Calibration of Permeation Passive Samplers with Silicone Membranes

Anal. Chem. 2003, 75, 3182-3192

Calibration of Permeation Passive Samplers with Silicone Membranes Based on Physicochemical Properties of the Analytes Boz3 ena Zabiegała,† Tadeusz Go´recki,*,† and Jacek Namies´nik‡

Department of Chemistry, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1 Canada, and Department of Analytical Chemistry, Chemical Faculty, Gdan´ sk University of Technology, 11/12 Narutowicza Str., 80-952 Gdan´ sk, Poland

Passive sampling is a very attractive alternative to active sampling due to its simplicity and low cost. Among the passive samplers used in air analysis, permeation passive samplers are the least affected by ambient conditions, including humidity, air currents, and temperature changes. The biggest drawback of permeation passive samplers is the need to calibrate them experimentally for each individual target analyte. The paper presents the results of research on the calibration of permeation passive samplers based on physicochemical properties of the analytes. Strong correlations were found between the calibration constants of the samplers and the number of carbon atoms among families of compounds (R2 ranging from 0.8507 for alcohols to 0.9995 for aromatic hydrocarbons), the molecular weights of the compounds (R2 ) 0.8742), their boiling points (R2 ) 0.8911), and linear temperature-programmed retention indexes (R2 ) 0.9225). The last correlation makes it possible to estimate the calibration constants for unidentified analytes, which is impossible when the conventional procedure is used. This makes it possible to deploy permeation passive samplers in the same way in which active sampling is deployed. Accurate and representative indoor air quality (IAQ) measurements are very important when building air is compared with guidelines and standards. The short-term measurements typically used for IAQ control may reflect temporary conditions that are not representative for longer periods of time and, in consequence, may lead to incorrect decisions aimed at improving the quality of air.1,2 Consequently, techniques allowing the measurement of the concentration of indoor air pollutants over extended periods of time become increasingly important.3 Passive sampling techniques fall within this category, as they yield time-weighted average concentrations of the analytes for the entire sampling period. In the case of indoor air quality measurements, they have the * Corresponding author. E-mail: [email protected]. † University of Waterloo. ‡ Gdan´sk University of Technology. (1) Luoma, M.; Batterman, S. A. AIHA J. 2000, 61, 658-668. (2) Schneider, Th. J. Environ. Monit. 1999, 1, 427-434. (3) Zabiegała, B.; Przyjazny, A.; Namies´nik, J. J. Environ. Pathol., Toxicol. Oncol. 1999, 18, 47-59.

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additional advantage of being much more acceptable by the inhabitants of the monitored areas compared to standard techniques based on dynamic sampling using sorption tubes.4 The use of passive sampling for analyte collection from different matrixes, including air, water, and soil, has been described in the literature.5 In the case of air quality monitoring, the two main types of passive samplers are diffusion samplers and permeation samplers. They do not involve any active devices (pumps, flow meters, etc). The main advantage of permeation samplers, collecting samples of gaseous pollutants at a rate controlled by permeation through a nonporous membrane, is their small sensitivity to varying ambient conditions (including humidity, air currents, and temperature variations). THEORY Mass transfer in permeation passive samplers is generally governed by Fick’s first law of diffusion. The mass (M) of a gaseous component transported by diffusion over a specific period of time (t) can be calculated from a simplified form of Fick’s first law:6,7

Ut ) M ) (AP/LM)p0t

(1)

where U is the diffusional mass-transfer rate (kg/min), M is the amount of a compound trapped on the sorbent bed (determined by an appropriate analytical method) (kg), A is the cross section of the diffusion path (cm2), LM is the membrane thickness (cm), P is the permeability coefficient of the sampled component (cm/ min), p0 is the partial pressure of the analyte near the outer membrane surface (atm), and t is the time (min). Partial pressure of the analyte at a given temperature can be easily converted to its mass concentration in air using ideal gas law:

p0 ) (n/V)R T ) aC0

(2)

where R is the gas constant (atm L mol-1 K-1), T is temperature (4) Zabiegała, B.; Go´recki, T.; Przyk, E.; Namies´nik, J. Atmos. Environ. 2002, 36, 2907-2916. (5) Go´recki, T.; Namies´nik, J. TrAC, Trends Anal. Chem. 2002, 21, 276-291. (6) Reiszner, K. D.; West, P. W., Environ. Sci. Technol. 1973, 7, 526-532. 10.1021/ac034087t CCC: $25.00

© 2003 American Chemical Society Published on Web 05/07/2003

(K), a ) RT/MW (MW is molecular weight of the analyte), and C0 is analyte concentration near the outer membrane surface (kg L-1). At constant temperature, the terms P, A, a, and LM are constant and can be replaced by

1/k ) PAa/LM

C0 ) k(M/t)

(4)

Based on this equation, analyte concentration in the air can be determined from the mass of the analyte trapped by the passive sampler (M) and exposure time (t), provided that the sampling rate (k) for the analyte is known. The nonporous membrane of permeation passive samplers determines the rate of analyte uptake from the surrounding atmosphere. Permeation is a three-step process, consisting of sorption of the analyte onto the external surface of the membrane, dissolution in the membrane material followed by diffusion of the dissolved analyte through the membrane, and desorption of the analyte on the opposite side of the membrane. In passive sampling, analyte molecules that cross the membrane are collected by the trapping medium. To achieve efficient trapping, the analyte distribution ratio between the membrane and the sorption medium should be small.8,9 When the analyte flux obeys Fick’s law, permeability of a polymer is given by10

(

)

NLM C0′ - C1′ ) D p0 - p 1 p0 - p 1

(5)

where N is the steady-state analyte flux through the polymer (kg cm-2 min-1), p0 is the analyte partial pressure near the outer surface of the membrane, p1 is the analyte partial pressure near the inner surface of the membrane, C0′ is the analyte concentration in the polymer at the outer surface of the membrane, C1′ is its concentration in the polymer at the inner surface of the membrane, and D h is the concentration-averaged diffusivity (cm2 min-1). When p1 is much lower that p0 (which is the usual case for passive samplers), the term in parentheses in eq 5 becomes C0′/p0, which is the analyte solubility coefficient S at pressure p0. Consequently, eq 5 can be rewritten as

