Uncertainty Associated with the Analysis of Secondary Organic Aerosol Compounds Formed in Smog Chambers by Gas Chromatography-Mass Spectrometry

This work assesses the main sources of uncertainty of the determination of several secondary organic aerosol (SOA) components. The evaluation of the uncertainty associated with analytical methods is essential in order to demonstrate that the results obtained in routine analysis are reliable. The current work has thoroughly evaluated the sources of uncertainties associated with the analytical method employed to quantify the SOA produced from photo-oxidation of complex mixtures of volatile organic compounds (VOCs) in smog chambers. Measurement uncertainties were calculated by applying a bottom-up approach. The combined uncertainty of the analytical method ranged from 8% for glyoxal to 29% for methyl benzoquinone. The results clearly show that the determination of some SOA compounds is associated with a high level of uncertainty, and thus the quantification process for these at lower levels remains challenging.


INTRODUCTION
Experiments performed in smog chambers offer a framework to reproduce chemical reactions under controlled conditions, and thus, they are a useful tool to investigate reactions and mechanisms involved in the secondary organic aerosol (SOA) formation.In consequence, the number of papers related to smog chambers has risen considerably during last years (Coeur-Tourneur et al., 2009;Kleindienst et al., 2009;Ortiz et al., 2009;Vivanco et al., 2011;Zhang et al., 2011;Zhou et al., 2011;Borrás and Tortajada-Genaro, 2012a, b;Santiago et al., 2012).Knowledge of the SOA formation and its composition presents a high interest for different scientific areas since some components of SOA have harmful effect on human health (Chuang et al., 2012;Sawyer et al., 2010) and particles contribute to the global radiative balance of the atmosphere by dispersing and absorbing light (IPPC, 2007).
There are some techniques to analyze SOA produced from smog chamber experiments.Installing a filter system below the chamber to collect those species is one of most employed.Regarding to sampling, Ortiz et al. (2009) have highlighted that the collection efficiencies from sampling must be deeply studied still.On the other hand, it is noteworthy that having an adequate analytical method to analyze those compounds deposited on filters is a main stage related to the SOA analysis.However, there is no single analytical method to analyze SOA products.In fact, each author develops own analytical methods, according to their needs (Forstner et al., 1997;Yu and Jeffries, 1997;Yu et al., 1997;Yu et al., 1998;Kleindienst et al., 2004;Chiappini et al., 2006;Bateman et al., 2010).Developing an analytical method is complex, long and rarely valued.The last stage, but unfortunately not always performed, is verifying analytical method can provide reliable results.In practice, the fitness for purpose of an analytical method is assessed through method validation studies (Rozet et al., 2011c).A typical validation study determines some parameters among which trueness, precision, bias, linearity, detection limit, robustness and selectivity are the main (Thompson et al., 2002;Rozet et al., 2011a;EURACHEM, 2012).
For this reason, the analytical method developed by the authors to quantify some products from the photo-oxidation of toluene, 1,3,5-thrimethylbenzene, o-xylene, octane, αpinene, limonene and isoprene has been already validated and their results have been published elsewhere (Pindado Jiménez et al., 2013).However, in routine application of a methodology, it is impossible evaluating dispersion of results and bias of the method because samples are usually analyze once.Therefore, it is imperative provide another system able to assess if results are reliable.This is why assessment of measurement uncertainty should be performed (Rozet et al., 2011b).Establishing the uncertainty gives us the possibility to compare between results and also is an index of the goodness of our measurement method.
In light of above, the aim of this article is assessing measurement uncertainty of some products formed from the photo-oxidation of complex mixtures of volatile organic compounds (VOCs) in a smog chamber.Specifically, the bottom-up approach to determine all the individual sources of uncertainty was performed.

Materials and Equipements
An Agilent 6890 chromatograph with automatic sampler, a split/splitless programmed temperature injector, equipped with a capillary column Zebron ZB-5MS (30 m. × 0.25 mm.× 0.25 µm) and coupled to an Agilent 5975 mass spectrometer was employed.Operating conditions were: He as carrier gas; flow rate of 1 mL/min; PTV injector had initial temperature of 90°C, held 0.1 min, then increased at a rate of 700 °C/min to 250°C; operation mode splitless with an injection of 1 µL; initial oven temperature 80°C for 5 min, increased at a rate of 10 °C/min to 210°C, held 3 min, later increased at a rate of 10 °C/min to 250°C and finally held 5 min; detector operated in electronic impact mode (70 eV) in SIM and SCAN mode.
Extraction was performed with an ultrasonic bath device (Selecta Ultrasons-H) being extracts filtered through a Teflon filters (0.2 µm) and concentrated under a gentle stream of nitrogen (> 99.999%).

