The recovery of n-heptane as a percent of the target concentration of the generated atmosphere was evaluated for intra-run variability at 40 ppmv, 400 ppmv, and 800 ppmv. The LCS samples had a mean recovery of 99.0% which was used to apply a correction to the sample recovery of all samples in the concentration study. For a target of 40 ppmv (n = 6), mean recovery was 103% with a relative standard deviation (RSD) of 6%, for 400 ppmv recovery was 111% with an RSD of 4%, and 800 ppmv recovery was 109% with an RSD of 3%. The RSD of the mean intra-run recovery versus concentration is plotted in Figure 3. The trend demonstrates that lower concentrations resulted in a higher RSD. Data was plotted with the concentration axis in log scale in Figure 3 to illustrate that the relationship between sample concentration and variability is more appropriately portrayed when the x-axis is plotted logarithmically so that it does not imply the extension of the trend line to the y-intercept (Horwitz 1982; Sáez and Rittmann 1992; Zorn et al. 1997).

The RSD of intra-run percent recoveries of 40 ppmv n-heptane from a data set of 16 runs of four samples per run are plotted in Figure 4 where they ranged from 0.24% to 3.95%. The mean of the intra-run RSD was 2.19 ± 1.02% for the 16 runs. There was a high degree of consistency of variability across the sample sets for the 16 runs. The mean intra-run RSD of 2.19% (n = 64) was less than the RSD of 6.19% (n = 6) at 40 ppmv from the concentration study, and closer to the RSD of 2.47% (n = 6) for the 800 ppmv samples in Figure 3.

The experiments for the n-heptane 40 ppmv samples in the concentration study and the 16-run study were done at separate laboratories by separate researchers. The larger RSD of the recovery could have been due to the researcher’s experience and technique. There was also a larger sample loading and sampling time (4.8 liters during 120 min) in the concentration study experiments than (1.5 liters during 30 min) in the 16 runs of the 40 ppmv dataset.

In a mixture of 10 VOCs, the intra-run RSD of the percentage of n-heptane recovery from 16 runs (Figure 5) ranged from 2.6% to 13.1% with a mean of 8.33 ± 3.4% for the 16 runs. This result was consistent with expectations that a lower concentration would result in larger variability (Taylor et al. 1977). The RSD of the recovery is comprised of several factors including atmosphere variability, analytical variability, and variability in desorption efficiency. The variability of the analytical spikes was relatively consistent for heptane between the 40 ppmv dataset and the 10 VOC mixture dataset (plotted in Figures S1 and S2 in the supplementary information), which indicated that the variability in the atmosphere and desorption efficiency were the larger influences on the differences in variability between the two datasets. Influences contributing to the greater variability of n-heptane recovery from the 0.1 ppmv VOC mixture versus the 40 ppmv n-heptane samples could include irreversible chemisorption on CSC which contains surface metal oxides and organic functional groups which becomes more of a factor at lower concentrations (Guenier and Muller 1984; Ballesta et al. 1999; Harper 2000). Variability in adsorption efficiency or the coefficient of desorption can both be affected by matrix effects in the presence of more than one compound (Ballesta et al. 1992).

The bias of the recovery was evaluated from three different VOC profiles from datasets of sixteen replicate runs, with 4 samplers in each run. For each run, the mean concentration of the intra-run result of analysis versus the target concentration of the generated atmosphere was calculated as a percent recovery. A Grubb’s test for rejection of an observation was applied to each of the datasets. Histograms showing the distribution of the percent recovery for each of the chemicals are included in the supplementary information in Figures S3 through S5. Most compounds had some variation of a bell-shaped distribution around a central maximum, however, there were outlying recovery bins, somewhat skewed distributions, and what appeared to be bi-modal distributions. In the case of toluene, the outlier which was identified from the Grubbs test was easily identifiable via a visual inspection of the histograms. In the case of toluene, the outlier which was identified from the Grubbs test was easily identifiable via a visual inspection of the histograms.

