Kinetic Study of Membrane Extraction with a Sorbent Interface for Air

the membrane probe is simply exposed to air with carrier gas .... Canada). Nitrogen, compressed air, and hydrogen gases for flame ionization detection...
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Anal. Chem. 1998, 70, 248-254

Kinetic Study of Membrane Extraction with a Sorbent Interface for Air Analysis Yu Z. Luo, Marc Adams, and J. Pawliszyn*

The GuelphsWaterloo Center for Graduate Work in Chemistry and the Waterloo Center for Groundwater Research, Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

This paper presents the theory and experimental implementation of the technique of membrane extraction with a sorbent interface for air analysis. A mathematical model was derived to predict the extraction process and the significant factors, such as membrane length and carrier gas flow rate. A benzene/nitrogen standard gas mixture was generated by the permeation tube method. Several parameters that affect the extraction efficiency are discussed. Among them, the membrane length, the flow rate of the carrier gas, and temperature strongly affected the extraction rate of analyte. The results demonstrated that the extraction rate of benzene was decreased with increase of the extraction temperature. Toluene, hexane, ethylbenzene, and trichloroethylene were selected to test the theory, and good agreement between theoretical predictions and experimental results was observed. The estimation of air concentration without experimental calibration is discussed. In the proposed estimation method, the diffusion coefficient of benzene in the membrane and the distribution constant between air and the membrane were measured experimentally. Common techniques for air sampling can be divided into two categories: solid sorbent techniques and whole air collection techniques. These common methods usually require dedicated separation instruments, are expensive, and are time-consuming. Although EPA Method To-141 provides sensitive and reliable measurements, it is unsuitable for automated or field monitoring. However, real-time or near real-time monitoring is becoming important for air pollution measurements. The membrane extraction with a sorbent interface (MESI) technique is amenable to automated and field monitoring.2,3 Pratt and Pawliszyn studied the extraction of water samples with a countercurrent flow system.4,5 In their research, a water sample was pumped through a hollow fiber membrane. The carrier gas flowed countercurrently around the exterior of the fiber. Analyte in the sample was extracted when water sample made contact with the membrane. Good sensitivity was obtained. In this paper, the membrane probe is simply exposed to air with carrier gas (1) Winberry, W. T.; Murphy, N. T.; Riggan, R. M. EPA To-14 Method, EPA600/4-89-017. U.S. EPA: Washington DC, 1988. (2) Yang, M. J.; Harms, S.; Luo, Y. Z.; Pawliszyn, J. Anal. Chem. 1994, 66, 1339-1346. (3) Yang, M. J.; Luo, Y. Z.; Pawliszyn, J. CHEMTECH 1994, 24, 31-37. (4) Pratt, K. F.; Pawliszyn, J. Anal. Chem. 1992, 64, 2101-2106. (5) Pratt, K. F.; Pawliszyn, J. Anal. Chem. 1992, 64, 2107-2110.

