Four-Way Data Coupled to Parallel Factor Model Applied to Environmental Analysis:  Determination of 2,3,7,8-Tetrachloro-dibenzo-para-dioxin in Highly Contaminated Waters by Solid−Liquid Extraction Laser-Excited Time-Resolved Shpol'skii Spectroscopy

Abstract

This article reports the first application of parallel factor analysis to high-order instrumental data generated from Shpol'skii matrixes at liquid helium temperature. Third-order data arrays-consisting of excitation modulated wavelength time matrixes-are collected with the aid of a cryogenic fiber-optic probe, a tunable dye laser, and a multichannel system for phosphorescence detection. The multidimensional data formats are applied to the analysis of 2,3,7,8-tetrachloro-dibenzo-para-dioxin in water samples. The experimental procedure is rapid and environmentally friendly. Complete sample analysis is accomplished in less than 15 min with only 100 muL of organic solvent (n-heptane). The feasibility to directly determine parts-per-trillion concentration levels of the target compound is demonstrated with heavily contaminated samples of unknown composition. The limits of detection, estimated from calibrations based on the univariate method and parallel factor analysis, are 0.060 and 0.092 ng.mL(-1), respectively; both referred to a 100 mL water sample.

Second- and higher-order data generation and calibration: A tutorial

“…Figure 14 A third alternative is based on laser-excited time-resolved EEM phosphorescence 769 data, using instrumental data generated from Shpol´skii matrices at liquid helium 770 temperature. In this case, the third-order data arrays, consisting of excitation modulated 771 wavelength-time matrices, were collected with the aid of a cryogenic fiber-optic probe, 772 a tunable dye laser, and a multichannel system for phosphorescence detection, and 773 applied to the analysis of 2,3,7,8-tetrachloro-dibenzo-para-dioxin [78]. 774…”

Third-order/Four-way Calibration and Beyond

“…Quadrilinear data can be conveniently analyzed with an algorithm whose internal model is quadrilinear. [5][6][7][8][9][10] As mentioned above, nonquadrilinear data of type 1 can be transformed into a trilinear threedimensional array to be decomposed with three-way PARAFAC. There are variants of PARAFAC that are also based on the quadrilinear model: alternating penalty quadrilinear decomposition 19 and alternating weighted residual constraint quadrilinear decomposition.…”

Four-way kinetic-excitation-emission fluorescence data processed by multi-way algorithms. Determination of carbaryl and 1-naphthol in water samples in the presence of fluorescent interferents

“…In these cases, a reaction may produce a fluorescent species from a non-fluorescent analyte, or a natively fluorescent analyte may generate a non-fluorescent species. The time dependence may also arise from naturally timedecaying EEM data [5]. In any case, only a few reports exist on the processing of kinetic-EEM data aimed at the determination of one or several analytes embedded in a complex background.…”

“…Quadrilinear models such as parallel factor analysis (PARAFAC) [5,6] and alternating quadrilinear decomposition [12] are appealing because they provide useful physicochemical information, in terms of kinetic and spectral profiles for the different sample components. However, kinetic systems pose challenges to these latter algorithms due to: (1) strong linear dependencies among component profiles, typical of kinetic systems, and (2) multi-linearity losses due to the fact that the reaction may progress during the time required for registering a complete EEM.…”