. In compound 2, the two [B10O16] triangles of the [V6B20O50] ¹⁶⁻cluster anion are staggered by 60 degrees, forming an isomer configurationally different from compound 1. The similarities and differences between the 2D-IR COS spectra of the two compounds are explained from the structural point of view. Theoretical calculation shows that two staggered cluster anions have similar in energies and thus should be able to coexist. This study not only fills the gap in the study of the isomer of vanadoborates, but also makes an outstanding contribution to the study of the self-assembly mechanism of polyoxometalates.
Article
We proposed a modified and improved approach to removing the interference of moisture from an IR spectrum and the corresponding second derivative spectrum. The temperature fluctuation in the air of the optical path and baseline-drift lead to the small but persistent presence of the interference of moisture. The problem has been successfully addressed by adopting a double-matching strategy. Additionally, two-dimensional correlationspectra (2D-COS) are generated using the second derivative or third derivative spectrum of the negative base 10 logarithms of the single-beam spectra, thereby removing the linear slope or quadratic portion of baseline-drift. Using the newly adopted approach, the residual interferences of moisture are attenuated. We applied the new approach to the IR spectra and the second derivative spectra of neat hexadecanol and biaxially oriented polypropylene (BOPP) film, and some promising preliminary results are obtained. In hexadecanol, two highly overlapping peaks at 1464 and 1463 cm⁻¹ are revealed. In BOPP, the envelope at 1458 cm⁻¹ is found to be composed of a number of sub-peaks.
Article
To accurately analyze strongly interfering species in a system, current analytical methodologies separate and purify each chemical species before individual characterization. Herein, we introduce a new concept to analyze individual molecules in interfering systems, provided the target molecules offer orthogonal modulation by external stimuli. Using optical and thermal modulation simultaneously, we demonstrated that two interfering molecules, one photoswitching while the other thermal switching, could be accurately identified in a mixture because they underwent orthogonal chemical reactions when stimulated by both light and heat. The broad impact of the newly developed molecular modulation spectroscopy (MMS) is significant because molecular species in interfering systems can be analyzed directly in situ and in detail without time-consuming chemical separation and purification. Conversely, such stimuli-induced switching molecules can function as molecular sensors, gauging the presence and magnitude of that specific external stimulus.
Article
The undeclared addition of soybean proteins in meats is a serious problem due to health and economic reasons. This paper proposes a methodology for quantitative determination and rapid visualization of soybean protein powder (SPP) addition in ground beef using hyperspectral imaging (HSI). Hyperspectral images of a total of 256 samples with different SPP contents were acquired by HSI system in spectral range of 400–1000 nm. Regions of interest (ROIs) were identified to withstand interference of background and containers to extract spectra. Principal component analysis (PCA) of extracted spectra found that PC1 and PC2 were effective for grouping samples into different levels. Gray level co-occurrence matrix (GLCM) algorithm was thus applied on the corresponding first two PC score images to extract eight texture features. Partial least squares regression (PLSR) was used to establish quantitative models, yielding the optimal correlation coefficient in prediction (Rp) of 0.9979 and residual predictive deviation (RPD) of 14.48 using standard normal variate (SNV) followed by detrending preprocessed spectra. Deming and Passing-Bablok regression were also conducted, and HSI results revealed high model performance which can be interchanged with laboratory standard. Key wavelengths were selected using PC loadings, two-dimensional correlation spectroscopy (2D-COS) and regression coefficients (RC), respectively. After that, PLSR models were evaluated with various inputs, and results showed spectra played predominate role rather than texture. Consequently, simplified PLSR model based on six selected wavelengths from PC loadings was retained with Rp = 0.9933, RPD = 8.45 and limit of detection (LOD) of 0.74%. Colorful spatial distribution maps were successfully created to clearly observe SPP adulteration levels. Current study indicates that HSI has high potential for determining and visualizing SPP adulteration in ground beef.
