Recent applications of multiway calibration methods in environmental analytical chemistry: A review

A tutorial on multi-way data processing of excitation-emission fluorescence matrices acquired from semiconductor quantum dots sensing platforms

This tutorial demonstrates how to exploit the second-order advantage on excitation-emission fluorescence matrices (EEFMs) acquired from sensing platforms based on analyte-triggered semiconductor quantum dots (QDs) fluorescence modulation (quenching/enhancing). The advantage in processing such second-order EEFMs data from complex samples, seeking successful quantification, is comprehensively addressed. It is worth emphasizing that, aiming to exploit the second-order advantage, the selection of the most appropriate advanced chemometric model should rely on the matching between the data structure and the physicochemical chemometric model assumption. In this sense, the achievement of second-order advantage after EEFMs' processing is extensively addressed throughout this tutorial taking into consideration three different analytical situations, each involving a specific data structure: i) parallel factor analysis (PARAFAC), which is applied in a real dataset stacked in a three-way data array containing a trilinear data structure acquired from QDs-based detection with non-selective species; ii) multivariate curve resolution - alternating least-squares (MCR-ALS), which is also employed in a real dataset arranged in an augmented data matrix containing non-trilinear data structure acquired from QDs-based detection with a single breaking mode caused by background signals; iii) unfolded partial least-squares with residual bilinearization (U-PLS/RBL), which is applied in a dataset containing non-trilinear data acquired from a classical fluorescence system with two breaking modes caused by inner filter effect (IFE) in both instrumental modes (excitation and emission). The latter challenging data structure can be acquired via fluorescence quenching from IFE-based sensing platforms and chemometrically handled in two main steps. First, a set of calibration EEFMs data is converted into an unfolded data matrix during the unfolding process, followed by applying U-PLS model. Second, a post-calibration procedure using RBL analysis is applied to a test sample of EEFM maintained in its matrix form, in order to handle potential interferents. In the last section, the state-of-the-art of second-order EEFMs data acquired from semiconductor QDs-based sensing platforms and coupled to multi-way fluorescence data processing to accomplish a successful quantification, even with substantial interfering species, is critically reviewed.

Application of alternating trilinear decomposition-assisted multivariate curve resolution to gas chromatography-mass spectrometric data for the quantification of polycyclic aromatic hydrocarbons in aerosols

For the first time, alternating trilinear decomposition-assisted multivariate curve resolution (ATLD-MCR) was applied to analyse complex gas chromatography-mass spectrometric (GC-MS) data with severe baseline drifts, serious co-elution peaks and slight retention time shifts for the simultaneous identification and quantification of polycyclic aromatic hydrocarbons (PAHs) in aerosols. It was also compared with the classic multivariate curve resolution-alternating least-squares (MCR-ALS) and the GC-MS-based external standard method. In validation samples, average recoveries of five PAHs were within the range from (96.2 ± 6.8)% to (106.5 ± 4.1)% for ATLD-MCR, near to the results of MCR-ALS ((98.0 ± 1.5)% to (106.7 ± 4.3)%). In aerosol samples, the concentrations of pyrene provided by ATLD-MCR were not significantly different from those of MCR-ALS. The other four PAHs including chrysene, benzo[a]anthracene, fluoranthene and benzo[b]fluoranthene were not detected by ATLD-MCR and the GC-MS-based external standard method. The results of figures of merit further demonstrated that ATLD-MCR achieved high sensitivities (8.9 × 104 to 1.7 × 106 mAU ml µg-1) and low limits of detection (0.003 to 0.087 µg ml-1), which were better than or similar to MCR-ALS, presenting a great choice to deal with complex GC-MS data for the simultaneous determination of targeted PAHs in aerosols.

Multilinear Mathematical Separation in Chromatography

Chromatography is a powerful and generally applicable method for the analytical separation and quantification of the chemical constituents in complex mixtures because chromatographic separation can provide high selectivity by isolating all analytes from interferences. Multiway analysis based on the multilinear model is an increasingly widely used method for interference-free and fast determination of the chemical constituents also in complex mixtures because multilinear mathematical separation can provide high selectivity by extracting the pure signal of the analyte from the mixed signal of a real sample. By combining chromatographic separation with mathematical separation, multiway calibration method, multiway standard additions method, and multiway internal standard method can be established. Chromatography assisted by multiway analysis can reduce the requirements for complete chromatographic separation, save elution time, and decrease the consumption of the mobile phase, particularly when the peak coelution problem is difficult to solve. This review presents the fundamentals and analytical applications of multilinear mathematical separation in chromatography.