Electronic waste analysis using laser-induced breakdown spectroscopy (LIBS) and X-ray fluorescence (XRF): Critical evaluation of data fusion for the determination of Al, Cu and Fe.

BACKGROUND: Electronic waste (e-waste) proliferation and its implications underscore the imperative for advanced analytical methods to mitigate its environmental impact. It is estimated that e-waste production stands at a staggering 20-50 million tons yearly, of which merely 20-25% undergo formal recycling. The e-waste samples evaluated contain computers, laptops, smartphones, and tablets. RESULTS: Forty-one samples were processed, involving the disassembly and separation of components. Subsequently, two analytical techniques, laser-induced breakdown spectroscopy (LIBS) and energy dispersive X-ray fluorescence (ED-XRF), were applied to quantify aluminum (Al), copper (Cu), and iron (Fe) in the e-waste samples. The samples were then analyzed after acid mineralization with 50% v v-1 aqua regia in a digester block and finally by ICP OES. A solid residue composed of Si and Ti was observed after the digestion of the samples. Multivariate calibration strategies such as partial least-squares regression (PLS), principal component regression (PCR), maximum likelihood principal component regression (MLPCR), and error covariance penalized regression (ECPR) were used for calibration. Finally, the figures of merit were calculated to verify the most suitable models. The results revealed robust models with notable sensitivity, varying from 8.98 to 35.04 Signal (a.u.)(% w w-1) -1, low Limits of Detection (LoD) within the range of 0.001-0.2 % w w-1, and remarkable relative errors ranging from 2% to 33%, particularly for Cu and Fe. SIGNIFICANCE: Notably, the models for Al faced inherent challenges, thus highlighting the complexities associated with its quantification in e-waste samples. In conclusion, this research represents an important step toward a more sustainable and efficient future for electronic waste recycling, signifying its relevance to global environmental welfare and resource conservation.

Data-Driven Version of Multiway Soft Independent Modeling of Class Analogy (N-Way DD-SIMCA): Theory and Application.

One-class classification (OCC) is discussed in the framework of the measurement and processing of multiway data. Data-driven soft independent modeling of class analogy (DD-SIMCA) is applied in the following formats: (1) multiblock and (2) Tucker 3 N-way SIMCA, which are shown to be useful tools for solving classification tasks. A new decision rule for N-way DD-SIMCA is adopted based on the conventional two-way DD-SIMCA model. Multiblock SIMCA is shown to be useful for variable selection, and Tucker 3 SIMCA to select the optimal model complexity when applying multiway data decomposition and to assess the role of individual samples in the classification model. Both approaches, together with the two-way DD-SIMCA version applied to the unfolded data, are compared regarding the analysis of an experimental data set including genuine and adulterated blueberry extract samples. The latter were employed to produce matrix spectral-time data matrices per sample within a flow injection system, taking advantage of the spectral changes in the sample constituents as a function of the pH of the carrier phase. The need to employ the Tucker 3 model instead of a trilinear decomposition is supported by a discussion on the lack of the trilinearity property of the studied data.

An exhaustive analysis of the use of image moments for second-order calibration. A comparison with multivariate curve resolution-alternating least-squares.

BACKGROUND: the chemometric processing of second-order chromatographic-spectral data is usually carried out with the aid of multivariate curve resolution-alternating least-squares (MCR-ALS). Recently, an alternative procedure was described based on the estimation of image moments for each data matrix and subsequent application of multiple linear regression after suitable variable selection. RESULTS: The analysis of both simulated and experimental data leads to the conclusion that the image moment method, although can cope with chromatographic lack of reproducibility across injections, it only performs well in the absence of uncalibrated interferents. MCR-ALS, on the other hand, provides good analytical results in all studied situations, whether the test samples contain uncalibrated interferents or not. SIGNIFICANCE: The results are useful to assess the real usefulness of newly proposed methodologies for second-order calibration in the case of chromatographic-spectral data sets, especially when samples contain unexpected chemical constituents.

A new constraint to model background signals when processing chromatographic-spectral second-order data with multivariate curve resolution.

BACKGROUND: the chemometric processing of second-order chromatographic-spectral data is usually carried out with the aid of multivariate curve resolution-alternating least-squares (MCR-ALS). When baseline contributions occur in the data, the background profile retrieved with MCR-ALS may show abnormal lumps or negative dips at the position of the remaining component peaks. RESULTS: The phenomenon is shown to be due to remaining rotational ambiguity in the obtained profiles, as confirmed by the estimation of the boundaries of the range of feasible bilinear profiles. To avoid the abnormal features in the retrieved profile, a new background interpolation constraint is proposed and described in detail. Both simulated and experimental data are employed to support the need of the new MCR-ALS constraint. In the latter case, the estimated analyte concentrations agreed with those previously reported. SIGNIFICANCE: The developed procedure helps to reduce the extent of rotational ambiguity in the solution and to better interpret the results on physicochemical grounds.

