Linear PLS regression to cope with interferences of major concomitants in the determination of antimony by ETAAS

Abstract

Most heavy metals are present in trace concentrations in many matrices whereas concomitants are, generally, several orders of magnitude higher. Thus, when Sb was determined in water samples by electrothermal atomic absorption spectrometry (ETAAS), typical major concomitant ions Ca²⁺, Fe³⁺, Na⁺, Mg²⁺, Cl⁻, PO₄³⁻ and SO₄²⁻ induced displacement, depletion and division of its atomic peak. These interferences were handled with partial least squares regression (PLS). Plackett–Burman experimental designs were implemented to develop the calibration matrix and assess which concomitants modified the atomic signal the most. Despite the concentration-dependent effects induced by the concomitants, linear PLS was a reliable way to predict the concentration of Sb in aqueous samples (standard error of prediction = 1.44 ng mL⁻¹). Polynomial PLS regression was also studied but it did not outperform the linear models. The multivariate-derived figures of merit were calculated: sensitivity (0.014 absorbance/(ng mL⁻¹)), characteristic mass (6.2 pg) and selectivity (using the net analyte signal concept, 83%); limit of detection (considering 5% of type-α and type-β risks, 5.6 ng mL⁻¹) and quantification (10.6 ng mL⁻¹), following recent IUPAC and ISO guidelines. The method was validated studying its robustness to current ETAAS problems and analysing several certified reference waters.

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Introduction

The World Health Organization included Sb in its guidelines for materials in contact with drinking water (20 µg L⁻¹).¹ The low concentration of Sb in the Earth’s crust (0.2–1 µg g⁻¹)² makes its natural input insignificant compared to the anthropogenic one, as many industrial processes use Sb compounds (e.g. manufacture of textiles, and glass products).³ Antimony in airborne samples was attributed mainly to coal and fuel combustion, pyrometallurgical Cu–Ni-based metal production, incinerators^2,4 and road traffic.⁵ Following that, Sb might become a potential source of concern. Although few studies dealt with Sb determination in soils and sediments, Cal-Prieto et al.⁶ proposed it as a suitable tracer of the anthropogenic influence in urban soils and marine sediments close to urban areas.

Despite electrothermal atomic absorption spectrometry (ETAAS) being a suitable and widely applied technique for analyzing trace metals, it can be severely restrained by concomitants (whose concentrations may be several orders of magnitude higher than that of the analyte) which can seriously affect precision and trueness. A good example is the determination of Cr by ETAAS in presence of Fe³⁺ in acid extracts of soils⁷ where concentrations of Fe³⁺ above 7.5 µg mL⁻¹ altered significantly (>15%) the signal. Another study⁸ proved that the determination of Sb in aqueous solutions was affected by Ca²⁺, Fe³⁺, Mg²⁺, Na⁺, Ni²⁺, CO₃²⁻, F⁻, PO₄³⁻, and SO₄²⁻.

Classical optimization in ETAAS implies proper temperature programs (the stabilized temperature platform furnace concept, STPF, is broadly applied⁹) and testing several modifiers (each at different concentrations) and their combinations (also at different ratios). This is time-consuming and expensive (graphite tubes, reagents, modifiers, etc.) and it may happen that the final working range becomes limited. A less time- and labor-intensive, cheap and efficient alternative is to model the signals of analyte standards (including concomitants) using multivariate calibration. Although this requires standards containing the most relevant interferences, such models are usually powerful and the analysis of unknown samples is really fast. Previous applications of multivariate calibration in this field are scarce and they include the use of ordinary multivariate linear regression (MLR) to determine several metals in preconcentrated sea water by ETAAS;^10–11 the use of backpropagation artificial neural networks (ANN) combined with flame AAS data¹² and the use of ANN to extend the calibration range to quantify high concentrations of Cd in drinking waters by ETAAS.¹³ Results were comparable to those from the standard additions method, but the method was faster. Main objections to these methodologies are that the MLR contains linear, quadratic and cross-product terms, not easy to explain chemically, and that ANNs models can not be interpreted. On the contrary, partial least squares regression (PLS) yields models that are easier to understand and that may constitute suitable, fast and convenient alternatives to cope with chemical and spectral interferences in ETAAS.^14–16 A recent example studied the interferences caused by a major metal, Fe³⁺, when determining another trace metal, Cr.¹⁷ There, three main typical ETAAS interferences (peak-shift, peak-enhancement /depletion and increased random noise) were simulated and satisfactorily handled by PLS.