Chapter
The diverse area of pigments and dyes and their degradation products is considered here commencing with the detailed historical chronology of Raman spectral studies and a comprehensive survey of the pigments and organic dyes used over many centuries. Advantages and drawbacks of Raman spectral studies. Comparison with elemental data obtained from SEM/EDAXS and Electron microprobe studies. Includes several case studies to illustrate the information obtained from Raman spectral studies and databases. Role of nondestructive and noninvasive Raman spectroscopic techniques.KeywordsRaman spectroscopyColoured pigments and dyesSERSDegradationNondestructive procedures
Article
Ionic liquids (ILs) have unique physicochemical features, such as insignificant vapour pressure, which make ILs excellent entrainers in extractive distillation to separate the azeotrope. For better utilization of the IL entrainer in extractive distillation, the microstructure properties of dimethyl carbonate (DMC)–ethanol azeotrope mixtures, before and after the separation breaking of the azeotrope by IL, were studied by Fourier transform infrared spectroscopy (FTIR) and density functional theory (DFT) calculations with focus on the vibrational region of the ethanol hydroxyl group. Excess spectroscopy followed by two-dimensional correlation spectroscopy (2D-COS) was performed on the original IR spectra to extract the microstructural features of different mixtures step by step. Different sizes of ethanol self-aggregations, DMC–ethanol interaction complex and different IL–ethanol interaction complexes were identified in different mixtures. Specifically, the DMC–ethanol interaction complex existed in both the DMC–ethanol and IL–DMC–ethanol systems at lower IL concentrations (x(IL) < 0.125) while broken out by IL at higher IL concentrations (x(IL) >0.125). The intrinsic cause of the azeotrope breaking by the 1-hexyl-3-methylimidazolium bis(trifluoromethyl)sulfonyl imide ([HMIM][Tf2N]) entrainer was revealed to be the disappearance of the DMC–ethanol interaction complex by the IL at higher IL concentrations. The hydrogen-bonds between DMC/IL and ethanol were also identified and confirmed in the DMC–ethanol and different IL–ethanol interaction complexes. Both the oxygen atom and the hydrogen atom in the hydroxyl group of ethanol participated in the hydrogen-bond, which confirmed the sensitivity of the hydroxyl group vibrational region. The hydrogen-bonds are weak strength, closed shells and electrostatic dominant interactions.
Article
Two-dimensional correlation spectroscopy (2D-COS) is a technique that permits the examination of synchronous and asynchronous changes present in hyperspectral data. It produces two-dimensional correlation coefficient maps that represent the mutually correlated changes occurring at all Raman wavenumbers during an implemented perturbation. To focus our analysis on clusters of wavenumbers that tend to change together, we apply a k-means clustering to the wavenumber profiles in the perturbation domain decomposition of the two-dimensional correlation coefficient map. These profiles (or trends) reflect peak intensity changes as a function of the perturbation. We then plot the co-occurrences of cluster members two-dimensionally in a manner analogous to a two-dimensional correlation coefficient map. Because wavenumber profiles are clustered based on their similarity, two-dimensional cluster member spectra reveal which Raman peaks change in a similar manner, rather than how much they are correlated. Furthermore, clustering produces a discrete partitioning of the wavenumbers, thus a two-dimensional cluster member spectrum exhibits a discrete presentation of related Raman peaks as opposed to the more continuous representations in a two-dimensional correlation coefficient map. We demonstrate first the basic principles of the technique with the aid of synthetic data. We then apply it to Raman spectra obtained from a polystyrene perchlorate model system followed by Raman spectra from mammalian cells fixed with different percentages of methanol. Both data sets were designed to produce differential changes in sample components. In both cases, all the peaks pertaining to a given component should then change in a similar manner. We observed that component-based profile clustering did occur for polystyrene and perchlorate in the model system and lipids, nucleic acids, and proteins in the mammalian cell example. This confirmed that the method can translate to "real world" samples. We contrast these results with two-dimensional correlation spectroscopy results. To supplement interpretation, we present the cluster-segmented mean spectrum of the hyperspectral data. Overall, this technique is expected to be a valuable adjunct to two-dimensional correlation spectroscopy to further facilitate hyperspectral data interpretation and analysis.
Article
Near infrared (NIR) spectroscopy has the characteristics of rapid processing, nondestructive analysis and on-line detection. This technique has been widely used in the fields of quantitative determination and substance content analysis. However, for complex NIR spectral data, most traditional machine learning models cannot carry out effective quantitative analyses (manifested as underfitting; that is, the training effect of the model is not good). Small amounts of available data limit the performance of deep learning-based infrared spectroscopy methods, while the traditional threshold-based feature selection methods require more prior knowledge. To address the above problems, this paper proposes a competitive adaptive reweighted sampling method based on dual band transformation (DWT-CARS). DWT-CARS includes four types in total: CARS based on integrated two-dimensional correlation spectrum (i2DCOS-CARS), CARS based on difference coefficient (DI-CARS), CARS based on ratio coefficient (RI-CARS) and CARS based on normalized difference coefficient (NDI-CARS). We conducted comparative experiments on three datasets; compared to traditional machine learning methods, our method achieved good results, demonstrating that this method has considerable prospects for the quantitative analysis of near-infrared spectroscopic data. To further improve the performance and stability of this method, we combined the idea of integrated modeling and constructed a partial least squares model based on Monte Carlo sampling for the samples obtained by CARS (DWT-CARS-MC-PLS). Through comparative experiments, we verified that the integrated model could further enhance the accuracy and stability of the results.