Analytical Procedure
SOA analysis was performed using an entirely developed methodology by the authors.Details of this procedure, as well as validation study, can see in Pindado et al. (2013).Briefly, a volume of 5 mL of water was added to the quartz filters, spiked with the objective compounds, and 750 µL of PFBHA (2000 µg/mL) were subsequently added.The first extraction was performed by shaking the mixture for 1 min and stored at room temperature and darkness overnight.The second extraction included the addition of 5 mL MeOH to the quartz filter, shaking it for 1 min and keeping it in the darkness at ambient temperature overnight.Later, mixture was shaken for 15 min in an ultrasonic bath.
Aqueous and methanolic extracts were joined and concentrated to 100 µL under a stream of nitrogen.Subsequently, 150 µL of PFBHA (2000 µg/mL) and 500 µL of acetonitrile were added and the mixture was stored 24 h at room temperature and darkness.Later, mixture was concentrated to dryness in a nitrogen stream and then 50 µL of BSTFA and 50 µL of pyridine were added and introduced into an oven for 40 min at 80°C.Finally, extract was concentrated to dryness under nitrogen stream, re-dissolved in 100 µL of dichloromethane and the internal standard was added.

UNCERTAINTY ESTIMATION
The term of uncertainty is widely known, but it is important to know that there are many possible sources of uncertainty in a measurement, and not all the components will make a significant contribution to measurement uncertainty.There are several approaches to evaluate measurement uncertainty.One of the most employed is the bottom-up approach that divides the analytical method into steps.Thus, uncertainty of each step consists of random and systematic components that can be assessment from a statistical analysis of repeated measurements.In this article, the authors have adopted the bottom-up approach for estimating measurement uncertainty because each sources of error can be easily identified allowing design potential improvements.This approach has already been satisfactorily used for complex analytical methods (Cuadros-Rodríguez et al., 2002;de Melo Abreu et al., 2006;Ratola et al., 2006;Yenisoy-Karakas, 2006;Fisicaro et al., 2007;Pindado Jiménez et al., 2010;Drolc and Pintar, 2011;Pindado Jiménez and Pérez Pastor, 2012).
Briefly, the estimation of uncertainty associated with a result involves four steps: first, specify the measurand, second, identify all uncertainty sources, later quantify uncertainty components and finally calculate the combined uncertainty.In order to calculate combined uncertainty, components have to be expressed as standard deviations, and combined it according to the appropriate rules.It is well known that not all uncertainty components contribute equally, but that is no reason to omit it, and each contribution must be calculated.The expanded uncertainty is the result of applying an appropriated coverage factor (A coverage factor of 2 is usually used.This implies that there is 95% probability that the result is within this interval).

RESULTS AND DISCUSSION
The first step in the assessment of uncertainty is to specify the measurand.Therefore, the expression to calculate the amount (expressed in ng) of SOA components produced from the photo-oxidation of VOCs in smog chambers is obtained from the Eq.(1): where C is the analyte concentration (in µg/mL) obtained from the calibration; V is the volume in which the sample was dissolved (in mL); R is the recovery for each compound.

