Environ. Sci. Technol. 2003, 37, 1633-1638
Reevaluation of the Employment of Fick’s Law for Diffusion Dosimeters JOHN H. CROSS* Environmental Sciences, School of Public Health, University of Texas-Houston Health Science Center, 1200 Hermann Pressler Drive, Houston, Texas 77030-3900
J ) SRCAIR
This paper reconsiders the means of applying Fick’s first law to passive diffusion dosimeters. The performance of the organic vapor monitor (OVM), a commercially available dosimeter, is modeled in terms of gradients, which are generated by evaporating a compound from the dosimeter. The fluxes induced by the gradients are determined gravimetrically. The ratio of a flux and a gradient is reported as a Fick’s law proportionality constant, the sampling rate. The sampling rate for the gradient across the OVM is calculated from a harmonic average of the sampling rates of two other gradients. The OVM sampling rates for nine compounds determined by the new methodology agree well with published values. Further analysis of the other two gradients provides a value for an apparent reduction in sampling rate in the absence of airflow across the dosimeter (a boundary-layer effect). Procedures are also described to validate measured air concentrations by determining the sampling rates before and after exposure and by correcting for the boundary-layer effect. Sampling rates were found to be stable during 2-4-day exposures in a variety of conditions. In contrast, the boundary-layer effect caused the measured air concentrations to be substantially lower than the estimated true air concentrations.
Introduction Diffusion dosimetry began in 1973 when Palmes and Gunnison (1) invented the concept. Their device was a length of plastic tubing with one open end and an adsorbent at the closed end. They presented data demonstrating that the quantities of water or sulfur dioxide collected on the adsorbents were related by Fick’s first law to the air concentrations external to the tube. They formulated Fick’s law in a format suitable for the design of their device:
J ) D(A/L)(CAIR - CPAD)
(1)
where J is the flux (mg/s), D is the diffusion coefficient in air (cm2/s), A is the diffusion cross-sectional area of the dosimeter (cm2), L is the diffusion path length from the inlet to the adsorbent (cm), CAIR is the analyte air concentration (mg/cm3), and CPAD is the analyte air concentration at an adsorbent pad (mg/cm3). The flux (J) is the measured quantity. It is calculated from the mass of analyte collected on the adsorbent as determined by an appropriate laboratory analysis divided by the time for which the dosimeter was exposed to the atmosphere. When the adsorbent functions as a perfect sink, CPAD equals zero and CAIR can be calculated from known values of D, A, and L or from a calibration that * Phone: (281)333-5869; e-mail:
[email protected]. Present address: 1789 Saxony Lane, Houston, TX 77058. 10.1021/es020706o CCC: $25.00 Published on Web 03/11/2003
2003 American Chemical Society
determines the proportionality constant DA/L. This constant is termed the sampling rate (SR) because it has the units of flow (volume/time). Its use facilitates comparisons with active sampling methods, which have a measurable flow rate (2). When SR is determined in a calibration method, eq 1 simplifies to
(2)
The most widely used calibration method utilizes an exposure chamber to generate a known concentration of analyte, CAIR. The flux is measured, and the sampling rate is calculated. Equation 1 has become the governing equation for diffusion dosimetry. It is used to guide design efforts and to assess performance. Equation 2 is used to calculate air concentrations from flux measurements (3). The devices described by Palmes and co-workers (1, 4) were found to perform as predicted by eq 1 when D was taken as the diffusion coefficient of the analyte in air. Within a few years, however, devices were available (5, 6) that did not perform according to eq 1 but that were claimed to function by Fick’s law. The advantage of the newer devices was a higher sampling rate, allowing shorter sampling times, or less sensitive analytical methods for the flux measurements. The “nonideality” was found to arise from mass transfer considerations (5). Briefly, the sampling rate calculated from D, A, and L was higher than mass transfer would allow. This effect became known by several names such as boundary-layer effect (7), starvation effect, or wind velocity effect. The latter refers to the finding that air moving across the inlet of the device would compensate for undersampling. It is sometimes advised that dosimeters, particularly those used for area monitoring, should be placed in a location where the air velocity is adequate to prevent monitor starvation (8). For dosimeters with short path lengths, eq 1 has a limitation. Fick’s first law describes the relationship between a flux and the concentration gradient that causes the flux as a direct proportionality. Furthermore, the value for the proportionality is a constant. Thus, a change in a gradient causes the associated flux to change but does not cause the proportionality constant to change. The law belongs to a class of similar laws collectively called transport phenomena, which include heat flow and electrical flow. In eq 1, the Fick’s law proportionality constant is D, the diffusion coefficient in air. It is customarily taken to be the same for all dosimeter designs. Since A is a scaling factor, the diffusion path length (L) is the parameter usually invoked to describe nonideal dosimeter performance. With L as the variable, eq 1 becomes a power equation. When