Chemometric tools in electroanalytical chemistry: Methods for optimization based on factorial design and response surface methodology

The aim of this paper is to give a brief overview of chemometric techniques based on factorial designs and response surface methodologies used in the optimization of electroanalytical methods. Chemometric techniques have several important advantages over one-way optimization for analytical applications, including a relatively low cost, a reduced number of experiments, and possibilities to evaluate interactions among variables. These techniques also enable the selection of optimal experimental conditions, helping to avoid trivial mistakes during optimization. Despite these facts, chemometric techniques have rarely been applied to electroanalytical data, especially in comparison with their use in spectroscopy. The application of chemometric methods in electroanalytical chemistry has been mostly used for solving overlapping signals, multivariate calibration methods, model identification and optimization of analytical procedures. This review is focused on the latter applications and overviews the role of full or fractional factorial designs (first-order designs), as well as second-order designs, such as central composite, Doehlert and Box-Behnken designs, for optimization of electroanalytical methods. A discussion of chemometric-related advantages is also given for stripping analyses, flow injection systems with amperometric detection, differential pulse voltammetry, square wave voltammetry and electrochemical sensor preparation.     

Strategies for solving matrix effects in the analysis of sulfathiazole in honey samples using three-way photochemically induced fluorescence data

A widely employed compound for honey treatment, sulfathiazole (ST), was determined in commercial honey samples, employing a combination of photochemically induced fluorescence excitation-emission matrices (EEMs) and chemometric processing of the recorded second-order data. Parallel Factor Analysis (PARAFAC) and Self-Weighted Alternating Trilinear Decomposition (SWATLD) methods were used for calibration. An appropriately designed calibration with a set of standards composed of 18 samples, coupled to the use of the second-order advantage offered by the applied chemometric techniques, allowed quantitation of sulfathiazole in spiked commercial honey samples. No previous separation or sample pretreatment steps were required. The results were compared with other calibration methods such as N-PLS and PLS-1 that produced good results on synthetic samples but not on the investigated commercial honey samples.     

Photoinduced spectrofluorimetric determination of fluoroquinolones in human urine by using three- and two-way spectroscopic data and multivariate calibration

Multivariate methods comprise of a group of chemometric tools allowing the analysis of different analytical data, i.e., spectroscopic, chromatographic obtained from multichannel detector systems. Second-way data are widely used in analytical applications in combination with multivariate calibration methods, but three- and higher-way data are yet not as widely applied. In complex biological samples, the employment of the three-way data is of special interest, as they may be combined with methods that exploit the second-order advantage allowing calculating individual concentrations of the analytes of interest in the presence of unknown interferences in untreated samples. A very sensitive and selective method is proposed, by coupling photoinduced fluorescence and multivariate analysis of the three-way data excitation-emission fluorescence matrices (EEMs), of the photoproducts obtained from UV irradiation of three fluoroquinolones: enoxacin (ENO), norfloxacin (NOR) and ofloxacin (OFLO). The application of a previous photoirrradiation process allows the determination of mixtures of ENO, NOR and OFLO, in urine samples at biological levels without sample pretreatments. The resolution ability of N-way partial least squares (N-PLS), parallel factor analysis (PARAFAC) and self weighted alternating trilinear decomposition (SWATLD), is compared with partial least squares (PLS) and unfolded-PLS (U-PLS), in the analysis of ENO, NOR and OFLO in human urine samples.     

A review of multivariate calibration methods applied to biomedical analysis

The determination of the contents of therapeutic drugs, metabolites and other important biomedical analytes in biological samples is usually performed by using high-performance liquid chromatography (HPLC). Modern multivariate calibration methods constitute an attractive alternative, even when they are applied to intrinsically unselective spectroscopic or electrochemical signals. First-order (i.e., vectorized) data are conveniently analyzed with classical chemometric tools such as partial least-squares (PLS). Certain analytical problems require more sophisticated models, such as artificial neural networks (ANNs), which are especially able to cope with non-linearities in the data structure. Finally, models based on the acquisition and processing of second- or higher-order data (i.e., matrices or higher dimensional data arrays) present the phenomenon known as “second-order advantage”, which permits quantitation of calibrated analytes in the presence of interferents. The latter models show immense potentialities in the field of biomedical analysis. Pertinent literature examples are reviewed.     