Here several major ubiquitous concomitants present in natural waters (Ca²⁺, Fe³⁺, Na⁺, Mg²⁺, Cl⁻, PO₄³⁻ and SO₄²⁻) are considered simultaneously in order to quantify trace amounts of Sb (it had previously been reported that they interfered with Sb determination in aqueous samples⁸). In general, concomitant concentrations are several orders of magnitude higher than the analyte; as an example, average gross values for (non or slightly polluted) river waters sampled along A Coruña (Galicia, N.W. Spain) were:¹⁸ 5 mg Ca²⁺ L⁻¹; 0.4 mg Fe³⁺ L⁻¹, 9 mg Na⁺ L⁻¹, 5 mg Mg²⁺ L⁻¹, 15 mg Cl⁻ L⁻¹, 0.35 mg PO₄³⁻L⁻¹ and 10 mg SO₄²⁻ L⁻¹. With the exception of Baxter and Ohman’s work,¹⁴ where they performed multicomponent standard additions and PLS modeling, to the best of our knowledge this is the first application where the effect of several concomitants on the atomic peak is studied and addressed using PLS regression.

The problem becomes complex because many different phenomena can well occur (more details are given in the following sections):

(i). The most sensitive spectral line for Sb (217.6 nm), employed currently, is not totally free of interferences. Particularly, Fe presents an almost adjacent line (217.8 nm)¹⁹ not resolved with the instrumental slit (0.7 nm). This spectral problem has also been reported elsewhere.^17,20

(ii). Chemical interferences are a real concern since Sb was reported to interact with many metals and other elements, giving intermetallic compounds.²¹

All chemical phenomena occurring in the graphite tube affected the atomic signal of Sb leading to peak displacement, peak broadening, peak splitting and peak depletion. Their magnitude depended on the concentration of Sb and the amounts of concomitants and they also occurred simultaneously (e.g., peak depletion and broadening).

Different PLS regression models were tested, including linear and non-linear (or polynomial) ones, from where the optimal model was selected and its performance studied. The International Union of Pure and Applied Chemistry (IUPAC) guidelines for single laboratory validation of methods²² defined a series of individual performance characteristics for describing analytical methods, including: applicability, selectivity, sensitivity, calibration, trueness, precision, limit of detection (LOD), limit of quantification (LOQ), and ruggedness. They are evaluated throughout this paper considering the optimal PLS model. The LOD was estimated applying an error propagation-based formula for standard error of prediction at zero concentration level²³ and also follows the latest IUPAC and ISO guidelines concerning the inclusion of both alpha and beta probabilities of error. In addition, multivariate estimates of sensitivity and selectivity are derived using the net analyte signal concept.

Experimental

Equipment

A 4100 Perkin-Elmer Atomic Absorption Spectrometer (Überlingen, Germany) equipped with an HGA-700 graphite furnace, an AS-70 autosampler and a deuterium-arc background correction was employed throughout. Argon was used as the inert gas; the flow rate was 300 mL min⁻¹ for all steps, except for atomization (gas, stopped). Measurements were made by using a hollow-cathode lamp (Perkin-Elmer), at 217.6 nm (0.7 nm slit). Pyrolytic coated tubes with preinserted L'vov platforms were purchased from Z-tek (Amsterdam, The Netherlands).

Reagents

All reagents were of analytical grade. Sb standards were prepared on a daily basis in HNO₃ (0.5% v/v, Baker Instra-analized grade, J. T. Baker, Phillipsburg, USA) from stock standard solutions of 1.000 g L⁻¹ (Panreac, Barcelona, Spain). High purity water (18 MΩ cm resistivity, Milli-Q Water System, Millipore, Madrid, Spain). Ca²⁺, Fe³⁺, Na⁺, Mg²⁺ stock solutions (1.000 g L⁻¹) were from Panreac; Cl⁻ (Baker), SO₄²⁻ and PO₄³⁻ (Merck, New Jersey, USA) standards were prepared from their corresponding suprapure acids.

All glassware and plasticware were soaked in 10% v/v HNO₃ for 24 h and rinsed with high purity water at least three times before use.

Analyical procedure

Aqueous samples and standards were directly analyzed by ETAAS; the final volume of the aliquots was 20 µL (0.5% v/v HNO₃ was added when needed). The furnace program had been optimized previously, as well as the effect of several chemical modifiers (nitric acid, sulfuric acid, magnesium nitrate, ammonium dihydrogen phosphate and the mixture palladium + magnesium nitrate at the 1.5 + 1 proportion), using STPF conditions, the pyrolysis temperature and atomization temperatures being 900 and 2000 °C, respectively.¹⁰ Nevertheless, the Sb peaks still got modified when high concentrations of several concomitants were included simultaneously in the standards. Although other approaches (for instance, the use of transversally-heated furnace and a Zeeman background corrector) could solve this problem, it was decided to apply PLS.