248 Analytical Chemistry, Vol. 70, No. 2, January 15, 1998

flowing inside the membrane to perform extraction. This simplification is beneficial to the practice of air monitoring, because the probe can be easily placed in pipes, in vents, or behind fans. In the MESI method, since the enrichment time of extraction is flexible within certain ranges, both a near real-time and a relatively long term time-averaged air monitoring are practical. For a low concentration of analyte in the air, the enrichment time can be longer to satisfy the detection limit. For a higher concentration, a short enrichment time is adopted, such as 40 s. This paper is a continuation of the study of membrane extraction by the MESI method. In the previous papers,6,7 headspace and direct aqueous sample extractions were studied, and this paper focuses on air extraction and analysis. THEORY The permeation of volatile organic compounds through a nonporous polymer membrane is generally described in terms of a “solution-diffusion” mechanism.8,9 The membrane used in this study is hollow fiber. The extraction processes consist of several steps, and they are described as follows: (1) mass flux of analyte from air to the boundary layer outside the membrane surface; (2) diffusion of analyte through the boundary layer to the membrane outer surface, a diffusion process; (3) partition of analyte between air and membrane at the membrane outer surface, a partitioning process; (4) random movement of the analyte in and through the membrane, a diffusion process; (5) release and stripping of analyte by carrier gas at the inner surface of the membrane, a partitioning process; (6) diffusion of analyte though the gas boundary layer which is close to the inner membrane surface, a diffusion process; (7) mass transfer of analyte to the sorbent interface by carrier gas. Since most volatile organic compounds have a large diffusion coefficient in air, mass transfer through air can be considered fast. When the membrane is exposed in a fast flowing gas stream, steps 1 and 2 are fast. Since carrier gas flows through the inside of the hollow fiber membrane, steps 6 and 7 are fast. Steps 3 and 5 are partitioning processes. These processes are relatively fast. Since most analytes have a low diffusion coefficient in the membrane, step 4 is slow and, hence, is the rate-determining step in the extraction process. In this paper, the studies were focused on (6) Yang, M. J.; Adams, M.; Pawliszyn, J. Anal. Chem. 1996, 68, 2782-2789. (7) Luo, Y. Z.; Adams, M.; Pawliszyn, J. Analyst 1997, 122, 1461-1469. (8) Stern, S. A. Membrane Separation Technology; Elsevier: Amsterdam, 1995. (9) Skelland, A. H. P. Diffusional Mass Transfer; John Wiley & Sons: New York, 1974. S0003-2700(97)00549-0 CCC: $15.00

© 1998 American Chemical Society Published on Web 01/15/1998

G(t) )

∂

{

Z(t) ) CsADKs

∂t

2

∞

∑e a

-DRn2t

1

+

θ + a ln(b/a)

}

J0(bRn)[θRnJ1(aRn) + J0(aRn)] F(Rn)

n)1

(2)

Figure 1. Geometry of the hollow fiber membrane.

where θ )ADKs f/Q, A is the membrane surface area, D is the diffusion coefficient in the membrane, Ks is the distribution constant between the air and the membrane, f ) Cg/Cg and Cg is the average lengthwise concentration in the carrier gas, and an are the positive roots of

-[θR J1(aR) + J0(aR)] Y0(bR) + [θR Y1(aR) + Y0(aR)] J0(bR) ) 0 (3) Formula 2 can be used to calculate the time to reach steady-state extraction rate. A computer program must be used to find the roots of eq 3 and then calculate extraction rate or extraction amount. At steady state, the formula for C(r,t) simplifies to Figure 2. Concentration profile during air extraction. The concentration at the outer surface is much higher than in the air because of the high partitioning. The concentration at the inner surface is low because of the concentration gradient and gas stripping.

θ + a ln(r/a) C(r) ) KsCs θ + a ln(b/a)

(4)

the extraction rate at steady state is extraction from a fast-flowing gas stream. To simplify the model, perfect agitation was assumed in the gas phase; hence the boundary layers were not considered in the calculations.10 The theoretical analysis treats the membrane as having a hollow cylinder geometry (Figure 1). The inner radius is a and outer radius is b. The membrane length is L. The stripping carrier gas is on the inside at the flow rate Q. Figure 2 shows the expected concentration profile of analyte across the membrane. The air temperature is assumed constant during the extraction. Cs represents the analyte concentration in the air stream flowing past the outside of the membrane. The air is assumed perfectly agitated and the concentration of analyte in air is assumed constant. C(r,t) is the analyte concentration in the membrane at position r and time t, and D is the diffusion coefficient of the analyte in the membrane. Initial analyte concentration in the membrane is assumed 0. The extraction rate of the MESI process can be predicted by solving the diffusion equation for the membrane geometry and boundary conditions. The details of the derivation of the equations are shown in the Supporting Information. The total amount extracted at time t can be expressed as