A review on advanced oxidation processes: From classical to new perspectives coupled to two- and multi-way calibration strategies to monitor degradation of contaminants in environmental samples

This paper offers a critical review from classical to new perspectives of advanced oxidation processes (AOPs) coupled to two- and multi-way calibration strategies based on multivariate curve resolution – alternating least-squares (MCR-ALS) and parallel factory analysis (PARAFAC) with various analytical techniques to monitor the degradation of contaminants in environmental samples. It focuses on the generation of highly reactive hydroxyl (HO•) radicals (classical AOPs with emphasis on Fenton, photo-Fenton and ozonation processes) and emerging reactive sulphate (SO₄^•−) radicals (new perspectives of AOPs) for effective degradation of recalcitrant compounds. Other new perspectives of AOPs were also addressed, namely semiconductor photocatalysis (TiO₂/UV), combination of processes involving at least one AOP (hybrid or single-step processes and sequential or two-step processes), novel advanced electrochemical oxidation technologies (electro-Fenton and electro-photo-Fenton) and nanocatalytic heterogeneous Fenton technology with high specific surface area. Literature reports since 2008 for real applications in the environmental remediation based on AOPs (from classical to new perspectives) coupled to PARAFAC and MCR-ALS with first-, second- and third-order data were reviewed and the improvements obtained were briefly discussed. The two- and multi-way calibration strategies allow one the successful decomposition of first-, second- and third-order data collected from different analytical techniques. Therefore, the respective profiles obtained allowed qualitative (spectral profiles) and quantitative (concentration profiles) analysis of complex samples during the degradation of contaminants through the second-order advantage. Finally, trends of future research directions for AOPs coupled to various analytical techniques and advanced chemometric models were provided.     

A chemometric sensor for determining sulphaguanidine residues in honey samples

The inclusion complex of sulphaguanidine (SGN) in β-cyclodextrin has been investigated. To avoid the problem of the low solubility of β-cyclodextrin in water, solutions of β-cyclodextrin in urea have been used. A 1:1 stoichiometry and an association constant of 450 M⁻¹ have been established for the complex. A new spectrofluorimetric method has been developed for the determination of SGN residues in honey samples. This sulphonamide is widely employed for honey treatment. The method for the determination is based on second-order multivariate calibration, applying parallel factor analysis (PARAFAC). No previous separation or samples pre-treatment were required. The calibration solutions were prepared in water, with concentrations in the range from 0.02 to 0.20 μg mL⁻¹ for SGN. The use of the second-order calibration method in the standard addition mode, using the excitation-emission matrices (EEMs) as analytical signal, allowed its determination in honey samples, even in the presence of interferences, with satisfactory results. The proposed procedure was validated by comparing the obtained results with a HPLC method, with satisfactory results for the assayed method.     

Three-way partial least-squares/residual bilinearization study of second-order lanthanide-sensitized luminescence excitation-time decay data: analysis of benzoic acid in beverage samples

Lanthanide-sensitized luminescence excitation-time decay matrices were employed for achieving the second-order advantage using as chemometric algorithms parallel factor analysis (PARAFAC) and multidimensional partial least-squares with residual bilinearization (N-PLS/RBL). The second-order data were measured for a calibration set of samples containing the analyte benzoic acid in the concentration range from 0.00 to 5.00 mg L⁻¹, for a validation set containing the analyte and the potential interferent saccharin (in the range 0.00–6.00 mg L⁻¹), and for real samples of beverages containing benzoic acid as preservant, saccharin, and other potentially interfering compounds. All samples were treated with terbium(III), trioctylphosphine oxide as a synergistic ligand, and contained a suitable imidazol buffer, in order to ensure maximum intensity of the luminescence signals. The results indicate a slightly better predictive ability of the newly introduced N-PLS/RBL procedure over standard PARAFAC, both in what concerns the comparison with nominal analyte concentrations in the validation sample set and with results provided by the reference high-performance liquid chromatographic technique for the real sample set.     

The role of chemometrics in single and sequential extraction assays: a review. Part II. Cluster analysis, multiple linear regression, mixture resolution, experimental design and other techniques

Single and sequential extraction procedures are used for studying element mobility and availability in solid matrices, like soils, sediments, sludge, and airborne particulate matter. In the first part of this review we reported an overview on these procedures and described the applications of chemometric uni- and bivariate techniques and of multivariate pattern recognition techniques based on variable reduction to the experimental results obtained. The second part of the review deals with the use of chemometrics not only for the visualization and interpretation of data, but also for the investigation of the effects of experimental conditions on the response, the optimization of their values and the calculation of element fractionation. We will describe the principles of the multivariate chemometric techniques considered, the aims for which they were applied and the key findings obtained. The following topics will be critically addressed: pattern recognition by cluster analysis (CA), linear discriminant analysis (LDA) and other less common techniques; modelling by multiple linear regression (MLR); investigation of spatial distribution of variables by geostatistics; calculation of fractionation patterns by a mixture resolution method (Chemometric Identification of Substrates and Element Distributions, CISED); optimization and characterization of extraction procedures by experimental design; other multivariate techniques less commonly applied.     