Standards and samples

Calibration and validation samples were prepared by mixing appropriate amounts of Sb stock solutions and concomitants. The experimental range for Sb was from 0 to 50 ng mL⁻¹, at 10 ng mL⁻¹ intervals, the linearity in this range had previously been verified without interfering concomitants.⁸ The amount of each concomitant in each mixture was defined by deploying a Plackett–Burman design, n = 8, at each concentration level of Sb (see Table 1). Note their closeness with the usual average values in Galician rivers, as explained in the introduction. In addition, a standard without interferents was measured at each Sb level; in total 54 solutions were used for calibration.

Table 1 Plackett–Burman experimental matrix to design the calibration set. The design was repeated for each level of Sb (from 0 to 50 ng mL⁻¹, at 10 ng mL⁻¹ intervals)

	Concentration of interferent/mg L^−1
Experience	Ca^2+	Fe^3+	Na^+	Cl^−	Mg^2+	PO4^3−	SO4^2−
1	5.00	5.00	5.00	0.50	5.00	0.10	0.10
2	0.25	5.00	5.00	5.00	0.25	1.00	0.10
3	0.25	0.25	5.00	5.00	5.00	0.10	1.00
4	5.00	0.25	0.25	5.00	5.00	1.00	0.10
5	0.25	5.00	0.25	0.50	5.00	1.00	1.00
6	5.00	0.25	5.00	0.50	0.25	1.00	1.00
7	5.00	5.00	0.25	5.00	0.25	0.10	1.00
8	0.25	0.25	0.25	0.50	0.25	0.10	0.10

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The external validation set (not employed during calibration) included nine Sb standards prepared with 10, 30 and 50 ng Sb mL⁻¹ and their levels of concomitants were defined by the 2nd, 4th and 6th experiments of the Plackett–Burman matrix. The methodology was further validated using four certified reference materials, Water SPS-SW1 (Spectrapure Standards AS, Norway), Water TM24 (National Water Research Institute, Canada), Estuarine water SLEW-3 (National Research Council, Canada) and Water LGC6017 (Laboratory of the Goverment Chemist, UK) as well as with spiked CRM aliquots since, unfortunately, not many CRMs have certified values for Sb.

Random variability on the ETAAS measurements was accounted for by measuring every standard and sample by triplicate, smoothing (Savitsky–Golay algorithm,²⁴ 11-points-window, 2nd order polynomial) because the atomic signals were noisy, and averaging them. Therefore, each solution is represented by an averaged peak profile, with negligible noise. In this way, we avoided some problems related to cross-validation of duplicated spectra on the calibration sets. Each spectrum (data acquisition time lasted for 2 s) was digitized to 108 variables.

Software

Home-made Matlab subroutines and the PLS-Toolbox²⁵ were employed throughout.

Partial least squares regression, PLS

The PLS foundations have been broadly presented elsewhere (see, e.g.ref. 24) and only brief details will be given just to summarize the working procedure. PLS regression is a linear multivariate calibration algorithm intended to extract the most of the information present in the spectra (X-variables) which is related to the concentration of Sb (Y-variable) using a series of latent variables (LV). Each LV is a linear combination of the original absorbances. The values of each sample (spectrum) on these latent variables are called scores whereas the participation of each spectral variable on the latent variables is called loading or weight. The regression model is built by regressing (through inner regression equations) those scores against the scores of the Sb concentration. If the inner relation is not linear, e.g. a polynomial, non-linear models can be obtained. Here, second-order and third-order polynomials were considered. Although the spectral and chemical interferences can introduce a nonlinear behavior, it has been proved that PLS can model slight nonlinearities by increasing the number of latent variables included in the model.²⁶ In this work, the number of latent variables that yielded the best predictive model was searched for by cross-validation. Whenever the minimum in the average leave-one-out cross-validation error²⁴ was not clearly definite, studies were made in the vicinity of the minimum using the external validation set.

Results and discussion

a. PLS models

Fig. 1 depicts the complex situation the interferents produced in the Sb peak. Two gross effects occurred: peak depletion + peak broadening and peak displacement (to the right) + peak splitting.

Fig. 1 Changes on the atomic profile of Sb caused by different combinations of concomitants given by the 8-trial experimental design ([Sb] = 20 ng mL⁻¹). “Original” means that no concomitant was added.

Preliminary PLS models were built in order to look for outliers by visual inspection of PLS graphs; mainly the “X-variables score plots (t)” (t₁versus t_k, where k is the order of the latent variable) and the “X–Y scores relationship” (t_kvs. u_k). Additionally, the presence of anomalous spectra and/or anomalous predictions in the calibration set was assessed by applying the studentized error vs. leverage plot, and the T² (the multivariate t-test) and Q (considering the residuals of the model) tests.²⁵ Outliers in the external validation (test) set were assessed by using the Mahalanobis distance.²⁴ The bias was studied regressing the PLS predicted values against the reference values and computing the F-test for the slope and intercept joint confidence intervals.

The complex behavior of the interferents, which caused different spectral effects depending on their concentration, impelled us to test non-linear PLS regression models to assess whether they could improve the results of the linear models. They were preferred instead of ANNs because their interpretation is simpler.