Identification of Uncertainty Sources
All parameters in Eq. ( 1) have an uncertainty associated with their values and are therefore potential uncertainty sources.Thus the authors have identified the estimation of the analyte concentration from the calibration curve, the dilution factor and the recovery as main uncertainty sources.However, there are other parameters that do not appear explicitly in Eq. ( 1) and could affect to the mass of SOA results.
The uncertainty associated to concentration of an analyte from the calibration curve is a combination of several uncertainties.Among all sources of uncertainty on the estimated concentration of an analyte from linear least squares calibration, the most significant and thus the unique evaluated in this study are random variations in peak area.Preparation of standard solutions is a major uncertainty source.This uncertainty involves preparation of calibration solutions from pure compounds, and therefore contribution of volume, purity and mass of each compound must be assessed.In addition there is the contribution of the internal standard employed, which has two uncertainty sources: purity and volume.The influence of repeatability has been calculated, where factors as instrument precision and interferences from the matrix or reagents have been considered.
The dilution factor has volume as main source of uncertainty.This uncertainty includes uncertainty of calibration, which is given by manufacturer of volumetric material, the uncertainty due to variations in filling of the volumetric material and also variations in temperature may be affecting to volume.
Several factors contribute to the uncertainty associated with the loss of SOA mass during each analytical operation; two extractions, three dryness under N 2 atmosphere, three derivatization reactions and one filtration.Because of lack of reference material for method, in-house bias has to be assessed by considering the uncertainties associated with whole procedure.This uncertainty has been evaluated as uncertainty derived from recovery.This recovery study take into account the influence of each stage of analytical procedure as well as other sources of uncertainty associated to sample preparation as being homogeneity of sample, dissolution and stoichiometry of derivatization reaction.
Fig. 1 shows the cause and effect diagram that facilitates identification of all contributions.

Quantification of Uncertainty Sources
This section shows the calculus of contributions to whole uncertainty.In order to facilitate quantification of each uncertainty source and methodology carried out, a scheme with all mathematical equations employed in the estimation of uncertainty are shown in Fig. 2. Because of the length of the article, the authors only describe in detail the estimation of uncertainty for pyruvic acid, because the procedure for the rest of compounds is similar.Nonetheless, results for all compounds studied are in the electronic supplementary material.

Uncertainty Derived from Analyte Concentration
The expression to calculate the analyte concentration by linear squares calibration is shown in Eq. ( 2): where A is the chromatographic area, a is the intercept and b is the slope.So this uncertainty is a combination of three contributions: uncertainty due to preparation of standard solutions, from calibration by a linear squares regression and from repeatability, which are in turn a combination of several uncertainties.

Uncertainty Derived from Calibration by a Linear Squares Regression
The chromatography device is calibrated by observing the areas of chromatographic peaks (A) to different levels of concentration for each analyte.The uncertainty in a predicted values (x pred ) due to variability in response (y signal ) can be estimated using the formula given in Eq. (3) (EURACHEM, 2012) The above formula considers variances of slope and intercept and also their covariance using the calibration data, where S is the residual standard deviation, b is the slope, p is the number of measurements to determinate concentration (p = 1), n is the number of measurements for the calibration (n = 5), x pred determined SOA concentration (10 mg/L), x is the mean value of the different calibration measurements (for pyruvic acid x is 9.03 mg/L) and S xx is the sum of squared deviations.As example, the evaluation of the uncertainty associated to calibration of pyruvic acid is shown in Eq. ( 4), meanwhile data for all compounds are summarized in Table 1.
According to Table 1, there are significant differences in sensitivity, as well as variations into linearity.As it can see, the compound has got the highest linearity is glyoxal, meanwhile hydroxyacetone and methyl benzoquinone showed the lowest linearity.These differences in linearity translate into the uncertainty associated with each compound.Therefore, the highest uncertainty corresponds to compounds with lower correlation coefficient.

Uncertainty Derived from Preparation of Standard Solutions
A stock solution of 500 µg/mL of each compound was prepared by dilution of pure compounds in an adequate solvent.Also six solutions, at different levels of concentration, were prepared by diluting stock solutions.