L is small, one can expect that sampling rates predicted from DA/L will be too high as has been reported. Using eq 1, it becomes difficult to decide if a sampling rate lower than predicted is due to the power equation or due to a physical cause, such as a boundarylayer effect. In addition, since L is not the Fick’s law proportionality constant, there is a lack of conceptual rigor in its use. In practice, the limitations of eq 1 have been overcome by devising values for L (9) or A/L (10) to correct the sampling rate. Perhaps because eq 1 or the correction factors fail to predict performance or to provide clear rationales, dosimeters are not recognized as primary analytical methods. This is surprising because their simplicity of construction and nominal adherence to one of the transport phenomenon should define their performance better than appears to be the case. Instead, they are usually validated by comparison VOL. 37, NO. 8, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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with a known, reliable method, usually an active sampling method (11, 12). Validation protocols, promulgated by professional organizations, are also used (13). These require extensive, expensive testing that probably discourages the selection of dosimeters for more applications. Equation 2, in contrast, is a simple proportionality equation. Since the sampling rate (SR) conceptually includes the path length, the inlet area, and the diffusion coefficient, it is unnecessary to specify values for them. This paper describes a performance model based on eq 2. As in almost all dosimeter research, gradients are established, and the resulting fluxes are measured. Since the model emphasizes gradients over path lengths, I have called it “gradient analysis”. The goal was to be able to use gradient analysis to predict performance and to detect and compensate for errors arising during exposure assessments in the field. Since an extensive literature on dosimetry has developed in the 30 years since the first Palmes and Gunnison paper, the progress of the research was judged by external consistency with published experimental results. This literature has been recently reviewed in a chapter in an industrial hygiene textbook (14). The proceedings of a symposium on diffusive dosimetry has been published recently (15). For gradient analysis to be successful, it is necessary to generate the gradients defining a dosimeter and subsequently to measure the resulting fluxes. The exposure chamber method has significant limitations. It is capital-, time-, and labor-intensive. In addition, the technical difficulties of controlling several variables for long periods can cause the results to be too imprecise to detect small performance differences. Furthermore, the adsorbent pads from exposed dosimeters must be analyzed. This is expensive, is timeconsuming, and confounds sampling errors with analytical errors. To collect the quantity and quality of data required to perform a gradient analysis on one type of dosimeter, I modified an existing method for measuring diffusion coefficients (16, 17). The basis of the method is to evaporate a compound from a capillary tube. The compound’s vapor pressure generates a gradient between the surface of the compound and the air above the tube. The flux is determined from the length of liquid that evaporates in a measured time. If the cross-sectional area of the tube is small as compared to the length, the proportionality constant is the diffusion coefficient of the compound in air. To simplify the method for gradient analysis, I measured the mass evaporated using an analytical balance. I validated the adapted method by comparing air diffusion coefficients measured by the adaptation with those reported by Lugg (17). The dosimeter used was the organic vapor monitor 3500 (OVM) manufactured and marketed by 3M. It has been available commercially for a number of years and has been used for both occupational (12) and environmental exposure assessments (18). The sampling rates for 63 volatile organic compounds (VOCs) have been measured with it, and sampling rates for many other compounds can be derived from the measured ones (3). It is supplied with a charcoal adsorbent pad for collecting VOCs. It has a “badge” configuration because the inlet area is large relative to the diffusion path between the inlet and the charcoal adsorbent pad (A ) 7.71 cm2, L ) 1 cm). For use with the evaporative analytical method, the charcoal pad was replaced with a paper dispenser. The device is reported to deviate from the performance predicted by eq 1 (10). This paper describes the application of gradient analysis to determining several performance characteristics of OVM dosimeters. The evaporative analytical method is described and validated by comparing air diffusion coefficients measured with it to Lugg’s diffusion coefficients (17). The method is then used to determine sampling rates, which are found 1634
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to be the harmonic average of two gradients formed during evaporation. Further analysis of the same two gradients provides a value for an apparent reduction in sampling rate in the absence of airflow across the dosimeter (a boundarylayer effect). Two procedures for validating air concentrations from dosimeters deployed in the field are included. The first is a method to assess if the calibration factor (sampling rate) remains constant throughout the sample collection time. The second is a test to estimate the true air concentration in the presence of a boundary layer.