Unraveling surface-enhanced Raman spectroscopy results through chemometrics and machine learning: principles, progress, and trends.

Surface-enhanced Raman spectroscopy (SERS) has gained increasing attention because it provides rich chemical information and high sensitivity, being applicable in many scientific fields including medical diagnosis, forensic analysis, food control, and microbiology. Although SERS is often limited by the lack of selectivity in the analysis of samples with complex matrices, the use of multivariate statistics and mathematical tools has been demonstrated to be an efficient strategy to circumvent this issue. Importantly, since the rapid development of artificial intelligence has been promoting the implementation of a wide variety of advanced multivariate methods in SERS, a discussion about the extent of their synergy and possible standardization becomes necessary. This critical review comprises the principles, advantages, and limitations of coupling SERS with chemometrics and machine learning for both qualitative and quantitative analytical applications. Recent advances and trends in combining SERS with uncommonly used but powerful data analysis tools are also discussed. Finally, a section on benchmarking and tips for selecting the suitable chemometric/machine learning method is included. We believe this will help to move SERS from an alternative detection strategy to a general analytical technique for real-life applications.

A Critical Review on the Development of Optical Sensors for the Determination of Heavy Metals in Water Samples. The Case of Mercury(II) Ion.

Recent publications are reviewed concerning the development of sensors for the determination of mercury in drinking water, based on spectroscopic methodologies. A critical analysis is made of the specific details and figures of merit of the developed protocols. Special emphasis is directed to the validation and applicability to real samples in the usual concentration range of mercury, considering the maximum allowed limits in drinking water established by international regulations. It was found that while most publications describe in detail the synthesis, structure, and physicochemical properties of the sensing phases, they do not follow the state of the art in the analytical developments. Recommendations are provided regarding the proper method development and validation, including the setting of the calibration concentration range, the correct estimation of the limits of detection and quantitation, the concentration levels to be set for producing spiked water samples, the number of real samples for adequate validation, the comparison of the developed method with a reference technique, and other analytical features which should be followed.

Linear or non-linear multivariate calibration models? That is the question.

Concepts from data science, machine learning, deep learning and artificial neural networks are spreading in many disciplines. The general idea is to exploit the power of statistical tools to interpret complex and, in many cases, non-linear data. Specifically in analytical chemistry, many chemometrics tools are being developed. However, they tend to get more complex without necessarily improving the prediction ability, which conspires against parsimony. In this report, we show how non-linear analytical data sets can be solved with equal or better efficiency by easily interpretable modified linear models, based on the concept of local sample selection before model building. The latter activity is conducted by choosing a sub-set of samples located in the neighborhood of each unknown sample in the space spanned by the latent variables. Two experimental examples related to the use of near infrared spectroscopy for the analysis of target properties in food samples are examined. The comparison with seemingly more complex chemometric models reveals that local regression is able to achieve similar analytical performance, with considerably less computational burden.

Sensitivity and generalized analytical sensitivity expressions for quantitative analysis using convolutional neural networks.

In recent years, convolutional neural networks and deep neural networks have been used extensively in various fields of analytical chemistry. The use of these models for calibration tasks has been highly effective; however, few reports have been published on their properties and characteristics of analytical figures of merit. Currently, most performance measures for these types of networks only incorporate some function of prediction error. While useful, these measures are incomplete and cannot be used as an objective comparison among different models. In this report, a new method for calculating the sensitivity of any type of neural network is proposed and studied on both simulated and real datasets. Generalized analytical sensitivity is defined and calculated for neural networks as an additional figure of merit. Moreover, the dependence of convolutional neural networks on regularization dataset size is studied and compared with other conventional calibration methods.

Chromatographic Applications in the Multi-Way Calibration Field.

In this review, recent advances and applications using multi-way calibration protocols based on the processing of multi-dimensional chromatographic data are discussed. We first describe the various modes in which multi-way chromatographic data sets can be generated, including some important characteristics that should be taken into account for the selection of an adequate data processing model. We then discuss the different manners in which the collected instrumental data can be arranged, and the most usually applied models and algorithms for the decomposition of the data arrays. The latter activity leads to the estimation of surrogate variables (scores), useful for analyte quantitation in the presence of uncalibrated interferences, achieving the second-order advantage. Recent experimental reports based on multi-way liquid and gas chromatographic data are then reviewed. Finally, analytical figures of merit that should always accompany quantitative calibration reports are described.