三维(二阶)算法在液相色谱分析中的应用

使用"垂线法"、"切线法"或"三角形法"等传统方法对液相色谱重叠峰分辨时经常会遇到误差过大的情况,而使用三维(二阶)算法对重叠和拖尾峰分辨可以最大限度地降低这种因几何分割而人为产生的误差。这样改进的色谱解析方法具有自动化程度高、抗干扰能力强、对重叠/拖尾峰定量准确等优点,甚至可以减少样品前处理和色谱条件优化。该方法的核心是基于化学计量学三维(二阶)算法抽取有效信息和建模的思想,三维色谱数据按照对三线性模型的符合程度有"三线性数据"和"非三线性数据"的区别,相应地将三维(二阶)算法分为"三线性算法"和"非三线性算法"。本文综述了近10年来国内外三维(二阶)算法在复杂体系液相色谱分析中的应用进展,侧重于样品前处理、辅助算法、校正算法间的联用和对比等问题。     

Multivariate calibration: What is in chemometrics for the analytical chemist?

Chemometrics has been used for some 30 years but there is still need for disseminating the potential benefits to a wider audience. In this paper, we claim that proper analytical chemistry (1) must in fact incorporate a chemometric approach and (2) that there are several significant advantages of doing so. In order to explain this, an indirect route will be taken, where the most important benefits of chemometric methods are discussed using small illustrative examples. Emphasis will be on multivariate data analysis (for example calibration), whereas other parts of chemometrics such as experimental design will not be treated here. Four distinct aspects are treated in detail: noise reduction; handling of interferents; the exploratory aspect and the possible outlier control. Additionally, some new developments in chemometrics are described.     

The application to wastewaters of chemometric approaches to handling problems of highly complex matrices

This overview covers current chemometric methodologies using second-order advantage to solve problems of analyzing highly complex matrices. Among the existing algorithms, it focuses on those most frequently used (e.g., the standard for second-order approaches to data analysis, PARAFAC (parallel factor analysis), and MCR-ALS (multivariate curve resolution alternating least squares), as well as the most recently implemented BLLS (bilinear least-squares), and U-PLS/RBL (unfolded partial least squares/residual bilinearization)). All of these are based on linear models. The overview also covers ANN/RBL (artificial neural networks followed by residual bilinearization), which achieves the second-order advantage in systems involving non-linear behavior. In addition, the overview deals with the drawbacks of these approaches, as well as other drawbacks that are inherent in the analytical techniques to question.     

Chemometrics in pharmaceutical analysis: an introduction, review, and future perspectives

Chemometrics is the application of statistical and mathematical methods to analytical data to permit maximum collection and extraction of useful information. The utility of chemometric techniques as tools enabling multidimensional calibration of selected spectroscopic, electrochemical, and chromatographic methods is demonstrated. Application of this approach mainly for interpretation of UV-Vis and near-IR (NIR) spectra, as well as for data obtained by other instrumental methods, makes identification and quantitative analysis of active substances in complex mixtures possible, especially in the analysis of pharmaceutical preparations present in the market. Such analytical work is carried out by the use of advanced chemical instruments and data processing, which has led to a need for advanced methods to design experiments, calibrate instruments, and analyze the resulting data. The purpose of this review is to describe various chemometric methods in combination with UV-Vis spectrophotometry, NIR spectroscopy, fluorescence spectroscopy, electroanalysis, chromatographic separation, and flow-injection analysis for the analysis of drugs in pharmaceutical preparations. Theoretical and practical aspects are described with pharmaceutical examples of chemometric applications. This review will concentrate on gaining an understanding of how chemometrics can be useful in the modern analytical laboratory. A selection of the most challenging problems faced in pharmaceutical analysis is presented, the potential for chemometrics is considered, and some consequent implications for utilization are discussed. The reader can refer to the citations wherever appropriate.     

