Nonequilbrium Quantitation of Volatiles in Air Streams by Solid-Phase

Anal. Chem. 1999, 71, 92-101

Nonequilbrium Quantitation of Volatiles in Air Streams by Solid-Phase Microextraction Robert J. Bartelt* and Bruce W. Zilkowski

Bioactive Agents Research Unit, National Center for Agricultural Utilization Research, USDA Agricultural Research Service, 1815 North University Street, Peoria, Illinois 61604

Solid-phase microextraction (SPME) is a valuable technique for analyzing air-borne organic compounds; one important application is measuring concentrations when these are constant over time. Quantitation normally relies on the SPME fiber being fully equilibrated with the sample medium. Unfortunately, relatively heavy compounds do not equilibrate within a reasonable amount of time, and this has limited the scope of SPME. The ability to quantitate during equilibration was needed and was the focus of this investigation. This entailed having an accurate description of SPME kinetics, and the kinetics of extraction by poly(dimethylsiloxane) fibers was studied for alkanes of 9-22 carbons, primary alcohols of 6-13 carbons, and methyl esters of 6-16-carbon acids. Sampling was from air streams in which analyte concentrations were effectively constant, and sampling times ranged from 30 min to 3 days. Other experimental variables included sampling temperature, fiber coating thickness, air flow rate, and tubing diameter in which the SPME sampling took place. Over 1900 data points were acquired. Previous theoretical kinetic models were not applicable to the present experimental conditions, but a simple kinetic equation was formulated that described the data very well; its key property is an explicit relationship between fiber sensitivity and equilibration time. Using nonlinear regression, the equation parameters were linked to known properties of the analyte (the functional group and GC retention index on a nonpolar column) and to certain sampling conditions (temperature, sampling duration, air flow rate, tubing diameter). The regression equation serves as a practical quantitation formula and allows the absolute concentration of the analyte in the air stream to be calculated directly from the amount extracted by the SPME fiber (which is easily measured by GC), regardless of whether equilibrium has been established or not, as long as the above analyte properties and sampling conditions are known. The residual variability for the model (RSD ) 9.4%) was only slightly larger than the variability inherent in SPME alone (∼5%). Considerations for SPME sampling from air are discussed, and new fiber calibration information is presented for the larger hydrocarbons, alcohols, and methyl esters. 92 Analytical Chemistry, Vol. 71, No. 1, January 1, 1999

Solid-phase microextraction (SPME) is a simple, convenient, and sensitive technique for analyzing organic compounds in air. Measurement of air-borne analyte concentrations is an important application and is meaningful when sampling is from a closed system (“headspace SPME”1) or when the analyte concentrations are effectively constant over time, which is the focus of the present investigation. (However, interpretation of SPME measurements when concentrations are not constant over time, such as in longterm environmental monitoring, could be very complex, and this situation is beyond the scope of the present study.) A fundamental property of SPME is that analytes partition between the fiber coating and the air,1 and calculations of concentration always involve the equilibrium relationship. At equilibrium, the concentration (or alternatively, the amount) of analyte in the fiber coating is directly proportional to the concentration in the air, and the proportionality constant (“calibration factor”) depends on the particular analyte, fiber type, and temperature. A number of these constants have been published, and it is also possible to calculate them from readily available physical parameters using regression equations.2,3 A viable approach to quantitation, then, is to sample long enough to ensure complete equilibration; measure the amount captured by the fiber, which is easily done by gas chromatography (GC); and then calculate the concentration in the air by applying the known proportionality constant. To the extent that the fibers are manufactured uniformly, absolute quantitation can be done with any individual fiber of a given type, without employing standards.4 Unfortunately, many compounds, such as the insect pheromones encountered in our research, do not equilibrate with the fiber within a reasonable amount of time. For example, compounds with a linear temperature-programmed retention index, relative to n-alkanes, (LTPRI) of >1300 on a nonpolar column do not equilibrate with a 100-µm poly(dimethylsiloxane) (PDMS) fiber within 30 min at 25 °C.2 For some compounds, many hours or even days would be required, even if fibers with thinner coatings are used. Such waits are impractical and would greatly limit the usefulness of SPME. A general method was needed that would permit quantitation from air samples even before the fiber was fully equilibrated. Such a method would necessarily be based on an accurate mathematical description of extraction kinetics. (1) Pawliszyn, J. Solid-Phase Microextraction: Theory and Practice; Wiley-VCH: New York, 1997. (2) Bartelt, R. J. Anal. Chem. 1997, 69, 364-372. (3) Martos, P. A.; Saraullo, A.; Pawliszyn, J. Anal. Chem. 1997, 69, 402-408. (4) Martos, P. A.; Pawliszyn, J. Anal. Chem. 1997, 69, 206-215. 10.1021/ac980785f Not subject to U.S. Copyright. Publ. Am. Chem. Soc.