Experimental Procedures Determination of Diffusion Coefficients of VOCs in Air. An Ohaus (Florham Park, NJ, model AP250D) analytical balance capable of reading to 0.01 mg was used. Fluxes were measured by evaporating VOCs from 10-mL graduate cylinders (Fisher Scientific, Houston, TX, catalog #085571A) placed on the weighing pan in the balance chamber. The cylinders were approximate substitutes for the capillary columns used by Desty et al. (16). The compounds tested were all reagentgrade or better quality derived from laboratory stocks. One thickness of flat finish brown paper towel at the bottom of the cylinder served as a dispenser for a quantity of liquid sufficient to provide a steady flux for the duration of the measurement. The air concentrations immediately above the dispensers were calculated from the ideal gas equation with vapor pressures calculated from the Antonine constants (19, 20). The vapor pressures were calculated at the temperatures inside the balance chamber at the time of flux measurements using a HOBO HO8 temperature/relative humidity sensor (Onset Computer Corporation, Pocassset, MA). The temperatures (near 25 °C) varied with the season and the operation of the air conditioning. The air concentrations of the VOCs inside the balance chamber were taken to be zero. Depending on the volatility of the VOC, mass readings were collected periodically for 10-20 min. Diffusion coefficients were calculated from Desty et al. (16) (eq 3). The symbols used in Desty et al. have been changed to conform to those used in eq 1:
J ) DMPA/RTL ln(P/(P - p))
(3)
where J is the flux (mg/s), D is the diffusion coefficient in air (cm2/s), M is the molecular weight of the analyte, P is the pressure above the mouth of the cylinder (taken to be 1 atm), A is the diffusion cross-sectional area of the cylinder (cm2), R is the gas constant (atm cm3 mol-1 K-1), T is the absolute temperature (K), L is the diffusion path length from the cylinder mouth to the adsorbent pad (cm), and p is the vapor pressure of the VOC (atm). The term ln(P/(P - p)) is a correction factor for the volatility of the VOC. Determination of Sampling Rates from OVMs. OVMs (Figure 1 with part of the windscreen cut away to show the configuration and Figure 2 shows the relative relationship between components) were assembled for each experiment by random selection from a supply of components. Plastic components of OVMs purchased from 3M (St. Paul, MN) were recovered after the OVMs had been used for air sampling and the charcoal pads had been removed for analysis. All four plastic components were reused, but care was required to reinstall the windscreens tautly. As for the air diffusion measurements, one thickness of flat finish brown paper towel served as a dispenser for a quantity of VOC (100-300 µL) sufficient to provide a steady flux for the duration of the measurement. (The dispensers were visibly damp after the measurements.) Two flux measurements were required to determine an OVM sampling rate. For one, a paper dispenser about the diameter of the adsorbent pad (3 cm) was placed on the bottom of the dosimeter body where the charcoal
FIGURE 1. OVM 3500 dosimeter. The windscreen is cut away to show the internal components. adsorbent pad had been. For the second, the windscreen was replaced with a circle of aluminum foil with one layer of paper on top of it. The windscreen retainer was clamped over both layers such that the foil was not visible in the area encompassed by the windscreen retainer. Flux measurements from the OVMs were more exacting than those from the graduate cylinders because the fluxes were significantly greater. An RS232 port on the balance transferred a mass reading to a computer at a predetermined interval from 1 to 15 s (HyperTerminal Version 4.0, Hilgraeve, Monroe, MI). Using Microsoft Excel 97, mass data (y-axis) were regressed (LINEST array function) against time points (x-axis). The SLOPE function multiplied by 1000 gave the flux in milligrams per second. An R 2 > 0.995 was the criterion to accept each set of experimental flux data. The data were discarded if curvature was detected at the beginning or end of the data series. Data were typically collected for 1-3 min after the balance pan was allowed to stabilize for about 1 min. One replicate flux measurement could be made in 5-7 min. Sampling rates were calculated from eq 2. No correction factor for the volatility of the VOC was used. Validation of Measured Air Concentrations. Sampling Rate Changes (Calibration Changes) during Sample Collection. New OVMs were exposed in the field for 2-4 days. The deployment conditions were representative of urban environments. In two instances, damaged dosimeters (one contaminated with cooking oil and a second with a split in the windscreen) from exposure assessment studies were analyzed to determine if the damage had changed the calibration factor significantly. After being recovered from the field, the sampling rates of the exposed dosimeters were measured using the procedure described in the previous section. That is, the dosimeters were disassembled, the charcoal pads were removed, and the dosimeters were reassembled with paper dispensers in place of the charcoal pads. Flux measurements were also made from the windscreen position. During the same measurement session, fluxes were measured from new dosimeters that had not been deployed in the field (lab blanks). Although the dosimeters could have been exposed to many compounds while they were exposed, the fluxes were usually measured with n-heptane because stable, replicable fluxes could be measured in a period of 1 min. A simplification of the standard procedure was also developed. In the simplified procedure, n-heptane was injected with a microliter syringe through the windscreen onto the carbon adsorbent pad. Surprisingly, the pad did not become warm, and the flux from it was comparable to that from a paper dispenser.