Achieving the analytical second-order advantage with non-bilinear second-order data.

Multi-way calibration based on second-order data constitutes a revolutionary milestone for analytical applications. However, most classical chemometric models assume that these data fulfil the property of low rank bilinearity, which cannot be accomplished by all instrumental methods. Indeed, various techniques are able to generate non-bilinear data, which are all potentially useful for the development of novel second-order calibration methodologies. However, the achievement of the second-order advantage in these cases may be severely limited, since methods for comprehensive modelling of non-bilinear second-order data remain only partially explored. In this research, the analytical performance of three well-known second-order models, namely non-bilinear rank annihilation (NBRA), unfolded partial least-squares with residual bilinearization (U-PLS-RBL) and multivariate curve resolution - alternating least-squares (MCR-ALS) is systematically assessed through sets of simulated and experimental non-bilinear second-order data, involving one analyte and one interferent. Although it is not possible to establish a single strategy to model any type of non-bilinear second-order data with the studied methods, each approach may lead to successful predictions under certain circumstances. It is shown that the prediction capacity is severely affected by data properties such as the level of instrumental noise, the rank of the response matrices and the signal selectivity pattern of the analyte.

Interference-free calibration with first-order instrumental data and multivariate curve resolution. When and why?

The possibility of building an interference-free calibration with first-order instrumental data with multivariate curve resolution-alternating least-squares (MCR-ALS) has been a recent topic of interest. When the protocols were successful, MCR-ALS proved to be suitable for the extraction of chemically meaningful information from first-order calibration datasets, even in the presence of unexpected species, i.e., constituents present in the test samples but absent in the calibration set. This may represent an interesting advantage over classical first-order models, e.g. partial least-squares regression (PLS). However, the predictive capacity of MCR-ALS models can be severely affected by rotational ambiguity (RA), which is usually present in first-order datasets when interferents occur, and has not been always characterized in the published analytical protocols. The aim of this report is to discuss important issues regarding MCR-ALS modelling of first-order data for a calibration scenario with a single analyte and one interferent through simulated and experimental data. Specifically, the question of when and why MCR-ALS allows one to build interference-free calibration models with first-order data is studied in terms of signal overlapping, extent of RA, and especially the role of ALS initialization procedures in prediction performance. The aim is to alert analytical chemists that interference-free MCR-ALS with first-order data may not always be successful.

A down-to-earth analyst view of rotational ambiguity in second-order calibration with multivariate curve resolution - a tutorial.

Rotational ambiguity is a phenomenon with the potential of generating an uncertainty in the estimation of analyte concentrations in protocols based on matrix instrumental data processed by multivariate curve resolution - alternating least-squares (MCR-ALS). This is particularly relevant when the second-order advantage is to be achieved, i.e., when selected analytes are determined in unknown samples having unexpected constituents, not considered in the calibration set of samples. It is therefore imperative that analytical chemists developing second-order multivariate calibration methods using MCR-ALS acknowledge the relevance of this issue, and more importantly, have access to the required tools to size the relative impact of this potential source of uncertainty on the estimated analyte concentrations. The purpose of this tutorial is to provide a down-to-earth view of rotational ambiguity, by studying in detail a synthetic example mimicking a typical chromatographic-spectral experiment, where a set of calibration samples is joined with an unknown sample having an uncalibrated interference. After explaining the background information needed to understand the origin of the phenomenon, the available tools for the estimation of the feasible MCR-ALS solutions and the derived uncertainty on analyte predictions will be discussed. A multi-component experimental system will also be discussed, stressing the fact that rotational ambiguity uncertainties, however small, should always be estimated and reported.

Sensitivity for Multivariate Calibration Based on Multilayer Perceptron Artificial Neural Networks.

The use of machine learning for multivariate spectroscopic data analysis in applications related to process monitoring has become very popular since non-linearities in the relationship between signal and predicted variables are commonly observed. In this regard, the use of artificial neural networks (ANN) to develop calibration models has demonstrated to be more appropriate and flexible than classical multivariate linear methods. The most frequently reported type of ANN is the so-called multilayer perceptron (MLP). Nevertheless, the latter models still lack a complete statistical characterization in terms of prediction uncertainty, which is an advantage of the parametric counterparts. In the field of analytical calibration, developments regarding the estimation of prediction errors would derive in the calculation of other analytical figures of merit (AFOMs), such as sensitivity, analytical sensitivity, and limits of detection and quantitation. In this work, equations to estimate the sensitivity in MLP-based calibrations were deduced and are here reported for the first time. The reliability of the derived sensitivity parameter was assessed through a set of simulated and experimental data. The results were also applied to a previously reported MLP fluorescence calibration methodology for the biopharmaceutical industry, yielding a value of sensitivity ca. 30 times larger than for the univariate reference method.