P ) SD h

KH′(≡ 1/Kp) ) KH(RT/MW)

(7)

(3)

where k is the so-called calibration constant of the sampler. The dimensions of 1/k are liters per minute; hence, this parameter describes the sampling rate of the permeation passive sampler. Combination of eqs 1 and 3 yields eq 4:

P)

For rubbery polymers with liquidlike properties (including poly(dimethyl siloxane), PDMS), the term C0′/p0 is equivalent to dimensional Henry’s law constant KH for the polymer, which can be easily converted to the dimensionless Henry’s constant KH′:

(6)

(7) Namies´nik, J.; Go´recki, T.; Kozłowski, E. Sci. Total Environ. 1984, 38, 225258. (8) van de Merbel, N. C.; Hageman, J. J.; Brinkman, U. A. Th. J. Chromatogr. 1993, 634, 1-29. (9) Zabiegała, B.; Zygmunt, B.; Przyk, E.; Namies´nik, J. Anal. Lett. 2000, 33, 1361-1372. (10) Merkel, T. C.; Bondar, V. I.; Nagai, K.; Freeman, B. D.; Pinnau, I. J. Polym. Sci., B 2000, 38, 415-434.

where Kp is the gas-membrane partition coefficient. According to eq 6, the permeation rate is controlled by the combination of analyte solubility in the membrane material and its diffusivity within the membrane. The solubility at constant operating conditions (temperature, pressure, composition) is mainly a function of analyte condensability,10 which typically increases with the size of a molecule. Diffusivity, on the other hand, is inversely related to the size of the molecule. This generally leads to a tradeoff in the overall magnitude of the permeability coefficient. However, since the liquidlike matrix of PDMS has a poor ability to sieve molecules based on their size, the differences between the permeability coefficients of different molecules for this polymer are mostly governed by the differences in their solubility in PDMS.10 The solubility, in turn, determines the magnitude of the partition coefficient between the air and the membrane material. Consequently, permeability through the membrane can be described by the equation

P ) De(Kp/LM)

(8)

where De is the effective diffusion coefficient of the analyte in the membrane material.11 In practice, effective diffusion coefficients of the analytes in the membrane material are unavailable; therefore, permeability (typically expressed through the calibration constant kssee eq 3) has to be determined experimentally for each individual analyte.7 This requirement constitutes the single most important drawback of permeation passive samplers. Only target analytes, for which the calibration constants were determined in advance in model experiments, can be quantified using this technique. This paper presents a new approach to the calibration of permeation passive samplers equipped with PDMS membranes, based on physicochemical properties of the analytes. The approach proposed vastly simplifies the calibration procedure by making it possible to estimate the calibration constants based on properties including the number of carbon atoms in a member of a homologous series of compounds, boiling point of a compound, its molecular weight, or GC retention index. EXPERIMENTAL SECTION Materials and Reagents. Poly(dimethyl siloxane) membrane of 50-µm thickness (SSP-M100) was from Specialty Silicone Products, Inc. (New York). Teflon FEP foil of 50- and 120-µm thickness was from Du Pont. Active carbon (40-60 mesh, specific surface area 1500 m2/g) was from Zakład Suchej Destylacji Drewna (Hajno´wka, Poland). Carbon disulfide was purchased from BDH (Toronto, ON, Canada). Stock solutions of the analytes were made from high-purity reagents by diluting them with CS2. Standards in CS2 were prepared fresh just before use. The stock (11) Audunsson, G. Anal. Chem. 1986, 58, 2714-2723.

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Figure 1. Design of the permeation passive sampler used in the study. Key: 1, screw cap; 2, protective screen mount; 3, protective screen; 4, PDMS membrane; 5, active carbon; 6, glass wool; 7, washer; 8, main body; 9, O-ring; 10, opening for a screw-in holder; 11, plug; 12, set screw.

solutions contained n-pentane, n-hexane, n-heptane, n-octane, n-nonane, n-decane (quality grade, Polyscience Corp., Niles, IL), benzene, toluene, ethylbenzene, butylbenzene, methyl acetate, ethyl acetate, methyl butyrate, ethyl butyrate, methyl heptanoate, 2-methyl-1-propanol, 2-pentanol, 2,3-dimethyl-2-butanol, 3-hexanol, 2-hexanol, 2,4-dimethyl-3-pentanol, 1-hexanol, 6-methyl-2-heptanol, 1-heptanol, and 2-ethyl-1-hexanol (98% or higher purity, Aldrich). Compressed helium, air, hydrogen, and nitrogen were from Praxair (Waterloo, ON, Canada). Methods of Sample Collection. (1) Passive Samplers. Passive sampling was carried out using custom-made permeation passive samplers equipped with PDMS membranes of 50-µm thickness. The design of the samplers, developed at the Gdan´sk University of Technology (Poland),12 is presented in Figure 1. The samplers were machined of polyamide. The membrane (4) was mounted in the sampler by placing it between a PTFE washer (7) and a metal protective screen mount (2). The assembly was held in place by tightening the screw cap (1). The screw cap was prevented from loosening by tightening the set screw (12). The opening in the screw cap (1) and the screen mount (2) defined the active surface area of the membrane. The stainless steel screen (3) protected the membrane from mechanical damage during handling of the sampler. Active carbon was used as the sorbent (5). It was held in place by glass wool (6) and plug (11), screwed into the main body (8). The internal chamber of the sampler was sealed with an O-ring (9). During the exposure, a holder screwed into the threaded opening (10) held the sampler in place. After the exposure, the sampler was sealed from the atmosphere by placing a polypropylene cap on (1). (2) Dynamic Method of Sample Collection. Dynamic sample collection was carried out by passing a known volume of the standard gas through sorption tubes filled with active carbon. The sample section of the tube contained 500 mg, while the backup section contained 200 mg of the carbon. Generation of Standard Gas Mixtures. Standard gas mixtures were generated dynamically using permeation sources. The custom-made standard gas mixture generator (Figure 2) was based on a Shimadzu GC 9A gas chromatograph (2). The permeation vessels (5) were made of 1.8-mL crimp-top glass vials (12) Namies´nik, J.; Go´recki , T.; Kozdron´-Zabiegała, B.; Janicki, W. Indoor Air 1992, 2, 115-120.