The recovery of n-heptane with a target concentration of 40 ppmv as an intra-run mean and standard deviation for each of the 16 replicate runs is shown in Table 1. The mean recovery of the 63 samples was 104 ± 3%. None of the intra-run mean recoveries were rejected via Grubb’s test. One sample tube from run 9 broke before it could be analyzed. Recovery was corrected for a desorption efficiency of 105% from the LCS recoveries. Analytical spike and LCS data have been included in the supplementary information in Table S1.

The intra-run mean recovery and the standard deviation of the mean recovery are shown in Table 2 from dynamically generated atmospheres containing BTEX at a target of 0.1 ppmv for each component. The mean recovery of benzene was 99 ± 5%. Toluene and ethylbenzene, both had a mean recovery of 100 ± 5%, and o-xylene, 97 ± 5%. The LCS mean desorption efficiencies of 95.3%, 95.2%, 97.6%, and 92.9% for the BTEX components, respectively, were used for the correction of the recoveries. No results in this set were rejected via Grubb’s test.

In a dynamically generated atmosphere of a 10 VOC mixture targeted at 0.1 ppmv of each component, the percent recovery of the intra-run mean (n = 4 samples per run) and standard deviation of each of the chemical components are shown in Table 3. Although chloroform was below the LOQ but above the LOD, the results have been included as contextual information. Grubb’s test rejected one sample result of toluene from run 15, which was identifiable in the histogram of recovery in the supplementary information Figure S3I.

Toluene had the highest percent recovery among the VOCs (excluding chloroform) with a 113% percent recovery in run 15. The identification of toluene as an outlier while the remainder of the VOCs were not identified as outliers suggests that the difference may be due to variability associated with the analysis of toluene, not the generation of the VOC atmosphere. However, toluene is also present in many lab environments and contamination cannot be ruled out as affecting this result. The lowest mean intra-run recovery was observed for n-heptane at 75% in run six, however, this was not excluded via the Grubbs test, though the lower recoveries of other VOCs in that run would suggest that there was a difference in performance in run six. The QC spikes, done during the analysis, produced a maximum desorption efficiency of 106% for heptane, and a minimum of 100% for o-xylene (analytical spike desorption efficiencies for all 10 VOCs shown in the supplementary information Table S2). The laboratory control spike recovery values were used to correct sample recovery results. Seven out of the ten analytes had their lowest recovery in run six, however, the variability for that run was not flagged as an outlier in the evaluations using Grubb’s test, or Bartlett’s test for homogeneity of variance.

There was an expectation of a relatively low bias from the sampling and analysis methods from previous evaluations of alkanes on CSC sampling media (NIOSH 2003a, 2003b). NIOSH Method 1500 lists biases between 1% and 10% for a range of comparable alkanes, which was within the range of the biases measured except for chloroform, which was below the LOQ (NIOSH 2003b). Recoveries from the 0.1 ppmv 10 VOC mixture had a larger bias on average than the other data sets, 40 ppm n-heptane, and BTEX.

A Bartlett’s test for homogeneity of variance was used to determine if all the samples in the 16-run set could be combined to calculate a pooled RSD. The Bartlett’s test was computed using the R language and environment for statistical computing using the Bartlett test function (R Core Team 2018). Bartlett’s test null hypothesis, p > 0.05, indicated that the intra-run RSD values could be pooled as shown in Table 4. The pooled RSD (sr,p) was determined using the formula in Equation 1 from (Olofsson et al. 1981; NIOSH 1995): (1) sr,p=[∑(si2x¯i2)(ni−1)/∑(ni−1)]1/2 where s is the standard deviation, x¯ is the mean, and n is the number of samples. The pooled RSD can be thought of as an improved estimate of the imprecision of the process (Olofsson et al. 1981). There are several contributing sources of uncertainty including inter-day and inter-run variabilities in the pooled RSD, which are not present in the intra-run imprecision. Thus, the pooled RSD should be considered a computation of the total imprecision or variability of the system.

