Using 2D Correlation Analysis to Enhance Spectral Information Available from Highly Spatially Resolved AFM-IR Spectra

Comprehensive modified approaches to reducing the interference of moisture from an FTIR spectrum and the corresponding second derivative spectrum

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.

Random swapping, an effective and efficient way to boost the intensities of cross peaks in a 2D asynchronous spectrum

Analysis of mixture via chromatographic-spectroscopic and analogous experiments is a common task in analytical chemistry. A 2D/nD asynchronous spectrum is effective in retrieving spectra of pure substances even if different components cannot be separated. However, noise in the 2D/nD asynchronous spectrum becomes a bottleneck in the analysis. Finding a suitable sequence of the 1D spectra used in constructing the 2D/nD asynchronous spectrum is helpful to improve the signal-to-noise level. A 2D/nD asynchronous spectrum is often produced via a large number of 1D spectra. The resultant colossal number of the possible sequences makes stochastic search the only possible way to find a suitable sequence. Random changing (RC) and random swapping (RS) are two ways to obtain a new sequence. We found that the possibility of finding a better sequence via an RS is significantly higher than that via an RC in the advanced stage of stochastic searching. This is the reason why the performance of RS is superior to that of RC in two model systems where 2D asynchronous spectra are used. We applied the RS approach on the analysis of water/isopropanol mixtures, and satisfactory sequences are acquired with affordable computational cost. Thus, the RS approach brings about an opportunity increase the signal-to-noise level of a 2D asynchronous spectrum in the analysis of the bilinear data from complex mixed samples.

A new approach to removing interference of moisture from FTIR spectrum

An approach is developed to remove the interference of moisture from FTIR spectra. The interference arises from two aspects: the fluctuation on the temperature of the HeNe laser and the fluctuation on the transient concentration of moisture in the light - path of an FTIR spectrometer. The temperature fluctuation on the HeNe laser produces a systematic spectral shift between single-beam sample and background spectra, which often makes spectral subtraction method invalid in removing the interference of moisture. Herein, the Carbo similarity metric (the C_AB value) is used to reflect the subtle spectral shift. A database of single-beam background spectra is established based on the concept of big-data and the pigeon-hole theory. The spectral shift is corrected by selecting suitable single-beam background spectra from the database to match with the given single-beam sample spectrum according to the C_AB value. The interference caused by the fluctuation of the transient concentration of moisture is removed using a comprehensive 2D-COS method. We apply the approach on two polymeric samples to retrieve high-quality spectra and reliable second derivative spectra without the interference of moisture. The present work provides a new opportunity of obtaining the reliable second derivative spectra in the spectral region masked by moisture.

Intensity Enhancement of a Two-Dimensional Asynchronous Spectrum Without Noise Level Fluctuation Escalation Using a One-Dimensional Spectra Sequence Change

Previously, we demonstrated that the intensities of cross-peaks in a two-dimensional asynchronous spectrum could be enhanced using sequence change of the corresponding one-dimensional spectra. This unusual approach becomes useful when the determination of the sequential order of physicochemical events is not essential. However, it was not known whether the level of noise in the two-dimensional asynchronous spectrum was also escalated as the sequence of one-dimensional spectra changed. We first investigated the noise behavior in a two-dimensional asynchronous spectrum upon changing the sequence of the corresponding one-dimensional spectra on a model system. In the model system, bilinear data from a chromatographic-spectroscopic experiment on a mixture containing two components were analyzed using a two-dimensional asynchronous spectrum. The computer simulation results confirm that the cross-peak intensities in the resultant a two-dimensional asynchronous spectrum were indeed enhanced by more than 100 times as the sequence of one-dimensional spectra changed, whereas the fluctuation level of noise, reflected by the standard deviation of the value of a two-dimensional asynchronous spectrum at a given point, was almost invariant. Further analysis on the model system demonstrated that the special mathematical property of the Hilbert-Noda matrix (the modules of all column vectors of the Hilbert-Noda matrix being a near constant) accounts for the moderate variation of the noise level during the changes of the sequence of one-dimensional spectra. Next, a realistic example from a thermogravimetry-Fourier transform infrared spectroscopy experiment with added artificial noise in seven one-dimensional spectra was studied. As we altered the sequence of the seven FT-IR spectra, the variation of the cross-peak intensities covered four orders of magnitude in the two-dimensional asynchronous spectra. In contrast, the fluctuation of noise in the two-dimensional asynchronous spectra was within two times. The above results clearly demonstrate that a change in the sequence of one-dimensional spectra is an effective way to improve the signal-to-noise level of the two-dimensional asynchronous spectra.