1 Gss ) CsADKs θ + a ln(b/a)

(5)

and the extraction rate is

EXPERIMENTAL SECTION Apparatus and Reagents. The membrane used was a silicon hollow fiber membrane (Baxter Healthcare Corp., McGaw Park, IL). The membrane had an inner diameter of 305 mm and a wall thickness of 165 mm. The membrane probe was constructed by connecting two 8-cm-long (0.53-mm o.d.) deactivated silica tubing (Supelco Canada, Mississauga, ON, Canada) to the ends of the membrane. For this connection, one end of the membrane was first immersed in toluene for about 10 s, and then a 0.5-cm length of the silica tubing was inserted into the swollen membrane. When the toluene evaporated, the membrane shrank and a tight seal formed between the membrane and the tubing. One silica tubing was then connected to a carrier gas feed line which was disconnected from the GC injector. The other one was connected to the sorbent interface. The sorbent interface has been described previously.11 The sorbent interface contains three parts: polymer sorbent, a pulse heating device and a cooling device. The polymer sorbent was a 1-cm-long poly(dimethylsiloxane) (PDMS)-coated fused-silica fiber (Supelco Canada). The fiber was located in a 6-cm-long, 0.53mm-i.d. deactivated fused-silica capillary tube (Supelco Canada). On the outside of the tubing, a 2-cm heating coil (Ni-Cr wire, 20 Cr, 0.1-mm diameter, 40-cm length, 47Ω total resistance, Johnson Matthey Metals Ltd. U.S.A) was tightly wrapped. The coil covered the entire region where the fiber was located. The tubing with the coil was placed on the top plate of a three-stage semiconductive

(10) Carslaw, H. S.; Jeaeger, J. C. Conduction of Heat in Solids, 2nd ed.; Clarendon Press: Oxford, U.K., 1986.

(11) Luo, Y. Z.; Yang, M. J.; Pawliszyn, J. J. High Resolut. Chromatogr. 1995, 18, 727-731.

{

Z(t) ) CsADKs 2

∞

t

+

θ + a ln(b/a)

∑ (1 - e aD

-DRn2t

)

n)1

}

J0(bRn)[θRnJ1(aRn) + J0(aRn)] F(Rn)R2n

(1)

Analytical Chemistry, Vol. 70, No. 2, January 15, 1998

249

cooler (top plate: 2 × 2 cm in size, Melcor Materials Electronic Products Corp., Trenton, NJ). The hot surface of the cooler made contact with an aluminum heat sink with thermal grease to facilitate heat release. A 2 × 2 × 0.4 cm aluminum plate with a slot through the center of the plate was used to cover the tubing. The slot was approximately 3 mm wide and 2 mm deep to allow the tubing to fit into the plate. Finally, a 6 × 6 × 3 cm piece of styrofoam was used to cover the cooling part to provide insulation. A 13-V dc power supply was used to maintain the cooler at -40 °C. The sorbent interface was placed just before the GC injector. The GC injector was modified, and the inlet of the column was pierced through the septum and extended to the sorbent trap. An SPB-5 column, 5 m × 0.32 mm i.d., with a stationary-phase thickness of 0.1 µm (Supelco Canada) was used. Nitrogen was the carrier gas, and the flow rate was 2.2 mL/min. A Varian model 3500 GC (Varian Canada Inc., Mississauga, ON, Canada) equipped with a flame ionization detector (FID) was operated isothermally with a column temperature of 40 °C. The FID was maintained at 250 °C, at range 12. A computer was used for the control of the pulse heating for the sorbent interface and the data acquisition. For the pulse heating, the computer sent a series of electric pulses of a preset duration to the solid-state relay which converted the pulses to more powerful electrical current pulses through the heating coil around the trap. The first pulse at time 0 cleared the trap. The following pulses, each after an equal trapping period, were sent to desorb all analytes into the carrier stream for GC analysis. The second pulse also started a computer program for real-time GC detector signal collection and display on the computer monitor. The cycle of trapping and desorption was repeated automatically for continuous monitoring. Benzene, toluene, ethylbenzene, n-hexane, and trichloroethylene, were purchased from Sigma-Aldrich (Mississauga, ON, Canada). Nitrogen, compressed air, and hydrogen gases for flame ionization detection were purchased from Praxair (Waterloo, ON, Canada). The certified permeation tubes of benzene, toluene, ethylbenzene, hexane, and trichloroethylene were purchased from Kin-Tek Co. (La Marque, TX). Procedure. Standard Gas Mixture Generation. The standard analyte/N2 mixture gas was generated by the permeation method.12,13 The permeation chamber was made of aluminum and shaped like an extraction chamber (20 cm long, 4.5 cm i.d.). The permeation tube was located inside the permeation chamber, and the chamber was wrapped with a heating tape. When a constant voltage was applied to the heating tape, constant temperature 60 °C was obtained for the standard gas mixture generation. The temperature was monitored by a digital temperature indicator (Cole-Parmer Instrument Co., Chicago, IL). Nitrogen gas flowed through the permeation chamber; the flow rate was controlled by a compressed gas regulator and can be monitored by using a calibrated flowmeter (Brooks Instrument Division, Emerson Electric Canada, Markham, ON, Canada). Then the gas mixture flowed through a glass extraction chamber (Supelco Canada). In the experiment, two different sizes of glass chambers were used: 1000 and 125 mL. Like the permeation chamber, the extraction (12) Andrew, P., Smith, A. F.; Wood, R. Analyst 1971, 96, 528-534. (13) Bertom, G.; Liberti, F. A.; Perrino, C. J. Chromatogr. 1981, 203, 263-271.