For 16 runs there were 15 degrees of freedom (DoF) or categories (runs) that were independent of each other. The closer that χ2 (the statistical result of the chi-squared test) divided by the DoF comes to unity is indicative of higher confidence in the data fitting. The maximum χ2 values for 15 DoF at the 5% significance level is 24.996. All values of χ2 indicated confidence in the fitting of the data, though the fitting of ethylbenzene and o-xylene in the 10-VOC mixture was approaching the limits of fitting and confidence in homogeneity.

The pooled RSD of the recovery showed an increase with a greater number of compounds in the generated atmosphere. Among the different atmospheres tested, the single component 40 ppmv n-heptane atmosphere exhibited the lowest pooled RSD as shown in Table 4. This was followed by the 0.1 ppmv BTEX atmosphere samples, while the 10 VOC mixture had the highest pooled RSD for both sample recovery and bias (mean recovery % – 100%). This was consistent with samples of test atmospheres containing a single VOC having been previously shown to have lower variability than samples of atmospheres containing mixtures of VOCs (Ballesta et al. 1992).

For air-sampling method development, NIOSH has defined total variability in Equation 2, which includes variability from aspects of sampling in Equation 3, and analysis in Equation 4 (NIOSH 1995). The estimate of the variability of the total procedure (S^rT) or method variability is the square root of the sum of the squares of variability in sampling (S¯rS), analysis and desorption efficiency (S¯rA+DE¯), and a pump error (srP) as in Equation 2 and shown in Table 5 for each of the VOC sets. (2) S^rT=(S¯rS)2+(S¯rA+DE¯)2+(SrP)2

The SrP, used to approximate variability due to personal sampling pumps used during field sampling, is typically estimated as 5%, which is added as a component of the total uncertainty of the method.

The variability of sampling and generation (S¯rS), shown in Equation 3, is the square root of the difference of squares of the pooled variability of generated samples (S¯r2) and the pooled variability obtained from the analysis of spiked samples (S¯r1). The S¯rS as an estimate of the precision attributed to sampling in the AGS is shown in Table 4 for each compound. In cases where S¯r1 was larger than S¯r2, S¯rS is set as zero, and alternative calculations are used to calculate the variability of the method (Taylor et al. 1977). (3) S¯rS=(S¯r2)2−(S¯r1)2

The S¯rS may have contributions from components of the AGS such as analyte and carrier air delivery systems, variability of the CSC sampling tubes such as charcoal packing, and the critical orifices used to control the sample flow rate. It is important to recognize that compounds applied as liquid spikes to generate analytical samples have the potential to desorb differently than compounds that were adsorbed via vapor pulled through the sorbent tube. There are a couple of factors that differentiate spiked samples from air samples. The amount of water present in the air samples has the potential to affect desorption efficiency, particularly for compounds that have some solubility in water (OSHA 2024). Second, spiked samples are injected into a small region of the sampling media rather than being distributed more evenly through the sorbent material as an air sample drawn through the media.

The analytical and desorption efficiency variability S¯rA+DE¯ is a derived correction to S¯r1 based upon sample size (n is the number of samples) as shown in Equation 4: (4) S¯rA+DE¯=S¯r1(n+1)n

The pooled variability from the analysis procedure (S¯r1) has contributions from both the sorbent desorption procedure and the instrumental analysis and was quantified using the quality control (QC) spike data. The experimental designs in this study included replicates of analytical spikes, which were used as variability of the analysis procedure. The pooled variability of the QC spikes done during analysis was calculated as S¯r1 from the RSD of the laboratory control spike replicates (S¯rLCS), the blind spike replicates (S¯rBS) and sample replicates (S¯rSR). Analytical spike targets and recoveries were included in the supplementary information Table S1, along with S¯r1, the pooled RSD of the analytical spikes in Table S3.

