Anal. Chem. 2000, 72, 1064-1071
Calibration of Membrane Extraction for Air Analysis Yu Z. Luo and J. Pawliszyn*
The GuelphsWaterloo Center for Graduate Work in Chemistry, Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Calibration methods based on the recently developed mathematical model are proposed for air monitoring by membrane extraction. In membrane extraction, analytes permeate through the membrane at a constant rate controlled by the distribution constant and the diffusion coefficient. The principle of the proposed calibration approach is based on either theoretical or experimental determination of both constants at the extraction conditions. A group of selected compounds was employed for the experimental testing, and the results indicated practical feasibility of the approach. On-line determination of partition coefficients and distribution constants was proposed and investigated, producing very promising results. Both approaches to calibration facilitate quantitative monitoring. Among the diverse sampling and sample preparation methods, membrane separation and introduction of analytes from numerous sample matrixes to GC2-5 and MS6-8 have drawn much attention, because they are solvent free, have high selectivity, and concentrate and enrich analytes during the separation. Membrane extraction is composed of two simultaneous steps: extraction of analytes from the sample matrix by the membrane probe and stripping of analytes from the other side of membrane into the flowing stripping gas, vacuum, or liquid. The membrane extracts some analytes and prevents others from passing through the membrane wall to the analytical system. Therefore, purified sample components are introduced into the chromatographic or MS system, which results in a longer instrument life due to less interference from sample matrix. Among the membranes available, nonporous membrane plays an important role in the extraction of volatile organic compounds because of its selectivity. Transport through nonporous membranes occurs by a solution-diffusion mechanism and separation is achieved by differences in solubility * Corresponding author: (tel) (519) 888-4641; (fax) (519) 746-0435; (e-mail)
[email protected]. (1) Luo, Y. Z.,; Adams, M.; Pawliszyn, J. Anal. Chem. 1998, 70, 248-254. (2) Pratt, K. F.; Pawliszyn, J. Anal. Chem. 1992, 64, 2101-2106. (3) Pratt, K. F.; Pawliszyn, J. Anal. Chem. 1992, 64, 2107-2110. (4) Mitra, S.; Zhang, L.; Zhu, N.; Guo, X. J. Chromatogr., A 1996, 736, 165173. (5) Luo, Y. Z.; Adams, M.; Pawliszyn, J. Analyst 1997, 122 (Dec), 1461-1469. (6) Kotiaho, T.; Lauritsen, F. R.; Choudhury, T. K.; Cooks, R. G.; Tsao, G. T. Anal. Chem. 1991, 63, 875A-883A. (7) Lauritsen, F. R. Int. J. Mass Spectrom. Ion Processes 1990, 95, 259-268. (8) LapPack, M. A.; Tou, J. C.; Enke, C. G. Anal. Chem. 1990, 62, 1265-1271
1064 Analytical Chemistry, Vol. 72, No. 5, March 1, 2000
and/or diffusivity,9 which means extraction of analytes with large partition coefficients (membrane/sample matrix) and large diffusion coefficients (in the membrane) can be greatly enhanced. Membrane extraction with a sorbent interface (MESI) combines the sampling, preconcentration, and sample introduction to analytical instruments in one step. It eliminates the steps in sample preparation that are the main sources of sample loss and contamination. MESI is a promising sample preparation technique for either routine analysis or continuous monitoring of organic compounds in various sample matrixes and is an excellent candidate method for field monitoring. The MESI technique has the advantages of simplicity, flexible sampling time, low cost, time efficiency, freedom from solvent use, durability, good selectivity, high sensitivity, and easy automation including continuous monitoring. A mathematical model has been derived to describe the membrane extraction process,1 and it indicates that diffusion in the membrane dominates the extraction process. To date, research efforts have focused on the optimization of the extraction conditions to improve the extraction efficiency. Calibration is an important issue in MESI analysis. By experimental investigation,10 external calibration shows good precision and wide linear range. However, for field application, because of the demands of fast, simple, and accurate analysis, the traditional calibration methods such as internal and external calibration are not appropriate choices, and in some cases they are not applicable. A new calibration method, which can answer the demands of field analysis, is introduced in this paper. This calibration method is based on the mathematical model that was derived previously.1 No additional external calibration effort is needed. In this study, the important parameters for calibration, including stripping gas flow rate and partition and diffusion coefficients, were evaluated mathematically and experimentally. It was found that partition coefficient and diffusion coefficient are the most important parameters in the calibration. These two parameters are not only determined by the characteristics of analyte itself but are also dependent on extraction conditions and, typically, are temperature related. An on-line determination of partition coefficient and distribution constant was also evaluated in this study, again operated without external calibration. The result was that the determinations of these two parameters could (9) Mulder, M. Basic Principles of Membrane Technology; Kluwer Academic Publishers: Dordrecht, 1991. (10) Luo, Y. Z. Membrane Extraction with a Sorbent Interface. Ph.D. Thesis, University of Waterloo, 1999. 10.1021/ac990746j CCC: $19.00
© 2000 American Chemical Society Published on Web 02/02/2000
Figure 1. Schematic of MESI system.