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Analytical Chemistry, Vol. 70, No. 2, January 15, 1998

chamber was also wrapped with a heating tape for temperature control. Measurements of Distribution Constants and Diffusion Coefficients. The distribution constants were measured by the solid-phase microextraction (SPME) method. Details of the SPME method are available in the literature.14-16 In the measurement, a SPME membrane device was used instead of SPME fiber. This device was a modification of the SPME fiber assembly. The original SPME fiber assembly was replaced with a length of stainless steel tubing (6 cm long, 18 gauge); stainless steel needle (8-cm length, 30 gauge) was used for supporting the membrane. The equilibrium time of extraction was checked before the constant measurement. The membrane was exposed to the flowing gas mixture stream for sampling. After the extraction reached equilibrium, the membrane was exposed in the GC injector for thermal desorption. The absorbed amount was calibrated with standard liquid injection. In the diffusion coefficient measurement, two methods were applied. One is the MESI method, in which the sorbent interface and the GC column were replaced by a 20 cm × 0.32 mm i.d. deactivated silica tubing. This tubing connected the extraction probe directly to the FID detector. The carrier gas flow rate was 25.0 mL/min for this specific determination. To obtain the permeation profile, the membrane probe was initially exposed in a clean empty vial for 1 min. Then, the membrane probe was exposed in the glass extraction chamber for the permeation. Another method is the SPME method. In this method, the SPME membrane was inserted into the glass extraction chamber to extract analyte. The following extraction times were selected: 10, 20, 30, 40, 50, 60, 80, 100, 120, 180, 300, and 600 s. The amount extracted at each time can be detected by exposing the membrane in the GC injector for thermal desorption, followed by GC analysis. In these measurements, the extraction chamber was maintained at 25 °C. Investigation of Factors in Extraction. In these studies, a 12.7 µg/L benzene/N2 gas mixture was used as the air sample. A 1-min trapping time and 10- or 20-min monitoring time were chosen. In the studies of the carrier gas flow rate, the flow rate was measured after the membrane by using a soap bubble meter. In the investigation of the membrane response to the concentration change, the membrane probe was initially exposed in the glass extraction chamber for 20 min, with a 12.7 µg/L benzene/ N2 gas mixture flowing through the chamber. The probe was then removed from this chamber and exposed in front of a fan. The air speed was 50 cm/s. Thus, the concentration at the outside membrane was suddenly changed to zero. In this time period, the computer recorded the permeation time profile. The profile indicated the response of the membrane to the concentration change. RESULTS AND DISCUSSION Measurements of Distribution Constant and Diffusion Coefficient. The theory presented incorporates analyte physical properties described by distribution constants between the membrane and gas phase and the diffusion coefficients in the (14) Zhang, Z.; Yang, M. J.; Pawliszyn, J. Anal. Chem. 1994, 66, 844A-853A. (15) Louch, D.; Motlagh, S. J. Anal. Chem. 1992, 64, 1187-1199. (16) Pawliszyn, J. Solid Phase Microextraction: Theory and Practice; Eley-VCH Press: New York, 1997.