Table 2 summarizes the main results, the root mean square error of calibration (RMSEC) and prediction (RMSEP, for the validation set), both calculated as [∑(c_predicted − c_true)²/n]^1/2 (n = number of samples) and the percentage of explained variance. It can be observed that linear PLS (with mean-centered data) was not outperformed by the polynomial models. This means that the non-linear effects produced by the interferences either are not too strong or (more likely) they can be modeled successfully by linear PLS, even all peak displacements and changes on the peak shapes.^26,27 Hereinafter, only linear models will be considered in detail. It is worth noting that despite seven concomitants were considered, only four latent variables were needed in the PLS models and three (sometimes four) experimental factors (concomitants) were significant on the Plackett–Burman designs (see the following sections on chemical interpretation for more details on this issue). Such agreement strongly suggests that the optimum number of latent variables is four, as verified by a clear and sharp minimum in the typical plot “predicted residual error sum of squares -PRESS- versus latent variables” (not shown here). Quite good linear relationships between the three first LVs and concentration of Sb were obtained. The 4th LV is not so clear and would manage minor spectral characteristics (see Fig. S1 in the ESI).†Fig. 2 displays the loadings of the X-block variables along with the most characteristic atomic peaks. The loadings of the 1st LV can be roughly identified with the average spectral profile. The loadings of the next LVs present a first-derivative shape with maxima and minima just where the atomic peaks have maxima or inflection points. This suggests that the model tries to solve some undesirable interferences that might be yielding some spectral artifacts on those regions. This appears more clear when the final regression coefficients are considered (Fig. 3) as the model has positive implications for those variables defining the secondary (frontal) peak and, surprisingly, those variables around the maxima of the atomic peaks which became displaced to the right (e.g. experience 1). Noteworthy, this location also coincides with a shoulder of the non-displaced peaks.

Fig. 2 Graphical representation of the X-block loadings for the 4 latent variables-PLS model (continuous lines) superimposed with the three types of spectra obtained in the study (dashed lines). See text for details.

Fig. 3 Graphical comparison between the regresion coefficients and three typical atomic profiles. “Original” means that no concomitant was added.

Table 2 Selection of the partial least squares model and scaling mode of the atomic signals

			[Sb]/ng mL^−1		% Information^a
PLS model		Number of LV	RMSEC	RMSEP	X	Y
a Total variance explained.
Linear	Mean	3	1.75	3.18	99.3	99.4
	Centering	4	1.55	1.44	99.7	99.5
	Autoscaling	4	1.45	2.45	67.4	99.2
		5	1.34	2.64	72.5	99.3
		6	1.25	1.83	76.0	99.4
2nd order	Mean	4	1.24	3.31	99.3	99.8
	Centering	5	1.10	3.37	99.5	99.9
		6	0.92	5.32	99.6	99.9
3rd order	Mean	4	1.25	2.32	98.9	99.8
	Centering	5	1.07	2.36	99.5	99.9
		6	0.92	11.4	99.6	99.9

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The model behaved satisfactorily and without bias. The fitted regression line in the “predicted” vs. “actual” plot was Predicted value = (0.2075 ± 0.3819) + (0.9915 ± 0.0128) * Actual value, with an acceptable correlation coefficient (0.9958) and a low standard error of the regression line (1.58 ng mL⁻¹). The joint confidence test for the slope and intercept revealed that there was not bias and that the method gives true results (F_exp = 0.22; F_tab,_95% = 3.18). The total variances explained by cross-validation on the X- and Y-blocks, were 99.7 and 99.5%, respectively.

The use of four CRM waters, analyzed exactly like the aqueous standards, can help in assessing trueness (in addition to the previous F-test) and traceability. If they were not certified for Sb, their “true” values were evaluated in the classical way (using either ad-hoc aqueous calibration or a standard addition calibration). If their concentrations were below the PLS detection limit, spiked aliquots were used. Table 3 shows good results for the analysis of the CRMs and the spiked aliquots, with some discrepancies for the high spikes. The fact that the highest spiked concentrations are not properly predicted indicates that the model is applicable (linear behaviour) up to 25–30 ng mL⁻¹ and it, therefore, includes the WHO maximum level.¹ This boundary corresponds to the similar concept of “working linear range” in classical calibration.