Article
Raman spectra of bioplastic poly(3-hydroxybutyrate-co-3-hydroxyhexanoate) (PHBHx at 13.8% Hx) were recorded between -250 cm⁻¹ and 3200 cm⁻¹ during isothermal crystallization at 25⁰C after quenching from the melt in liquid nitrogen. At room temperature the crystallization proceeds slowly, so spectra were recorded over a 14-hour period. While there are spectral changes throughout the spectrum, the focus was on interpretable bands known to be sensitive to crystalline form. These bands included the carbonyl band that sharpens and shifts, a pair of bands on the high energy side of the carbon-hydrogen stretch, and a low frequency band that we assign to the molecular phonon in the crystal unit cell. After appropriate pre-processing of the spectra, they were further analyzed by 2D-COS (two-dimensional correlation spectroscopy) that provides determination of the order in which the polymer functional regions assemble into the crystalline state. According to this analysis one of the methyl CH’s interacts with the carbonyl bond to produce a line at 3000 cm⁻¹. Following that, multiple changes appear in the carbonyl region, the strong CH band at 2930 cm⁻¹ of the crystalline phase grows, then the 80 cm⁻¹ phonon band, and the splitting of the methyl CH only appears after the phonon. From this sequence one can derive a picture of how the polymer unit locks into the crystal form. This can be of interest to commercialization of the materials because mechanical properties are intimately controlled by the crystallinity of the material. By understanding how the crystallization process proceeds, it can be engineered to be “fit for purpose” for a polymer targeted for a specific use.
Article
As an important resource in many prescriptions, the geographical origins of Gentiana rigescens Franch. influences its chemical characteristics, quality and price greatly. Hence, a simple and rapid method for the correct classification and identification of the geographical origins of G. rigescens is of significance. In this work, marker components of iridoids were measured by high performance liquid chromatography (HPLC) and were applied as a reference to characterize chemical profiles of samples from different geographical origins. The effects of climate factors on the content differences of G. rigescens were examined by correlation analysis. Afterward, a novel two-dimensional correlation spectroscopy (2DCOS) images acquired based on Fourier transform infrared (FT-IR) spectroscopy was proposed combined to deep learning to identify geographical origins of G. rigescens. Through analyzing the iridoid components of G. rigescens, which discovered that there were significant differences in its five marker components. In addition, the marker components of gentiopicroside based on Northwestern Yunnan (DXB) were higher, and the climate environment of low temperature, temperate, and high precipitation was more suitable for the cultivation and growth of G. rigescens. In the residual convolutional neural network (ResNet), the train set and test set accuracy of synchronous 2DCOS images for the feature bands (1800–400 cm-1) was 100%, and the external validation set of all samples was correctly identified. The results indicated the synchronous 2DCOS images of feature bands were suitable for the correct identification of the geographic origin of G. rigescens, and it reduced the amount of computation and time, and saved computing resources. This study provided a powerful and useful tool for the cultivation and geographical origins identification of G. rigescens.
Article
The solvent of the oral liquid formulations of traditional Chinese medicine is mainly water, but the variation of the absorption band of water in the infrared (IR) spectrum was often...
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To address the challenge of realizing multifunctional polymers simultaneously exhibiting high strength and high toughness through molecular engineering, we fabricated ultra‐strong and super‐tough shape memory poly(urea‐urethane)s by regulating (i) the reversible cross‐links composed of rigid units and multiple hydrogen bonds and (ii) the molecular weight of soft segments. The optimal material exhibited an unparalleled strength of 84.2 MPa at a large elongation at break of 925.6%, a superior toughness of 322.8 MJ m−3, and remarkable fatigue resistance without fracture. The repeated stretching of this material induced an irreversible deformation, which, however, could be rapidly recovered by heating. Moreover, all samples were capable of temporary shape fixation at −40°C (recovering the original shape at 30°C) and exhibited blue fluorescence when excited at the optimum wavelength, which was ascribed to clusterization‐triggered emission due to the formation of microphase separation structures. Thus, the adopted approach provides a solution to a long‐standing problem and paves the way to the realization of intrinsically luminescent shape memory materials exhibiting both ultrahigh strength and ultrahigh toughness. This article is protected by copyright. All rights reserved
Article
In response to the growing need for development of modern biomaterials for applications in regenerative medicine strategies, the research presented here investigated the biological potential of two types of polymer nanocomposites. Graphene oxide (GO) and partially reduced graphene oxide (rGO) were incorporated into a poly(ε-caprolactone) (PCL) matrix, creating PCL/GO and PCL/rGO nanocomposites in the form of membranes. Proliferation of osteoblast-like cells (human U-2 OS cell line) on the surface of the studied materials confirmed their biological activity. Fluorescence microscopy was able to distinguish the different patterns of interaction between cells (depending on the type of material) after 15 days of the test run. Raman micro-spectroscopy and two-dimensional correlation spectroscopy (2D-COS) applied to Raman spectra distinguished the nature of cell-material interactions after only 8 days. Combination of these two techniques (Raman micro-spectroscopy and 2D-COS analysis) facilitated identification of a much more complex cellular response (especially from proteins) on the surface of PCL/GO. The presented approach can be regarded as a method for early study of the bioactivity of membrane materials.