Published on Web 12/01/1998

Quantitation in the absence of equilibrium and the kinetics of extraction have been addressed.1,5 In both publications, the rate of analyte extraction is understood to depend on the rates of diffusion within the fiber coating and through a boundary layer. The boundary layer is the zone of the sample medium adjacent to the fiber and is characterized by the presence of analyte concentration gradients. This layer exists because of diffusion and viscosity effects. The boundary layer can significantly retard movement of analyte from the bulk sample into the fiber, and the degree of retardation depends strongly on the thickness of the layer. However, the publications are not clear how this thickness is determined in practice. Also, it was not clear whether these models, which focused primarily on extraction of fairly small analytes from water, would be relevant for larger analytes being extracted from air. A data set was acquired with which to study the SPME kinetics. The chosen experimental conditions differed from most earlier studies in that sampling from large, closed containers was avoided; rates of mixing, diffusion, and bulk flow would be poorly defined and nearly impossible to control in such vessels. Instead, we focused on SPME measurements from air that was flowing through a tube at a constant rate and that had effectively constant analyte concentrations, somewhat as in the study by Martos and Pawliszyn.4 Not only were the movements and concentrations of volatiles easier to control and describe in such a system, but moving air streams can also be particularly relevant for biological measurements, as discussed below. Our experimental setup had spatial characteristics that put it beyond the scope of the previous boundary layer diffusion models, but an alternative kinetic model was proposed that was consistent with the data. The parameters of this model were then linked by nonlinear regression to easily obtained chemical information for the analytes and to physical measurements of the sampling apparatus. The final result is a practical and general approach for measuring absolute analyte concentrations in uniform air streams, and the approach is appropriate even before the fiber has equilibrated. Notation. From SPME theory,1 the equilibrium concentration of analyte in the fiber coating divided by the concentration in the sample medium is equal to the partition coefficient, Kfg, where f and g refer to the fiber coating and gas phase:

Cfiber,∞/Cair ) Kfg

(1)

But the equilibrium concentration in the fiber coating is equal to the mass of analyte in the fiber at equilibrium, Mfiber,∞, divided by the volume of the fiber coating, Vfiber. Only the amount in the fiber coating, not the concentration, is of practical interest, and the volume of the fiber coating is a constant for each fiber type, by manufacture. (For the 100-µm fiber coating, the volume is ∼0.69 mm3 ) 0.000 69 mL). Thus the equilibrium equation is rearranged, and a new symbol, K*, is defined, which we call the calibration factor:

Mfiber,∞/Cair ) KfgVfiber ) K*

(2)

In this report, K* always has units of milliliters. (It is easily derived (5) Ai, J. Anal. Chem. 1997, 69, 1230-1236.