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(Agilent Technologies) capped with membranes made of thin Teflon film and filled with pure chemicals of interest (one chemical per vial). The vials were placed in a glass impinger (6) kept inside the GC oven at a constant temperature of 30 ( 1 °C. High-purity nitrogen was supplied to the bottom of the impinger at a constant flow rate of 300 ( 2 mL/min, controlled by the gas chromatograph’s carrier gas flow controller (4). The nitrogen was purified using a charcoal-filled hydrocarbon trap (1) before entering the generator. The standard mixture generated in this way was supplied directly to the calibration chamber (10). Three separate standard gas mixtures were generated. The first mixture contained the n-alkanes (n-pentane, n-hexane, nheptane, n-octane, n-nonane, n-decane) and the aromatic hydrocarbons (benzene, toluene, ethylbenzene, butylbenzene). The second mixture contained the esters (methyl acetate, ethyl acetate, methyl butyrate, ethyl butyrate, methyl heptanoate), and the third contained the alcohols (2-methyl-1-propanol, 2-pentanol, 2,3dimethyl-2-butanol, 3-hexanol, 2-hexanol, 2,4-dimethyl-3-pentanol, 1-hexanol, 6-methyl-2-heptanol, 1-heptanol, 2-ethyl-1-hexanol). Teflon membranes of different thicknesses were used in the permeation vessels, depending on the volatility of the component of interest. The 30-µm Teflon membrane was used for 1-hexanol, 6-methyl 2-heptanol, 1-heptanol, 2-ethyl-1-hexanol, and methyl heptanoate; the 120-µm membrane was used for all the remaining compounds. The calibration chamber (10) was made of an amber glass jar of 4-L volume. The jar was wrapped tightly along its entire height with a coil made of 1/4-in. copper tubing (11) and thermally insulated (9). The coil was connected to a thermostat, which maintained the chamber temperature at 25 ( 1 °C. The lid of the jar had two holes made in it to accommodate the standard mixture inlet and outlet manifolds. A 1/4-in.-thick PTFE disk, machined to 1/ -in. thickness at the edge and held in place with the lid, was 8 used to seal the jar. Four posts made of 3/4-in. PTFE rods were attached to the PTFE disk with screws. The posts were of two different lengths, 6 and 4 in., arranged alternately. They held the passive samplers (8) in place during exposure. The standard gas mixture from the generator was delivered to the bottom of the calibration chamber through 1/8-in. stainless steel tubing. The flow rate of the standard gas at the outlet of the calibration chamber was controlled periodically with a bubble flow meter. Analyte concentrations at the outlet of the calibration chamber were validated using the standard technique (sorption tubes filled with active carbon (7)) on a daily basis. In addition, average inlet concentrations were determined from the difference between the masses of the permeation vessels before and after the experiment and the diluting gas flow rate. The concentrations of the individual compounds were calculated from the equation

C (ng/mL) ) R/Q

(9)

where R is analyte permeation rate (ng/min, determined from the mass difference and the time between the weightings) and Q is nitrogen flow rate (mL/min). Calibration of the Permeation Passive Samplers. Four samplers were simultaneously exposed to the standard gas mixtures in the calibration chamber. The exposure time was varied from 1 to 14 days. Each experiment was repeated at least three

Figure 2. Schematic diagram of the passive sampling calibration apparatus. Key: 1, hydrocarbon trap; 2, standard gas generator based on a Shimadzu GC 9A gas chromatograph; 3, rotameter; 4, flow controller; 5, permeation vessels; 6, glass impinger; 7, sorption tube filled with active carbon; 8, passive samplers; 9, thermal insulation; 10, calibration chamber; 11, thermostating coil (1/4-in. brass tubing). Table 1. Conditions of Analyte Desorption from the Sorbent and GC Analysis of the Extracts 30-min desorption (after transferring the active carbon to a glass vial) gas chromatograph detector injection mode split ratio injection volume carrier gas temperature program data acquisition and processing capillary column calibration method

Analytical Procedure 1 mL of CS2 for aliphatic and aromatic hydrocarbons or 1 mL of mixture of CS2 + 1% 2-propanol for esters and alcohols Hewlett-Packard, GC System 5890 FID, 280 °C split, 250 °C 1:10 1 µL helium at 1.2 mL/min 35 °C, 7 °C/min to 220 °C, held for 2 min ChemStation software HP-1, 32 m × 0.25 mm, 0.25-µm film thickness external standard (ESTD) multipoint calibration curve

times. The experiments were carried out under the conditions of 0% relative humidity (RH), temperature (T) of 25 ( 1 °C, and standard mixture flow rate (Q) of 300 ( 2 mL/min. The active carbon sorbent was removed from the samplers after each exposure and analyzed for the content of the organic compounds trapped. The calibration constants k for the target analytes were calculated from eq 4 based on the amounts of the analytes trapped, their concentrations in the standard gas mixture, and the exposure time. Gas Chromatographic Analysis. All experiments were performed using an HP 5890 gas chromatograph (Hewlett-Packard) equipped with an FID detector and a split/splitless injector. Following each exposure, the carbon sorbent was transferred into 4-mL glass vials equipped with PTFE-lined septa. The analytes were liberated from the sorbent by desorption with 1 mL of CS2 or CS2 with 1% 2-propanol. In the case of the sorption tubes, the sample and the back-up sections were analyzed separately. The results of gas chromatographic determination were corrected for the blank value. The details of analyte desorption and GC analysis conditions are given in Table 1. All the reagents and materials coming into contact with the sample and the standards were randomly tested for contamination. Determination of the Recovery Coefficient from Active Carbon. Analyte recovery was determined for each component

of the standard gas mixture. Ten 500-mg samples of active carbon placed in 4-mL Teflon-capped vials were spiked with known amounts of the analytes. After 24 h, the samples were extracted with CS2 (or CS2 containing 1% of 2-propanol in the case of alcohols and esters) and analyzed by GC. The recovery coefficients obtained are listed in Table 2. They were taken into account in all determinations of the mass of the analyte trapped by the active carbon (both in the passive samplers and in the sorption tubes). RESULTS AND DISCUSSION Experimental Determination of the Calibration Constants. Air may contain a large number of organic compounds, and their composition may change over time. Consequently, the need to calibrate permeation passive samplers for each individual target compound is the single biggest obstacle in the widespread adoption of these samplers for air sampling. Thorough calibration of the samplers is very important, as it determines the accuracy and reliability of any further measurement results.12,13 The membrane of the permeation passive sampler used in our investigations has a well-defined surface area, which is mandatory for quantitative measurements. The calibration constants k for target analytes can be determined from eq 4 by exposing the (13) Kozdron´-Zabiegała, B.; Przyjazny, A.; Namies´nik, J. Indoor Build. Environ. 1996, 5, 212-218.

