Multivariate calibration applied to simultaneous chemiluminescence determination of cobalt and chromium

The simultaneous determination of chromium and cobalt in water samples has been studied. Chemiluminescence registers based on the luminol-hydrogen peroxide reaction have obtained by a batch procedure. PLS algorithms have employed to model the time-response (formation and destruction of emitter).The influence of the presence of two metals and the non-linearity relationship between response and concentration have been evaluated in the signal. Different experimental designs and the selection of variables have been tested. The calibration set has been selected based on two criteria: unicomponent and/or bicomponent standard solutions and the slope calculated from linear univariate calibration. The response has been modelled providing high percentages of explained variance, robust models and low prediction errors.The proposed methodology has been validated using test standard solutions and a standard reference material of fresh water. Accurate results have proved the advantages of this method for the simultaneous determination of chromium and cobalt in water samples.     

Use of multivariate curve resolution for determination of chromium in tanning samples using sequential injection analysis

We report a method for determining total chromium in tanning samples using sequential injection analysis (SIA) with a diode-array spectrophotometric detector. With a suitable analytical sequence CrO₄^2– is converted to Cr₂O₇^2– inside the tubes of the SIA system, after total oxidation of chromium(III). A data matrix is obtained and analysed by several chemometric techniques based on multivariate analysis: principal components analysis, simple-to-use interactive self-modelling mixture analysis, and multivariate curve resolution-alternating least-squares. We studied several samples from different stages of a tanning process. Two of these samples were easily oxidized but the others needed more extreme conditions. The analytical sequence prepared, which was based on obtaining a pH gradient and used H₂SO₄ as reagent, is valid and independent of the level of oxidation needed for the sample. We established a calibration model and evaluated the figures of merit. In some samples we found interferents. With this method the amounts of chromium in each sample were quantified and the results were statistically similar to those obtained by use of the reference method, atomic absorption spectrometry.     

Factorial design for optimising chromium determination in tanning wastewater

A totally automatized procedure for determining chromium by sequential injection analysis (SIA) linked to multivariate curve resolution with alternating least squares (MCR-ALS) is proposed. With this system Cr(III) is oxidised to chromate (Cr(VI)) and this form is then converted to dichromate in order to obtain second order data. The experimental design method was used to establish the best conditions. The identification of the most influential factors was validated using ANOVA tests. We used this method to successfully analyse total chromium in several aqueous tannery samples from various steps of a tanning process. The results from this method and those from the atomic absorbance spectroscopy (AAS) method are comparable. Sample frequency was 30 samples h^− 1.     

First- and second-order multivariate calibration applied to biological samples: determination of anti-inflammatories in serum and urine

First- and second-order multivariate calibration of fluorescence data have been compared as regards the determination of anti-inflammatories and metabolites in the biological fluids serum and urine. The simultaneous resolution of naproxen-salicylic acid mixtures in serum and naproxen-salicylic acid-salicyluric acid mixtures in urine was accomplished and employed for a discussion of the relative advantages of the applied chemometric tools. The analysis of second-order fluorescence excitation-emission matrices was performed using iteratively reweighted generalized rank annihilation method (IRGRAM), parallel factor analysis (PARAFAC), and self-weighted alternating trilinear decomposition (SWATLD). The results were compared with first-order fluorescence emission data analyzed with partial least-squares regression (PLS). In all cases, the performance of the methods was improved through the formation of inclusion complexes of the analytes with beta-cyclodextrin. The concentration ranges in which the analytes could be determined were as follows: naproxen, 0-250 ng mL(-1) in serum and 0-200 ng mL(-1) in urine; salicylic acid, 0-500 ng mL(-1) in serum and 0-300 ng mL(-1) in urine, and salicyluric acid, 0-300 ng mL(-1) in urine.     

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.     

