Validation and uncertainty estimation of an analytical method for the determination of phenolic compounds in concrete

Organic contaminants from building materials negatively affect the health of people. This study presents an analytical method for the simultaneous identification and quantification of 9 phenolic compounds, i.e., phenol, 2-chlorophenol, 2,4-dimethylphenol, 2,4-dichlorophenol, 2,6-dichlorophenol, 4-chloro-3-methylphenol, 2,4,6-trichlorophenol, 2,3,4,6-tetrahlorophenol and pentachlorophenol, in concrete by a gas chromatographic method with mass spectrometric detection (GC–MS). By comparing the MS spectra of the test compounds with MS spectra of analytical standards, reliable identification was achieved. The method could be applied in a given range (from 0.01 to 7.5 mg kg-1) with appropriate parameters of precision, accuracy, repeatability and linearity. The developed method could be used for quality control testing of phenols in concrete during the construction of new buildings, old residences and construction waste. The measurement uncertainty of the phenolic compounds in concrete was evaluated using two approaches, i.e., GUM recommendations and a Monte Carlo method. Disagreement of those methods was observed. The Monte Carlo method could be used in the evaluation of combined measurement uncertainty for the determination of phenolic compounds in concrete.


INTRODUCTION
Phenol and phenol derivates represent a very important group of pollutants that are ubiquitous in the environment.Due to the exceptional toxicity of most phenolic compounds with bioaccumulation effect in animals and plants, and carcinogenicity to human health, the US Environmental Protection Agency -USEPA has classified phenolic compounds as a group of hazardous pollutants. 1 Similarly, ANALITYCAL METHOD FOR DETERMINATION OF PHENOLIC COMPOUNDS IN CONCRETE 57 analysis of phenolic compounds in concrete.Each of these methods has its adventages in different areas: chemistry, 23,24 pharmacy, 25 geodesy, 26 spectrometry, 27 biomedical science, 28 etc.

Sampling
Sampling of concrete walls was performed in the dimensions 10 cm×10 cm using a drill, with a diamond plate to the depth of 2 cm.The concrete was then collected in a hermetically sealed container and transported to the laboratory.Further, the sample was homogenized to a particle size <1 µm using a hydraulic press without heating.

Extraction
Powdered concrete (10 g) was mixed with 75 mL of methanol and the pH was adjusted to <3 by adding concentrated hydrochloric acid.Extraction was performed by sonification for 10 min and then 30 min on a mechanical shaker (200-300 rpm).After the particles had settled, the supernatant was filtered.An aliquot of 10 mL was transferred to a 100-mL separation funnel and 50 mL of aqueous potassium carbonate solution (0.1 M) was added.Then, 2 mL of sodium hydroxide (0.5 M) and 1 mL of acetic anhydride were added to the extract.The extract was gently rotated for 2 min in the separating funnel during the release of carbon dioxide and left to stand 10 min with occasional shaking.Thereafter, 10 mL of cyclohexane was added, the mixture intensely shaken and the two phases were separated.The cyclohexane phase (upper phase) was transferred to a 20-mL headspace bottle in which 2 g of anhydrous sodium sulfate had previously been added.The extract was stored in a refrigerator at 4 °C and analyzed within 48 h; 1 mL of extract was taken for GC-MS analysis.Blank and spiked samples were prepared in the same way as a real sample.
Identification of compounds from the standard solution was performed by comparing the characteristic mass spectrum of the compound from the library with the characteristic MS spectrum of the individual phenol in the standard solution.

Instrument and analytical conditions
Chromatographic analyses were performed on the gas chromatograph with mass detector, Agilent Technologies 7890B GC System, Agilent Technologies 5977MSD.A fused silica GC capillary column Agilent J&W (HP-5ms 30 m×0.25 mm i.d., film thicknesses 0.25 μm) was used.The gas chromatographic conditions were a programmed temperature of the capillary column from 60 °C (0.2 min hold) at 30 °C min -1 to 150 °C (0 min hold), 8 °C min -1 to 179 °C ________________________________________________________________________________________________________________________ (CC) 2019 SCS.
Available on line at www.shd.org.rs/JSCS/58 S A V I Ć et al.
(0 min hold), 20 °C min -1 to 240 °C (2 min hold), 50 °C min -1 to 320 °C (hold 5 min constant).The temperature of the splitless injector was 250 °C.The injection volume was 1 μL.Helium, grade 5.0 was used as the carrier gas at constant flow rate of 1.9 mL min -1 .The transfer line temperature was 310 °C.The ionization occurred with a kinetic energy of the impacting electrons of 70 eV.Mass spectra and reconstructed chromatograms (total ion current [TIC]) were obtained by automatic scanning in the mass range m/z 45-300.The GC-MS data were processed with Agilent GC-MS MassHunter software and the NIST 14 mass spectral library.