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Table 2. Recovery of the Analytes from Active Carbon recoverya

compound Esters (CS2 + 1% methyl acetate ethyl acetate methyl butyrate ethyl butyrate methyl heptanoate

2-Propanol)b

Aliphatic Hydrocarbons (CS2) n-pentane n-hexane n-heptane n-octane n-nonane n-decane

a

(%)

Table 3. Calibration Constants k Determined Experimentally k (min mL-1)

96 ( 3 98 ( 3 100 ( 3 100 ( 3 90 ( 3 102 ( 3 101 ( 3 100 ( 3 100 ( 3 98 ( 3 98 ( 3

Aromatic Hydrocarbons (CS2) benzene toluene ethylbenzene butylbenzene

96 ( 3 96 ( 3 97 ( 3 92 ( 3

Alcohols (CS2 + 1% 2-Propanol) 2-methyl-1-propanol 2-pentanol 2,3-dimethyl-2-butanol 3-hexanol 2-hexanol 2,4-dimethyl-3-pentanol 1-hexanol 6-methyl-2-heptanol 1-heptanol 2-ethyl-1-hexanol

90 ( 3 85 ( 3 85 ( 3 71 ( 3 71 ( 3 85 ( 3 70 ( 3 82 ( 3 75 ( 3 85 ( 3

P ) 95%, fn-1)9. b Desorption medium.

samplers to known, constant concentrations of these analytes in a standard gas mixture for known periods of time. Each sampler has to be calibrated individually for each individual target compound, with replicate experiments carried out for each exposure time. Assuming that the permeation rate of a given analyte through the membrane remains constant for a constant analyte concentration in the calibration mixture, the plots of the amount of analyte trapped versus the exposure time should be linear. The calibration constants k can be found from the reciprocals of the slopes of these lines (plotted individually for each compound). Calibration constants determined in this way for the 25 analytes used in the study are presented in Table 3 together with the total number of experiments on which the determination was based and the standard deviations of the results. The stability of analyte concentration in the calibration mixture plays an extremely important role in the calibration of permeation passive samplers. To avoid errors, care should be taken to make sure that the concentration remains constant and stable in the calibration chamber throughout all the measurements. In our experiments, analyte concentrations were monitored at the inlet to the calibration chamber and at its outlet, both during and after the exposure (with no samplers in the chamber). The concentrations of the components of the standard gas mixture measured at the inlet (gravimetric method) and at the outlet of the calibration chamber, with and without the passive samplers inside, are presented in Table 4. The results indicate that the concentrations measured at the outlet of the chamber when it contained the passive samplers were 3186 Analytical Chemistry, Vol. 75, No. 13, July 1, 2003

group of compds esters

alcohols

aliphatic hydrocarbons

aromatic hydrocarbons

target compd

exptl data

STD

methyl acetate ethyl acetate methyl butyrate ethyl butyrate methyl heptanoate 2-methyl-1-propanol 2-pentanol 2.3-dimethyl 2-butanol 3-hexanol 2-hexanol 2,4-dimethyl 3-pentanol 1-hexanol 6 methyl 2-heptanol 1-heptanol 2-ethyl-1-hexanol n-pentane n-hexane n-heptane n-octane n-nonane n-decane benzene toluene ethylbenzene butylbenzene

0.185 0.155 0.131 0.103 0.064 0.185 0.160 0.142 0.122 0.117 0.115 0.110 0.095 0.085 0.075 0.230 0.184 0.160 0.132 0.100 0.064 0.166 0.142 0.117 0.072

0.011 0.017 0.013 0.009 0.008 0.028 0.043 0.023 0.030 0.035 0.018 0.018 0.022 0.016 0.024 0.026 0.020 0.021 0.011 0.021 0.023 0.009 0.011 0.013 0.010

no. of expts n)8

n)8

n ) 12

n ) 12

always lower than the concentrations measured when no samplers were present in the chamber. This was expected considering that the thin PDMS membranes used in the samplers were characterized by high permeability toward the analytes. Taking into account that four passive samplers were present in the chamber during each exposure, they were able to remove a significant fraction of the analytes from the standard gas mixture delivered to the chamber in unit time, especially when the rate of analyte delivery was relatively low. The reduction in the concentration of the analytes in the chamber can be estimated from the magnitude of the calibration constants k and the rates of permeation of the analytes from the permeation sources (determined gravimetrically). The former allows the calculation of the rate of analyte removal from the chamber, while the latter gives information on the rate of analyte delivery. Table 5 summarizes the results of such a comparison for n-alkanes. In general, the effect was more pronounced for less volatile analytes, with the drop for n-decane reaching 21%. Again, this result was expected considering that these compounds are characterized by high partition coefficients between air and PDMS (hence small calibration constants). Consequently, for a given rate of standard gas mixture delivery, a larger fraction of the analyte delivered to the chamber was removed by the samplers in unit time than was the case for more volatile analytes. Analyte depletion in the exposure chamber might lead to incorrect determination of the calibration constants k, which, in turn, would lead to incorrect results in field measurements. Thus, the effect should always be either accounted for or eliminated. One way to reduce the magnitude of this problem would be to use fewer samplers in the chamber (note that, even for n-decane, the decrease in concentration would be only ∼5.5% if a single sampler was present in the chamber instead of four samplers at