Article
A simple and effective method based on in situ infrared spectroscopy and two-dimensional (2D) correlation analysis was applied to research the chemical changes and curing reaction mechanism of epoxy resin and amine curing agents. It is generally agreed that the epoxy groups in epoxy resin react with amino groups to form new C–N and hydroxyl groups during the curing reaction process. However, detailed information about the curing reaction mechanism of epoxy resin and amine curing agents has rarely been reported. In this work, the curing reaction mechanism can be deeply understood from the results of 2D correlation analysis. Due to the nucleophilic addition reaction of amino and epoxy groups, the nitrogen atoms of primary amines easily combine with the carbon atoms in epoxy groups, which forms new C–N groups. Then, the C–O bonds in epoxy groups break; finally, as the N–H bonds in primary amines break, the hydrogen atoms combine with the oxygen atoms to form new hydroxyl groups. In situ infrared spectroscopy and two-dimensional (2D) correlation analysis was applied to research the chemical changes and curing reaction mechanism of epoxy resin and amine curing agents. The curing reaction mechanism can be deeply understood from the results. Due to the nucleophilic addition reaction of amino and epoxy groups, the nitrogen atoms easily combine with the carbon atoms, which forms new C-N groups. Then, the C-O bonds break; finally, as the N-H bonds in primary amines break, the hydrogen atoms combine with the oxygen atoms to form new hydroxyl groups.
Article
Raman spectra of water and supercooled water were measured in the temperature range of ‐6 to 18°C with every 2°C step. The obtained spectra were analyzed for the 3750‐2850 cm‐1 and 400‐100 cm‐1 regions by two‐dimensional correlation (2D‐COS) Raman spectroscopy. As previously reported, there are three bands at around 3620, 3420, and 3200 cm‐1 in the OH stretching region. These bands were assigned to the OH‐stretching modes of dangling (Dang) bonds of water, destructured, and structured water species, respectively. A pair of clear peaks appear in asynchronous 2D‐COS maps in the 3750‐2850 cm‐1 region of Raman spectra of water developed using the spectra measured in the temperature‐ranges of ‐6 to 0°C, 0 to 8°C, and 8 to 18°C, and they are similar to each other, suggesting non‐linear (covex) temperature‐dependent increase and decrease of the two kinds of water species. A power spectrum calculated along the diagonal line in the synchronous spectrum in the ‐6 to 18°C range has a peak at 3171 cm‐1 with a broad shoulder at around 3400 cm‐1. These peaks at 3171 and 3400 cm‐1 may be assigned to the collective mode and its local mode of structured water, respectively. In the 400‐100 cm‐1 region there is a broad feature centered at 185 cm‐1 assigned to the intermolecular stretching mode of water molecule. Close inspection of the low‐frequency region by the baseline corrected spectra and the second derivative spectra shows that the broad feature consists of a major band at around 185 cm‐1 and a weak shoulder at around 150 cm‐1. We have assigned these two peaks at 185 and 150 cm‐1 to the structured and destructured water, respectively, based on the results of 2D‐COS and the comparison with the results of multivariate curve resolution‐alternative least square (MCR‐ALS) reported by Hamaguchi et al. A hetero 2D correlation synchronous map between the 3750‐3000 and 400‐100 cm‐1 regions reveals that there is a cross peak between the structured water band at around 3200 cm‐1 and the 185 cm‐1 band, confirming that the 185 cm‐1 band comes from the structured water.
Article
To master the fundamental knowledge of the tobacco thermal degradation process is of great significance for the utilization of tobacco waste. Thermogravimetric analysis coupled with Fourier transform infrared spectrometer was used to analyze the thermal degradation of tobacco lamina and the release behavior of small molecular gas products. Based on the composition and component characteristics of tobacco lamina, the process was divided into four stages to elucidate its thermal degradation mechanism. Tobacco lamina pyrolysis at 200–800 °C was carried out on a microreactor with the products analyzed by gas chromatography-mass spectrometry. On the basis of obtaining variation rule of products belonging to different families of organic compounds with temperature, the evolution properties of products within the same family were summarized. Thereinto, the compositions of nitrogen-containing heterocyclic compounds and hydrocarbons were most affected by temperature. The in-situ infrared of the solid residue during tobacco lamina pyrolysis and the corresponding two-dimensional perturbation correlation infrared spectroscopy were performed to reveal the evolution of functional groups on the surface of the pyrolytic char. The results showed that the dehydration and ring-opening reaction of polysaccharides were earlier than the decomposition of carbonyl containing compounds.