Estimation of the True Air Concentration in the Presence of a Boundary Layer. Measured air concentrations from dosimeters exposed to outdoor air were corrected by the method of Persoff and Hodges (21). This method uses a relationship between measured air concentrations and fluxes at several diffusion path lengths to estimate a true air concentration. The path lengths chosen for this example were 0.55, 1.0 (standard), and 1.55 cm. Placing 0.5 cm thick PTFE cylinders inside the dosimeter bodies made OVMs with a measured diffusion path length of 0.55 cm. Placing PTFE cylinders inside OVM 3500 dosimeters, which have an extension section that doubles the path length, made OVMs with a path length of 1.55 cm. The sampling rates for the 0.55- and 1.55-cm dosimeters were determined by the evaporative method as described above. Two sets of dosimeters (with charcoal adsorbent pads) were exposed to outdoor air under two conditions, airflow and stagnant air. For airflow exposures, three dosimeters with each diffusion path length were hung where they were exposed to the prevailing wind. The samples were collected in April when the wind speeds were subjectively judged to be higher than normal. For stagnant air exposure, three dosimeters of each path length were placed in a 25-cm-deep box covered with cheesecloth. The dosimeters exposed to airflow and stagnant air were placed close together such that the only environmental condition differing between them was the air speed. After an exposure of 63 h, sampling was halted by replacing the windscreens with an impervious plastic cap (22), the dosimeters were returned to the laboratory in individual cans with sealed tops, and the adsorbent pads were removed and analyzed by a GC/MS analysis (23). Carbon tetrachloride was the only compound detected above a signal-to-noise ratio of 3. To estimate the true air concentration, the measured air concentrations of carbon tetrachloride at each path length were plotted against the fluxes at that path length. Extrapolation to zero flux (the y-axis) gave the corrected air concentration (21).
Results and Discussion This reevaluation of the use of Fick’s first law with diffusion dosimeters, which I have called gradient analysis, is based on two ideas. First, the gradients are described with a Fick’s law proportionality constant, the sampling rate (eq 2). Experimentation based on eq 1 is generally expressed in terms of path length. Second, the sampling rates are determined by a fast, simple, accurate, and precise evaporative technique. The evaporative technique was initially developed by Desty et al. (16). It was subsequently used by Lugg (17) to measure the diffusion coefficients in air of more than 130 VOCs considered to be important in environmental studies. In addition, Lugg compared his experimental diffusion coefficients with values calculated by several widely used methods. Thus, I judged the data set to be comprehensive and reliable. The modified evaporative method differed in two ways from the procedures reported by Desty et al. (16) and Lugg (17); the OVM is wider and shorter than a capillary tube, and the mass measurements were made by weighing. To validate the changes to the evaporative method, air diffusion coefficients were measured by the adapted method and compared with the same values reported by Lugg (17). To be relied on, the method had to provide accurate air diffusion coefficients. The air diffusion coefficients were found to be within 2-6% of the reference values (Table 1). Since the agreement between experimental and calculated values reported in Lugg’s paper (17) were of about this magnitude, I judged the adapted method to be acceptable. Sampling Rates for VOCs. In initial experiments, the sampling rates measured from the position of the adsorbent pad were lower than those reported by 3M (3). Since earlier VOL. 37, NO. 8, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 1. Comparison of Experimental and Reference Values of Diffusion Coefficients compound
DAIR (cm2/s)
DREFa (cm2/s)
differencea (%)
acetone benzene dichloromethane n-octane toluene p-xylene
0.0988 0.0916 0.1060 0.0593 0.0874 0.0657
0.1049 0.0932 0.1037 0.0616 0.0849 0.0670
6 2 2 4 3 2
a
From ref 16.