Figure 1. Diagrammatic view of air sampling apparatus.

that if a gas-phase analyte sample is present in a bottle whose volume (in mL) is equal to K* for the analyte, then exactly half of the analyte mass will move into the SPME fiber coating during equilibration.) EXPERIMENTAL SECTION Sampling Apparatus. The sampling apparatus used in the study was quite simple and small in size and is shown diagrammatically in Figure 1. The test analytes evaporated slowly from a piece of rubber (serum vial stopper or “septum”) and were entrained in the air stream. The air stream flowed past the SPME fiber, which was positioned along the central axis of the sampling port, and then exited through a trap connected to the port’s sidearm. The trap contained a small amount of the porous polymer, Super Q (Alltech Associates, Deerfield, IL). The Super Q (10 mm in the 3-mm-i.d. glass trap) was held between a 300mesh stainless steel screen (that was fused into the glass) and a plug of silanized glass wool. Any analyte not retained by the fiber was caught by the trap. The usual sampling port internal diameter was 4.5 mm, but this could be reduced to 1.5 mm with a Teflon tubing insert. All of the SPME fibers had a PDMS coating and were obtained from Supelco (Bellefonte, PA). Fibers with a 100-µm coating were used for most measurements, but fibers with 7- and 30-µm coatings were also used. The SPME needle was inserted into the port through a silicone rubber septum which had a Teflon barrier on the inside to minimize sample adsorption. The fiber itself was positioned 7 cm from the enlarged tube holding the septum and 3 cm upstream of the Super-Q trap. Amounts of analyte extracted by the fiber and captured in the trap were measured by GC. Septum Preparation. The rubber septa (natural red rubber, 18 mm long ×10 mm in diameter, Wheaton, Millville, NJ) were extracted in a Soxhlet apparatus for 6 h with methylene chloride and stored dry until needed. They were loaded by applying a solution of n-alkanes (9-22 carbons), primary alcohols (6-13 carbons), or methyl esters (of 6-16-carbon acids) in hexane. Amounts were ∼5 mg of each component per septum. Exact release rates were not known beforehand but were calculated from the quantities of compounds in the fiber and trap. After the solvent had evaporated, the septum was placed into the sampling apparatus (Figure 1) for 1 day with air flow so that analyte emission would stabilize before data collection began. Air Flow and Temperature Control. Dry compressed air from a tank, suitable for use with a GC FID, was directed through a fine needle valve, through a filter of porous polymer to remove impurities, and finally into the sampling apparatus. Flow was measured at the outlet with an electronic meter (Alltech Flow Check), which was periodically checked for accuracy with a Analytical Chemistry, Vol. 71, No. 1, January 1, 1999

93

Table 1. Experimental Parameters for Tests

test

compd type

fiber coating (µm)

temp (°C)

sampling port i.d. (mm)

1 2 3 4 5 6 7 8 9 10 11

alkanes alkanes methyl esters alcohols alkanes alkanes alkanes alkanes alkanes alkanes alkanes