greatly aid the calibration. Finally, a group of volatile organic compounds was chosen to test the precision and accuracy of the calibration. EXPERIMENTAL SECTION The MESI system contains four major sections: a membrane probe, sorbent interface, chromatographic device, and computer.11 The operation of MESI includes two steps in sequence, trapping and desorption, which correspond to sample preconcentration and injection.12 Figure 1 depicts a schematic of the system and the two operational modes. The probe used in this study was a hollow fiber silicon membrane (Baxter Healthcare Corp., McGaw Park, IL). The inner diameter of the hollow membrane was 305 µm and the wall thickness was 165 µm. The sorbent module consisted of another section of the membrane positioned inside a section of 0.53 mm o.d. deactivated fused-silica tubing (Supeco Canada, Mississauga, ON). For the sorbent, membrane was cut in two pieces along the axis and one cut piece was weighed to determine its volume. A piece of membrane 0.5 cm long (1.36 mm3) was used as the sorbent. An SPB-5 column, 30 m × 0.32 mm i.d., with a stationary-phase thickness of 1 µm, (Supelco Canada) was used. A Varian model 3500 GC (Varian Canada Inc., Mississauga, ON) equipped with a flame ionization detector (FID) was operated isothermally with a column temperature of 40 °C. The FID was maintained at 250 °C, attenuation 8, and range 12. Nitrogen was used as the carrier gas at a flow rate of 2.2 mL/min. The detector gas flow rates were set to 290 mL/min for air, 35 mL/min for nitrogen makeup, and 30 mL/min for hydrogen. A computer was used for control of the pulse heating of the sorbent interface and 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 (11) Luo, Y. Z.; Yang, M. J.; Pawliszyn, J. J. High Resolut. Chromatogr. 1995, 18, 727-731. (12) Yang, M. J.; Harms, S.; Luo, Y. Z.; Pawliszyn, J. Anal. Chem. 1994, 66, 1339-1346.
electrical current pulses passed through the heating coil around the trap. The first pulse at time 0 cleaned the trap. The following pulses, each after an equal trapping period, desorbed 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.13,14 Benzene, toluene, ethylbenzene, o-xylene, n-hexane, and trichloroethylene were purchased from Sigma-Aldrich (Mississauga, ON, Canada). Nitrogen (UHP), compressed air (zero gas), and hydrogen (UPH) gases for flame ionization detection were purchased from Praxair (Waterloo, ON, Canada). Certified permeation tubes of benzene, toluene, ethylbenzene, n-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.11,12 The permeation chamber was made of aluminum and shaped liked 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 heating tape. When a constant voltage was applied to the heating tape, a constant temperature of 60 °C was obtained for the standard gas mixture generation. Nitrogen gas flowed through the permeation chamber; the flow rate was controlled by a compressed gas regulator and could be monitored using a calibrated flowmeter (Brooks Instrument Division, Emerson Electric Canada, Markham, ON, Canada). The gas mixture then flowed through a glass extraction chamber (Supelco Canada). In the experiment, a 500 mL glass bulb was used as the extraction chamber. Like the permeation chamber, the extraction chamber was also wrapped with a heating tape for temperature control. The standard gas concentration was verified by SPME. The concentration of the generated standard gas mixture can be expressed as
Cmix ) K0(ng/min)/F where F is dilution gas flow (in mL/min at STP), K0 is the permiation constant, and Cmix is the concentration at 60 °C. To convert Cmix to the concentration Cs at room temperature (25 °C), the following equation can be used:
Cs ) 333K0(ng/min)/298 The determination of the FID response factor was performed by injecting a standard mixture (in methanol) into the same instrument for analysis. For the measurement, the GC conditions including the carrier gas flow rate and oven and detector temperatures were the same as for the MESI analysis. For the on-line measurement of diffusion coefficient and partition coefficient, the sorbent interface was held at room temperature during trapping. The pulse voltage for heating the membrane sorbent was carefully adjusted to avoid both overly high temperatures, which could cause membrane degradation, and low temperatures, which would cause serious carryover. (13) Yang, M. J.; Luo, Y. Z.; Pawliszyn, J. CHEMTECH 1994, 24, 31-37. (14) Yang, M. J.; Adams, M.; Pawliszyn, J. Anal. Chem. 1996, 68, 2782-2789.