Table 4. Concentrations of the Components of the Standard Gas Mixture Determined by Two Different Methods concentration of the analyte in the calibration chamber (µg/L), n ) 30 chromatographic method target compound

with samplers in the chamber

without samplers in the chamber

STD

STD

gravimetric method

n-pentane n-hexane n-heptane n-octane n-nonane n-decane

5.17 1.83 1.35 0.60 0.26 0.12

Aliphatic Hydrocarbons 1.164 0.412 0.312 0.142 0.075 0.036

5.88 1.91 1.55 0.71 0.31 0.14

1.199 0.487 0.313 0.143 0.068 0.051

5.94 1.89 1.53 0.78 0.32 0.13

benzene toluene ethylbenzene butylbenzene

1.84 1.20 0.47 0.08

Aromatic Hydrocarbons 0.372 0.347 0.112 0.021

2.02 1.51 0.53 0.10

0.442 0.395 0.104 0.035

2.74 2.23 0.58 0.22

methyl acetate ethyl acetate methyl butyrate ethyl butyrate methyl heptanoate 2-methyl-1-propanol 2-pentanol 2,3-dimethyl-2-butanol 3-hexanol 2-hexanol 2,4-dimethyl-3-pentanol 1-hexanol 6-methyl-2-heptanol 1-heptanol 2-ethyl-1-hexanol

80.69 56.79 43.68 10.76 2.43

Esters 4.696 3.680 3.507 0.805 0.611

91.52 60.01 45.38 10.89 2.69

4.130 2.960 3.057 0.710 0.561

89.66 61.00 49.32 11.07 3.54

7.17 5.81 9.39 4.20 3.68 6.11 1.16 0.90 0.58 0.34

Alcohols 1.961 1.913 2.045 0.626 1.094 1.302 0.253 0.288 0.101 0.091

7.45 5.91 9.48 4.21 3.87 6.20 1.32 0.98 0.61 0.40

0.961 1.113 2.135 0.613 0.909 1.202 0.325 0.128 0.091 0.091

7.51 5.60 9.51 4.21 3.99 6.21 1.61 1.02 0.64 0.44

Table 5. Effect of the Rate of Analyte Delivery to the Calibration Chamber on the Calibration of Passive Samplers Determined for n-Alkanes

analyte

C (ng cm-3)

n-pentane n-hexane n-heptane n-octane n-nonane n-decane

5.17 1.83 1.35 0.60 0.26 0.12

a

calibration chamber k rate of analyte (calibration uptake by a single -3 const) (min cm ) passive samplera (ng min-1) 0.230 0.184 0.160 0.132 0.100 0.064

22.49 9.94 8.44 4.55 2.60 1.88

Std gas mixture generator permeation rate (R) (ng‚min-1)

decrease in analyte concn in calibration chamber caused by passive samplers (%)

1782 576 405 180 78 36

5 7 8 10 13 21

(1/k)c equation used to calculate the analyte amount taken up by the passive sampler from the standard gas mixture during calibration.

a time). This approach is not practical, however, as it would be too labor- and time-consuming. Another way to eliminate this problem would be to make sure that the rate of analyte delivery from the standard gas generator is much greater than the rate of analyte removal by the samplers. In the case of permeation-based standard gas mixture generators, this can be accomplished by simultaneously increasing the rate of analyte permeation and the flow rate of the diluting gas. Permeation rate can be increased by increasing the temperature of the sources, by increasing the surface area of the permeation barrier, and by reducing its thickness. The calibration constants k presented in Table 5 were calculated using analyte concentrations at the outlet of the chamber, which were the steady-state concentrations the samplers

were effectively sensing. This minimized the effect of analyte depletion in the chamber on the results of determination of k. Estimation of the Calibration Constants Based on Physicochemical Properties of the Analytes. Experimental determination of the individual calibration constants k of permeation passive samplers is time-consuming and costly. The main goal of our study was to simplify the calibration process by making it possible to estimate the value of the calibration constant for any compound without the need for calibration in the standard gas mixture. Equation 6 indicates that permeability of a compound through a polymeric membrane depends on the solubility and diffusivity of the chemical in the membrane material. Since diffusivity in the PDMS polymer depends only weakly on the Analytical Chemistry, Vol. 75, No. 13, July 1, 2003

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Figure 3. Relationships between the number of carbon atoms in a homologous series of compounds and the calibration constants for the permeation passive samplers equipped with PDMS membranes. The equations of the lines: Y ) -0.0317x + 0.383 (R2 ) 0.9932) for n-alkanes, Y ) -0.0236x + 0.307 (R2 ) 0.9995) for aromatic hydrocarbons, Y ) -0.0247x + 0.278 (R2 ) 0.8507) for alcohols, and Y ) -0.0241x + 0.253 (R2 ) 0.9928) for esters.

structure of a compound, permeability should be primarily determined by the solubility coefficient S, equivalent to Henry’s law constant for analyte partitioning between air and the polymer. It is well known when considering partitioning between two phases that free energy of transfer of a molecule from one phase to the other changes consistently with incremental changes in the structure of the molecule. This observation forms the foundation of linear free energy relationships, used for example to estimate octanol-water partition coefficients of chemicals from various physicochemical properties of the molecules.14 We decided to use a similar approach to try to estimate the calibration constants of permeation passive samplers equipped with thin PDMS membranes. Addition of a certain fragment to a molecule should cause a consistent change in the free energy of transfer of this molecule between the two phases involved in partitioning. Consequently, in a homologous series of compounds, a unit change in the number of carbon atoms should cause a constant change in the partitioning coefficient, thus also the calibration constant k. Figure 3 presents the relationships between the number of carbon atoms and the calibration constants k for four families of organic compounds, including n-alkanes, aromatics, alcohols, and esters. The k value decreased linearly with increasing number of carbon atoms for all four series. The linear correlation coefficients (see figure caption) were generally very high. The scatter of results observed for alcohols with six, seven, and eight carbon atoms was fully expected considering the different structures of the molecules with the same number of carbon atoms. Branching and different positions of the alcohol group are obviously not reflected in the number of carbon atoms, while the free energy of transfer of the molecule from the gas phase to PDMS depends on the geometry of the molecule. The data presented in Figure 3 clearly demonstrate that it is possible to predict the value of the calibration constant k for a member of a homologous series of compounds if the structure of (14) Schwarzenbach R. P.; Gschwend P. M.; Imboden D. M. Environmental Organic Chemistry; J. Wiley & Sons: New York, 1993.