FIGURE 2. Schematic depiction of the gradient model for the OVM. workers had described undersampling due to a boundary layer, I inferred that the lower sampling rates were an effect of a boundary layer. To account for a boundary-layer gradient, I formulated the model shown in Figure 2. This model was analogous to a dosimeter with two gradients whose sampling rate had been described by Palmes and Lindenboom (24). They reported that the gradients acted in series and that the sampling rate of the series could be calculated from the harmonic average of the gradients. Equation 4 is the harmonic average required for the OVM dosimeter. The sampling rate at the position of the adsorbent pad was designated SRTOTAL. It is the harmonic average of the gradients across the dosimeter (SROVM) and the boundary layer (SRBL):
1/SRTOTAL ) 1/SROVM + 1/SRBL
(4)
With three gradients, it was necessary to determine the sampling rates for two gradients to calculate the third. Thus, SRTOTAL and SRBL were measured for nine VOCs. Although the procedure is described in the Experimental Methods section, several critical measurement parameters were defined during the experimental effort. (i) Since the balance pan was enclosed and mass data were acquired after a 15-60-s delay, the air surrounding the dosimeter was quiescent if not stagnant, and the boundary layer was maximized at a constant value. (ii) A substantial concentration gradient existed throughout the measurement period. A worst-case scenario is given as an example. Evaporation of acetone from the windscreen level to determine SRBL had a flux of about 1.5 mg/s. For a 60-s measurement, the total evaporated was about 90 mg into the 5-L balance pan chamber giving a concentration of about 0.018 mg/cm3. The concentration generated by the vapor pressure of acetone just above the paper dispenser was 0.72 mg/cm3. The concentration gradient was thus a minimum of about 40:1. (ii) Valid measurements required that the paper dispensers remained saturated with liquid VOC and that the liquid temperatures remained reasonably constant throughout the measurement period. If the pads dried out or the temperature decreased, the fluxes decreased as the measurement time increased. The rationale for obtaining the fluxes as the slopes of regression curves was to detect the resulting curvature. (iv) For SRBL, the inlet area was critical. This was achieved by surrounding the paper pad at the windscreen level with the windscreen retainer. If the dispensing area was not welldefined, the precision of the measurements was lower. 1636
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(v) Better results were obtained when SROVM was calculated from measurements of SRTOTAL and SRBL made during the same measurement session. (vi) Reassembly of the dosimeters had little effect on the sampling rates. When these parameters were understood and controlled, the sampling rates obtained by the evaporative method compared well with previously published values. I found that relative standard deviations of 3-5% for three replicate measurements could be obtained readily. For the less volatile compounds, the relative standard deviation would often be less than 1% for three replicates. Table 2 includes both of the gradient measurements required to calculate SROVM from eq 4. It also contains the standard deviations for the measured quantities. Only for dichloromethane, the most volatile compound, was SROVM greatly different from the published value. This VOC was observed to undergo evaporative cooling during measurement of SRBL, and the flux decreased from the beginning of the measurement period. The use of the volatility correction factor from eq 3 did not compensate. Since the SROVM for acetone agreed with the reference value, the evaporative procedure may be best applied to compounds boiling above about 60 °C. The close correspondence between the sampling rates measured by 3M in an exposure chamber (3) and those determined by the evaporative method validate the gradient analysis approach. The way SROVM depended on SRBL was unexpected. It confirms earlier work that demonstrates undersampling in badge dosimeters (5). I had expected that the OVM sampling rate would be attributable to the components of the dosimeter with the windscreen contributing most to the nonideal sampling rates that had been reported (10). Instead, the conclusion to be drawn is that a Fick’s law calculation with two gradients is a good model for OVM performance. A connection that has not been made previously is that the boundary layer can be described by a Fick’s law proportionality constant. Tompkins and Goldsmith (5) originally described the boundary layer in terms of mass transfer. A boundary layer so described cannot be easily compared with a sampling rate. Gillett et al. (9) have recently reported boundary-layer resistance measurements made at the surface of a dosimeter as were the values of SRBL, but they reported the resistance in terms of length. Although the boundarylayer length can be readily compared with the dosimeter length, a Fick’s law proportionality constant is more conceptually rigorous. Sampling Rate Reduction due to the Boundary Layer. The effect of the boundary layer was estimated using the following argument. If Fick’s law is rigorously applicable to diffusion dosimeters, SROVM will not vary with wind speed, but the total gradient will vary. In stagnant air, the boundarylayer gradient will be maximized, and it will decrease to zero as the air speed increases. When the boundary layer decreases to zero, the gradient across the OVM remains, and SRTOTAL equals SROVM (see eq 4 and Figure 2). Thus, the difference between SRTOTAL and SROVM represents the magnitude of the boundary layer. In stagnant air, the sampling rate should decrease by the percentage calculated from eq 5:
100 × (SROVM - SRTOTAL)/SROVM
(5)
In Table 3, this percentage is reported for eight VOCs with a range of chemical properties and volatilities. In all cases, the percentage reduction in sampling rate is about 30%. On the basis of these results, it is reasonable to predict that the maximum sampling rate reduction for any compound sampled by an OVM will be 30%. An experimental determination of the effect of airflow on toluene concentration showed about a 30% reduction for a decrease in airflow from 0.5 m/s to zero (25).
