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When diffusion coefficients of different components in a mixture are similar, NMR spectra of pure individual components are difficult to be obtained via a diffusion-ordered spectroscopy (DOSY) experiment. Two-dimensional correlation spectroscopy (2D-COS) is used to analyze the data from the DOSY experiment. Through the properties of the systematic absence of cross-peak (SACP) in the 2D asynchronous spectra, spectra of pure components can be obtained even if their diffusion coefficients are similar. However, fluctuations in peak-position and peak-width are often unavoidable in NMR spectra, which makes SACPs unrecognizable. To address the problem, a 2D quotient spectrum is used to identify the masked SACPs. However, undesirable interference peaks due to the fluctuations in peak-position and peak-width are still present when we extract a spectrum of a component by slicing the 2D asynchronous spectrum across the SACP. A genetic algorithm (GA) is used to select a suitable subset of spectra where the diversities of peak-position and peak-width are significantly reduced. Then, we used the selected spectra to construct a refined 2D asynchronous spectrum so that the spectra of pure components with significant attenuated interference can be obtained. The above approach has been proven to be effective on a model system and a real-world example, demonstrating that 2D-COS possesses a bright perspective in the analysis of the bilinear data from DOSY experiments.

Estimation of the stoichiometric ratio of a supramolecular aggregate formed by different compounds is very important in elucidating the structure and function of the aggregate. Many spectroscopic methods used to estimate the stoichiometric ratios of coordination complexes become invalid when characteristic peaks of the aggregate overlap with peaks of compounds that form the aggregate. Previously, we combined the asynchronous orthogonal sample design with Job's method to address the abovementioned problem. However, the interference of noise may lead to incorrect results. Herein, a new method has been developed. In the generation of corresponding Job's curve, the intensity of a cross peak at a single apex is replaced by the volume of the cross peak. Since most noise is canceled in the calculation of the volume of the cross peak, resultant Job's curve is robust to noise. Moreover, the Jonckheere-Terpstra statistical test, a famous nonparametric method to detect whether the data has an upward or downward trend, could further reduce the risk of yielding incorrect results caused by noise. We have applied this approach to two real-world examples (resveratrol/β-Cyclodextrin (β-CD) andiN, N/i-diethyl-iN/i'-benzoylthiourea (DEBT)/Cusup2+/sup) with satisfactory results. The method described in this paper provides a robust way to measure the stoichiometric ratio in supramolecular systems.

An approach to construct a secondary asynchronous spectrum via sample-sample correlation (SASS) is proposed to analyze bilinear data from hyphenated spectroscopic experiments. In SASS, bilinear data is used to construct a series of two-dimensional (2D) sample-sample correlation spectra. Then a vertical slice is extracted from each 2D sample-sample correlation spectrum so that a secondary 2D asynchronous spectrum is constructed via these slices. The advantage of SASS is demonstrated by a model system with the following challenging situations: (1) Temporal profiles of different components severely overlap, making spectra of pure components difficult to directly obtain from either original bilinear data or multivariate curve resolution-alternating least squares (MCR-ALS) with non-negativity and unimodality constraints. (2) Every peak in the spectra of the eluted samples contains contributions from at least two components. Hence, two-dimensional correlation spectroscopy (2D-COS) and n-dimensional (nD) asynchronous spectroscopic method developed in our previous work, which previously worked so well, are now invalid. SASS managed to reveal different groups of systematic absences of cross peaks (SACPs) that reflect the lack of spectral contributions of different components at different regions in the second asynchronous spectrum. Spectra of different components can still be faithfully retrieved via MCR-ALS calculation using constraints revealed by different groups of SACPs. The results demonstrate that implicit but intrinsic information revealed by SASS is indispensable in solving challenging bilinear data as the model system. We applied SASS on two real-world examples from thermogravimetry-Fourier transform infrared spectroscopy (TG-FT-IR) experiments of mixtures (H2O/HOD/D2O and H2O/isopropanol/pyridine). FT-IR spectra of different components were successfully recovered. Moreover, FT-IR spectrum of HOD, which is difficult to obtain, was successfully extracted. SASS can be applied in the analysis of gaseous mixtures from TG-FT-IR experiment and a combination of quantum cascade lasers with substrate-integrated hollow waveguides in environmental monitoring and biomedical diagnosis. Furthermore, SASS is also useful in various advanced hyphenated spectroscopic experiments.