100 100 100 100 100 100 100 100 100 30 7

27 27 27 27 15 35 27 27 27 27 27

4.5 4.5 4.5 4.5 4.5 4.5 4.5 1.5 1.5 4.5 4.5

air flow rate volume linear (mL/min) (cm/min) 20 20 20 20 20 20 200 20 2 20 20

130 130 130 130 130 130 1300 1200 120 130 130

bubble flowmeter. The whole sampling apparatus was placed inside an incubator which controlled temperature to the nearest 1 °C. Experimental Design. The experimental parameters were compound class, fiber coating thickness, sampling temperature, sampling port inside diameter, and air flow rate (Table 1). The “standard” test involved hydrocarbons, the 100-µm fiber coating, 27 °C sampling temperature, and 4.5-mm sampling port i.d. with 20 mL/min volumetric air flow rate. (A volumetric flow rate of 20 mL/min through a 4.5-mm-i.d. tube represents a linear velocity of 130 cm/min past the fiber.) Two complete tests were conducted under the standard conditions; then the measurements were repeated, varying the experimental parameters one at a time while keeping all other parameters as in the standard test. This approach isolated the effect of each experimental parameter and prevented confounding. Each test ran for 6 days, during which 17 consecutive SPME samples and 12 trap collections were analyzed. SPME sampling times were 30, 60, 120, 240, 480, 960, and 3840 min. There were four replications at 30 and 960 min and one at 3840 min; for all other times, there were two replications. During each of the first 4 days of a test there were two 240-min trap collections; there were also three 960-min overnight collections and a final collection of 3840 min. The trap collections did not parallel those for SPME exactly because durations of less than 4 h did not provide sufficient amounts of the less volatile compounds for quantitation. Gas Chromatography. Two Hewlett-Packard 5890 Series II instruments were used for all analyses. One was equipped with a split/splitless inlet, always operated in splitless mode. For SPME injections a 0.75-mm-i.d. glass inlet liner was used, but for liquid injections it was replaced with a 4-mm-i.d. liner. The other instrument was equipped with a cool on-column inlet. The inlet was fitted with a 10-cm retention gap of deactivated fused-silica tubing (0.53-mm-i.d., large enough to accommodate SPME injections). The narrow-bore analytical column was attached to the retention gap with a press-fit connector. Both instruments had flame ionization detectors and autosamplers and were connected to a Hewlett-Packard ChemStation data system. Carrier gas was helium. Initial analyses of hydrocarbons were through the splitless inlet into a 15-m DB-1 column with 0.25-mm-i.d. and 0.25-µm film thickness (J & W Scientific, Folsom, CA). Later analyses were through the on-column inlet into a 30-m DB-5-MS column with 0.25-mm-i.d. and 1.0-µm film thickness (J & W) because this column gave better peak shapes, particularly with the alcohols. Oven temperature programs started at 50 °C and increased at 10 94

Analytical Chemistry, Vol. 71, No. 1, January 1, 1999

°C/min until all analytes had emerged (final temperature was 250 or 300 °C). Detector temperature was the same as the final oven temperature. FID Response Factors and Retention Indexes. Response factors (nanogram per integration unit) were determined from liquid samples. The samples were prepared gravimetrically in volumetric flasks, diluted so that peak areas would be similar to those encountered with volatile samples, and injected with the autosampler (five replications). Response factors were checked weekly during the study. LTPRI3 for each ester and alcohol was determined on the DB-1 column with the oven temperature increasing at 10 °C/min. SPME Analyses. The GC inlet temperature was 200 °C. Injection time was 30 s. The fiber was conditioned in an additional split/splitless inlet for at least 2 min at 200 °C prior to reuse. Peak areas were converted to nanograms using the previously determined response factors. Analyses of Trap Collections. The Super Q trap was removed from the apparatus and back-flushed with 500 µL of hexane into an autosampler vial. Internal standard was added (40 µg of pentacosane), and the sample was sealed, mixed, and analyzed by GC. Mass of analyte in the sample was calculated from the internal standard and FID response factors. Initial tests with filters in tandem indicated that the analytes were trapped quantitatively by the first filter. Sequential elutions of a filter with hexane indicated that no detectable analyte remained after the first 500µL rinse. Calculation of Concentrations. The total amount of material released from a septum during a Super-Q trapping interval was calculated as the sum of all of the SPME collections (Mfiber) during that period plus the particular trap collection (Mtrap). This total could be converted to a mean concentration in the air stream during the period:

C h air ) (

∑M

fiber

+ Mtrap)/Ft

(3)

where F is the volumetric flow rate (mL/min) and t is the time period (min). Release of volatiles from rubber septa is first order;6 thus plotting the logarithm of concentration in the air versus the time after setting up a septum gives a straight line. Graphing the mean concentrations for the Super-Q trapping intervals (eq 3) versus time would produce a series of “steps”, and converted to logarithms, the midpoints of these steps defined exactly the straight line describing first-order release. The equation of this line was determined by linear regression for each analyte in each test, and from these equations, the concentration of any analyte impinging on the fiber at any instant could be calculated. For the most volatile compounds such as nonane and methyl hexanoate, the decrease in air stream concentration was clearly noticeable in consecutive collections, but concentrations of the larger compounds (those less volatile than tridecane) were essentially constant throughout the entire test period. The concentration at the end of each SPME sampling period was used in the subsequent calculations. This concentration effectively applied to the entire period if there was negligible (6) McDonough, L. M. In Naturally Occurring Pest Bioregulators; Hedin, P. A., Ed.; ACS Symposium Series 449; American Chemical Society: Washington, DC, 1991; Chapter 8.

change during the lesser of two times: the sampling time and the SPME equilibration time. (The fiber has no “memory” of what was experienced during the early portion of a long sampling period if the equilibration time is relatively short.) This criterion was met for all compounds, with the typical amount of change being 1500) can be extracted from the air stream virtually quantitatively. In fact, when these flow conditions were used (test 9), only traces of the heavier alkanes got past the SPME fiber into the Super Q trap. In such circumstances, SPME closely matches the trapping efficiency of a porous polymer. Efficiency Factor A. No theoretical model is proposed for predicting the parameter A. However, certain physical factors probably affect its value. First is the linear velocity of air past the fiber. Intuitively, the slower the air is flowing, the higher the probability of an analyte molecule interacting with the fiber. The other significant factor is sampling port diameter. A large-diameter port would lower the probability of a molecule diffusing all the way to the fiber coating before bulk flow carried the molecule beyond the fiber. It is reasonable that slowing the linear velocity could compensate for a larger port diameter so that there would be no net change in A. Expressing air flow as a volume per time (rather than linear velocity) incorporates this compensation, and Analytical Chemistry, Vol. 71, No. 1, January 1, 1999

97

Table 3. Final Regression Model for Thick-Film Fiber

both fitted values of A for a volumetric air flow of 20 mL/min (Table 3) were very similar, despite very different linear velocities and port diameters. It is suggested that air flow rate expressed as volume per time will be the best predictor of A, but port diameter may provide important additional information for “finetuning” such predictions. Thin- and Medium-Film Fibers. The fitted values of K* for the alkanes with the thin- and medium-film fibers (tests 10 and 11, Table 1) are given in Table 6, and the estimated parameter values for the regression model are given in Table 2. The estimated equilibration times for these fibers are consistent with earlier results1 in that equilibration is faster for thin-film fibers; for example, times for hexadecane are 104, 288, and 1240 min for the 7-, 30-, and 100-µm films, respectively. However, even with 98


the 7-µm film, equilibration can become impractically long with sufficiently large compounds. Thus, simply using a thin-film fiber does not guarantee that equilibrium will be established during sampling. The efficiency parameter, A, was lower for the thin- and medium-film fibers (0.147 and 0.221, respectively) than for the thick-film fiber under the same air flow conditions (0.258). The thinner-film fibers have smaller surface areas and could therefore be expected to interact less efficiently with the analytes in the air stream. It can be shown that because both A and K* are highest for the thick-film fiber, it will always absorb more total analyte than a thinner-film fiber in a side-by-side comparison, regardless of analyte, length of sampling time, and whether equilibration has occurred. The thick-film fiber will provide the greatest sensitivity

Table 4. Values of K*, log K*, and Equilibration Time Calculated from Regression Model, for Alkanes, Methyl Esters, and Alcohols, Sampled at 27 °C with the Thick-Film Fiber and with a Volumetric Air Flow Rate of 20 mL/min and Sampling Port i.d. of 4.5 mm compd

LTPRI

K*

log K*

1.5-mm i.d.

equilibn time (h) comp

nonane decane undecane dodecane tridecane tetradecane pentadecane hexadecane heptadecane octadecane nonadecane eicosane heneicosane docosane

n-Alkanes 900 2.12 1000 5.70 1100 15.3 1200 41.2 1300 111 1400 297 1500 798 1600 2140 1700 5750 1800 15400 1900 41500 2000 111000 2100 299000 2200 804000