Second-order multivariate calibration procedures applied to high-performance liquid chromatography coupled to fast-scanning fluorescence detection for the determination of fluoroquinolones

Different second-order multivariate calibration algorithms, namely parallel factor analysis (PARAFAC), N-dimensional partial least-squares (N-PLS) and multivariate curve resolution-alternating least-squares (MCR-ALS) have been compared for the analysis of four fluoroquinolones in aqueous solutions, including some human urine samples (additional four fluoroquinolones were simultaneously determined by univariate calibration). Data were measured in a short time with a chromatographic system operating in the isocratic mode. The detection system consisted of a fast-scanning spectrofluorimeter, which allows one to obtain second-order data matrices containing the fluorescence intensity as a function of retention time and emission wavelength. The developed approach enabled us to determine eight analytes, some of them with overlapped profiles, without the necessity of applying an elution gradient, and thus significantly reducing both the experimental time and complexity. The study was employed for the discussion of the scopes of the applied second-order chemometric tools. The quality of the proposed technique coupled to each of the evaluated algorithms was assessed on the basis of the figures of merit for the determination of fluoroquinolones in the analyzed water and urine samples. Univariate calibration of four analytes led to limits of detection in the range 20–40 ng mL⁻¹ and root mean square errors for the validation samples in the range 30–60 ng mL⁻¹ (corresponding to relative prediction errors of 3–8%). The ranges for second-order multivariate calibration (using PARAFAC and N-PLS) of the remaining four analytes were: limit of detection, 2–8 ng mL⁻¹, root mean square errors, 3–50 ng mL⁻¹ and relative prediction errors, 1–5%.     

Heteroscedastic controlled calibration model applied to analytical chemistry

In chemical analyses performed by laboratories, one faces the problem of determining the concentration of a chemical element in a sample. In practice, one deals with the problem using the so‐called linear calibration model, which considers that the errors associated with the independent variables are negligible compared with the former variable. In this work, a new linear calibration model is proposed assuming that the independent variables are subject to heteroscedastic measurement errors. A simulation study is carried out in order to verify some properties of the estimators derived for the new model and it is also considered the usual calibration model to compare it with the new approach. Three applications are considered to verify the performance of the new approach. Copyright © 2010 John Wiley & Sons, Ltd.     

A multivariate calibration procedure for the tensammetric determination of detergents

A multivariate calibration procedure based on singular value decomposition (SVD) and the Ho-Kashyap algorithm is used for the tensammetric determination of the cationic detergents Hyamine 1622, benzalkonium chloride (BACl), N-cetyl-N,N,N-trimethylammonium bromide (CTABr) and mixtures of CTABr and BACl. The sensitivity and accuracy depend strongly on the nature of the detergent. Acceptable accuracy is obtained with a two-step calculation procedure in which calibration constants for the total concentration range of interest are used to guide the choice of a more specific set of calibration constants which are valid for a much smaller concentration span. For Hyamine 1622, concentrations in the range 5 × 10^?6?2 × 10^?4 M could be determined with an accuracy of ± 10^?6 M. For CTABr, these numbers were 3 × 10^?6?2 × 10^?4 M and ± 5 × 10^?7 M; for BACl, they were 2 × 10^?3?9 × 10^?2 g l^?1 and ± 1 × 10^?3 g l^?1. In the mixtures of CTABr and BACl, the accuracies were ± 3 × 10^?6 M and × 1 × 10^?3 g l^?1, respectively.     

Second-order and higher-order multivariate calibration methods applied to non-multilinear data using different algorithms

We discuss and evaluate the current state of second-order and higher-order multivariate calibration methods devoted to the determination of compounds in non-multilinear data systems. We examine possible causes of multilinearity deviations:

(1)

a non-linear relationship between signal and analyte concentration;

(2)

a signal for a given sample that is non-multilinear; and,

(3)

component profiles that are not constant across the different samples.

We discuss the advantages and the limitations of the algorithms available to cope with these different situations.The review covers relevant analytical problems found in samples of environmental and biological interest, highlighting some significant examples, and evaluating the advantages and the limitations of the different algorithms available.     