Table 1. Parameters of Benzene distribution const diffusion coeff D concn in air (25 °C) extraction temp

485 2.12 × 10-6 cm2/s 12.7 µg/L 25 °C

membrane. In order to test the theory, these parameters must be measured separately. For most analytes, these parameters are not available from the literature and must be determined experimentally. (a) Distribution Constant (K) Measurement. The distribution constant is an important consideration in membrane extraction. Table 1 lists the distribution constant of benzene. It is interesting that benzene has a larger K value for the membrane material as compared to the pure PDMS of the SPME fiber.16 This indicates that benzene partitions easily into the membrane outer surface and has a relatively high concentration there. However, this would also mean benzene is relatively more difficult to remove from the inner membrane surface. (b) Diffusion Coefficient (D) Measurement. There are a number of ways to measure the diffusion coefficient of an analyte in the membrane.17-20 In this paper, the measurement of the diffusion coefficient is based on eq 6,17,19,20 where d is the

D ) 0.14 d2/t1/2

Figure 3. Permeation versus time profile of benzene.

(6)

membrane wall thickness and t1/2 is the half-time of the permeation reaching steady state. In eq 6, the membrane thickness d is known. t1/2 can be obtained by experiment. Thus, the D value can be calculated. It should be pointed out that eq 6 is only valid when the concentration at one side of the membrane is constant and zero at the other side. In this study, the concentration at an outside of the membrane was constant. Inside, to let the concentration be zero, a high flow rate has to be used. By the theory, the flow rate needs to be greater than 25 mL/min for a 4-cm length of membrane. The t1/2 was checked experimentally with different flow rates from 1 to 30 mL/min. It was found that the t1/2 reached a minimum and remained constant above 25 mL/ min. Thus, 25 mL/min was used for D value measurement. Figure 3 shows the permeation time profile of benzene. It can be seen that an increase in intensity appeared within 1 min, and then a stable flat signal line was observed. The t1/2 was 18 s, and Table 1 lists the D value of benzene obtained by this method at 25 °C. Investigation of Extraction Parameters. Understanding of the extraction process is important in this study. Figure 4 shows a comparison between theoretical and experimental results. Curve A shows the theoretical prediction of the extraction time profile for benzene. This profile indicates the extraction is composed of two permeation processes: non-steady-state permeation and (17) Ziegel, K. D.; Frensdorff, H. K.; Blair, D. E. J. Polym. Sci., Part A-2 1969, 7, 809-819. (18) Vieth, W. R. Diffusion in and through Polymers, Principles and Applications: Oxford University Press: Oxford, U.K., 1991. (19) Crank, J.; Park, G. S. Diffusion in Polymers; Academic Press: London, 1968. (20) LaPack, M. A.; Tou, J. C.; McGuffin, V. L.; Enke, C. G. J. Polym. Sci. 1994, 86, 263-280.

Figure 4. Air extraction time profiles of benzene: (A) theoretical prediction; (B) experimental curve.

steady-state permeation. The term non-steady-state permeation refers to the process of forming the concentration gradient of analyte in the membrane. The term steady-state permeation refers to the process after the concentration gradient is formed, when a constant permeation through the membrane wall is reached. In curve A, the rising curve corresponds to the non-steady-state permeation process and the flat line corresponds to the steadystate permeation process. An experimental extraction time profile was obtained, and it is shown as curve B. Comparing curves A and B, it can be seen that the theoretical predication and the experimental result are close. The time at which the signal intensity reached 90% of the steady-state permeation signal was considered the steady-state time. The experimental result showed the steady-state time was 66 s and the theoretical prediction was 62 s. In a sealed extraction chamber, the extraction process continuously removed analyte via the membrane probe, so the amount of analyte was reduced with time. With the decrease of analyte amount, the concentration in the air was decreased, so the extraction rate was reduced since the extraction rate is proportional to the sample concentration. Obviously, a larger sample volume can buffer the concentration change, because the extracted portion would be small in a large sample for a short extraction time. In the experiment, we found that, in a 20-min continuous extraction, there was no peak decrease for the 1.0-L extraction Analytical Chemistry, Vol. 70, No. 2, January 15, 1998

251

Table 2. Relationship between Membrane Length and Extraction Rate of Benzene membrane length (cm)

extraction rate (ng/s) theory experiment

2a

4a

8a

8b

0.18 0.19

0.29 0.28

0.41 0.31

0.60 0.49

a Carrier gas flow rate, 2.2 mL/min. b Carrier gas flow rate, 5.0 mL/min.