Identification of systematic absence of cross-peaks (SACPs) in a two-dimensional asynchronous Spectrum using an auxiliary 2D quotient Spectrum and a statistical test

Systematic Absence of Cross Peaks (SACPs) in a two-dimensional (2D) asynchronous spectrum, a sensitive indicator of the signal purity, is very important in analyzing bilinear data. However, identification of SACPs in practice remains a challenge because of noise in the corresponding 2D asynchronous spectrum. We firstly show that SACP can be identified via a statistical test using a large amount of 2D asynchronous spectra. To meet the practical demand that SACPs must be identified based on a single 2D asynchronous spectrum in many cases, we use a 2D quotient spectrum (Q (x, y)) as an effective auxiliary tool to recognize SACPs. The expectation of Q(x, y) is zero when (x, y) is within SACP or background regions in the corresponding 2D asynchronous spectrum. When (x, y) is in a cross-peak region, the expectation of the absolute value of Q(x, y) is a constant regardless of whether the cross-peak in a 2D asynchronous spectrum is strong or weak. Thus, a unified threshold can be set up to differentiate the SACP region from cross-peak region via the auxiliary 2D quotient spectrum. We have applied this approach on two real-world examples and satisfactory results have been obtained. This result demonstrates that the statistical test with a 2D quotient spectrum is applicable in real-world systems.

Two-dimensional correlation analysis of highly spatially resolved simultaneous IR and Raman spectral imaging of bioplastics composite using optical photothermal Infrared and Raman spectroscopy

Optical photothermal infrared (O-PTIR) and Raman spectroscopy and imaging was used to explore the spatial distributions of molecular constituents of a laminate sample consisting of the bioplastics, polyhydroxyalkanoate (PHA) and polylactic acid (PLA), near the interfacial boundary. Highly spatially resolved simultaneous IR and Raman spectra were sequentially collected at 100 nm increments along a line traversing the interface. The set of spectra were subjected to 2D-COS analysis to extract the detailed nature of the spatial distribution of the laminate constituents. It was revealed that the laminate is not a simple binary system of two non-interacting polymers, but consists of different constituents with more complex spatial distributions. Some portion of PLA seems to penetrate into the PHA layer. The crystallinity of PHA near the interface is reduced compared to the rest of the PHA layer. The result suggests the existence of some partial molecular mixing even for these seemingly immiscible polymer pairs. The mixing probably occurs at the segmental level confined to only several hundred nanometers of space at the interface. Such partial mixing may explain the high compatibility between the two bioplastics.

A novel systematic absence of cross peaks-based 2D-COS approach for bilinear data

A novel approach to use two-dimensional correlation spectroscopy (2D-COS) to analyze bilinear data is proposed. A phenomenon called Systematic Absence of Cross Peaks (SACPs) is observed in a 2D asynchronous spectrum. Two theorems relevant to SACPs have been derived. The SACP-based 2D-COS method has been successfully applied on analyzing bilinear data from mixed samples (including one model system and two real systems). Implicit isolated peaks can be identified and assigned to different components based on characteristic pattern of SACPs even if the time-related profiles of different components are severely overlapped. Based on the results of SACPs, spectra of pure components can be retrieved. Identification of SACPs can still be achieved in the presence of artifacts. Thus, neither noise nor baseline drift can produce significant influence on the results obtained from the approach described in this paper. We have used several well-established chemometric methods, including N-Findr, VCA, and MCR with various initial settings, on two systems that can be successfully solved using the 2D-COS method. The chemometric methods mentioned above cannot provide correct spectra of pure components because of severe problem of rotational ambiguity derived from severe overlapping of the time-related profiles. Only when the information from SACPs in 2D-COS is used as additional constraints in MCR calculation, correct spectra can be obtained. That is to say, the SACP-based 2D-COS method provides intrinsic information which is crucial in the analysis of chromatographic-spectroscopic and analogous data even if the time-related profiles of different components overlap severely.

A Novel Approach Based on Two-Dimensional Correlation Spectroscopy to Determine the Stoichiometric Ratio of Two Substances Involved in Intermolecular Interactions

A novel technique called AOSD@Job's, combining asynchronous orthogonal sample design scheme (AOSD) with Job's method, is proposed to estimate the stoichiometric ratio of two substances that form a supramolecular aggregate under intermolecular interactions. First, a mathematical analysis was performed along with the procedure of the AOSD@Job's method. Then, the validity of the AOSD@Job's method was manifested by computer simulation on two model systems. Finally, the AOSD@Job's method was applied on two real chemical systems. The stoichiometric ratio between the coordination complex of Ni²⁺ and ethylenediaminetetraacetic acid disodium salt (EDTA) was estimated to be 1.0. Benzyl alcohol (BA) and β-cyclodextrin (β-CD) were determined to form a 1 : 1 host-guest complex. These values were consistent with the values reported in the literature. Compared with the traditional Job's method, the AOSD@Job's method has an evident advantage since it is still valid even if all the peaks of the supramolecular aggregate severely overlap with the peaks of the substances that form the aggregate.