Multivariate standardisation for non-linear calibration range in the chemiluminescence determination of chromium

Multivariate standardisation is proposed for the successful chemiluminescence determination of chromium based on luminol-hydrogen peroxide reaction. In an extended concentration range, non-linear calibration model is needed. The studied instrumental situations were different detection cells, instruments, assemblies, time and their possible combinations. Chemiluminescence kinetic registers have been transferred using piecewise direct standardisation (PDS) method. The optimisation of transfer parameters has been carried out based on the prediction residual error criteria.Non-linear principal component regression (NL-PCR) and non-linear partial least square regression (NL-PLS) were chosen for modelling the relationship signal-concentration of transferred registers.Good accuracy and precision were obtained for water samples. The concentrations of chromium were statistically in agreement with reference method values and with recovery studies. Therefore, it is possible to transfer chemiluminescence curves without loosing ability of prediction, even the presence of a non-linear behaviour.     

A photoplate calibration technique applied to the determination of hafnium in zirconium by SSMS

A photoplate calibration procedure is suggested for spark source mass spectrometry /SSMS/ with photoplate detection. The technique uses the Churchill two-line method applied to the two stable isotopes of copper. The calibration curve thus obtained is split into fragments and each fragment is approximated by a polynomial. The method was applied for the quantitative determination of Hf as impurity in zirconium sponge obtained from a pilot plant dedicated to the depletion of the hafnium content in zirconium by fractional crystallization.     

Use of glyoxal in production of a composite chromium tanning agent

Conditions in which a composite chromium tanning agent can be obtained in the presence of glyoxal were studied. It was found that the expenditure of the aldehyde and sulfuric acid affects the reduction kinetics of hexavalent chromium. Spectrophotometry and conductometry were used to examine the composition of composite tanning agents. It was shown that chromaldehyde tanning agents can be applied in manufacture of leather and fur.     

A study of robustness with multivariate calibration. Application to the polarographic determination of benzaldehyde

A procedure to evaluate the robustness of an analytical method when there are changes in some experimental variables, when using multivariate calibration, is proposed. The procedure consists of analysing the root mean square error of prediction (RMSEP) as a response to a Plackett–Burman experimental design, through which the influence of several experimental factors on the prediction capability of the multivariate partial least squares (PLS) models built is studied. Two different ways of analysing the experimental design response are considered: establishing the residual variance with replicates and using Lenth's method. The proposed methodology has been applied to estimate the robustness of the polarographic determination of benzaldehyde when PLS calibration is used.     

Spectrophotometric determination of organic dye mixtures by using multivariate calibration

The simultaneous determination of organic dye mixtures by using spectrophotometric methods is a difficult problem in analytical chemistry, due to spectral interferences. By using multivariate calibration methods such as partial least-squares regression (PLSR), it is possible to obtain a model adjusted to the concentration values of the mixtures used in the calibration stage. In this study, the calibration model is based on absorption spectra in the 350-650-nm range for a set of 16 different mixtures of reactive red 195, reactive yellow 145 and reactive orange 122 dyes, and made the determination of the dye concentrations possible in a validation set with significantly greater accuracy than the conventional univariate calibration method. By using the developed model it was possible to monitor the decolorization kinetic of one dye (reactive orange 122), when the mixture of the three dyes was previously submitted to an ozonation process.     

Simultaneous spectrophotometric determination of diuretics by using multivariate calibration methods

The wavelength range and number of factors used in partial least-squares (PLS) calibration for the resolution of the dihydralazine (DHZ)-hydrochlorothiazide (HCT) binary mixture and the dihydralazine-hydrochlorothiazide-reserpine ternary mixture were optimized in terms of the relative standard error (R.S.E.) and relative mean standard error (R.M.S.E.). Under the optimum conditions thus established, synthetic mixtures of the analytes can be resolved with errors and relative standard deviations (R.S.D) less than 4.5 and 1.0%, respectively. The ensuing method, which was validated by comparison with high performance liquid chromatography (HPLC), also gives good results with real samples (pharmaceutical preparations).     