Figure 5. Theoretical prediction of the relationship between membrane wall thickness and extraction.

chamber. However, for the 0.125-L chamber, the peaks were dropping after a 7-min extraction. As the model predicts, a large membrane surface results in a high extraction rate. A longer membrane length means a larger surface area, hence, a higher extraction rate. Experimentally, to simplify the analysis, only the extraction rate under the steadystate permeation processes was investigated. Table 2 lists the comparisons of the theory and experimental results. An agreement was obtained for 2- and 4-cm membrane extraction. The agreement did not follow for the 8-cm membrane. However, when the flow rate was change from 2.2 to 5.0 mL/min, the extraction rate was increased to 0.49 ng/s; the theoretical prediction is 0.60 ng/s at this flow rate, so an improvement in agreement was observed. For this improvement, we can see that the carrier gas flow rate impacts the extraction rate. According to the theory, the extraction rate should increase with a decrease of the membrane wall thickness. The reason for this increase is apparent considering the concentration gradient along the membrane thickness (Figure 2). A higher concentration at the inner surface of the membrane leads to a higher flux of analyte into the carrier gas, and a higher overall extraction rate. Figure 5 illustrates the relationship. From this figure we can see that when the thickness is reduced to 82.5 mm, half of the original thickness, the extraction rate at the steady-state diffusion is increased from 0.27 to 0.36 ng/s. If the thickness doubles, to 330 mm, for example, the extraction rate is decreased to 0.19 ng/ s. It can be seen that when the membrane wall thickness is halved, the time to reach the steady state is much shorter. Obviously, a longer time is needed to reach the steady-state point when the thickness is doubled. No data were obtained to prove this prediction as no membrane with different thicknesses but 252

Analytical Chemistry, Vol. 70, No. 2, January 15, 1998

the same inner diameter and material of construction is commercially available. As mentioned before, the carrier gas flow rate affects the extraction rate. The theory predicts this effect. Table 3 shows the theoretical relationship between flow rate and extraction rate of benzene. This table indicates that a high flow rate leads to a high extraction rate and a low flow rate results in a low extraction rate. At low flow rate, since the carrier gas has a relatively long time in contact with the inner membrane surface, the analyte easily reaches partition equilibrium between the gas and the inner surface; although the carrier gas can obtain a relatively high concentration, only a small amount of analyte can be stripped off from the inner surface per time unit; thus the overall extraction rate is low. At higher flow rate, the carrier gas either does not reach partition equilibrium or reaches partition equilibrium near the membrane exit; though the carrier gas has a relatively low concentration compared to that in a lower flow rate, the overall extraction rate is higher because of the higher flow rate. Table 3 suggests that good agreement with the theory exists when the flow rate is between 1 and 5 mL/min. At higher flow rate, 10 mL/min, for example, the extraction rate was significantly decreased in the experiment. This is attributed to breakthrough at the sorbent interface. Here, breakthrough refers to the analytes in the carrier gas not being trapped at the sorbent interface and entering into the GC column directly. Experimentally, the extraction rate at high flow rate actually represents the amount trapped per time unit; this rate was lower than the permeation rate at the membrane because of the breakthrough. The breakthrough can be reduced by reducing the linear flow rate at the sorbent interface; in this way the detected extraction rate will be higher. Experimentally, increasing the linear flow rate at the membrane probe and decreasing the linear flow rate at the sorbent interface can significantly enhance the overall extraction rate. The extraction rate is pressure-dependent. A pressure difference between the outside and inside of the membrane changes the diffusion coefficient in the membrane.19 This effect results in an extraction rate change. By experimental investigation, when the pressure at the outside of the membrane was changed from 1 to 2 atm, the extraction rate was increased less than 8%. Normally, air extraction with the MESI technique is performed under atmospheric pressure, so a change in extraction rate caused by a change of pressure can be considered of minimal importance. The effect of humidity on the extraction rate is an important factor. The membrane used in the experiment is hydrophobic, so water does not penetrate the membrane wall at room temperature. Experimentally, when the humidity was increased to 80%, no effect on extraction rate was observed. When the humidity was higher, 100%, for example, the extraction rate was 5% lower. Thus, the effect of humidity on air extraction is negligible. Extraction temperature changes the K and D values. The influence on the K value can be expressed as19