Uncertainty from Stock Solution
The uncertainty associated to the stock solution depends upon the weight of the standard, its purity and volume of liquid in which it was dissolved.Thus, uncertainty is given by Eq. ( 5): To begin with, 5 mg of pyruvic acid were weighted, so uncertainty associated with this mass was given by manufacturer as 7 × 10 -3 mg.
Then the mass of pyruvic acid was dissolved in water using a flask of 10 mL, so that uncertainty of volume had three contributions, temperature, tolerance and repeatability.The uncertainty associated to temperature was calculated from the coefficient of expansion of solvent assuming a rectangular distribution for a temperature variation (20°C ± 5°C).Manufacturer quoted a volume for the flask of 10 ± 0.02 mL so the uncertainty of tolerance was calculated assuming a triangular distribution.The uncertainty of repeatability was calculated by the standard deviation obtained from the weight (10 times) of a flask full of solvent.To sum up, the estimation of uncertainty due to volume is given in Eq. ( 6): The purity of the pyruvic acid was given by the manufactures as 0.98 ± 0.02, and thus standard uncertainty was calculated assuming triangular distribution.
To sum up, the contribution to uncertainty of the preparation of the stock solution of pyruvic acid is given by Eq. ( 7).
Uncertainty from Calibration Solutions Calibration solutions were prepared by dilution of the stock solution according to Eq (8).
Pindado Jiménez and Pérez Pastor, Aerosol and Air Quality Research, 14: 642-652, 2014 647 where C cal is the concentration of a solution of calibrate, C stock is the concentration of the stock solution, V o is the volume of stock solution, V f is the final volume of calibrate solution and F is the dilution factor.Therefore, this uncertainty was calculated according to Eq. ( 9) and Eq (10): Regarding to calculate uncertainties of volume in each calibration solutions, only two contributions were considered; tolerance (manufacture certifies 1% of volume displaced) and repeatability.Table 2 shows information of volumetric material used for preparing calibration solutions.
On the other hand, the uncertainty of dilution factor for calibration solutions of pyruvic acid is summarized in Table 3.
And finally, contribution to uncertainty of calibration solutions for pyruvic acid is given in Table 4.

Uncertainty from Internal Standard
Quantification is based on the internal standard method so the uncertainty due to the stock solution of phenatrene deuterated must be evaluated.The stock solution has a concentration of 10 mg/L with a purity of 0.995, employing 10 µL of stock solution as internal standard.To calculate uncertainty of purity, a triangular distribution is assumed, meanwhile the volume has three influences; calibration, repeatability and temperature effects, as was given in Eq. ( 6).According that, the uncertainty of phenetrane deuterated is given by Eq. ( 11):

Uncertainty Derived from Repeatability
The uncertainty derived from repeatability was due to variation between analyses.Hence the method to determinate this contribution was through calculating the standard deviation obtained from 8 spiked aliquots at a concentration of 10 µg/mL at intermediate precision conditions.Table 5 summarizes results of uncertainties due to repeatability.
That completes evaluation of each contribution to uncertainty from analyte concentration measured by GC/MS.To sum up, the uncertainty due to analyte concentration for pyruvic acid is given by Eq. ( 12) meanwhile results for the rest of compounds are summarized in Table 6: Uncertainty Derived from Recovery In order to examine the bias of the method, and thus estimate its accuracy, a recovery study was performed by the authors.Results showed recovery factors different than 100%.The uncertainty derived from recovery is another contribution to uncertainty, and it can be assessed according to Eq. ( 13): This uncertainty was calculated using eight spiked samples at a concentration of 10 µg/mL.Result of the uncertainty associated to recovery of pyruvic acid is given in Eq. ( 14): The standard deviation associated to recovery ranged between 2% to 23%.Methyl glyoxal showed the highest standard deviation, and thus was the compound with contribution to uncertainty higher.In any case, the authors wish to highlight that no significant differences between compounds were found.
It has been realized that calibration by linear regression gives the largest contribution to uncertainty.It is especially remarkable for hydroxyacetone and methyl benzoquinone, which uncertainties are close to 25%.In both cases was due to those compounds showed lower linearity.Nevertheless, Adipic acid 3.39 × 10 -02 2.84 × 10 -05 9.54 × 10 -04 5.17 for the rest of compounds, this contribution was also high, except for glyoxal and methyl glyoxal because these compounds showed high linearity and sensitivity.The second main source was associated to recovery, which ranged between 3-10%.This uncertainty takes into account the influence of each stage of the analytical procedure assessing loss of SOA mass during each analytical operation.Because of SOA compounds were measured at trace level, we might be concluded those results are acceptable.As general rule, the uncertainty from repeatability is below 5%.However, it must be highlighted that adipic acid and norpinonic acid showed values higher, close to 5%.These values might be due to derivatization reaction was not carried out properly.
The contribution of the stock solution and internal standard to uncertainty was low, being the contribution of calibration solutions slightly higher, ranged between 3 to 6%.On the other hand, the uncertainty components from volume measuring were lower than 0.7%.