Uncertainty estimation
In order to achieve a standardized way of expressing measurement results, in 1993 seven international organizations prepared the GUM. 21GUM embraces many aspects of uncertainty evaluation.Therefore, it was widely used, respected and recognized by many as the basic document for uncertainty estimation.However, some deficiencies and limitations were noticed in this document.In order to revise and promote the use of GUM and the International Vocabulary of Basic and General Terms in Metrology (VIM), and prepare supplemental guides for GUM, 21,22,[29][30][31][32] the Joint Committee for Guides in Metrology (JCGM) was formed.The basic document in the JCGM 100 series 21 is based on the law of propagation of uncertainty (LPU). 33LPU can be used under the following conditions: only one output quantity appears in the model; the model is explicit, i.e., it can be written as c = f (X 1 ,…, X N ) (although the function c does not need to be analytic); and, the model is well approximated by its linear expansion around the best estimates of the input quantities.
After obtaining the standard uncertainty using LPU, the GUM approach uses the Welch--Satterthwaite formula to obtain the effective degrees of freedom, necessary to calculate the expanded uncertainty.Since the analytical evaluation of the effective degrees of freedom is still an unsolved problem, the GUM is not always appropriate.Moreover, GUM assumes the validity of the central limit theorem, i.e., it assumes that the probability density function (PDF) of the output is approximately normal and can be represented by a Student t-distribution.In some cases, this resulting distribution may have an asymmetric behavior or tend to a normal distribution, which implies less validity of GUM. 34ne way to overcome these constraints is to use methods that contain more information for estimation of measurement uncertainty than GUM.This work presents a methodology that uses the Monte Carlo method for propagation of distributions, which is described in JCGM 101. 22The difference between the two approaches is illustrated by Fig. 1a and b, which present propagation of uncertainties and propagation of distributions, respectively.In the case of distributions propagation, complete information of the input quantities is available, while in the case of propagation of uncertainties, the input contains only expectation and standard deviation of the input quantities (only the first and the second central moments).The Monte Carlo approach for the evaluation of uncertainty is a reliable tool when the GUM framework is not adequate.Therefore, besides analysis of the measurement uncertainty by the GUM method, the Monte Carlo method used for an estimation of measurement uncertainty in the C++ programming language is implemented.
A procedure for application of Monte Carlo method was performed in the following way: the number of histories M in the MC simulation was selected; N input values and an estimate of their distribution functions were defined; M vectors were generated, by sampling from the PDFs assigned to the input quantities X i , i = 1,…,N; for each vector, the corresponding model Y was created; the obtained values of the models were sorted into increasing order; the output value was estimated and the uncertainty was measured; for the chosen coverage probability p, an appropriate coverage interval was formed (in case of asymmetric PDF, it is the shortest 100 p percentage coverage interval).

Selectivity
Selectivity describes the ability of an analytical method to differentiate various substances in the sample and is applicable to a method in which two or more components are separated and quantified in a complex matrix. 35The selectivity of the presented method was tested by recording the chromatogram of a spiked sample (7.5 mg kg -1 ) and blank sample under the previously established chromatographic conditions (see Fig. 2).The resolution successive peak, as a quantification measure of selectivity, was calculated by Eq. ( 1): ( ) where t R 1 is the retention time, in seconds, of the first peak, t R 2 is the retention time, in seconds, of the second peak, w 1 is the peak width on the time axis, in s, of first peak and w 2 is the peak width on the time axis, in seconds, of the second peak.Resolution for all selected peaks was in the range from 0.5-1.4.The indicated values satisfy the criteria defined in the Eurochem guide, 36 implying that a good selectivity is obtained when using the proposed method for most phenolic compounds.

Linearity
Linearity was tested by linear regression analysis using a calibration standard of acetylated phenolic compounds at five concentration levels (0.05-1.0 mg L -1 ).For each concentration level, three consecutive measurements were performed.The chromatogram corresponding to the lowest level of the calibration curve is shown in Fig. 2.
Based on the results, parameters of the regression equations (the slope, intercept and correlation coefficient) were determined, Table I.
Examination of the regression line showed that the method is linear with a regression coefficient, R > 0.99 for all phenolic compounds in the examined range.
The limits of detection (LOD) and quantification (LOQ) were determined statistically using regression analysis functions obtained from linearity according to the equations: where b is the slope of the calibration curve and SD is the residual standard deviation.The obtained LOD and LOQ values are presented in Table I.