K ) K0 exp

[ (

)]

1 ∆H 1 R T T0

(7)

where K is the distribution constant at temperature T in degrees kelvin, K0 is the distribution constant at temperature T0, ∆H is the change in enthalpy when analyte goes from air into the

Table 3. Relationship of Flow Rate of Carrier Gas and Extraction Rate of Benzene flow rate (mL/min)

extraction rate (ng/s) theory experiment

1

3

5

10

12

15

20

25

30

0.19 0.19

0.32 0.29

0.36 0.33

0.39 0.32

0.4 0.31

0.41 0.28

0.42 0.24

0.43 0.21

0.43 0.15

Table 4. Experimental Results and Theoretical Predictions

TCE toluene hexane ethylbenzene

extraction amt (ng)

distribution const K

diffusion coeff (10-6 cm2/s)

Cg (mg/L)

theory

expnt

RSD (%)

443 1872 224 3379

1.81 1.59 2.27 1.09

21 1.4 8.2 1.2

0.41 0.05 0.11 0.04

0.42 0.04 0.12 0.04

6.2 3.4 2.8 3.6

membrane, and R is the gas constant. ∆H is considered constant for the ambient temperature range and is close to the value of ∆Hv, the enthalpy change of vaporization of the pure analyte. From this equation, we can see that the K value decreases with an increase in temperature. A low K value results in a low concentration at the membrane outer surface, hence, a lower permeation driving force in the membrane and a low extraction rate. On the other hand, an increase in extraction temperature accelerates the molecular motion in both air and the membrane, so the diffusion coefficient is increased. The diffusion coefficients of many penetrating gases in polymers exhibit an exponential temperature dependence over a limited range of temperatures.19

D ) D0 exp(-Ed/RT)

(8)

In this equation D0 is a pre-exponential factor and Ed is the apparent activation energy for diffusion. Over a certain range of temperatures, Ed is constant and a plot of the logarithm of D versus 1/T is linear.16,17 When the diffusion coefficient is increased, the diffusion rate in both air and the membrane is increased and the extraction rate is increased. The effect of extraction temperature on distribution constant and diffusion coefficient are opposite. The total effect depends on which factor is more important under temperature change. Experimentally, two temperatures were investigated. We found that the extraction rate of benzene was decreased significantly when temperature was increased from 23 to 40 °C. This result indicates the temperature effect on the distribution constant was more important than on the diffusion coefficient in the extraction. In air monitoring, the membrane probe is required to respond to a concentration change as fast as possible. To simplify the investigation, the benzene/nitrogen mixture concentration was suddenly changed from 12.70 to g/L, Figure 6 shows the response. The ideal response should exactly follow the air concentration change, which is indicated as a dotted line in the figure. However, due to the small diffusion coefficient in the membrane and the membrane thickness, benzene continues to partition out of the membrane for a few seconds after the change. In this figure, the time for the signal change from 100 to 10% is 36 s. Obviously, a thinner wall membrane could produce a faster response.

Figure 6. Response time profile of the membrane to the concentration change of benzene.