Article
This comprehensive survey review compiles noteworthy developments and new concepts of two-dimensional correlation spectroscopy (2D-COS) for the last two years. It covers review articles, books, proceedings, and numerous research papers published on 2D-COS, as well as patent and publication trends. 2D-COS continues to evolve and grow with new significant developments and versatile applications in diverse scientific fields. The healthy, vigorous, and diverse progress of 2D-COS studies in many fields strongly confirms that it is well accepted as a powerful analytical technique to provide an in-depth understanding of systems of interest.
Chapter
To effectively classify imported frozen fish, we propose a characteristic wavelength selection method based on two-dimensional correlation spectroscopy (2DCOS), which reduces spectral variables required for analysis and improves the accuracy and efficiency of classification, among the data obtained by near-infrared spectroscopy (NIRS). In the experiments, near-infrared spectral were collected from Pollachius, Theragra chalcogramma, Gadous macrocephaius, and Melanogrammus aeglefinus of the family Gadidae, comparing different preprocessing algorithms and selecting multiple scattering corrections. The 2DCOS between the four Cod samples were then constructed. Based on the autocorrelation spectrum of the synchronous 2DCOS, the relative intensities at wavelengths 1580 nm, 1744 nm, and 1900 nm were obtained to be almost zero, and the two highest peaks in the autocorrelation spectrum were at 1550–1580 nm and 1744–1900 nm, as well as the spectra in these two bands, were highly correlated, so the two bands 1550–1580 nm and 1744–1900 nm were filtered out from the complete spectrum. The results are the accuracy of the training set of the waveband SVM filtered based on the 2DCOS is 94.58%, and the accuracy of the validation set can reach up to 97.30%. The study shows that the proposed spectral data compression method based on the 2DCOS technique has a high compression rate and high classification accuracy.
Article
Herbal medicines (HMs) have been utilized to prevent and treat human ailments for thousands of years. Especially, HMs have recently played a crucial role in the treatment of COVID-19 in China. However, HMs are susceptible to various factors during harvesting, processing, and marketing, affecting their clinical efficacy. Therefore, it is necessary to conclude a rapid and effective method to study HMs so that they can be used in the clinical setting with maximum medicinal value. Non-targeted analytical technology is a reliable analytical method for studying HMs because of its unique advantages in analyzing unknown components. Based on the extensive literature, the paper summarizes the benefits, limitations, and applicability of non-targeted analytical technology. Moreover, the article describes the application of non-targeted analytical technology in HMs from four aspects: structure analysis, authentication, real-time monitoring, and quality assessment. Finally, the review has prospected the development trend and challenges of non-targeted analytical technology. It can assist HMs industry researchers and engineers select non-targeted analytical technology to analyze HMs’ quality and authenticity.
Article
The application of two-trace two-dimensional (2T2D) correlation analysis to a number of spectra consisting of more than a simple pair is explored, especially when such spectra are randomly collected without knowing the sampling order. Calculation and interpretation of 2T2D correlation spectra are briefly reviewed, and a systematic procedure to identify the set of characteristic bands, which are mutually asynchronous and least overlapped with each other, is described. 2T2D correlation is applied to individual spectra by selecting a representative reference spectrum, such as the average of the whole dataset. A slice of an asynchronous 2T2D spectrum at a characteristic band is devoid of the spectral contribution from the species represented by the band. Since 2T2D analysis may be applied to the whole set of spectra, and each 2T2D asynchronous spectrum yields a set of slices for different characteristic bands, it is possible to generate a series of 2T2D slices obtained at a given characteristic band. By applying the generalized 2D correlation or a successive 2T2D analysis to such slices, one can obtain excellent estimates of the pure component spectra of the mixture, which are comparable to the results from other curve resolution techniques.
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Proefschrift Delft. Met lit. opg. - Met samenvatting in het Nederlands. Auteursnaam op omslag: Ad Bax.