Table 3 Sb concentrations ± standard deviation (n = 3) predicted by the PLS model for different original and spiked samples (see text for details)

	Concentration of Sb/ng mL^−1
	True	Predicted
a LOD for classical measurements, 95% confidence. b LOD for the PLS model, 95% confidence.
Water SPS-SW1	<1.64^a	<5.6^b
Water SPS-SW1 + spike 1	10.0	9.9
Water SPS-SW1 + spike 2	20.0	19.8
Water SPS-SW1 + spike 3	40.0	32.5
Water TM-24	9.6	10.8
Water TM-24 + spike 1	17.1	16.8
Water TM-24 + spike 2	24.6	22.4
Water TM-24 + spike 3	39.6	31.6
Estuarine water SLEW-3	<1.64^a	<5.6^b
Estuarine water SLEW-3 + spike 1	25.0	19.2
Water LGC 6017	<1.64^a	<5.6^b
Water LGC 6017 + spike 1	15.0	15.5
Water LGC 6017 + spike 2	30.0	24.6

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Robustness

Once a satisfactory model was developed, it should remain “robust” to small changes in the experimental conditions. In this sense, the performance of the graphite atomizers varies due to ageing, and this modifies the atomic profiles. In a previous work¹⁷ three peak features were simulated to see how they influenced the models; namely, peak shift (in general tube ageing leads to longer atomization times, “to the right”); signal enhancement or depletion, and an increase in the random noise of the atomic peak. Here, random noise was not studied because the Savitsky–Golay pretreatment largely precluded its influence. Peak shift was an inherent issue in the problem presented here and, therefore, no more simulations were carried out. Finally, peak enhancement and peak depletion were studied by means of a simulation. It consisted on selecting two extreme atomic peaks and reproducing them as close as possible with two and three Gaussian peaks (visual inspection revealed a good agreement among the real and reproduced signals except for random noise). Then, modification of the peaks (peak enhancement/depletion) is straightforward, see Fig. 4. The predicted Sb concentrations (see Table 4) revealed that the model is robust to “vertical” variations in the atomic peak profile within current ETAAS fluctuations, thus variations lower than 10% in peak height yielded acceptable predictions within ±10% the Sb concentration, as usually accepted for trace metal determination by ETAAS. As expected, predictions were slightly worse for the lowest Sb concentration (the lowest absorbances) when the signal decreased as much as ca. 8% simultaneously in both Gaussian functions (i.e., the main atomic signal and the smaller frontal peak).

Fig. 4 Stacked profiles simulating peak enhancement and/or peak depletion effects induced by the concomitants (the inserts correspond to two typical atomic profiles).

Table 4 Studies to assess the robustness of the multivariate model to typical signal variations in ETAAS, linear PLS, mean centered data

	Signal variation (%)		% Error in prediction^a
Analyte level	1st peak	2nd peak
a Error = (predicted value − original value)/(original value) × 100.
[Sb] = 10 ng mL^−1	+8	+6	−0.3
	+4	+3	−4.6
	−4	−3	−12.4
	−8	−6	−15.9
[Sb] = 20 ng mL^−1	+8	+6	+7.9
	+4	+3	+2.8
	−4	−3	−3.5
	−8	−6	−8.3

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Chemical interpretation of the interferences

Although PLS gave some rough information about the underlying interferences, the Plackett–Burman designs used to prepare the calibration mixtures yielded further insight into this issue. The Birbaun’s plots developed for each level of Sb allowed discrimination of highly influential from not influential concomitants. The response variable was 1000 × peak height/(1 + |t_{original peak} − t|), where t is the number of the variable where the maximum of the atomic peak appears. This equation considers—simultaneously—peak displacement and changes on the peak height (Fig. S2 in the electronic supplementary material,† shows a Birbaun’s plot²⁸ where Na⁺, SO₄²⁻ and Fe³⁺ appeared as the most influential ions; however, the order was not the same along the different levels of Sb). Some explanations can be hypothesized to justify the interfering effects:

Na⁺ can form several compounds with Sb, such as sodium antimonate and antimonite (that are used as fire retardants²⁹) and their formation might explain the drift of the maximum of the atomic profile to higher times. Welz et al.³⁰ reported on the displacement of the atomic peak of Sb when SO₄²⁻ was present. The effect was attributed to a distortion of the atomic peak caused by a high increase on the background during the first stages of its appearance, resulting in an apparent displacement. They considered it as a typical interference occurring into the gas phase. We did not observe the increment on the background but a clear peak displacement.

Regarding Fe³⁺, it can give rise to both physical and chemical interferences. First, a spectral interference of Fe³⁺ can not be neglected because one of its secondary lines (217.8 nm)¹⁹ can not be instrumentally resolved from that of Sb (217.6 nm) (which makes the signal not totally specific of Sb). Indeed it has been reported that Fe decreased the Sb signal due to an overcorrection caused by the D₂ background correction system^30,31 (the Zeeman system is not available for our equipment). Nevertheless, this interference was disregarded because: (i) an overcorrection was not observed; (ii) despite it was observed that the atomic peak splits in several experiments, the total integrated area remains constant; (iii) analysis of samples containing only the interferents yielded good blanks, without clear atomic peaks; and (iv) peak splitting could not be corrected by increasing the pyrolysis and atomic temperatures (as it is generally done). This leads to the conclusion that Sb atomization is mainly suffering chemical interferences and that the spectral ones can be disregarded. In order to confirm that high concentrations of Fe³⁺ caused chemical interferences, a new Sb standard (30 ng mL⁻¹) with high levels of all concomitants (except Fe³⁺) was measured again (this corresponded to the 1st trial of the Plackett–Burman designs) and the peak did not split. In addition, Fe³⁺ and Sb can form an intermetallic compound whose boiling point is greater than that of Fe³⁺ or Sb. This would justify the two peaks since part of the analyte would react with Fe³⁺ and become stabilized.