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Figure 4. Relationship between the molecular weight of a compound and the calibration constant for the permeation passive sampler equipped with the PDMS membrane. Equation of the regression line is Y ) -0.00188x + 0.3268 (R2 ) 0.8742). Regression lines for the individual classes of compounds: Y ) -0.00227x + 0.3875 (R2 ) 0.9932) for n-alkanes, Y ) -0.00168x + 0.2965 (R2 ) 0.9995) for aromatic hydrocarbons, Y ) -0.00178x + 0.3099 (R2 ) 0.8507) for alcohols, and Y ) -0.00172x + 0.3080 (R2 ) 0.9928) for esters.

the compound and the relationship between k and the number of carbon atoms for this series are known. The average difference between the experimental and the predicted value was -0.4%. While this very small difference was impressive, in our opinion it did not reflect the true magnitude of the difference between the estimate and the experimental value one could expect for any individual compound in real life. We decided therefore to calculate also the average of the absolute values of the differences, to eliminate the effect of the sign of the difference on the average. The calculated value of the average of the absolute values of the differences was 5.4%. The absolute difference was less than 10% for 21 of the 25 compounds studied. When only the true homologous series were taken into account (i.e., alcohols were excluded), all the differences were lower than 6.5%. Overall, the differences were in general much lower than typical uncertainty in field measurements. The use of this approach should result in significant time and cost savings. The sampler can be calibrated using just two or three members of a homologous series, and the resultant correlation could then be used to estimate the k values for any other member of the series, including compounds for which standards are unavailable. Physicochemical properties of a compound, including its molecular weight and boiling point, are more closely related to the structure of a molecule than just the number of carbon atoms. Thus, they should be more useful when trying to predict the calibration constants for a broader range of compounds (not necessarily members of a homologous series). Selected properties of the analytes used in the study are listed in Table 6. Figure 4 presents the relationship between the molecular weight of a compound (for all four classes of compounds used in the study) and the calibration constant k. In general, the relationship was linear, with a relatively high value of the linear correlation coefficient (R2 ) 0.8742). The differences between the experimental and the predicted values (see Table 7) exceeded 20% only for two compounds, which is well within satisfactory

Table 6. Physicochemical Properties and Chromatographic Retention Parameters of the Components of the Standard Gas Mixture group of compds esters

alcohols

aliphatic hydrocarbons

aromatic hydrocarbons

target compound

boiling point (°C)

molecular wt (amu)

est RIa

retention timeb

LTPRIc cal

methyl acetate ethyl acetate methyl butyrate ethyl butyrate methyl heptanoate 2-methyl-1-propanol 2-pentanol 2,3-dimethyl-2-butanol 3-hexanol 2-hexanol 2,4-dimethyl-3-pentanol 1-hexanol 6-methyl-2-heptanol 1-heptanol 2-ethyl-1-hexanol n-pentane n-hexane n-heptane n-octane n-nonane n-decane n-undecane n-dodecane benzene toluene ethylbenzene butylbenzene

56.9 77.1 102.0 136.0 172.0 107.9 118.0 120 135.0 136 139 156.0 172 176 183 36.1 69.0 98.4 126.0 150.8 171.0 195.9 216.3 80.1 110.6 136.2 183.0

74 88 102 116 144 74 88 102 102 102 116 102 130 116 130 72 86 100 114 128 142 156 170 78 92 106 134

500 600 700 800 1000 500 600 700 700 700 800 700 900 800 900 500 600 700 800 900 1000 1100 1200 600 700 800 1000

2.346 2.780 3.888 5.176 10.306 2.874 3.010 4.024 5.119 5.202 5.894 6.506 8.809 8.888 10.309 2.166 2.794 3.814 5.475 7.634 9.989 12.337 14.597 3.227 4.638 6.463 11.041

529 598 704 782 1013 608 621 713 779 784 819 848 950 953 1014 500 600 700 800 900 1000 1100 1200 642 750 846 1045

a Retention Index (RI) estimated from the empirical formula of the analyte. (If the retention index of a compound is unknown, it can be estimated from empirical considerations of the elements and partial structure present in the molecule. Rough approximation can be made using the empirical formula of the analyte.15 b Retention time of the analyte obtained for the chromatographic conditions given in Table 1. c Linear temperatureprogrammed retention index (LTPRI) calculated from the equation: LTPRI ) 100x(t(A) - t(n)/t(n + 1) - t(n)) + 100n, where t(A) is retention time of the analyte, t(n) is retention time of the n-alkane eluting directly before the analyte, t(n + 1) is retention time of the n-alkane eluting directly after analyte, and n is number of carbon atoms for the n-alkane eluting directly before the analyte.

limits in many field measurements. Overall, the differences ranged from a low of -16.8% for n-pentane to a high of +27.9% for 1-heptanol. The average difference was only 0.9%; the average of the absolute values of the differences between the experimental and the estimated k value was 9.8%. A closer look at the data indicates that molecular weight tended to underestimate the calibration constants for nonpolar and slightly polar aliphatic compounds and overestimate the values for the most polar alcohols and the aromatics. In general, molecular weight of a compound proved to be a reasonably good predictor of the k values of the analytes studied; thus it could be used to estimate these values without the need for calibration of the samplers for each individual analyte. When better accuracy of estimation is required, regression lines for the individual classes of compounds (see figure caption) can be used instead of the “universal” regression line for all compounds. Boiling point of a compound depends mostly on the strength of intermolecular interactions in the liquid phase, which is determined by the structure of a compound and the nature of the functional groups present in the molecule. The same factors affect the solubility of a compound in PMDS; therefore, the calibration constant of a permeation passive sampler should be correlated to the boiling point of the analyte. Figure 5 presents the relationship between the calibration constants determined in the study and the boiling points of the analytes. Again, a linear relationship was obtained, with the linear correlation coefficient of R2 ) 0.8911, which indicates that this correlation should be slightly better for

Figure 5. Relationship between the boiling point of a compound and the calibration constant for the permeation passive sampler equipped with the PDMS membrane. Equation of the regression line is Y ) -0.00099x + 0.2531 (R2 ) 0.8911). Regression lines for the individual classes of compounds: Y ) -0.00117x + 0.2716 (R2 ) 0.9889) for n-alkanes, Y ) -0.000923x + 0.2417 (R2 ) 0.9976) for aromatic hydrocarbons, Y ) -0.00122x + 0.2971 (R2 ) 0.8986) for alcohols, and Y ) -0.00101x + 0.2370 (R2 ) 0.9929) for esters.