Trueness
To test the trueness of the method, a recovery test was applied.Spiked samples of concrete were prepared for three concentration levels in the range of the calibration curve.The determined concentrations were compared with the spiked amounts.The ratio between the obtained and expected concentrations was calculated and expressed as a percentage, which represents the recovery.The mean value, standard deviation and relative standard deviation (RSD) were calculated.For GC-MS analysis, the obtained recoveries ranged from 79 to 91 %, except for 2,4-dimethylphenol (see Table I).According to Eurachem, 36 these mean values of the recoveries were within the acceptable range.

Repeatability
The repeatability of a method is one way of expressing precision within the laboratory, under the same operating conditions over a short period of time, with the same analyst on the same equipment.Repeatability represents agreement 62 S A V I Ć et al.
between the independent test results and it is expressed in the form of the standard deviation or the relative standard deviation (RSD).The RSD or the coefficient of variation (CV), as it is alternatively termed, can be useful in order to eliminate the influence of the concentration.For the determination of the repeatability of the method, six spiked samples with 3.75 mg kg -1 of phenols solution were prepared and the GC-MS analysis was performed.
The mean values of concentration and RSD were calculated.The obtained results are given in Table I.The RSD values ranged from 0.03 to 0.05 %.Based on Eurachem, 36 the calculated RSD values were within the acceptable range.

Intermediate precision
The purpose of this test was to check the trueness of the analytical method and to prove that the impact of small variations in the method parameters (different analysts and times of operation) on the trueness was negligible.For this validation characteristic, samples spiked with 3.75 mg kg -1 of phenols solution were prepared and injected in triplet during five days.The obtained results were compared with the results of the previous day.The SD and the RSD were calculated, Table I.

Determination of measurement uncertainty
The content of phenol in a concrete sample was determined according to Eq. ( 4): where y is the peak area of a phenol compound, a and b are the intercept and the slope of straight-line fit to a data set, respectively obtained by the application of the method of least squares, V is the volume of solution, m is the mass of sample and R is the recovery.
In accordance with the GUM, 21 all potential sources of uncertainty in the measurement were considered.In addition, the contribution to the uncertainty of the measurements was estimated in a way that uses all available information about the measurement procedure (considering that during propagation of uncertainty and propagation of distribution, no further information than that already known was transmitted).In order to identify all relevant uncertainty sources, a cause-effect diagram was drafted (Fig. 3).All necessary information for uncertainty calculations for both methods are summarized in Table II presenting the data for phenol and in Tables S-I, S-III, S-V, S-VII, S-IX, S-XI, S-XIII and S-XV of the Supplementary material to this paper for the eight other compounds.________________________________________________________________________________________________________________________ (CC) 2019 SCS.
Available on line at www.shd.org.rs/JSCS/The last parameter to be defined is the number of histories M in the Monte Carlo calculations.According to the "Evaluation of measurement data -Supplement 1" the "Guide to the expression of uncertainty in measurement'' -Propagation of distribution using a Monte Carlo method", 22 this number can be chosen as a priori in the following way: M > 10 6 (100-p) -1 ( 5 ) where p is a selected coverage probability.Therefore, when the coverage probability is 95 % (as in the present case), M should be at least higher than 2×10 5 .Since a larger number of histories M causes better convergence of the result, M was chosen to be 5×10 6 .The results were obtained by processing the set of available information using the GUM uncertainty approach.Corresponding statistical parameters were obtained by Monte Carlo simulation for the compound phenol and the results are presented in Table III.The results for the eight other compounds are presented in Tables S-II, S-IV, S-VI, S-VIII, S-X, S-XII, S-XIV and S-XVI of the Supplementary material.The following parameters were obtained S A V I Ć et al.
in the Monte Carlo simulation: low endpoint for 95 % and high endpoint for 95 %.They represent the low and high limit of the shortest-length 95 % confidence interval, respectively.It could be seen that for all compounds, the Monte Carlo approach predicts a larger spread of data around a central value.For example, from Table III, it could be noticed that one half of the shortest interval is 1.29 mg kg -1 compared to the expanded uncertainty of 0.95 mg kg -1 .Deviation of the PDF of the output estimated by Monte Carlo simulation from the distribution assigned to the measured and through GUM analysis is shown in Fig. 4. It could be seen that these two ways of expressing the measurement results are in disagreement, i.e., the resulting PDFs from Monte Carlo simulations are skewed to the right and their coverage intervals are larger than the coverage intervals obtained by the GUM approach.Since these disagreements come from the assumptions and approximation included in the GUM Uncertainty Framework, the Monte Carlo method described in JCGM 101:2008 is proposed for the analysis of this kind of uncertainty.

CONCLUSIONS
The gas chromatographic method with mass spectrometric detection was used for the simultaneous identification and quantification of nine phenolic compounds in concrete.The analytical technique was developed in the presented study.

Fig. 1 Monte
Fig. 1 Monte Carlo method for propagation of distributions, a) propagation of uncertainties; b) propagation of distributions.