Analytical Chemistry, Vol. 72, No. 5, March 1, 2000
1065
In some experiments, a piece of heating wire was coiled around the hollow fiber membrane. The heating pulse applied to the membrane released absorbed analytes to the flowing gas stream, which then carried it to the sorbent interface. RESULTS AND DISCUSSION In MESI analysis, the extraction process dominates the analysis time and governs the sensitivity and selectivity of the method. In air monitoring, extraction can be regarded as three major processessanalyte partitioning on the membrane outer surface, analyte diffusion through the membrane, and analyte removal by the stripping gas from the membrane inner surface. The amount extracted Z at time t can be expressed as
{
Z(t) ) ACsDKs 2
∞
∑
aDn)1
t
θ + a ln b/a
(1 - e-DRn t) 2
-
}
J0(bRn)[θRnJ1(aRn) + J0(aRn)] F(Rn)Rn2
where θ ) ADfKg/Q. At steady-state extraction, the amount extracted, Z, can be expressed as1
Z)
ACsDKt ADfK/Q + a ln(b/a)
(1)
where a and b are the inner and outer radius of the hollow fiber membrane, respectively. A is the membrane inner surface area, Cs is the concentration in air, D is the diffusion coefficient in the membrane, f is the ratio of the average concentration of the stripping gas and the concentration of the stripping gas at the exit of the end of the membrane (constant at steady-state conditions), K is the membrane/air partition coefficient, Q is the stripping gas flow rate, and t is the trapping time. To express the relationship between the concentration in air, Cs, and other parameters, eq 1 can be rearranged to
Cs )
(
)
a ln(b/a) Z f + t Q ADK
(2)
In eq 2, a, b, A, and Q are constants. The trapping time (t) can be experimentally fixed. D and K are constant if the extraction temperature is constant (assuming low sample concentration). K and D values are available in the literature or can be measured on site. Parameter f is a constant when extraction conditions, such as stripping gas flow rate and extraction temperature, are constant. Therefore, eq 2 can be simplified to
Cs ) BZ
(3)
where the constant B ) (1/t)(f/Q + a ln(b/a)/ADK) and can be calculated using experimental dimensions and parameters. Equation 3 shows that, at steady-state extraction, the concentration in air is proportional to the amount extracted. In other words, if the amount extracted is known, the concentration in air can be calculated. The amount extracted, Z, can be obtained from the 1066
Analytical Chemistry, Vol. 72, No. 5, March 1, 2000
Table 1. Variation of K and D Values at Different Temperatures temperature (°C)
K change of K (%) D (10-6 cm2 s-1 change of D (%)
25
30
35
485 35 2.12 -11
358
290 -19 3.18 33
2.39
analyte peak area and the flame ionization detector (FID) response factor. Thus, no external calibration is need. The above discussion is true if extraction conditions are stable. In some circumstances, however, the conditions are not stable, mainly because of temperature variation. Temperature variation results in changes in the stripping gas flow rate, the size of the membrane probe, and K and D values. The effect on probe size is usually very small and can be ignored. The effect on the flow rate of the stripping gas can be calculated by use of Gay-Lussac’s law (pressure is constant):15
V1/V2 ) T1/T2
(4)
where V1 and V2 are the volumes at temperatures T1 and T2 (kelvin), respectively. The gas volume V is equal to the flow rate, Q, multiplied by the time, t. So, eq 4 can be expressed as
Q1t/Q2t ) Q1/Q2 ) T1/T2
(5)
where Q1 and Q2 are the stripping gas flow rates at temperatures T1 and T2, respectively. If the temperature change is in the range of (5 °C at 25 °C, the change in flow rate is only (1.7% and is regarded as insignificant. However, temperature effects on K and D values are significant. The values of K (membrane/air) and D (in the membrane) for benzene are affected by temperature as shown in Table 1. Methods for determining K and D have been described elsewhere.1 It is apparent that when the temperature changes by (5 °C at 30 °C, K and D values change significantly and implies that the effects of temperature on these two parameters should be of