0.327 0.756 1.185 1.615 2.044 2.473 2.902 3.331 3.760 4.189 4.618 5.047 5.476 5.905

0.02 0.06 0.15 0.40 1.1 2.9 7.7 21 56 150 400 1100 2900 7800

methyl hexanoate methyl heptanoate methyl octanoate methyl nonanoate methyl decanoate methyl undecanoate methyl dodecanoate methyl tridecanoate methyl tetradecanoate methyl pentadecanoate methyl hexadecanoate

Methyl Esters 905 2.81 1005 7.55 1107 20.7 1207 55.5 1306 148 1407 401 1507 1080 1607 2890 1707 7760 1806 20600 1907 56000

0.449 0.878 1.320 1.745 2.169 2.603 3.032 3.461 3.890 4.315 4.748

0.03 0.07 0.20 0.54 1.4 3.9 10 28 75 200 540

Primary Alcohols 849 2.94 949 7.90 1052 21.9 1154 59.9 1256 164 1356 440 1457 1190 1558 3240

0.469 0.898 1.340 1.777 2.215 2.644 3.077 3.511

0.03 0.08 0.21 0.58 1.6 4.3 12 31

1-hexanol 1-heptanol 1-octanol 1-nonanol 1-decanol 1-undecanol 1-dodecanol 1-tridecanol

Table 5. Equilibration Times (Hours) for Alkanes under Four Sets of Conditions with Respect to Volumetric Flow Rate and Inside Diameter of Sampling Port (Sampling at 27 °C)a

under any conditions, and we see no advantage of using the thinner-film fibers in the present situation. Comparison of Present Results with Previous Research. The fitted values of log K* for the alkanes for a sampling temperature of 25 °C are shown in Figure 6, plotted against LTPRI. Also shown in the graph are observed values of log K* for alkanes obtained previously by sampling from sealed bottles.2 Both sets of values lie nearly on the same line. There were deviations from linearity around 12 and 13 carbons in the previous data set. Probably, equilibrium was not fully established during the sampling time (as assumed in the earlier calculations), or the heaviest analytes were especially prone to adsorption onto the walls of the sampling vessel. Nevertheless, the data sets agreed remarkably well, despite the determinations being made by entirely different methods. The slope of the line in Figure 6 is 0.004 35; this and the values of Q in Table 2 compare favorably with the value, 0.004 15, obtained in an earlier study by another laboratory.1 The values of the functional group parameter, G, for alcohols were almost identical between this study and the previous one,2 0.36 (Table 3) and 0.35, respectively. The value for methyl esters in this study (0.10) did not agree as well with that for esters in


log K*

4.5-mm i.d.

2 20 20 200 mL/min mL/min mL/min mL/min (A ) 0.98) (A ) 0.28) (A ) 0.26) (A ) 0.051)

0.327 0.05 0.756 0.15 1.185 0.39 1.615 1.1 2.044 2.8 2.473 7.6 2.902 20 3.331 55 3.760 150* 4.189 390* 4.618 1100* 5.047 2800* 5.476 7600* 5.905* 21000*

0.019 0.052 0.14 0.37 1.0 2.7 7.2 19 52 140* 380* 1000* 2700* 7300*

0.021 0.055 0.15 0.40 1.1 2.9 7.7 21 56 150* 400* 1100* 2900* 7800*

0.010 0.028 0.075 0.20 0.54 1.5 3.9 10 28 75* 200* 540* 1500* 3900

a Asterisk values are extrapolations calculated from formula; experimental data were not obtained beyond 64 h.