Initialization effects in two-component second-order multivariate calibration with the extended bilinear model.

Bilinear decomposition of an augmented data matrix is usually complicated by the phenomenon of rotational ambiguity. If the latter is significant, quantitative and qualitative information of the recovered profiles may be less useful. Although constraints can reduce the extent of feasible regions and the degree of rotational ambiguity, the estimation of initial parameters to start the decomposition is an important phase in multivariate curve resolution-alternating least-squares (MCR-ALS) studies. Dealing with a bilinear decomposition of an augmented data matrix where rotational ambiguity persists, the question remains whether it is possible to still develop a successful calibration protocol. Indeed, literature reports indicate that various analytical systems have been experimentally developed, in which substantial rotational ambiguity exists, yet the experimental results confirmed that accurate analyte quantitation was possible. In this research, we further investigate on the effect of the initialization step for a two-component second-order multivariate calibration with the extended bilinear model. It is shown that the selection strategy based on the so-called purest variables can be helpful in achieving a correct profile resolution, depending on which data direction it is applied. Finally, some data-driven guidelines for analytical chemists are suggested, to identify the potential degree of rotational ambiguity and the correct choice of the initialization strategy.

A New Parameter for Measuring the Prediction Uncertainty Produced by Rotational Ambiguity in Second-Order Calibration with Multivariate Curve Resolution.

Multivariate curve resolution-alternating least-squares (MCR-ALS) is the model of choice when dealing with matrix data that cannot be arranged into a trilinear three-way array, that is, mostly from chromatographic origin with spectral detection. A range of feasible solutions may be found in MCR studies, due to the phenomenon of rotational ambiguity associated with bilinear decompositions of matrices. The application of chemically driven constraints is vital to achieving an adequate solution and minimizing the degree of rotational ambiguity present in the system. However, when studying complex samples, it may not be possible to recover unique solutions, even under the application of proper constraints. In such cases, it is important to be able to assess the propagation of rotation uncertainty to the estimated analyte concentrations, which stems from the existence of a finite range of feasible solutions. In this work, we present a new analytical parameter to estimate the potential uncertainty in analyte prediction brought about by rotational ambiguity, in the form of an associated root-mean-square error, named RMSERA. The proposed parameter comes in the form of a range of values, whose limits are δRA/(12)1/2 and δRA/(3)1/2, with δRA being defined as the difference between the maximum and minimum values of the analyte concentration that would be predicted by the MCR model from its concentration profiles lying in the range of feasible solutions, and corresponding to maximum and minimum area, respectively. We support our proposal on extensive simulations for systems of varying composition, and demonstrate its application on experimental data aimed at the determination of four pollutants in environmental water samples.

Why should the pharmaceutical industry claim for the implementation of second-order chemometric models-A critical review.

Today, pharmaceutical products are submitted to a large number of analytical tests, planned to either ensure or construct their quality. The official methods of analysis used to perform these determinations are very different in nature, but almost all demand the intensive use of reagents and manpower as major drawbacks. Thus, analytical development is continuously evolving to find fast and smart approaches. First-order chemometric models are well-known in the pharmaceutical industry, and are extensively used in many fields. Such is the impact of chemometric models that regulatory agencies include them in guidelines and compendia. However, the mention or practical application of higher-order models in the pharmaceutical industry is rather scarce. Herein, we try to bring a brief introduction to chemometric models and useful literature references, focusing on higher-order chemometric models (HOCM) applied to reduce manpower, reagent consumption, and time of analysis, without sacrificing accuracy or precision, while gaining selectivity and sensitivity. The advantages and drawbacks of HOCM are also discussed, and the comparison to first-order chemometric models is also analyzed. Along the work, HOCM are evidenced as a powerful tool for the pharmaceutical industry; moreover, its implementation is shown during several steps of production, such as identification, purity test and assay, and other applications as homogeneity of API distribution, Process Analytical Technology (PAT), Quality by Design (QbD) or natural product fingerprinting. Among these topics, qualitative and quantitative applications were covered. Experimental approaches of chemometrics coupled to several analytical techniques such as UV-vis, fluorescence and vibrational spectroscopies (NIR, MIR and Raman), and other techniques as hyphenated-chromatography and electrochemical techniques applied to production and analysis are discussed throughout this work.