concern. To evaluate the effect of changes of these parameters on the calibration, the mathematical model was tested by varying K and D. The change ranges selected were (2, (5, and (10%. The results of the calculations are listed in Table 2. It is apparent from this table that varying the stripping gas flow rate has little impact on the extraction rate, but K, D, and membrane length have a large effect. The impact of membrane length can be avoided by carefully measuring the probe. In general, temperature variations do not cause significant changes in membrane dimensions. In Table 2, when a single parameter effect was considered, the effect on extraction was significant when a (10% change was assumed. However, the percentage change of these parameters was for the theoretical calculation only. For real-case modeling, two important factors should be consideredsreasonable values for the change ratio and combination effects. In the above testing, a (10% change in the stripping gas flow rate was unrealistically (15) Atkins, P. W. Physical Chemistry; Oxford University Press: London, 1978.
Table 2. Effect of Parameter Change (%) on the Extraction Rate (%)a) flow rate Q (mL/min) (%)
membrane length L (cm) (%)
partition coeff K (%)
diffusion coeff D (%)
change of extrn rate (%)
(2 (5 (10 (20
(0.9 (1.8 (3.6 (1.3 (3.1 (5.9 (0.9 (3.2 (6.3 (0.9 (3.2 (6.3 (2.3
(2 (5 (10 (2 (5 (10 (2 (5 (10
(2
(1
(20
a The parameter variation was based on the following values: Q ) 2.2 mL/min, L ) 4 cm, K ) 485, and D ) 2.12 × 10-6 cm2 s-1.
largesthis would require a 30 °C change in the extraction temperature, which would be rare for air extraction. For K and D values, however, a 10% change can be caused by temperature change of ∼1 °C, which is quite reasonable. When the total effect is assessed for a real situation, a positive or negative contribution of the parameters to the amount extracted should be obtained. In Table 2, for example, a temperature change has opposite effects on K and D, so when the change in K is positive, that in D is negative (last row of the table). When the total effect was assessed, (20% variation of K and D values was used; this corresponds to a temperature change of (3 °C. It can be seen that the total effect was not significant. In other words, temperature variation during an extraction will not result in a large calibration error. Experimentally, for a temperature change of (3 °C, variations in the amounts of selected analytes extracted were (5-10%, slightly more than the method precision of RSD 3-6%. A small temperature change does not, therefore, affect the calibration. An interesting option is to design membranes that have similar absolute value temperature effects on diffusion coefficients as distribution constant. This would result independent permeation rates of temperature. In field analysis, the temperature can vary from day to day and from place to place. Temperature differences can be several degrees to several tens of degrees in different applications. For example, the temperature in a chimney vent can be greater than 100 °C; that in a meat storage room can be below 0 °C. In these situations, the effect of temperature on the amount extracted is no longer insignificant. In Figure 2 we see the chromatogram obtained during continuous monitoring of BTEX during a temperature change from 97 to 25 °C. In the experiment, a 4 cm membrane was used. The flow rate of stripping gas was 2.2 mL L-1. The concentrations of BTEX components were as follows: benzene 12.7 µg L-1, toluene 15.2 µg L-1, ethylbenzene 15.7 µg L-1, and o-xylene 12.5 µg L-1. Obviously, in this case, K and D values calculated at room temperature should not be used, because this would cause a large calibration error. K and D values obtained at different temperatures should be used to ensure the calibration is correct. The partition coefficient K (membrane/air) and diffusion coefficient D values (in the membrane) for analytes at different
Figure 2. (A) Monitoring chromatogram of BTEX during extraction temperature change. (B) Plot of temperature change. Key: (1) benzene, (2) toluene, (3) ethylbenzene, and (4) o-xylene.