On the other hand, the latter statement suggests that Fe³⁺ itself could serve as a chemical modifier for Sb. This was evaluated using 30 ng mL⁻¹ Sb standards where all concomitants were set either to zero or to their highest concentrations (within the experimental design) and Fe³⁺ varied from 0 to 100 µg mL⁻¹. Their behaviour was twofold (see Fig. 5):

Fig. 5 Atomic profiles for a 30 ng mL⁻¹ Sb standard plus (a) 0.25 µg Fe mL⁻¹ and (b) 5.00 µg Fe mL⁻¹.

(a) In absence of other concomitants, low Fe³⁺ concentrations (0.25 µg mL⁻¹) originated a second peak, which disappeared at higher concentrations (>5 µg mL⁻¹). In the latter situation, the Sb peak was narrow, well defined, single and displaced to higher atomization times (as expected). This fact strongly suggested that Fe³⁺ might be a suitable modifier for Sb, as it was already reported for Ni.³²

(b) When all other concomitants are present, up to 50 µg mL⁻¹ Fe³⁺ were needed to stabilize Sb. Such large amount of Fe³⁺ implies that there could be an interaction or competition with other interferents (but it could not be ascertained fully).

The potential use of Fe³⁺ as chemical modifier for Sb was tested on a CRM (Water TM24). Unfortunately, some spectral artifacts were observed (mainly, a D₂ background overcorrection) which were attributed to the TM24 matrix. Further, classical methods (aqueous calibration and the standard additions method) suffered the same problems. Accordingly, the use of Fe³⁺ to stabilize Sb needs to be fully confirmed by separate studies (not presented here).

b. Multivariate figures of merit

The description of a multivariate method of analysis must also include the corresponding estimated figures of merit;²² among others: applicability, selectivity, sensitivity, calibration, trueness, precision, limit of detection (LOD), limit of quantification (LOQ), and robustness. These parameters were evaluated for the method which includes the optimal PLS model. Some of them (sensitivity, selectivity) are based on the Net Analyte Signal, NAS, concept and the others (LOD and LOQ) are calculated following the latest advances in uncertainty evaluation in multivariate calibration.

Pseudo-univariate plot and sensitivity. In multivariate calibration not all the recorded signal is used for prediction. The part of the recorded signal that is confounded with the signal from the concomitants is lost. Only the part that can be uniquely assigned to the analyte is used. This part, called the net analyte signal (NAS), is calculated for sample i as³³r^*_i = c_is*, where c_i is the predicted concentration for sample i and s* is the net sensitivity vector. Since the PLS model is calculated on mean-centered data, c_i is the mean-centered prediction and r_i* is the NAS for the mean-centered spectrum.

The net sensitivity characterizes the model and is calculated as s* = b/‖b‖², where b is the vector of regression coefficients and ‖·‖ indicates the Euclidean norm.³³ Using the NAS, the PLS model can be represented like a usual univariate calibration model, i.e., as a scatter plot of the concentrations of standards and their signal (a pseudo univariate presentation can be seen in Fig. S3 of the ESI for the optimal PLS model based on four latent variables). The sensitivity of the method is the inverse of the slope of the regression line (which is also the norm of the net sensitivity vector), s = ‖s*‖ = 1/‖b‖= 0.0142 absorbance/(ng mL⁻¹), for this method.

The multivariate sensitivity can be used to evaluate a ‘multivariate characteristic mass’ (m₀); considering that 20 µL were injected, m₀ = 0.02 (mL) × 1000 (pg mL⁻¹) × 0.0044/0.0142 = 6.2 pg.

Selectivity. In multivariate calibration, selectivity is commonly used to measure the amount of signal that cannot be used for prediction because of the overlap between the signal of the analyte and the signal of the interferences.^34,35 For inverse models, selectivity is usually calculated for each calibration sample as ξ = ||r_i*||/||r_i||, where r_i * and r_i are the NAS and the spectrum of sample i, respectively. Notice that samples with the same amount of analyte but different amounts of interferences will have the same ||r_i*|| but different ||r_i|| and hence, a different selectivity value. This poses a problem for defining a unique selectivity value that characterizes the PLS model. However, we can take advantage of the experimental design of the calibration standards and calculate a global measure of selectivity. A plot of the norm of the NAS (mean-centered data) vs. the norm of the measured spectra will follow a linear trend (Fig. S3b of the ESI)† whose slope (here 0.83) is a global measure of selectivity that represents the model. This value indicates that approximately 83% of the measured signal is used for prediction and that a 17% of the measured signal is lost due to presence of the interferences.