Table 6. Fitted Values of log K* for Alkanes at Three Fiber Coating Thicknesses and Three Temperaturesa 100 µm film compound

15 °C

27 °C

35 °C

30 µm 27 °C

7 µm 27 °C


0.635 1.099 1.562 2.025 2.488 2.952 3.415 3.878 4.341 4.805 5.268 5.731* 6.194* 6.658*

0.327* 0.756 1.185 1.615 2.044 2.473 2.902 3.331 3.760 4.189 4.618* 5.047* 5.476* 5.905*

0.122* 0.529 0.935 1.341 1.747 2.154 2.560 2.966 3.372 3.779 4.185 4.591 4.997 5.404

-0.333* 0.090 0.513 0.936 1.359 1.782 2.205 2.628 3.051 3.474 3.897 4.320* 4.743* 5.166*

-0.930* -0.510* -0.090 0.330 0.750 1.170 1.590 2.010 2.430 2.850 3.270* 3.690* 4.110* 4.530*

a Volumetric flow rate was 20 mL/min and sampling port i.d. was 4.5 mm. * indicates that the value is an extrapolation from formula; no data could be obtained for the compound under the given conditions.

the earlier study (0.22); this corresponded to predicted concentrations differing by a factor of 1.3. A possible explanation is that all esters do not interact with the fiber in exactly the same way, and more than one kind of “ester parameter” will eventually be needed. Nevertheless, the present study was consistent with the earlier study in that the sensitivity of the PDMS fibers is higher for the more polar analytes, after allowing for differences in GC retention index. (The values of G for alcohols and methyl esters correspond to the fiber being 130 and 26% more sensitive to these compounds, respectively, than to hydrocarbons.) It is suggested that the more extensive list of G parameters presented in the earlier paper2 may also be useful with the present model, although additional research will be needed to further refine these values. In the earlier report,2 the relationship between log K* and sampling temperature was modeled as being approximately linear (at least within a narrow temperature range of 15-35 °C). The present study gave a clearer view of temperature effects because of the smaller residual error and because acceptability of data did Analytical Chemistry, Vol. 71, No. 1, January 1, 1999

99

Figure 4. Observed values of Mfiber/Cair for three alkanes with very different equilibration characteristics and the kinetic curves calculated with the regression model. Sampling was with the 100-µm poly(dimethylsiloxane) fiber at 27 °C; volumetric flow rate was 20 mL/ min through the sampling port with 4.5-mm i.d. There are 28 observations plotted for each compound.

Figure 6. Plots of log K* versus LTPRI for alkanes from an earlier study2 (filled circles) and from the present study (open squares). The values are for the 100-µm poly(dimethylsiloxane) fiber at 25 °C but were determined under very different experimental conditions (see text).

concentration in the moving air. The concentration is not of direct interest, but multiplying this by the volumetric air flow rate gives the emission rate of the volatile (e.g., in nanograms per minute), and this is the biologically relevant quantity. This approach would allow simple, rapid, and very flexible measurement of nearly any kind of biological volatile, without the use of solvents, and it brings the many practical advantages of SPME to bear on some otherwise difficult biological problems.

Figure 5. Approximation of the kinetic curve with a straight line during the early stages of absorption. Extraction kinetics are independent of K* wherever the straight line approximation is appropriate (see text). The data are for pentadecane.

not depend on judging whether equilibration was complete. Here, temperature entered the model most effectively as an adjustment to the slope for LTPRI (Table 3). Imposing a linear relationship between log K* and sampling temperature would have led to an inflated residual error. The present form of the model with respect to temperature is supported on empirical but not theoretical grounds. Practical Application to Biological Systems. It is often of interest to measure the rate at which particular volatiles are emitted from biological samples, such as pheromones from insects or fermentation volatiles from microbial cultures. SPME measurements from moving air streams, as described above, can meet this need nicely. If air is passed through a closed vessel containing such organisms, their emitted volatiles will be entrained in the air stream. If emission from the organisms is nearly constant, then the concentration in the exiting air will reach a steady state. Once a steady state is achieved (indicated by consecutive SPME measurements giving similar results), the rate of release by the organisms equals the rate at which the compound is swept away, and this rate is measurable, given that the steady state persists for an interval of time suitable for SPME sampling. The procedures descibed above will lead to an absolute measurement of the volatile 100 Analytical Chemistry, Vol. 71, No. 1, January 1, 1999