temperatures can be obtained from the literature or can be measured by methods described elsewhere.1 The MESI method can be employed for on-line determination of the K and D values of analytes without external calibration. To measure the K and D values, the PDMS sorbent used in the previous work was replaced by a piece of membrane which was the same material as that used for the membrane probe. The sorbent tube was kept at the same temperature as the membrane probe. No cooling or heating was used for room-temperature extraction. In this example, the measured D value corresponds to that at room temperature. In an absorption process, before equilibrium, the amount absorbed by the sorbent increases as the absorption time is extended. The diffusion process can, therefore, be monitored by monitoring the increase in the absorption amount. The amount absorbed by the sorbent can be thermally desorbed into the GC column and then detected. To monitor the amount absorbed with time, a series of absorption times were used. To ensure, initially, a constant concentration in the stripping gas, the membrane probe was left to equilibrate with the sample matrix while the stripping gas did not pass through the sorbent. After a constant concentration had been obtained in the stripping gas, the gas was switched to flow through the sorbent. The heating pulse was then sent to the sorbent at different times, e.g., 10, 20, 30, 40, 50, 60, 80, 100, 120, 150, 180, and 200 s, until a constant signal was obtained. A time profile was obtained and is shown in Figure 3. This time profile can be used to calculate the diffusion coefficient by use of the equation D ) d2/2t1/2, where d is the membrane wall thickness and t1/2 is the half-time to reach steady-state diffusion. By use of this method, the D values for three compounds shown in Figure 3 were found to be 2.70 ((0.05) × 10-6, 1.70 ((0.06) × 10-6, and 0.91(0.04) × 10-6 cm2 s-1, respectively. These values are relatively close to values determined previously1s2.12 ((0.03) × 10-6, 1.59 ((0.05) × 10-6, and 1.09 ((0.05) × 10-6 cm2 s-1, respectively. Analytical Chemistry, Vol. 72, No. 5, March 1, 2000
1067
Figure 3. Diffusion time profiles of benzene, toluene, and ethylbenzene in the membrane at room temperature (25 °C).
The partition coefficient K is the ratio of the concentrations in the two phases at equilibrium. This can be expressed as
K ) Cm/Cc
(6)
where Cm and Cc are the concentrations in the membrane and the carrier gas, respectively. Equation 6 can be rearranged to
K ) (nm/Vm)/Cc
(7)
where nm and Vm are, respectively, the amount absorbed by the membrane sorbent at equilibrium and the volume of the membrane used as a sorbent. The membrane volume Vm can be obtained by determining the membrane density and weight (by use of a microbalance). The amount absorbed can be determined by desorbing the analyte from the sorbent on to the GC column and can be expressed as
nm ) Hmrf
(8)
where Hm is peak area counts (or peak height) and rf is FID response factor. The analyte concentration Cc can be obtained by determining the amount of analyte flowing through the stream in a defined time period and can be expressed as
Cc ) nc/vc ) nc/Qt
(9)
where nc is the amount of analyte in the stripping gas of volume vc. Q is the stripping gas flow rate, and t is the trapping time. To determine nc, the trapping mode of MESI was used. Experimentally, the sorbent interface was cooled to -40 °C by use of a threestage semiconductive cooler,1 and the trapping time was 1 min. Like nm, the amount of analyte in the stripping gas can be expressed as
nc ) Hcrf
(10)
where Hc is the peak area counts from the carrier gas stream (or peak height) and rf is the FID response factor for the analyte. Combining eqs 8-10, eq 7 can be rewritten as
K ) HmQt/Hcvm 1068 Analytical Chemistry, Vol. 72, No. 5, March 1, 2000
Figure 4. Chromatograms of benzene, toluene, and ethylbenzene in the measurement of distribution constant. Chromatograms were obtained under (A) cryofocusing trapping and (B) room-temperature trapping.