On second-order calibration based on multivariate curve resolution in the presence of highly overlapped profiles.

Multivariate curve resolution has been applied to both simulated and experimental data sets where high or even complete overlapping occurs between component profiles in one data mode. It is shown that rotational ambiguity exists in the bilinear decomposition of the augmented data matrices built with second-order data for pure analyte standards and test samples containing uncalibrated interferents. However, even in the presence of rotational ambiguity, initialization based on the so-called purest variables in one of the data modes may allow one to develop analytical protocols with reasonable statistical indicators for the prediction of the analyte of interest. In one of the explored experimental systems, the analyte ciprofloxacin was determined in the presence of the interferent salicylate, measuring time decay-luminescence matrix data. The average prediction error was 0.02 mg L-1 in the test set, corresponding to a relative error of ca. 8%. In the second system, capillary electrophoresis with UV detection was employed to determine ciprofloxacin in aqueous samples in the presence of other fluoroquinolones, achieving analyte recoveries in the range 101-113%. Although further theoretical work may still be needed, the present analysis of the feasible component profiles after bilinear decomposition provides some clues to interpret the phenomenon.

Interpretation of matrix chromatographic-spectral data modeling with parallel factor analysis 2 and multivariate curve resolution.

Parallel factor analysis 2 (PARAFAC2) is still being advocated for the processing of second-order chromatographic-spectral data, both for qualitative and quantitative applications. However, neither classical PARAFAC2 nor the newly developed flexible non-negative NN-PARAFAC2 version can adequately model these data in a general situation. In quantitative analysis, considerable bias may result in the estimation of analyte concentrations, due to the fact that both PARAFAC2 models apply an artificial constraint to the retrieved profiles, requiring constant cross-product, i.e., constant overlapping, between all pairs of component elution profiles in all samples. This only occurs under limited conditions. In this report, simulations help to understand, visualize and interpret these PARAFAC2 features. Experimental data are also studied concerning the determination of a fluoroquinolone antibiotic in bovine liver samples by liquid chromatography with multi-wavelength fluorescence detection. Both for simulated and experimental data, the PARAFAC2 versions provide poor analytical results, while correct data processing and reasonable analytical indicators can be achieved using multivariate curve resolution - alternating least-squares (MCR-ALS). For the simulated data sets, root mean square errors/relative errors of prediction were 0.01 concentration units/2% for MCR-ALS, compared to 0.02-0.06 units/4-12% for both PARAFAC2 and NN-PARAFAC2. For the experimental data sets, they were 0.025 µg mL-1/11% for MCR-ALS, 0.09 µg mL-1/40% for PARAFAC2 and 0.16 µg mL-1/71% for NN-PARAFAC2, with average recoveries (standard deviation) of 91(14)%, 185(135)% and 69(35)% respectively.

Contribution to second-order calibration based on multivariate curve resolution with and without previous chromatographic synchronization.

Rotational ambiguity in the bilinear solutions provided by multivariate curve resolution - alternating least-squares (MCR-ALS) leads to an additional source of uncertainty in the estimation of analyte concentrations by second-order multivariate calibration. The phenomenon is particularly important when measuring matrix instrumental data derived from liquid chromatography with spectral detection, where elution time profiles usually vary from sample to sample both in position and shape. This makes the data non-trilinear, precluding the use of unique trilinear decomposition models. The present report compares some analytical results achieved by: (1) the usual MCR-ALS analysis of augmented matrices built from raw matrix data and (2) a previously reported procedure based on synchronizing the MCR-ALS elution time profiles using correlation optimized warping (COW), reconstructing the augmented matrix with the spectra and the aligned chromatograms, and then applying MCR-ALS again with the trilinearity constraint, leading to unique solutions, which is possible because the warping process restores the trilinearity of the data. We show that alternative (2) does not solve the rotational ambiguity issues and artificially modifies the original data, without significant improvements in analytical performance. In the simulated systems, the best average errors for alternative (1) were about 2%, whereas for alternative (2) they were in the range 4-11%. For the experimental system, the corresponding errors were 2-3% and 3-4% respectively, i.e. with no significant improvement in going to alternative (2). All efforts should be directed to reduce the degree of rotational ambiguity by applying a full battery of chemically reasonable constraints.

Analytical chemistry assisted by multi-way calibration: A contribution to green chemistry.

A review is presented of recent multi-way calibration protocols involving three-, four- and five-way data. A brief description of the various data structures and processing models is shown, with emphasis on model selection based on the matching between the data structure and the physicochemical model assumptions. Calibration research works are then discussed, classified according to the type of measured instrumental data and model/algorithm selection.