Simultaneous spectrophotometric determination of paracetamol, ibuprofen and caffeine in pharmaceuticals by chemometric methods

In this study, the simultaneous determination of paracetamol, ibuprofen and caffeine in pharmaceuticals by chemometric approaches using UV spectrophotometry has been reported as a simple alternative to using separate models for each component. Spectra of paracetamol, ibuprofen and caffeine were recorded at several concentrations within their linear ranges and were used to compute the calibration mixture between wavelengths 200 and 400 nm at an interval of 1 nm in methanol:0.1 HCl (3:1). Partial least squares regression (PLS), genetic algorithm coupled with PLS (GA-PLS), and principal component-artificial neural network (PC-ANN) were used for chemometric analysis of data and the parameters of the chemometric procedures were optimized. The analytical performances of these chemometric methods were characterized by relative prediction errors and recoveries (%) and were compared with each other. The GA-PLS shows superiority over other applied multivariate methods due to the wavelength selection in PLS calibration using a genetic algorithm without loss of prediction capacity. Although the components show an important degree of spectral overlap, they have been determined simultaneously and rapidly requiring no separation step. These three methods were successfully applied to pharmaceutical formulation, capsule, with no interference from excipients as indicated by the recovery study results. The proposed methods are simple and rapid and can be easily used in the quality control of drugs as alternative analysis tools.     

Fluorescence determination of metoprolol in human plasma by trilinear decomposition-based calibration techniques

In this study a new spectrofluorimetric method for the direct determination of metoprolol in human plasma is presented and discussed. It is based on the use of fluorescence excitation–emission matrices (EEMs) and second-order calibration performed with parallel factor analysis (PARAFAC) or alternating trilinear decomposition (ATLD). This methodology enables accurate and reliable discrimination of the analyte signal, even in the presence of unknown and uncalibrated fluorescent component(s), which is often referred to as the second-order advantage. No separation or sample pretreatment steps were required. Satisfactory results were obtained. Metoprolol recoveries in plasma were determined as 87±2% and 90±4% with PARAFAC and ATLD, respectively. All RSD values of intra- and interday assays were below 5%. Figure A three-dimensional plot of EEMs for a plasma sample and metoprolol solution     

Partial least-squares with residual bilinearization for the spectrofluorimetric determination of pesticides. A solution of the problems of inner-filter effects and matrix interferents

This paper demonstrates for the first time the power of a chemometric second-order algorithm for predicting, in a simple way and using spectrofluorimetric data, the concentration of analytes in the presence of both the inner-filter effect and unsuspected species. The simultaneous determination of the systemic fungicides carbendazim and thiabendazole was achieved and employed for the discussion of the scopes of the applied second-order chemometric tools: parallel factor analysis (PARAFAC) and partial least-squares with residual bilinearization (PLS/RBL). The chemometric study was performed using fluorescence excitation-emission matrices obtained after the extraction of the analytes over a C18-membrane surface. The ability of PLS/RBL to recognize and overcome the significant changes produced by thiabendazole in both the excitation and emission spectra of carbendazim is demonstrated. The high performance of the selected PLS/RBL method was established with the determination of both pesticides in artificial and real samples.     

Determination of vinegar acidity by attenuated total reflectance infrared measurements through the use of second-order absorbance-pH matrices and parallel factor analysis

Univariate (zero-order), multivariate (first-order) and multiway (second-order) calibrations were assayed for the determination of vinegar acidity using a mechanized procedure based upon vibrational spectroscopy and the emerging multicommutation methodology. The second-order methodology relies on the use of a flow system based on multicommutation and binary sampling. The flow network comprises a set of three-way solenoid valves, computer-controlled to provide facilities to handle the sample and to generate a time-dependent pH gradient using two carrier solutions. The procedure is based on the volumetric fraction variation approach that maintains the same volume of sample solution and dynamically varies its pH. The analysis of second-order absorbance-pH matrices was performed using parallel factor analysis (PARAFAC). Results were compared with first-order absorbance data analyzed with linear calibration and partial least squares regression (PLS) and they were employed for a discussion of the relative advantages of the applied chemometric tools. As excellent accuracy is obtained without the need of any sample pre-treatment, the procedure can be fully mechanized (i.e., by means of an auto-sampler device). Accuracy of the different strategies assayed was assessed by comparing the results achieved with those obtained by titration reference procedure.     