(11)
Equation 11 indicates that the value of K can be calculated by use of MESI by measuring the peak area (or height) counts. It can be seen that no additional external calibration is needed for calculation of K. The chromatogram obtained from the analytes after cryofocusing trapping is shown in Figure 4A, and the chromatogram of the same analytes under room-temperature trapping is shown in Figure 4B. The results of from the calculation are listed in Table 3. It can be seen that this approach is in very good agreement with the SPME method described previously. The determinations of K and D are only based on the chromatograms of the analytes, and no additional external calibration was used. For unknown analytes, if the K and D values are obtained, the unknown analyte could be identified by comparing these two parameters with literature or other data, because it is rare to find two compounds with the same K and D values. In other words, the K and D values might be useful for qualitative analysis, although further investigation is needed. Occasionally, identification is not necessary, because the total amount of a series of homologous compounds is important, such as in the monitoring of total alkanes or alkenes. Each compound’s K and D values can be measured, and an equal detector response factor for all organic compounds is assumed. Calibration can then be performed on the basis of the above discussion. The calibration results from the analysis of a standard gas mixture of benzene, toluene, ethylbenzene, o-xylene, n-hexane, and 1,1,1-trichloroethylene are shown in Table 4. It can be seen that the method gives good accuracy. There is a possibility to determine K and D values and to estimate air concentration in a single experiment. The SPME device is suitable for measurement of distribution constant K. In SPME, at equilibrium, the concentration in the liquid polymer coating is uniform. In MESI we know that for steady-state extraction there is a constant concentration gradient in the membrane.1 If the difference between the amounts absorbed by
Table 3. K Value Measurement by Different Means
benzene toluene ethylbenzene a
conc in carrier gas (peak area counts/cm3) (RSD %)a
conc in membrane (peak area counts/cm3) (RSD %)a
K value detnd by present method
K value detnd by SPMEb method in ref 1
1 051 000 (2.5) 35 900 (3.2) 12 300 (3.8)
541 000 000 (4.2) 62 300 000 (3.8) 39 100 000 (4.9)
514 1740 3180
485 1870 3380
RSD was obtained from five measurements. b Solid-phase microextraction.
Table 4. Estimation of Air Concentration without External Calibration (25 °C)
benzene toluene ethylbenzene o-xylene 1,1,1-trichloroethylene n-hexane
B
area counts (av of 5 reps)
FID response factor (area ng-1)
air concn (expt) (µg L-1)
std air concn (µg L-1)
0.71 0.58 0.44 0.38 0.69 0.65
214 700 000 208 500 000 136 500 000 126 500 000 46 550 000 24 850 000
25 600 30 200 33 700 38 800 7 600 22 000
1.19 ((0.05) 1.18 ((0.04) 0.92 ((0.06) 0.86 ((0.07) 1.49 ((0.05) 1.71 ((0.05)
1.25 1.12 0.94 0.88 1.58 1.62
the SPME and MESI techniques can be determined, K can be calculated from an MESI experiment. In MESI-GC the amount absorbed can be obtained by thermal desorption of the membrane probe. To perform membrane heating, the membrane probe is wrapped with a heating coil, which can be the same coil used in the sorbent interface. During membrane heating, however, the absorbed analyte cannot be completely desorbed into the stripping gas, as some analytes return to the air stream, so only a fraction can be detected. Experimental examination showed that the amount desorbed into the stripping gas was constant if the extraction and desorption conditions were constant. Thus determination of the difference between the amounts absorbed by the SPME and MESI techniques is equivalent to determination of the difference between the amount absorbed by the SPME technique and the fraction of the amount absorbed which is desorbed by the MESI technique. To obtain the fraction of the amount absorbed by the MESI technique, which is subsequently desorbed, pulse heating is applied to