In the above investigations, we employed benzene to test extraction rate. We found that the model had a good agreement with the experimental results. When other selected analytes (toluene, ethylbenzene, hexane, trichloroethylene) were tested, good agreement also existed. Table 4 summarizes the results. Estimation of Air Concentration. Quantitative analysis is usually done by external or internal calibration methods. For onsite monitoring, air concentration needs to be known as soon as possible; thus, a method for air concentration measurement without separate calibration has an advantage if it is fast, accurate, and convenient. A method to estimate air concentration by MESI without external or internal calibration is proposed. From eq 5, we know the relationship between the extraction rate and the air concentration. If we rewrite eq 5, the air concentration can be expressed as

θ + a ln(b/a) Cs ) Gss ADKs

(9)

In eq 9, if the D and Ks values are known, the membrane length and the flow rate are fixed, then eq 9 can be simplified as

Cs ) GssK′

(10)

Analytical Chemistry, Vol. 70, No. 2, January 15, 1998

253

A thinner walled membrane would be beneficial for the applications. Temperature is an important factor in the extraction. It affects both the distribution constant and the diffusion coefficient of an analyte. The effects are opposite for these two parameters. A relatively low extraction temperature results in a higher extraction rate. An exhaustive extraction method11 can be applied for the calibration. However, a method without external calibration to estimate air concentration makes the MESI method more advantageous. This study shows the potential applications of the MESI method in air monitoring.

Figure 7. Extraction time profile of benzene by the SPME method.

where K′ ) (θ + a ln(b/a))/ADKs, is a known constant. In eq 10, the extraction rate Gss can be calculated using FID response factors when the GC conditions are kept constant.21 For air monitoring, the only important impact factor in the extraction is temperature. We know the temperature affects both K and D. The K and D values of an analyte at different temperatures can be determined with the methods discussed in this paper or can be calculated by using eqs 7 and 8. In eq 7, K0 and ∆Hv are available in the literature or can be determined experimentally for most analytes.22 An alternative method called the “linear temperature-programmed retention index system” 23 can be used for the estimation of the air/membrane distribution constant. The D value can also be obtained by the SPME method. Figure 7 shows the extraction time profile of benzene by the SPME method. This profile indicates the extraction process, hence, the diffusion process in the membrane. The D value then can be calculated by using the appropriate model,15 in which D was expressed as D ) d2/2t1/2. From Figure 7, the t1/2 is 65 s and the D is 2.09 × 10-6 cm2/s. This value is close to the measurement in the MESI method (2.12 × 10-6 cm2/s). After K and D values are determined, the air concentration can be calculated using eq 10. CONCLUSIONS The model derived in this paper has successfully predicted the extraction processes. Good agreements with experimental results were obtained. In air analysis with MESI, several parameters affect the extraction efficiency. A longer membrane probe leads to a higher extraction rate if carrier gas flow rate is high enough. However, a higher carrier gas flow rate results in breakthrough at the sorbent interface. If a higher linear carrier gas flow rate and optimized mass flow rate can be applied at the membrane probe, a higher extraction rate without breakthrough will be achieved. Membrane thickness is another factor affecting extraction rate and the membrane response time for an analyte. (21) Tong, H. Y.; Karasek, F. W. Anal. Chem. 1984, 56, 2124-2128. (22) Martos, P. A.; Pawliszyn, J. Anal. Chem. 1997, 69, 206-215. (23) Martos, P. A.; Saraullo, A.; Pawliszyn, J. Anal. Chem. 1997, 69, 402-408.

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Analytical Chemistry, Vol. 70, No. 2, January 15, 1998

ACKNOWLEDGMENT This work has been financially supported by the Dow Chemical Co. and the Natural Sciences and Engineering Research Council of Canada. SUPPORTING INFORMATION AVAILABLE Derivation of the theory (4 pages). Ordering information is given on any current masthead page. GLOSSARY a

inner diameter of the membrane

A

membrane surface area

b

outer diameter of the membrane

Cs

concentration in air

Cg

average lengthwise concentration in the carrier gas

d

membrane wall thickness

D

diffusion coefficient in the membrane

Ed

activation energy

f

Cg/Cg

Ks

distribution constant between membrane and air

G

extraction rate

Gss

extraction rate at steady-state permeation

∆H

enthalpy change

J

Bessel function of the first kind

L

membrane length

Q

carrier gas flow rate [mL/min]

r

radius of the hollow fiber membrane

R

gas constant

t

time

T

temperature, in kelvin

Y

Bessel function of the second kind

Z

extraction amount

θ

)fKsDA/R

Rn

roots in the equations

Received for review May 29, 1997. Accepted November 4, 1997.X AC970549P X

Abstract published in Advance ACS Abstracts, December 15, 1997.