Chemometric determination of the length distribution of single walled carbon nanotubes through optical spectroscopy

Current synthesis methods for producing single walled carbon nanotubes (SWCNTs) do not ensure uniformity of the structure and properties, in particular the length, which is an important quality indicator of SWCNTs. As a result, sorting SWCNTs by length is an important post-synthesis processing step. For this purpose, convenient analysis methods are needed to characterize the length distribution rapidly and accurately. In this study, density gradient ultracentrifugation was applied to prepare length-sorted SWCNT suspensions containing individualized surfactant-wrapped SWCNTs. The length of sorted SWCNTs was first determined by atomic force microscope (AFM), and their absorbance was measured in ultraviolet-visible near-infrared (UV-vis-NIR) spectroscopy. Chemometric methods are used to calibrate the spectra against the AFM-measured length distribution. The calibration model enables convenient analysis of the length distribution of SWCNTs through UV-vis-NIR spectroscopy. Various chemometric techniques are investigated, including pre-processing methods and non-linear calibration models. Extended inverted signal correction, extended multiplicative signal correction and Gaussian process regression are found to provide good prediction of the length distribution of SWCNTs with satisfactory agreement with the AFM measurements. In summary, spectroscopy in conjunction with advanced chemometric techniques is a powerful analytical tool for carbon nanotube research.     

Interference-free determination of Sudan dyes in chilli foods using second-order calibration algorithms coupled with HPLC-DAD

This paper presents a new method for the determination of Sudan dyes contained in hot chilli samples. The method employs second-order calibration algorithms to handle the recorded data. The second-order calibration algorithms are based on the popular parallel factor analysis (PARAFAC), alternating trilinear decomposition (ATLD) and self-weighted alternating trilinear decomposition (SWATLD), respectively. These chemometric methodologies have the second-order advantage, which is the ability to get accurate concentration estimates of interested analytes even in the presence of uncalibrated interfering components. The results on a set of spiked chilli test shows that low contents of Sudan I and Sudan II in complex chilli mixtures can be accurately determined using the new method. The sample preparation was based on solvent extraction, and internal standard was not required. Quantification was carried out with simple mobile phase.     

A novel second-order standard addition analytical method based on data processing with multidimensional partial least-squares and residual bilinearization

In the presence of analyte-background interactions and a significant background signal, both second-order multivariate calibration and standard addition are required for successful analyte quantitation achieving the second-order advantage. This report discusses a modified second-order standard addition method, in which the test data matrix is subtracted from the standard addition matrices, and quantitation proceeds via the classical external calibration procedure. It is shown that this novel data processing method allows one to apply not only parallel factor analysis (PARAFAC) and multivariate curve resolution-alternating least-squares (MCR-ALS), but also the recently introduced and more flexible partial least-squares (PLS) models coupled to residual bilinearization (RBL). In particular, the multidimensional variant N-PLS/RBL is shown to produce the best analytical results. The comparison is carried out with the aid of a set of simulated data, as well as two experimental data sets: one aimed at the determination of salicylate in human serum in the presence of naproxen as an additional interferent, and the second one devoted to the analysis of danofloxacin in human serum in the presence of salicylate.     

The maintenance of the second-order advantage: second-order calibration of excitation-emission matrix fluorescence for quantitative analysis of herbicide napropamide in various environmental samples

A rapid non-separative spectrofluorometric method based on the second-order calibration of excitation-emission matrix (EEM) fluorescence was proposed for the determination of napropamide (NAP) in soil, river sediment, and wastewater as well as river water samples. With 0.10 mol L⁻¹ sodium citrate-hydrochloric acid (HCl) buffer solution of pH 2.2, the system of NAP has a large increase in fluorescence intensity. To handle the intrinsic fluorescence interferences of environmental samples, the alternating penalty trilinear decomposition (APTLD) algorithm as an efficient second-order calibration method was employed. Satisfactory results have been achieved for NAP in complex environmental samples. The limit of detection obtained for NAP in soil, river sediment, wastewater and river water samples were 0.80, 0.24, 0.12, 0.071 ng mL⁻¹, respectively. Furthermore, in order to fully investigate the performance of second-order calibration method, we test the second-order calibration method using different calibration approaches including the single matrix model, the intra-day various matrices model and the global model based on the APTLD algorithm with nature environmental datasets. The results showed the second-order calibration methods also enable one or more analyte(s) of interest to be determined simultaneously in the samples with various types of matrices. The maintenance of second-order advantage has been demonstrated in simultaneous determinations of the analyte of interests in the environmental samples of various matrices.