CONCLUSION The regression model allows calculation of analyte concentration in an air stream directly from the amount captured by the SPME fiber, if just sampling temperature, sampling time, analyte functional group, and analyte GC retention index are known and if one of the four studied configurations of air flow rate and sampling port diameter is used. In practice, it is not even necessary to use a sampling port as described in Figure 1 because postfiber trap collections would not be made; sampling can be done by simply inserting the SPME fiber into the open end of a propersized tube through which the analyte air stream is flowing. As suggested previously,2,4 the calibration information implicit in a fiber would allow determination of absolute vapor-phase concentrations with essentially no need to employ standards (except to determine GC detector response factors for converting peak areas to nanograms). The calculations are more complicated than the simple ratios usually associated with SPME measurements (as described in the introduction), but this complication is outweighed by the major benefit that equilibration is no longer an issue. Furthermore, macroprograms can be written for modern GC data systems that will do the necessary calculations automatically as peaks are detected within selected retention time windows; the analyte concentration could be printed out on the GC report, right along with retention time, peak area, or other items. APPENDIX A personal computer program (available on request from R.J.B.) was written in the Quick Basic language to calculate specific solutions for the extraction model presented in Appendix

2 of Pawliszyn’s book.1 By this model, analytes diffuse from the perfectly mixed sample medium, through a boundary layer, and into the fiber coating in accordance with Fick’s second law (we assume that no chemical change or “derivatization” of the analyte occurs). The underlying system of partial differential equations and the general solution are

[

]

∂ui(r,t) ∂2ui 1 ∂ui ) Di + ∂t r ∂r ∂r2 ∞

ui(r,t) )

∑F [A J (λ r) + B Y (λ r)] exp(-D λ j

ij 0

ij

ij 0

ij

2 1 1jt)

j)0

where ui(r,t) is the analyte concentration at distance r from the central axis of the SPME fiber at time t and in layer i (i ) 1 for fiber coating and i ) 2 for boundary layer); Di are the diffusion coefficients in the two layers; J0 and Y0 are zero-order Bessel functions of the first and second kind, respectively; and Fj, Aij, Bij, and λij are parameters that depend on the experimental conditions to be simulated. (See Pawliszyn1 for details of boundary conditions, initial conditions, and calculation of parameters.) The program calculates the first 200 terms of the infinite series solution, ui(r,t), that correspond to the chosen fiber coating and

boundary layer thicknesses, diffusion coefficients (Di), and partition coefficient (Kfg). (Bessel functions are not among the standard Quick Basic functions, so these must be evaluated; Chebishev polynomials9 are used for arguments less than 4 and numerical formulas10 are used for arguments greater than or equal to 4.) The program displays the values of ui(r,t) at selected distances from the fiber axis and also the integral of u1(r,t) over the entire fiber, for any time, t. This integral represents the amount of analyte in the fiber coating after sampling for the particular amount of time. The program presents this amount as a percentage of the maximum (equilibrium) amount; thus, the progress of equilibration is readily followed. The program was validated by recalculating examples in Pawliszyn’s book.1 Received for review July 16, 1998. Accepted October 19, 1998. AC980785F (9) Luke, Y. L. Mathematical Functions and Their Approximations; Academic Press: New York, 1975. (10) Olver, F. W. J. In Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables; Abramowitz, M., Stegun, I. A., Eds.; U.S. Department Commerce, Nat. Bur. Standards, Applied Mathematics Series 55; U.S. Government Printing Office: Washington DC, 1964; Chapter 9.


101

Nonequilbrium Quantitation of Volatiles in Air Streams by Solid-Phase

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