Chapter
Two-dimensional infrared (2D IR) spectroscopy [1–5] is a novel analytical technique based on a time-resolved IR measurement. The basic concept of 2D IR is somewhat analogous to the 2D correlation technique used extensively in NMR [6]; however, the experimental approach used in 2D IR is quite different. In 2D IR, a spectrum defined by two independent wavenumbers is generated by applying a correlation analysis to the dynamic fluctuation of infrared signals induced by an external macroscopic perturbation. A perturbation, such as small-amplitude oscillatory strain with an acoustic-range frequency, creates time-dependent reorientation of molecular constituents which can be monitored with a polarization-modulated IR probe produced by a photoelastic modulator [7]. Because of the specificity of absorption to individual chemical groups, fluctuations of IR signals contain detailed information about highly localized submolecular-level reorientation and relaxation processes.
Article
The crystalline/amorphous interface is a region where there is a transition from the ordered to disordered state. It must accommodate chain folds and defects which cannot lie within the crystal. This transition must occur over a finite distance, estimated to be of the order of 20A and represents a zone of intermediate mobility and order. Consequences are (1) an intermediate Tg, (2) loss peaks associated with limited mobility, (3) lower miscibility in this region arising from the lower entropy of mixing, and (4) concentration of excluded species in this region. Evidence for this comes from (1) Kratky analysis of small-angle x-ray scattering data, (2) observation of an enhanced concentration of excluded species by small-angle neutron scattering, and (3) rheo-optical studies of mobility. Previous NMR studies can also be interpreted in terms of this model. The model suggests how this “interphase” may be controlled via the nature and amount of the excluded species.
Chapter
Polyvinyl methyl ether) PVME with polydispersity of less than 1.1 has been synthesized. This material has been used to study the effects of molecular weight on the phase diagram of blends of PVME with polystyrene (PS). The role of specific interactions in the phase behavior of the PS/PVME system also was studied using specifically deuterated PVME. Dynamic infrared linear dichroism (DIRLD), has indicated that two different chemical environments for the methoxyl groups of PVME may exist. One type of methoxyl interacts with the PS phenyl group such that their reorientational motions under oscillatory strain are synchronized, while another substantial population of methoxyl groups shows no such synchronization.
Article
Two-dimensional (2D) homonuclear correlated spectra manifest connectivities between spin-coupled nuclei and can thus provide assignments of individual spin systems in complex 1H NMR spectra. Two experimental techniques discussed in this paper, spin-echo correlated spectroscopy and foldover-corrected correlated spectroscopy, are particularly suitable versions for handling the large data matrices encountered in work with biological macromolecules. This paper explains the fundamental aspects of these two techniques and the relations with the conventional 2D correlated spectroscopy technique.
Article
The possibilities for the extension of spectroscopy to two dimensions are discussed. Applications to nuclear magnetic resonance are described. The basic theory of two‐dimensional spectroscopy is developed. Numerous possible applications are mentioned and some of them treated in detail, including the elucidation of energy level diagrams, the observation of multiple quantum transitions, and the recording of high‐resolution spectra in inhomogenous magnetic fields. Experimental results are presented for some simple spin systems.
Article
The application of step-scan interferometry to two-dimensional infrared (2D IR) spectroscopy is described. In this 2D FT-IR experiment, a step-scan interferometer is used to study a system undergoing dynamic changes induced by an external perturbation. Because step-scanning removes the spectral multiplexing from the temporal domain, the time dependence of the sample response to the perturbation can be retrieved more conveniently, in comparison to conventional rapid-scan techniques. Time-resolved IR data are then converted to 2D IR correlation spectra. Peaks located on a 2D spectral plane provide information about interactions among various functional groups associated with the IR bands. In the step-scan mode, the FT-IR multiplex advantage is retained; thus, spectral regions far removed from each other can be correlated with the use of 2D analysis from a single scan. 2D FT-IR spectra for a composite film of isotactic polypropylene and poly(γ-benzyl-L-glutamate) subjected to a small-amplitude sinusoidal strain are presented. The 2D FT-IR spectra clearly differentiate bands arising from the polyolefin and polypeptide. Overlapped bands are deconvoluted into individual components on the 2D spectral plane due to their different dynamic behavior. The applicability of step-scan 2D FT-IR to a variety of dynamic experiments is discussed.
Article
Nanosecond two-dimensional resonance Raman spectroscopy was used to investigate the photochemistry of the production and decay of the radical anion of benzil in various solvents. A newly developed correlation formalism was applied to a set of time-resolved resonance Raman spectra of the benzil radical anion to generate two-dimensional Raman spectra. Unlike the 2D correlation method previously developed for IR spectroscopy, which was based on signals induced by a sinusoidally varying external perturbation, the new correlation formalism is generally applicable to the studies of any transient spectroscopic signals having an arbitrary waveform. This makes it ideally suited for the analysis of time-resolved spectroscopic signals following photoexcitation. 2D Raman spectra effectively accentuate certain useful information which is sometimes obscured in the original time-resolved spectra. Spectral intensity changes and peak shifts arising from the photochemical reaction processes were clearly observed by the synchronous and asynchronous correlation.