estimation of the calibration constants of the passive samplers than the relationship presented in Figure 4. The average difference between the experimental and the predicted value was 1.4%; the average of the absolute values of the differences between the experimental and the estimated k value was 8.5%, which was lower Analytical Chemistry, Vol. 75, No. 13, July 1, 2003

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Table 7. Comparison of the Calibration Constants (k) Obtained from Experimental Data and Estimated from the Equations of the Regression Linesa parameter used for the estimation of the calibration constant no. of C atoms

bp (°C)

MW

av MW - bp

LTPRI

target compound

kExp

kCA

% diff

kMW

% diff

kBP

% diff

kAV

% diff

kLTPRII

% diff

methyl acetate ethyl acetate methyl butyrate ethyl butyrate methyl heptanoate 2-methyl-1-propanol 2-pentanol 2,3-dimethyl-2-butanol 3-hexanol 2-hexanol 2,4-dimethyl-3-pentanol 1-hexanol 6-methyl-2-heptanol 1-heptanol 2-ethyl-1-hexanol n-pentane n-hexane n-heptane n-octane n-nonane n-decane benzene toluene ethylbenzene butylbenzene

0.185 0.155 0.131 0.103 0.064 0.185 0.160 0.142 0.122 0.117 0.115 0.110 0.095 0.085 0.075 0.230 0.184 0.160 0.132 0.100 0.064 0.166 0.142 0.117 0.072

0.180 0.156 0.132 0.108 0.060 0.178 0.153 0.128 0.128 0.128 0.103 0.128 0.078 0.103 0.078 0.224 0.193 0.161 0.129 0.097 0.066 0.165 0.142 0.118 0.071

2.2 -0.9 -1.0 -5.1 6.2 3.8 4.4 9.8 -5.0 -9.5 10.3 -16.4 17.7 -21.3 -4.2 2.4 -4.6 -0.4 1.9 2.8 -2.7 0.3 0.2 -1.1 0.8

0.188 0.161 0.135 0.109 0.056 0.188 0.161 0.135 0.135 0.135 0.109 0.135 0.082 0.109 0.082 0.191 0.165 0.139 0.112 0.086 0.060 0.180 0.154 0.128 0.075

1.7 4.0 3.1 5.5 -12.4 1.4 0.8 -4.9 10.7 15.4 -5.5 22.8 -13.3 27.9 9.9 -16.8 -10.4 -13.4 -14.6 -14.1 -6.5 8.7 8.4 9.1 4.5

0.197 0.177 0.152 0.118 0.083 0.146 0.136 0.134 0.119 0.118 0.115 0.099 0.083 0.079 0.072 0.217 0.185 0.156 0.128 0.104 0.084 0.174 0.144 0.118 0.072

6.6 14.0 16.1 15.0 29.3 -21.0 -14.9 -5.5 -2.1 1.2 0.4 -10.3 -12.9 -7.3 -4.1 -5.5 0.3 -2.9 -2.5 3.5 30.9 4.8 1.1 1.1 0.4

0.192 0.169 0.144 0.114 0.069 0.167 0.149 0.135 0.127 0.127 0.112 0.117 0.083 0.094 0.077 0.204 0.175 0.147 0.120 0.095 0.072 0.177 0.149 0.123 0.073

4.2 9.0 9.6 10.3 8.5 -9.8 -7.0 -5.2 4.3 8.3 -2.5 6.2 -13.1 10.3 2.9 -11.1 -5.0 -8.1 -8.6 -5.3 12.2 6.8 4.7 5.1 2.4

0.193 0.175 0.148 0.128 0.068 0.173 0.169 0.146 0.129 0.127 0.118 0.111 0.085 0.084 0.068 0.201 0.175 0.149 0.123 0.097 0.072 0.164 0.136 0.111 0.060

-4.7 -13.1 -12.9 -24.2 -6.7 6.6 -5.8 -2.6 -5.5 -9.0 -2.8 -0.9 10.9 1.4 9.0 12.8 5.1 7.0 6.4 2.8 -12.1 1.2 4.0 4.6 16.0

average

-0.4

0.9

1.4

1.2

-0.5

a Equations for the families of compounds were used for the correlation with the number of C atoms; in all other cases, regressions including all the compounds were used.

by 1.3% than the value for the estimates based on molecular weight. On the other hand, the differences between the experimental and the predicted values (see Table 7) exceeded 20% for three compounds, one more than was the case for molecular weight. The estimated k values were generally lower than the experimental values for most alcohols and higher than the experimental values for the esters. In general, however, the data indicate that the boiling point of a compound is also a useful predictor of the k values for the compounds studied. Similarly, as before, even better estimates can be obtained from the regression lines for the individual classes of compounds. The results presented in Figure 4 and Figure 5 demonstrate that the calibration constant k of a permeation passive sampler can be estimated with reasonable accuracy from the molecular weight of a compound or its boiling point, without the need for experimental calibration for each individual compound. The choice of one of the two descriptors is somewhat arbitrary and depends on the nature of the compound. In fact, the best results were obtained by averaging the k values obtained by the two methods. The differences between the experimental and the estimated values ranged in this case from -13.1% for 6-methyl-2-heptanol to +12.2% for n-decane, with the average difference of 1.2% and the average of the absolute values of the differences equal to 7.2%. The difference was less than 10% for 20 of the 25 compounds studied. These numbers would be acceptable in most fieldwork, where uncertainty of the measurements is usually higher than that. 3190

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Our experiments were carried out for analytes whose molecular weights ranged from 72 (n-pentane) to 144 (methyl heptanoate), and the boiling points ranged from 36 (n-pentane) to 183 °C (butylbenzene). These ranges cover many volatile organic compounds relevant to air analysis. The correlations established in this study could probably be applied for compounds outside of these ranges, but care should be exercised when this approach is used. For example, the course of the regression line obtained for the relationship between the boiling point of a compound and the calibration constant of the passive sampler indicates that this regression can only be used for compounds whose boiling point is below 250 °C. In field measurements, very often the identity of all compounds present in the sample is not known. The approaches proposed thus far cannot be used for obvious reasons for unknown analytes, which normally precludes even rough estimation of the total load of organics in the air when permeation passive samplers are used. It would be very advantageous to be able to estimate the calibration constants for all compounds present in a sample. The knowledge of the calibration constants could then be used to quantify the unknown compounds provided that the response factors of the detector toward these compounds were known. In the process of identification of organic compounds in complex mixtures, the use of retention indexes is becoming more important despite the wide use of GC/MS systems. This is a result of the outstanding stability of fused-silica capillaries and the