TABLE 2. Sampling Rates for Nine VOCs compound
boiling point (°C)
SRTotala (cm3/min)
SRBLa (cm3/min)
SROVM (cm3/min)
SROVM (3M) (cm3/min)
acetone benzene carbon tetrachloride dichloromethane ethylbenzene n-heptane n-octane toluene p-xylene
56.0 80.0 76.8 40.1 136.1 98.4 125.6 110.6 138.3
29.1 ( 0.19 25.7 ( 0.14 23.1 ( 0.46 32.5 ( 1.4 21.2 ( 0.17 20.7 ( 0.10 18.6 ( 0.93 22.0 ( 0.46 20.4 ( 0.46
113 ( 2.3 85.4 ( 4.6 78.2 ( 3.8 119 ( 3.7 67.7 ( 4.3 76.4 ( 2.1 62.4 ( 3.7 72.5 ( 1.4 64.3 ( 0.46
39.1 36.8 32.8 44.7 30.9 28.5 26.5 31.6 29.8
40.1 ( 0.9 35.5 ( 0.6 30.2 ( 0.4 37.9 ( 0.3 27.3b 28.9 ( 0.7 26.6 ( 0.6 31.4 ( 0.6 27.3 ( 0.5c
a
Average of 2-4 replicates ( SD.
b
Interpolated. c Unspecified isomer.
TABLE 3. Magnitude of the Boundary Layer in Stagnant Air compound acetone benzene carbon tetrachloride ethylbenzene n-heptane n-octane toluene p-xylene average ( SD
sampling rate reduction (%) 25.8 30.2 29.6 31.4 27.4 29.7 30.5 31.8 29.6 ( 2.0
TABLE 4. Stability of Sampling Rates (Calibration) during Sample Collection sampling scenario
post-deployment difference from lab blanks (%)
oily windscreen (1)a split windscreen (1) urban outdoors, field (3) urban outdoors, street corner (3) smoker’s house (3) sea air personal indoor air, residential (4) indoor air, warehouse (2)
-7 -6 +6 +4 +4 +5 +5 +4 +11
a
The conclusion that the sampling rate reduction is a predictable property of the dosimeter design does not seem to have been made before. In fact, a method to validate dosimeters for use in occupational environments implies that the boundary-layer effect varies with the chemical being collected (13). Validation of Measured Air Concentrations. Gradient analysis can also be applied to sample collection. Analyzing the contribution of a boundary layer to a measured air concentration is of obvious interest. More essential, however, is questioning the stability of SROVM, which is the calibration factor, because changes in SROVM would systematically bias the measured air concentrations. This is equivalent to measuring the flow rates for samples actively collected by pulling air through a collector. I am aware of no study that assesses if SROVM remains constant throughout sample collection. A recent symposium included several papers based on sampling times of 1 week or more (15). Sampling Rate Changes (Calibration Changes) during Sample Collection. Dosimeters were deployed in a variety of urban environments to determine if the sampling rates would be constant for several days under field conditions. The exposure times varied between 2 and 4 days. After the dosimeters were retrieved, their sampling rates were compared to those determined from unused dosimeters (lab blanks), because day-to-day variation in the analytical method was often greater than the differences between exposed dosimeters and lab blank dosimeters. These relative sampling rates were determined using the evaporative analysis or the simplified analysis described in the Experimental Procedures. Surprisingly, injecting toluene or heptane onto the charcoal adsorbent pad did not cause significant warming. Thus, solvent was injected into dosimeters through the windscreen with a microliter syringe. Of course, the carbon pad could no longer be analyzed for its VOC content. When it was necessary to remove the adsorbent pad for VOC analysis, the sampling rate was determined from a reassembled dosimeter with a paper circle in place of the adsorbent pad. In general, I found that the sampling rates remained constant throughout deployment (Table 4). This
Number of replicates.