Article
Most commercially available FUR instruments operate in the rapid-scan mode. In the rapid-scan mode, the moving mirror of the interferometer is scanned repeatedly at a constant velocity, thus every wavelength present is modulated at its own Fourier frequency. The sum of the sinusoids for all wavelengths in the bandwidth of the instrument is the recorded interferogram. Repeated interferograms are usually coadded before transformation in order to achieve the desired SNR. However, the rapid scan mode is difficult to apply to dynamic systems, especially when the relaxation time of the system is in the range of the commonly used Fourier modulation periods.1 This convolution of the temporal aspects of the experiment with the spectral multiplexing is avoided, and most of the advantages of (rapid-scan) FT interferometry are retained, by proper application of step-scan techniques of data acquisition. In the step-scan mode the moving mirror is stopped at, or vibrated about, each data collection point and data can be collected either in the impulse/response mode at discrete intervals of time following the impulse or in the synchronous modulation mode as in-phase and quadrature components of the signal with respect to the modulation. This modulation can be imposed either on the IR beam, or the sample's absorption, reflection or emission can be modulated by exciting the sample itself. For dynamic IR spectroscopy, the step-scan FUR mode simplifies data collection and allows relatively simple retrieval of the signal phase separate from the instrument phase. Applications illustrating how these advantages are realized in classical time-resolved spectroscopy and in phase-resolved two dimensional IR spectroscopy are illustrated below. The design principles of the step-scan interferometer used for the experiments described in this paper are covered in the paper by Manning, Palmer and Chao, in this volume (see also reference 2). In brief, the instrument is a modified IBM-IR-44; stepping is controlled by the application of a synchronous modulation to the moving mirror position and use of lock-in feedback loops to monitor the resulting modulation of the HeNe laser interference pattern. The mirror position is electronically and viscously damped. Data are collected at intervals corresponding to integral multiples of λ/4HeNe; depending on the desired free spectral range, at stepping paces as slow as desired and up to 10 Hz. The design is adapted from that originally published by Debarre, Boccara and Fournier.3
Article
A novel approach, utilizing a two-dimensional (2D) statistical correlation of mid- and near-infrared spectra, is presented as a means to assist with qualitative spectral interpretation. The method utilizes cross-correlation by least-squares to assess changes in both regions that result from changes in sample composition. The technique has been applied to complex agricultural samples that differ in wax (cuticle), carbohydrate, protein, and lignin content. Dispersive near-infrared (NIR) and interferometric mid-infrared (FT-IR) diffuse reflectance spectra were obtained on each of the samples, and point-for-point 2D cross-correlation was obtained. The technique permits the correlation of the combination and overtone region of the NIR to the fundamental vibrations in the mid-infrared (MIR) region. This allows the determination of the most probable source of NIR signals and verification of the "real" information content of the purely statistically derived signals whose intensities currently are used for quantitative analysis in this spectral region.
Article
The introduction of Fourier transform methods has not only remarkably enhanced the sensitivity of high-resolution NMR spectroscopy, thus allowing measurements to be made on less sensitive nuclei of the Periodic Table, but also has paved the way for the development of a large number of new experimental techniques. On the one hand, procedures already known have been improved and can now be performed more rapidly, and, on the other, completely new experimental approaches have become available. This situation resulted mainly from the introduction of programmable pulse transmitters and the separation of the experiment into preparation, evolution, and detection. In particular, the concept of two-dimensional spectroscopy has opened up new possibilities important for the analysis of complicated spectra and is able to provide information previously not accessible. As elsewhere, optimum application of the techniques and correct interpretation of the results require sound understanding of the underlying physical principles. Since a rigorous mathematical treatment is complicated and does not necessarily improve the comprehensibility, this article attempts to give an illustrative presentation of the new pulse techniques within the framework of the Bloch vector model. After a short introduction covering the basic principles, one-dimensional pulse techniques that can be applied using standard experimental equipment are dealt with. The main areas of application are signal assignment, sensitivity enhancement for measurements on less abundant nuclei, and selective excitation of individual resonances. Subsequently, the various techniques of two-dimensional NMR spectroscopy are treated: these enable shift correlations for different types of nuclei to be made, the presentation of spin multiplets without overlap, and the analysis of geometrical relations as well as of chemical exchange phenomena.
Article
Transient two-dimensional infrared (2D IR) correlation spectroscopy coupled with real-time Fourier transform infrared (RT FT-IR) measurement was used to analyze the reaction processes of photopolymerization systems. Unlike the previously developed 2D IR methods based on sinusoidally varying IR signals, a newly developed 2D correlation formalism applicable to transient spectroscopic signals having an arbitrary waveform was used. By this method, features associated with spectral intensity changes and peak shifts arising from polymerization reactions were clearly observed.