A preliminary study on constructing a high-dimensional asynchronous spectrum to analyze bilinear data

A novel approach to constructing high-dimensional asynchronous spectra (nD-Asyn) is proposed. Three theorems relevant to 1D slices of nD-Asyn are revealed. nD-Asyn is used to analyze bilinear data from mixtures containing multiple components obtained via hyphenated techniques. The spectral contribution of different components can be removed in a stepwise manner by increasing the dimensions of asynchronous spectra. As a result, the spectra of different components can be faithfully recovered even if the time-related profiles of different components severely overlap. Moreover, correct results can still be obtained via the nD-Asyn even if a considerable level of noise and baseline drift are present. The nD-Asyn approach is compared with MCR-ALS using different constraints in analyzing the data for a simulated and also for a real system. The nD-Asyn produced correct spectrum of every component. Only when complete constraints obtained from nD-Asyn method is utilized in the MCR-ALS calculation, correct spectra of all the components can be obtained. Thus, nD-Asyn can be used alone or in conjunction with MCR-ALS to analyze bilinear data containing contributions of multiple components.

Two-Dimensional Correlation Spectroscopy (2D-COS) for Analysis of Spatially Resolved Vibrational Spectra

The last two decades have seen tremendous progress in the application of two-dimensional correlation spectroscopy (2D-COS) as a versatile analysis method for data series obtained using a large variety of different spectroscopic modalities, including infrared (IR) and Raman spectroscopy. The analysis technique is applicable to a series of spectra recorded under the influence of an external sample perturbation. Two-dimensional COS analysis is not only helpful to decipher correlations, which may exist between distinct spectral features, but can also be utilized to obtain the sequence of individual spectral changes. The focus of this review article is on the application of 2D-COS for analyzing spatially resolved data with special emphasis on hyperspectral imaging (HSI) study. In this review, we briefly introduce the fundamentals of the generalized 2D-COS analysis approach, discuss specific points of 2D-COS application to spatially resolved spectra and demonstrate essential aspects of data pre-processing for 2D-COS analysis of spatially resolved spectra. Based on illustrative examples, we show that 2D-COS is useful for spectral band assignment in HSI applications and demonstrate its utility for detecting subtle correlations between spectra features, or between features from different imaging modalities in the case of heterospectral (multimodal) HSI. Furthermore, a short overview on existing 2D-COS software tools is provided. It is hoped that this article represents not only a useful guideline for 2D-COS analyses of spatially resolved hyperspectral data but supports also further dissemination of the 2D-COS analysis method as a whole.

The Relationship of Collagen Structural and Compositional Heterogeneity to Tissue Mechanical Properties: A Chemical Perspective

Collagen is the primary protein component in mammalian connective tissues. Over the last 20 years, evidence has mounted that collagen matrices exhibit substantial heterogeneity in their hierarchical structures and that this heterogeneity plays important roles in both structure and function. Herein, an overview of studies addressing the nanoscale compositional and structural heterogeneity is provided and connected to work exploring the mechanical implications for a number of tissues.

Vibrational spectroscopic techniques to assess bone quality

Although musculoskeletal diseases such as osteoporosis are diagnosed and treatment outcome is evaluated based mainly on routine clinical outcomes of bone mineral density (BMD) by DXA and biochemical markers, it is recognized that these two indicators, as valuable as they have proven to be in the everyday clinical practice, do not fully account for manifested bone strength. Thus, the term bone quality was introduced, to complement considerations based on bone turnover rates and BMD. Bone quality is an "umbrella" term that incorporates the structural and material/compositional characteristics of bone tissue. Vibrational spectroscopic techniques such as Fourier transform infrared microspectroscopy (FTIRM) and imaging (FTIRI), and Raman spectroscopy, are suitable analytical tools for the determination of bone quality as they provide simultaneous, quantitative, and qualitative information on all main bone tissue components (mineral, organic matrix, tissue water), in a spatially resolved manner. Moreover, the results of such analyses may be readily combined with the outcomes of other techniques such as histology/histomorphometry, small angle X-ray scattering, quantitative backscattered electron imaging, and nanoindentation.

Vibrational spectroscopic imaging for the evaluation of matrix and mineral chemistry

Metabolic bone diseases manifesting fragility fractures (such as osteoporosis) are routinely diagnosed based on bone mineral density (BMD) measurements, and the effect of various therapies also evaluated based on the same outcome. Although useful, it is well recognized that this metric does not fully account for either fracture incidence or the effect of various therapies on fracture incidence, thus, the emergence of bone quality as a contributing factor in the determination of bone strength. Infrared and Raman vibrational spectroscopic techniques are particularly well-suited for the determination of bone quality as they provide quantitative and qualitative information of the mineral and organic matrix bone components, simultaneously. Through the use of microspectroscopic techniques, this information is available in a spatially resolved manner, thus, the outcomes may be easily correlated with outcomes from techniques such as histology, histomorphometry, and nanoindentation, linking metabolic status with material properties.