Estimation of the Combined Uncertainty
Estimating the combined uncertainty is the final step in the assessment of uncertainty.The relationship between the combined standard uncertainty of mass of SOA and the uncertainties of the dependent parameters on which it depends is given in Eq. ( 16): In order to estimate the combined uncertainty, all individual uncertainties must be expressed as standard deviations.The present work has used a numerical method, suggested by Kragten (1994), to provide a combined standard uncertainty from input standard uncertainties.Estimation of the combined uncertainty for pyruvic acid is in Fig. 4.
Finally, Table 7 shows the combined and expanded uncertainty for each SOA components studied.Due to values used to estimate random effects were higher than six, it is recommended set a coverage factor k = 2 to calculate expanded uncertainty.This choice relies on an assumption of normality in the results.
Combined uncertainty ranged from 8% for glyoxal to 29% for methyl benzoquinone, as can see in Table 7.These results can be comparable with those published by others authors regarding to evaluation of uncertainty associated to analysis of organic species in environmental matrices (Hund et al., 2003;Díaz et al., 2004;Štĕphan et al., 2004).Unfortunately, within the extensive bibliography search made by the authors, any journal had evaluated the uncertainty associated to analysis of SOA compounds deposited onto filters.However, it is remarkable the work of Zádor et al. (2005), which have applied an uncertainty analysis to a wide range of species measured in a smog chamber.They realized that results suggest systematic disagreement between measurements and model calculations.That is consistent with our results, once it has been demonstrated that analysis of these species has great uncertainty.

CONCLUSIONS
An easy to follow guide for calculating the uncertainty of a chromatography mass spectrometry method to analyse SOA compounds has been described.Uncertainty sources  have been identified, a detailed analysis of contributions of each uncertainty source was carried out and the combined uncertainty established.
The largest contribution to uncertainty was calibration of components by linear regression followed by uncertainty from recovery.According to results, remaining contributions might be omitted.In order to decrease the combined uncertainty, authors should proceed in reducing those contributions.Authors propose further development by simplifying the analytical procedure as much as possible, using more efficiently extraction stages or novel derivatization agents.
The combined uncertainty was calculated and ranged between 8% for glyoxal to 29% for methyl benzoquinone.According to results, the authors have demonstrated that the analysis of SOA components at trace level have a considerable uncertainty so it must taken in consideration by the authors in the future.
1. Equations to calculate uncertainty components.

Uncertainty derived from repeatability.
Table 12: Uncertainty derived from repeatability.

Uncertainty derived from recovery.
Table 13: Uncertainty derived from recovery.

Fig. 1 .
Fig. 1.Cause and effect diagram of uncertainty associated to SOA analysis.

Fig. 2 .
Fig. 2. Mathematical equations employed in the estimation of uncertainty associated to SOA.

Fig. 3 .
Fig. 3. Standard uncertainties associated to the analysis of SOA.

Fig. 4 .
Fig. 4. Combined uncertainty, calculated by the method of Kragten, for the analysis of pyruvic acid.

Table 1 .
Calibration parameters of compounds studied.Mean value of calibrate concentrations (µg/mL); S, residual standard deviation; S xx sum of squared deviation. *

Table 2 .
Uncertainty associated to volumetric material employed to prepare calibration solutions.

Table 3 .
Uncertainty associated to dilution factor of calibration solutions of pyruvic acid.

Table 4 .
Contribution to uncertainty of calibration solutions for pyruvic acid.

Table 6 .
Uncertainty associated to analyte concentration measured by GC/MS.

Table 7 .
Combined and expanded uncertainty associated to the analysis of SOA.

Table 1 :
Uncertainty from calibration by a linear squares regression.

Table 2 :
Uncertainty of stock solution: influence of purity.

Table 3 :
Uncertainty of stock solution: influence of mass.

Table 4 :
Uncertainty of stock solution: Influence of volume (contribution of temperature).

Table 5 :
Uncertainty of stock solution: Influence of volume (contribution of tolerance of flask).

Table 6 :
Uncertainty of stock solution: Influence of volume (contribution of repeatability).

Table 7 :
Uncertainty of calibration solution: Influence of dilution factor (Uncertainty of syringe).

Table 8 :
Uncertainty of calibration solution: Influence of dilution factor.

Table 9 :
Uncertainty of each calibration solution I.

Table 10 :
Uncertainty of each calibration solution II.

Table 11 :
Uncertainty of each calibration solution III.