Article
Two-dimensional infrared (2D IR) spectroscopy, a novel technique based on time-resolved IR spectroscopy, is introduced. In 2D IR, a system is excited by an external perturbation, which induces a dynamic fluctuation of the IR spectrum. A correlation analysis is applied to the time-dependent IR signals to yield a spectrum defined by two independent wavenumbers. By spreading IR peaks over the second dimension, a complex spectrum consisting of overlapped peaks can be substantially simplified, and spectral resolution is enhanced. Peaks located on a 2D spectral plane provide information on connectivity and interactions among functional groups associated with the IR bands. 2D IR spectra are presented for a system consisting of a mixture of atactic polystyrene (PS) and low-density polyethylene (PE) to illustrate these features. The spectroscopic evidence clearly shows PS and PE in a blend are segregated at the molecular level, allowing the components to respond to an applied external perturbation independently of each other. A substantial difference is observed in the local mobility of the backbone and side-group functionalities of PS. On the basis of this observation, it is possible to assign the 1459-cm-1 component of the broad IR band centered around 1454 cm-1 to the backbone CH2 deformation in PS.
Article
Research News: The orientation of polymer molecules has a significant effect on the mechanical properties of polymeric materials. Infrared dichroism spectroscopy is a highly sensitive, chemically specific technique for examining the orientation of the electrical dipole moments in molecules and as such can be applied to the study of the mechanisms of orientational relaxation in entangled polymer melts. The technique and some of its recent applications are presented.
Article
Two-dimensional infrared (2D IR) spectroscopy is used to study atactic polystyrene. 2D IR is a technique based on time-resolved detection of IR signals in response to an external perturbation, such as mechanical strain. Since different chemical functional groups respond to the applied perturbation at unique and often different rates, characteristic time-dependent variations of the IR-band intensities are observed. Correlation analysis of the dynamic variation of the IR signals yields a new spectrum defined by two independent wave numbers. Peaks located on a 2D IR spectral plane imply interactions and connectivities among chemical functional groups. By spreading convoluted IR bands over two dimensions, the spectral resolution is also greatly enhanced.
Article
Infrared and Raman band frequencies, intensities and line shapes are often sensitive to the local molecular environment determined by molecular conformation, surrounding matrix, temperature, pressure, etc. The variety of local environments experienced by a condensed-phase molecule can lead to vibrational spectra with broad bands containing many overlapped spectral features. The spectral resolution of these overlapped features can be enhanced by making perturbations to the sample environment. Examples of perturbations which can be applied to the sample to enhance the information content of infrared spectra are changes in temperature, concentration and mechanical strain. In each instance, the spectra obtained as a function of the perturbation can be cross-correlated to produce a two-dimensional correlation map defined by two independent wavenumber axes. in this representation, infrared bands which respond to the perturbation in a similar or different manner can be clearly identified. This information can be used to help resolve overlapped bands and make unambiguous band assignments.
Article
A study of the kinetics of reorientation of a uniaxially aligned nematic liquid crystal (4-pentyl-4-′-cyanobiphenyl) under the influence of an external ac electric field is reported. Step-scan FT-IR was employed for the acquisition of the dynamic linear dichroism spectra. 2D FT-IR frequency correlation maps indicate that the rigid core of the nematic molecule reorients as a unit and suggest that the phenyl chain may reorient more rapidly than the core.
Article
A novel concept in vibrational spectroscopy called two-dimensional infrared (2D IR) spectroscopy is described. In 2D IR, a spectrum defined by two independent wavenumbers is generated by a cross-correlation analysis of dynamic fluctuations of IR signals induced by an external perturbation. 2D IR spectra are especially suited for elucidating various chemical interactions among functional groups. Notable features of the 2D IR approach are: simplification of complex spectra consisting of many overlapped peaks; enhancement of spectral resolution by spreading peaks over the second dimension; and establishment of unambiguous assignments through correlation analysis of bands selectively coupled by various interaction mechanisms. The procedure for generating 2D IR correlation spectra and the properties of the 2D spectra are discussed in detail. Examples of 2D IR spectra are presented for atactic polystyrene and the proteinacious component of human stratum corneum to demonstrate the utility of this technique.
Article
In some cases there are hidden correlations in a highly fluctuating signal, but these are lost in a conventional averaging procedure. Covariance mapping allows these correlations to be revealed unambiguously. As an example of the applicability of this technique, the dynamics of fragmentation of molecules ionized by an intense picosecond laser are analyzed.
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