Limits of detection and quantification. The limit of detection of the method (for the optimal PLS model: mean centered, 4 LV) was estimated using an equation based on an approximate expression for the sample-specific standard error of prediction (SEP), as derived by Faber and Bro³⁶ and that has been shown to provide good results at low concentration levels.

LOD = Δ(α, β, ν) × RMSEC√1 + h₀

The RMSEC is obtained from the squared fit errors of the PLS model as [(c_predicted − c_true)²/ν]^1/2 where the sum extends to all samples in the calibration set, and ν is the degrees of freedom, which are calculated (for a centered model) as ν = n − F − 1, with F being the number of latent variables considered in the model and n the number of samples in the set.

The leverage, h₀, quantifies the distance of the predicted sample (at zero concentration level) to the mean of the calibration set in the F-dimensional space. For a centered model it is calculated as h₀ = 1/n + t₀^T(T^TT)⁻¹t₀, where t₀ is the (Fxn) score vector of the predicted sample and T the nxF matrix of scores for the calibration set. In this work, h₀ was estimated as an average value of the leverages of the cross-validation samples having zero concentration of Sb.

Finally, the term (Δ(α,β,ν)) is a statistical parameter that takes into account the α and β probabilities of falsely stating the presence/absence of analyte, respectively, as recommended elsewhere.^37,38 When the number of degrees of freedom is high (ν ≧ 25), as is usually the case in multivariate calibration models, and α = β, Δ(α,β,ν) can be safely approached to 2 t_1−α,ν. Thus, the estimated LOD, for α = β = 5% and ν = 48 degrees of freedom, was 5.6 ng mL⁻¹ (4.3 ng mL⁻¹ if α = β = 10%). The limit of quantification was evaluated as the concentration having a relative standard deviation (RSD) of 15%. Although some guidelines recommended the use of RSD values of 10%, the value chosen was thought to be acceptable at the concentration level we are dealing with (around 10 ng mL⁻¹). This is supported by Horwitz equation, which predicts a reproducibility RSD of 22% at this concentration level. Since we want to determine an intralaboratory LOQ, we took an intermediate (intralaboratory) RSD of 15% (that is about 2/3 of 22%). So, finally, the LOQ was evaluated as LOQ = 100 × (RMSEC × (1 + h₀)^1/2)/RSD(%), where RMSEC was calculated as above and h₀ was calculated as the average value of the leverages of the cross-validation samples having 0 and 10 ng mL⁻¹ of Sb. The estimated LOQ was 10.6 ng mL⁻¹ of Sb. Both LOD and LOQ values are higher than those obtained previously for aqueous standards, without concomitants, in a classical way (LOD = 1.64 ng mL⁻¹ and LOQ = 5.48 ng mL⁻¹).⁹

Conclusions

It was shown that linear PLS models (using mean centered data) can satisfactorily predict the concentration of a trace metal (Sb) when several concomitants are present, even when one of them gives a quite complex chemical interference (Fe³⁺). The performance of the PLS model was tested by analyzing aqueous standards, four CRMs and several spiked CRM aliquots. The predictions were good for Sb concentrations ranging from 0–30 ng mL⁻¹, with as high concentrations of concomitants as 5 µg mL⁻¹. Although this is not the solution to any interference in ETAAS measurements, it opens up a reliable and convenient alternative to handle complex problems. The overall methodology proposed here (ETAAS-PLS) is simple, yields low turnaround times without large requirements on time or labor (i.e., analytical protocols can be developed quickly) and it is cheap. Further, the multivariate studies associated to the PLS models drew attention on important phenomena underlying the ETAAS measurement (e.g., the potential use of Fe³⁺ as a chemical modifier).

In addition, the ETAAS-PLS approach is robust to typical variations in atomic peaks when they are measured by ETAAS (ca. 10% peak enhancement or depletion).

Acknowledgements

MFS acknowledges the University of A Coruña for a PhD grant.