the membrane probe after steady-state permeation. Figure 5 shows a chromatogram obtained for benzene by membrane pulse heating. The two highest peaks, 1 and 2, correspond to two heating pulses, hence thermal desorption from the membrane. The two peaks are the same height, which means that a constant amount was desorbed. The fraction desorbed into the stripping gas is represented by the difference between the intensity of peak 1 (or peak 2) and the average intensity of the peak obtained at steady state, which aligns with curve a. Curve a is a smooth plot of each peak height from non steady state to steady state. Table 5 lists the K values that were measured by experiments at different temperatures. This table verifies that when the electrical heating pulse was fixed, the percentage desorbed from the membrane to the stripping gas was constant. The amount desorbed by MESI was ∼38% of the amount absorbed by SPME. After use of an adjustment factor of 38%, the K values determined by MESI are close to those obtained by SPME. In MESI, because the analytes that penetrated the membrane cannot immediately arrive at the detector, the permeation process
Figure 5. Chromatogram of benzene in probe pulse heating. Concentration 12.7 µg L-1; membrane probe length 4 cm; flow rate of stripping gas 2.2 mL min-1; extraction temperature 25 °C; pulse voltage on the membrane probe and sorbent interface 38.6 V; pulse width 1 s; trapping temperature at sorbent interface -40 °C; trapping time 40 s. Table 5. K Value Measurement and Adjustment (Benzene) temperature (°C)
K value by SPME method K value by membrane heating pulse in monitoring (before adjustment) difference before adjustment (%) K value after adjustment (adjust ratio 38%)
23
25
30
35
40
550 208
485 183
358 139
290 112
242 94
37.8 547
37.7 481
38.8 365
38.6 294
38.8 247
in the membrane cannot be detected instantly. Sorbent trapping is the major reason for the delayed detection of the penetrated analytes. For example, 40 s trapping results in 40 s delay. In Figure 5, curve b is a permeation time profile of benzene at high flow rate (25 mL/min). Curve b indicates more closely the permeation process of benzene in the membrane. Because a high flow rate of stripping gas and no sorbent trap were included, the analytes were quickly transported to the detector by the stripping gas after Analytical Chemistry, Vol. 72, No. 5, March 1, 2000
1069
Table 6. D Value Measurement and Adjustment (Benzene)a temperature (°C)
t1/2 (s) D (10-6 cm2 s-1) ) 0.14d2/t1/2 t1/2′ (s) D′ (10-6 cm2 s-1) ) 0.42 d2/t1/2
22
25
30
35
20 1.91 59 1.94
18 2.12 55 2.08
16 2.39 50 2.29
12 3.18 35 3.27
aConcentration 12.7 µg L-1; membrane probe length 4 cm; flow rate of stripping gas 2.2 mL min-1, extraction temperature 25 °C. Note that t1/2 and D were obtained with no trapping and at a high flow rate (25 mL min-1) and that t1/2′ and D′ were obtained with sorbent trapping and at a low flow rate (2.2 mL min-1).
Figure 6. Temperature vs time pulse heating profile.
membrane permeation. Compare curves a and b; t1/2 is larger for curve a. The membrane permeation processes are, however, similar in both measurements; therefore D is the same. The difference between the t1/2 values for curves a and b can be found experimentally. On the basis of this difference, D can be measured using curve a. Another way of measuring D is to detect the permeation process of the analyte in the membrane probe. In this method, the MESI setup is modified. The sorbent interface and the GC column are replaced by 20 cm × 0.32 mm i.d. deactivated silica tubing connected directly to the extraction probe and the FID detector. The measurement is based on eq 12.16
D ) 0.14d2/t1/2
actual air concn (µg L-1)
external calibration (µg L-1)
membrane probe heating (µg L-1)
0.12 0.53 0.91 1.24 5.31 8.25 11.7
0.13 ((0.03) 0.55 ((0.02) 0.85 ((0.03) 1.31 ((0.03) 5.17 ((0.05) 7.97 ((0.05) 11.4 ((0.6)
0.10 ((0.04) 0.62 ((0.02) 0.75 ((0.06) 1.11 ((0.06) 4.84 ((0.07) 9.05 ((0.05) 12.9 ((0.9)
aExtraction temperature 25 °C; membrane length 4 cm; flow rate of stripping gas 2.2 mL min-1.