Figure 6. Relationship between the linear temperature-programmed retention index of compound and the calibration constant for the permeation passive sampler equipped with the PDMS membrane. Equation of the regression line is Y ) -0.000258x + 0.3293 (R2 ) 0.9225). Regression lines for the individual classes of compounds: Y ) -0.000317x + 0.3830 (R2 ) 0.9932) for n-alkanes, Y ) -0.000235x + 0.3172 (R2 ) 0.9993) for aromatic hydrocarbons, Y ) -0.000240x + 0.3144 (R2 ) 0.9500) for alcohols, and Y ) -0.000243x + 0.3041 (R2 ) 0.9703) for esters.

excellent reproducibility of gas chromatographs now available.15 However, instead of the Kovats retention indexes, the linear temperature-programmed retention index system (LTPRI) is extensively used these days.16 Martos et al.17 demonstrated that LTPRI determined for a PDMS-coated capillary column could be used to estimate the partition coefficients of organic compounds between air and the PDMS coating of the SPME fiber. Since the solubility coefficient in eq 6 is related to the partition coefficient, there should also be a relationship between the LTPRI determined on PDMS-coated capillary columns and the calibration constant of a given compound for permeation passive samplers equipped with PDMS membranes. This relationship would not require knowledge of the identity of the compound for determination of its calibration constant. Data required for the calculation of LTPRI of the components of the standard gas mixture used in the study and the values of LTPRI for these compounds are listed in Table 6. The relationship between LTPRI and the calibration constant k is illustrated in Figure 6. The relationship was linear, with the highest value of the linear correlation coefficient of the three correlations examined (molecular weight, boiling point, LTPRI). In all cases, the estimates obtained using this correlation were within 25% of the experimental value (see Table 7), with the average difference of -0.5%, and the average of absolute values of the difference equal to 7.5%. The difference was less than 15% for 22 of the 25 compounds studied. Taking into account that the estimates of k were obtained in this case from retention parameters, without the need to know the identity of the analytes, we consider this an excellent result. The quality of the estimates obtained in this way can often be further improved if the chemical class to which the analyte belongs is known, as evidenced by the values of the linear correlation coefficients obtained for the correlations between (15) Hu ¨ bschmann H. J. Handbook of GC/MS: Fundamentals and Applications; Wiley-VCH: Toronto, 2001. (16) Gonzalez, F. R.; Nardillo, A. M. J. Chromatogr., A 1999, 842, 29-49. (17) Martos, P. A.; Saraullo, A.; Pawliszyn, J. Anal. Chem. 1997, 69, 402-408.

LTPRI and k for the individual families of the analytes (see figure caption). The positive correlation between LTPRI and the calibration constant of a permeation passive sampler for a given compound makes it possible to estimate the k value for any analyte found in the sample. If the identity of the analyte is unknown, the compound can be quantified with the use of a detector with a known, uniform response factor for organic compounds (e.g., FID or atomic emission detector), assuming that the recovery of the compound from the active carbon is 100%. This approach makes it possible to use permeation passive samplers for the estimation of the total load of organics in a sample or to determine group parameters such as total petroleum hydrocarbons. With a selective detector, determination of other group parameters becomes possible. For example, total organic halogen could be estimated with the use of an electrolytic conductivity detector. If the identity of the unknown analyte is determined, for example, by means of a mass spectrometric detector, the accuracy of the measurement result can be further improved by calibrating the response of the detector toward this particular compound. The additional step (calibration of the detector toward the new analyte) does not differ in this case from what would have to be done for a sample collected by active means (for example, using sorption tubes). Thus, the correlation between LTPRI and the calibration constant of a permeation passive sampler makes it possible to use the latter as efficiently as sorption tubes, while preserving all the advantages of passive sampling. In essence, the approach proposed makes it possible to perform qualitative and quantitative analysis of virtually any gaseous sample by this technique. CONCLUSIONS Passive sampling has numerous advantages. It is much less expensive and easier than active sampling. Samplers can be deployed unattended for prolonged periods of time without the annoyance unavoidable in the case of active sampling. Timeweighted average concentrations can be determined using passive sampling without the need for averaging the results. Permeation passive samplers offer an effective solution to several problems typical of other passive sampling techniques. They are generally less sensitive to air currents. With the right membrane, they can eliminate entirely problems caused by humidity. Finally, the sampling rate of permeation passive samplers depends only weakly on temperature. The single biggest obstacle in a wider acceptance of permeation passive samplers thus far has been the need to calibrate the samplers for each individual compound of interest. This limited the applicability of permeation passive samplers exclusively to target compound analysis. The approach proposed in this paper eliminates this fundamental limitation of permeation passive sampling. The PDMS membrane used in this study not only assured high sampling rates but also made it possible to estimate the values of the calibration constants based on physicochemical properties of the analytes, their retention parameters, or both. This makes it possible to deploy permeation passive samplers in the same way in which active sampling is deployed. The samplers can be exposed to an unknown sample without the need to calibrate their response toward all analytes in advance. Once the compounds present in the sample are identified, only the detector needs to be calibrated toward them. Alternatively, target compounds can be quantified, Analytical Chemistry, Vol. 75, No. 13, July 1, 2003

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and the total load of the organics or selected group parameters can be estimated using the right detectors. Further research required to demonstrate this is under way. Overall, we firmly believe that the results presented in this paper will help permeation passive sampling become a mainstream analytical technique. ACKNOWLEDGMENT This work has been financially supported by the NATO postdoctoral fellowship program, Natural Sciences and Engineer-

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ing Research Council of Canada, and Polish National Scientific Committee (KBN, project 3T09A 01319).

Received for review January 29, 2003. Accepted March 31, 2003. AC034087T