References

1. WHO Guidelines for drinking water quality, 3rd edn, http://www.who.org, 2004.
2. A. Kabata-Pendias and H. Pendias, Trace elements in soils and plants, CRC Press Inc., Boca Raton, Florida, 1992.
3. J. O. Nriagu, Environment, 1990, 32, 7.
4. G. B. van der Voet and F. A. de Wolff, in Toxicology of metals, ed. L. Chang, L. Magos and T. Suzuki, CRC Press, Boca Raton, FL, 1996.
5. C. Dietl, W. Reifenhauser and L. Peichl, Sci. Total Environ., 1997, 205, 235.
6. M. J. Cal-Prieto, A. Carlosena, J. M. Andrade, M. L. Martínez, S. Muniategui, P. López-Mahía and D. Prada, Water, Air, Soil Pollut., 2001, 129, 333.
7. A. Carlosena, P. López-Mahía, S. Muniategui, E. Fernández and D. Prada, J. Anal. At. Spectrom., 1998, 13, 1361.
8. M. J. Cal-Prieto, A. Carlosena, J. M. Andrade, S. Muniategui, P. López-Mahía and D. Prada, At. Spectrosc., 2000, 21(3), 93.
9. M. J. Cal-Prieto, A. Carlosena, J. M. Andrade, P. López-Mahía, S. Muniategui and D. Prada, Afinidad, 1999, 56(480), 105.
10. M. Grotti, M. L. Abelmoschi, F. Soggia, C. Tiberiade and R. Frache, Spectrochim. Acta, Part B, 2000, 55, 1847.
11. M. Grotti, R. Leardi and R. Frache, Anal. Chim. Acta, 1998, 376, 293.
12. J. Hou, G. S. Chen and Z. P. Wang, Spectrosc. Spectral Anal., 2001, 21(3), 387.
13. E. A. Hernández-Caraballo, R. M. Ávila-Gómez, F. Rivas, M. Burguera and J. L. Burguera, Talanta, 2004, 63, 425.
14. D. C. Baxter and J. Ohman, Spectrochim. Acta, Part B, 1990, 45(4–5), 481.
15. D. C. Baxter, W. French and I. Berlund, J. Anal. At. Spectrom., 1991, 6, 109.
16. E. M. M. Flores, J. N. G. Paniz, A. P. F. Saidelles, E. I. Müller and A. B. Costa, J. Anal. At. Spectrom., 2003, 18, 769.
17. M. Felipe-Sotelo, J. M. Andrade, A. Carlosena and D. Prada, Anal. Chem., 2003, 75, 5254.
18. J. M. Andrade, MSc thesis, University of Santiago, 1990.
19. CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton, FL, 83rd edn, 2002.
20. B. Baraj, A. Bianchini, L. F. H. Niencheski, C. C. R. Campos, P. E. Martínez, R. B. Robaldo, M. M. C. Muelbert, E. P. Colares and S. Zarzur, Fresenius Environ. Bull., 2001, 10(12), 859.
21. http://www.webelements.com/webelements/elem .
22. M. Thompson, S. L. R. Ellison and R. Wood, Pure Appl. Chem., 2002, 74, 835.
23. A. Höskuldsson, J. Chemom., 1988, 2, 11.
24. B. G. M. Vandeginste, D. L. Massart, L. M. C. Buydens, S. De Jong, P. J. Lewi and J. Smeyers-Verbeke, Handbook of Chemometrics and Qualimetrics, Elsevier, Amsterdam, 1998.
25. B. M. Wise and N. B. Gallahger, PLS Toolbox for Matlab v.1.5 Eigenvector Technology, Manson, WA, USA, 1996.
26. R. DiFoggio, Appl. Spectrosc., 1995, 49(1), 67.
27. J. M. Andrade, M. S. Sánchez and L. A. Sarabia, Chemom. Intell. Lab. Syst., 1999, 46, 41.
28. K. Jones, Int. Lab., 1986, 32.
29. http://minerals.usgs.gov/minerals/pubs/commodity/antimony .
30. B. Welz and M. Sperling, Atomic absorption spectrometry, Wiley-VCH, Weinheim, 1999.
31. I. Martinsen, B. Radziuk and Y. Thomassen, J. Anal. At. Spectrom., 1988, 3, 1013.
32. Y. Morishige, K. Horokawa and K. Yasuda, Fersenius’ J. Anal. Chem., 1994, 350, 410.
33. J. Ferré and N. M. Faber, Chemom. Intell. Lab. Syst., 2003, 60, 123.
34. K. Lorber, N. M. Faber and B. R. Kowalski, Anal. Chem., 1997, 69, 1620.
35. N. M. Faber, A. Lorber and B. R. Kowalski, J. Chemom., 1997, 11, 419.
36. N. M. Faber and R. Bro, Chemom. Intell. Lab. Syst., 2002, 61, 133.
37. L. A. Currie, Pure Appl. Chem., 1995, 67, 1699.
38. ISO 11843-1:1997: Capability of detection. Part 1: Terms and definitions, ISO, Genève.

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Footnote

† Electronic supplementary information (ESI) available: PLS model with four latent variables to test for linear relationships between predictors and predictand (Fig. S1); Birbaun’s curve for assessing which concomitants will mainly modify the atomic signal (Fig. S2); pseudo-univariate presentation of the PLS model (Fig. S3). See DOI: 10.1039/b506783a

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