(12)
where d is the membrane wall thickness and t1/2 is the half-time of permeation reaching steady state. In eq 12, the membrane thickness d is known and t1/2 can be obtained by experiment. In eq 12, the constant 0.14 is valid for a high stripping gas flow rate without trapping. At a low flow rate with trapping, to get the same D value (because D is not changed) the 0.14 value must be adjusted because t1/2 has changed. The adjustment factor can be obtained by comparing t1/2 for curves a and b. Experimentally, the adjustment factor was obtained by measuring t1/2 at different temperatures. The results are listed in Table 6. The adjustment factor 0.42 was obtained from the comparisons. From this table it is apparent that when extraction and GC conditions are constant, D for benzene can be estimated from curve a. An alternative method for estimation of D is based on membrane pulse heating under conditions of steady-state permeation. In Figure 5, curves a and c are similar (curve c is the smooth line of the peak heights after second pulse heating); they overlap each other if the two curves are moved together. This is easily understood. A certain amount of benzene in the membrane was desorbed during the pulse heating (peak 1). As the extraction conditions were restored after desorption, the same concentration gradient was formed in the membrane. The permeation followed the same evolution as in the initial extraction from the non steady state to the steady state. In the experiment, the pulse heating required ∼1 s to heat the membrane to 263 °C and 30 s to cool to room temperature. The profile of membrane temperature (16) Crank, J. The Mathematics of Diffusion; Oxford University Press: London, 1975.
1070 Analytical Chemistry, Vol. 72, No. 5, March 1, 2000
Table 7. Estimation of Benzene Concentration in Air by the External Calibration and Membrane Probe Heating Methodsa
against time is shown in Figure 6. For 40 s trapping, the first peak after peak 1 was not counted, because during this time the membrane temperature was decreasing, and this causes the D value to change. The permeation curve was counted from the second peak after the heating pulse. In these circumstances the D value can be calculated in the same way as in the method based on curve a. It is clear that this method for measurement of D is easy to handle, because it is not necessary to measure the exposure time of the membrane probe to the air. The K and D values for benzene can be obtained from the chromatogram shown in Figure 5. Under conditions of steadystate permeation, the peak area or height count can be used to calculate the amount extracted by use of the FID response factor. Then the concentration in air can be calculated by use of eq 3. In practice, the equation and the adjustment factors can be stored in a computer in advance. A calculation program can be developed for frequent reporting of the results of air analysis. The results obtained for air concentration measurements by the external calibration method and by the membrane probe heating method are shown in Table 7. It is apparent there is a good agreement between the two methods and the estimate of the air concentration is close to the real value. CONCLUSIONS Modeling of fundamental processes in the membrane extraction system led to on-line calibration methods for a very simple, but very useful analytical monitoring system. The calibration under good convection conditions can be performed based on diffusion coefficient and distribution constant related to membrane material
and given analyte. These values can be stored in the data analysis unit or can be determined experimentally on-line. The advantages of performing calibration on-line include compensation for changes in membrane properties with time, quantification of unidentified compounds, and even possible identification of unknown analytes based on their distribution constants and diffusion coefficients. The calibration approach described above can also be extended to quantification of analytes in well-agitated aqueous and solid matrixes by the headspace membrane arrangement14 as long as gas/matrix distribution constant (Henry constant for aqueous (17) Saraullo,; Martos, P.; Pawliszyn, J. Anal. Chem. 1997, 69, 1992-1998. (18) Luo, Y. Z.; Pawliszyn, J. Anal. Chem., 72, 1058-1063.
samples) is known. This approach to calibration is analogous to one recently described for SPME technique.17 Practically, the headspace membrane extraction arrangement can be implemented by using the “Cap” sampling system.18 ACKNOWLEDGMENT This work has been financially supported by Chrompack and the Natural Sciences and Engineering Research Council of Canada. Received for review July 8, 1999. Accepted December 15, 1999. AC990746J
Analytical Chemistry, Vol. 72, No. 5, March 1, 2000
1071