suggests that passive dosimeters will remain in calibration for at least 4 days. The first two entries in Table 4 are from damaged dosimeters that were recovered from an exposure assessment study. The oily windscreen was contaminated with oil while frying food. The split windscreen had a single split across the middle of the inlet. One expects damage to change the calibration factor, but the magnitude of the change helps determine if the data point should be rejected. The evaporative analysis detected a small decrease in the sampling rate for both. Estimation of True Air Concentrations in the Presence of a Boundary Layer. When a dosimeter is used for sampling, the measured air concentration reflects the value for SRTOTAL, because the sampling process does not differentiate the two gradients that contribute to it. Since SRBL has different values at different airflows, SRTOTAL varies continuously and unpredictably between 70% and 100% of SROVM. An air concentration determined by a dosimeter will be the true air concentration only if SRTOTAL equals SROVM throughout the sampling period. This condition is inherent in the design of the Palmes dosimeter (1, 4). It is not true for badge-type dosimeters. Samples collected in these dosimeters will underestimate the true air concentration unless a continuous airflow above some minimum value is assured. A gradient analysis approach to estimate true air concentrations from measured concentrations has been reported by Persoff and Hodges (21). They found a linear relationship between fluxes and measured air concentrations at different diffusion path lengths. Extrapolation to zero flux gave an estimate of the true air concentration. The design of the OVM allows the path length to be changed easily. I selected one path length longer and one shorter than the standard 1 cm. For both nonstandard path lengths, the evaporative analysis was used to determine the sampling rates and the sampling rate reduction due to the boundary layer (Table 5). The data in Table 5 make it clear that both the gradient across the dosimeter (the sampling rate) and the boundary-layer gradient vary with path length. This is the basis for performing a gradient analysis. VOL. 37, NO. 8, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 5. Effect of Path Length on Sampling Rates for Carbon Tetrachloride path length (cm)
sampling rate (cm3/min)
sampling rate reduction from boundary layer (%)
0.55 1.00 1.55
56.2 32.8a 18.0
42 30a 19
a
From Tables 2 and 3.
FIGURE 3. Estimated true air concentrations of carbon tetrachloride. Dosimeters of each path length were exposed outdoors to both moving and stagnant ambient air. The moving air exposure was to assess if dosimeters deployed in a standard scenario might underestimate air concentrations. The stagnant air exposure was designed to reveal if the maximum boundary-layer effect was 30%. The only VOC detected above a signal-to-noise ratio of 3 was carbon tetrachloride. (The detection of carbon tetrachloride owed much to its absence as a contaminant on the carbon adsorbent pad.) The air concentrations were calculated from eq 2 using the sampling rates in Table 5. The calculated air concentrations were plotted against the fluxes for each path length. Separate trend lines were fit through the data points for moving and stagnant air. According to Persoff and Hodges (21), the y-intercept is the true air concentration (Figure 3). For moving air the intercept was 0.618 µg/m3. Since the measured air concentration at the standard 1-cm path length was 0.500 µg/m3, the dosimeter underestimated the true air concentration by about 20%. As one replicate of one sampling scenario, it cannot be considered a definitive result. Nevertheless, the substantial underestimation warrants further investigation. The dosimeters exposed to stagnant air appear to have underestimated the true air concentration by about 38% (0.44 instead of 0.700 µg/m3). Although slightly greater than the predicted value of 30%, it is a rough confirmation of the predicted underestimation.
Acknowledgments The author thanks the Southwest Center for Occupational and Environmental Research, Houston, TX, for a Pilot Project Research Training grant to conduct the validation experiments, Dr. Thomas Stock for useful discussions during the genesis of the ideas presented here, and the scientists whose reviews helped shape the final manuscript.
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Received for review April 23, 2002. Revised manuscript received November 23, 2002. Accepted December 23, 2002. ES020706O