Four-way calibration applied to the simultaneous determination of folic acid and methotrexate in urine samples

First-, second- and third-order calibration methods were investigated for the simultaneous determination of folic acid and methotrexate. The interest in the determination of these compounds is related to the fact that methotrexate inhibits the body’s absorption of folic acid and prolonged treatment with methotrexate may lead to folic acid deficiency, and to the use of folic acid to cope with toxic side effects of methotrexate. Both analytes were converted into highly fluorescent compounds by oxidation with potassium permanganate, and the kinetics of the reaction was continuously monitored by recording the kinetics curves of fluorescence emission, the evolution with time of the emission spectra and the excitation–emission matrices (EEMs) of the samples at different reaction times. Direct determination of mixtures of both drugs in urine was accomplished on the basis of the evolution of the kinetics of EEMs by fluorescence measurements and four-way parallel-factor analysis (PARAFAC) or multiway partial least squares (N-PLS) chemometric calibration. The core consistency diagnostic (CORCONDIA) was employed to determine the correct number of factors in PARAFAC and the procedure converged to a choice of three factors, attributed to folic acid, methotrexate and to the sum of fluorescent species present in the urine.      

Capillary electrophoresis speciation of chromium in leather tanning liquor

We present a method for the speciation of chromium by capillary electrophoresis. Cr(III) was complexed with diethylenetriaminepentaacetic acid (DTPA) to form a negatively charged complex. Using 20 mM phosphate buffer of pH 8 containing 0.5 mM tetradecyltrimethylammonium hydroxide (TTAOH) at a separation voltage of -15 kV, both forms of chromium CrDTPA(2-) and CrO(4) (2-) were separated in less than 6 min. Direct UV detection at 214 nm was used. The effect of the presence of interfering ions was investigated. The application of the developed method to speciation of chromium in tanning liquor is demonstrated. The obtained results have shown a good correlation with those of flame atomic absorbance spectrometry (FAAS), inductively coupled plasma-mass spectrometry (ICP-MS) and UV/VIS spectrophotometry.     

Employing multivariate calibration for the determination of radionuclides by inductively coupled plasma-mass spectrometry

A method for the simultaneous ICP-MS determination of α- and β-emitting radionuclides in acid digested samples of concrete without further sample pretreatment is presented. Spectral and non-spectral interferences are corrected for by combining systematic internal standardization with bilinear multivariate calibration. Consequently, especially for radionuclides with long half-lives, ICP-MS is an alternative to radiometric analytical methods. The optimal multivariate calibration approach is the PLS1-model with preselected variables.     

Sequential injection wetting film extraction applied to the spectrophotometric determination of chromium(VI) and chromium(III) in water

The spectrophotometric determination of Cr(VI) and Cr(III) via sequential injection was used to demonstrate the sensitivity enhancement provided by a newly developed wetting film extraction system. The reaction product of Cr(VI) with 1,5-diphenylcarbazide was ion-paired with perchlorate and extracted into an organic wetting film consisting of octanol and 4-methyl-2-pentanone on the inner wall of a Teflon tube. The wetting film, with the extracted analyte, was then eluted with 100 mul acetonitrile and the analyte determined spectrophotometrically at 546 nm. Important optimized parameters were the selection of wetting film and elution solvents, the flow rate, the length and diameter of the extraction coil and the conditions for the formation of the ion paired chelate. Cr(III) was previously oxidized to Cr(VI) and calculated as the difference between total Cr and Cr(VI). An enrichment factor of 25 and a detection limit of 2.0 mug l(-1) Cr(VI) were achieved with a sampling frequency of 17 h(-1). The calibration curve was linear up to 100 mug l(-1) Cr(VI) (r = 0.999). The relative standard deviations were 2.8 and 2.0% at the 25 and 100 mug l(-1) levels.