For all analytes, there was low analytical variability S¯r1 and additional variability from contributions due to generation and sampling in S¯r2: The analytical variability S¯r1 was similar to and in some cases lower than the historical data in Table 6. One exception was benzene, which was larger in the NIOSH source data in Table 6. Compared to the other compounds, there was a relatively large contribution of the analytical variability of trichloroethylene in our study as shown in Table 5 which was also present in Table 6.

S¯rS calculated from the total variability of the generated samples S¯rS and the analytical variability S¯r1 has contributions from two distinct sources, the generation process, and the sampling. The variability from generation and variability from the sampling method cannot be easily separated using the data available in the experiments that have been presented. However, a low S¯r2 indicates that both the variability attributable to the generation system and the variability attributable to the sampling method are low. The low S¯r2 of 0.0243 for n-heptane in the 16-run set was consistent with historical data in Table 6 and was an indication that the AGS had low variability on par with previous AGSs used to produce the data in Table 6. At lower concentrations of n-heptane in the 0.1 ppmv 10 VOC mixture, the generated sample variability, S¯rS, was 0.0944 and was consistent with expectations of increased variability at lower concentrations.

The S^rT denotes an estimated total precision of the method and was largely influenced by the inclusion of SrP, compared to the contributions of S¯rS in Table 6. S¯rS in Table 6 was calculated using Equation 3 from S¯r1 and S¯r2 data provided by Taylor et al. (1977). Generally, lower concentrations and mixed VOC samples had a larger total variability S^rT in Table 5 than the historical data from Table 6. The S^rT in Table 6 does not consider concentration dependence though it was derived from single-compound evaluations at three relatively high concentrations related to exposure limits. Also, the effects of multiple VOCs were not present in the Table 6 data. The S^rT of the historical data at 5% for toluene was not far from the 7% at the lower concentration BTEX data set. Additionally, it was found that the variability of tetrachloroethylene at 0.1 ppmv was 9%, whereas the historical data at a much larger concentration was 5%. The similarity of S^rT for trichloroethylene in our data at 9% and the 8% from the historical data was particularly remarkable given the significant difference in the concentration of the samples. The larger S^rT from our BTEX and the 10 VOC mixture studies were consistent with the variability of sampling of multi-analyte mixtures at low concentrations versus single analytes at the higher concentration ranges in the data from NIOSH methods. The mesitylene data from OSHA 1012 was generated using sampling concentrations closer to the concentration of the 10 VOC mix and had an overall precision of 10.5%, which is similar to the 9.65% from our observations of mesitylene in the 10 VOC mixture. Differences in method development procedures did not enable direct comparison for several components of the mesitylene evaluation and, thus were not applicable (n/a).

For some aspects of the sample generation, collection, and analysis there was no way to isolate individual components for an independent measure of variability. This limited the ability to assign sources of variabilities. The data upon which this paper is based were assembled from independent studies and some of the differences in these studies limit the ability to draw conclusions that otherwise might have been determinable from a different experimental design. The set of VOCs studied was representative of a small number of compound types. There may be VOC-dependent variabilities that were not observed in the limited VOC set. The conclusions drawn have made the best use of the experimental design and available data to understand the observed variabilities.

When generating dynamic atmospheres for method development it is important to design experiments that enable analysis of the variability of the sample results, which be used to distinguish between multiple sources of variability. If possible, determining the variability and/or bias inherent to the AGS, and subtracting that from the overall observed variability and bias during method evaluation can give a more accurate measure of the sampling and analytical method variability and bias. Historically, much of the work related to the variability of samples from dynamically generated atmospheres and environmental air monitoring has focused on concentration ranges around exposure limits. The studies in this manuscript show that variability for lower concentrations of analytes can increase compared to variability at moderate concentrations near the exposure limits. With current trends for existing exposure limits to be revised to lower concentrations and increased interest in low-level chronic exposures, it is important to characterize generation system variability at low levels as part of method development.