Second-order advantage obtained from standard addition first-order instrumental data and multivariate curve resolution-alternating least squares. Calculation of the feasible bands of results

Abstract

In order to achieve the second-order advantage, two-way data per sample are usually required, e.g., kinetic spectrophotometric data. In this study, instead of monitoring the time evolution of spectra (collecting kinetic-spectrophotometric data) replicate spectra are used to build a spectrophotometric data matrix which is rank deficient. Augmentation of these data with standard addition data [or standard sample(s)] will break the rank deficiency. making the quantification of the analyte of interest possible. These data correspond to the kinetics of all sample constituents being identical when employing second-order kinetic-spectroscopic measurements. The MCR-ALS algorithm has been applied for the resolution and quantitation of the analyte in both simulated and experimental data sets. In order to evaluate the rotational ambiguity in the retrieved solutions, the algorithm MCR-BANDS has been employed. The reliability of the quantitative results significantly depends on the amount of spectral overlap in the spectral region of occurrence of the compound of interest and the remaining constituents. The ability of the proposed algorithm to quantitate the analyte is illustrated both with simulated data systems as well as with binary experimental mixtures.

Assessment of the Kernel Gram Matrix Representation of Data in Order to Avoid the Alignment of Chromatographic Signals

“…The baseline component was generated using the bilinear model given by Equation (2). The resulting data matrix with the baseline component, B, has the same dimensions as the pure chromatographic signal.…”

“…Nonetheless, essential analytical information is often extracted from data that were recorded using advanced multichannel detectors. A unique advantage of the multichannel detectors, such as a diode-array detector, multiple fluorescence detector, or mass spectrometry is based on recording the existing differences in physicochemical properties of individual mixture components (absorption differences in the UV and/or Vis spectral range, ion velocity, and specific emission spectra), referred to as the second-order advantage in the literature [ 1 , 2 ]. Compared to the classic mono-channel counterparts, the subsequent portions of eluent are characterized by a multichannel detector to a larger extent in addition to the chromatographic separation that is carried out along the time domain.…”

Modeling and optimization of simultaneous degradation of rhodamine B and acid red 14 binary solution by homogeneous Fenton reaction: a chemometrics approach

“…Where C is the matrix of species' concentrations, S T is their corresponding pure spectra at the initial dye concentration, and E is the part of data that cannot be expressed by the model and contains an experimental error and/or noise. The ALS algorithm uses initial estimates of C 0 or S T 0 and optimizes them iteratively by least-square solution and the implementation of proper constraints such as nonnegativity, unimodality, equality and closure to find the best answers [32,33]. The optimized concentration profiles for each component can be applied to calculate the degradation efficiency values (Q) at each experiment using Eq.…”

MCR-ALS of voltammetric data for the study of environmentally relevant substances

“…If the signals of the different analytes are not well resolved, calibration can be problematic. In the case of spectrophotometric measurements, second order information can be helpful to carry out calibration by standard addition, even using replicates of the samples to exploit the second-order advantage with first-order data [68]. In a recent work, our group has shown that the shape constraint characteristic of voltammetric measurements is a key factor to apply MCR-ALS to multivariate standard addition with no need of second order data.…”