Anal. Chem. 1999, 71, 4587-4593
Theoretical Analysis of Non-Steady-State, Pulse Introduction Membrane Extraction with a Sorbent Trap Interface for Gas Chromatographic Detection Xuemei Guo and Somenath Mitra*
Department of Chemical Engineering, Chemistry and Environmental Science, New Jersey Institute of Technology, Newark, New Jersey 07102
Polymeric membranes have been used for extraction of organic compounds from an aqueous matrix, where the analysis is carried out on-line using a GC, a HPLC, or a mass spectrometer. High extraction selectivity and permeation rate can be achieved by choosing an appropriate membrane and optimum operating conditions. The sample can be introduced either continuously or as a pulse into the membrane. The former approach is based on steadystate permeation, while the latter is not. In this paper, pulse introduction membrane extraction is presented for on-line gas chromatography using a sorbent trap as an interface. A mathematical model that incorporates boundary layer effects has been developed, and the process parameters that affect sensitivity and lag time have been studied. It is observed that there is a trade-off between sensitivity and lag time; larger sample volume and lower flow rate enhance sensitivity but also increase lag time. Analytical methods for the measurement of volatile organic compounds (VOCs) in water include purge and trap, headspace analysis, and solid-phase microextraction. All these techniques involve a separation/extraction step for the isolation of analytes from the aqueous matrix prior to GC or GC/MS analysis. Although these methods have some excellent merits, none are designed for continuous real-time extraction, which is desirable for the development of automated, on-line instrumentation. The use of a polymeric membrane for the extraction of organic compounds from an aqueous matrix has received much attention,1-15 where * Corresponding author: (phone) (973) 596-5611; (e-mail) mitra@ megahertz.njit.edu. (1) Hoch, G.; Kok, B. Arch. Biochem. Biophys. 1963, 101, 160. (2) Zhang, L.; Guo X.; Mitra, S. Environ. Monit. Assess. 1997, 44, 529-540. (3) Mitra, S.; Zhang, L.; Zhu, N.; Guo, X. J. Microcolumn Sep. 1996, 8 (1), 21-27. (4) Xu, Y.; Mitra, S. J. Chromatogr., A 1994, 688, 171-180. (5) Bier, M. E.; Cooks, R. G. Anal. Chem. 1987, 59, 597-601. (6) Westover, L. B.; Tou, J. C.; Mark, J. H. Anal. Chem. 1974, 46, 568-571. (7) Lapack, M. A.; Tou; J. C.; Enke, C. G. Anal. Chem. 1990, 62, 1265-1271. (8) Slivon, L. E.; Bauer, M. R.; Ho, J. S.; Budde, W. L. Anal. Chem. 1991, 63, 1335-1340. (9) Kotiaho, T.; Lauritsen, F. R.; Choudhury, T. K.; Cooks, R. G. Anal. Chem. 1991, 63, 875A-883A. (10) Virkki, V. T.; Ketola, R. A.; Ojala, M.; Kotiaho, T.; Kompa, V.; Grove, A.; Facchetti, S. Anal. Chem. 1995, 67, 1421-1425. (11) Rivlin, A. A., Rapid Commun. Mass Spectrom. 1995, 9, 397. (12) Brodbelt, J. S.; Cooks, R. G.; Tou, J. C.; Kallos, G. J.; Dryzga, M. D. Anal. Chem. 1987, 59, 454-458. 10.1021/ac981226b CCC: $18.00 Published on Web 09/18/1999
© 1999 American Chemical Society
the analysis can be carried out on-line using a GC, HPLC, or mass spectrometer as the detection device. A variety of porous (involving pore flow) and nonporous membrane materials have been evaluated for membrane extraction.2-4,14,15 High extraction selectivity and permeation rate can be achieved for organic analytes by choosing an appropriate membrane and optimum operating conditions. Poly(dimethylsiloxane) membranes provide high diffusivity for different molecules due to the large free volume inside the polymer matrix and are widely used. The solubility of target organic analytes in silicone is higher than that of water; therefore, membrane extraction achieves high selectivity. In such nonporous structures, the organic molecules first dissolve in the membrane and then diffuse under a concentration gradient. The rate of diffusion depends on the size and the chemical nature of the molecule. Fick’s first law describes steady-state permeation flux:
J ) -D(δc/δx)
(1)
where D is the diffusivity and δc/δx is the concentration gradient. Analytical applications of membrane sampling were first published by Hoch and Kok1 in 1963. Since then different approaches have been reported, most focusing on membrane interface for mass spectrometry (MIMS).5-13 In MIMS, the sample is in contact on one side of the membrane and the other side is directly exposed to the ion source of a mass spectrometer. Limited data on membrane extraction with GC detection are available.2-4,14,15 A sorbent or a cryogenic trap is usually used to preconcentrate the sample prior to GC analysis. In both GC and MS applications, the major advantage of membrane extraction is that the sample can be extracted continuously by the membrane for automated on-line analysis.2-4,10-12 These techniques have demonstrated high selectivity, large linear dynamic range, sensitive response, and the capability of real-time measurements.4 Sample can be introduced either continuously or as a pulse (flow injection type) during membrane extraction. In the former approach, measurements are made after permeation reaches steady state. It can take a fairly long time to reach steady state since the diffusion through the membrane and the boundary layer (13) Melcher, R. G.; Morabito, P. L. Anal. Chem. 1990, 62, 2183-2188. (14) Pratt, K. F.; Pawliszyn, J. Anal. Chem. 1992, 64, 2107-2110. (15) Pratt, K. F.; Pawliszyn, J. Anal. Chem. 1992, 64, 2101-2106.
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Figure 1. Schematic diagram of the pulse introduction membrane extraction (PIME)-GC system. The water passed through the tube side while the stripping gas flowed countercurrent on the shell side.
on the membrane surface are slow processes. The system does not instantly respond to concentration changes but slowly attains equilibrium. Any measurement during this transition period does not truly reflect the analyte concentration. The time taken to complete the permeation process is referred to as the lag time. The lag time is much longer in a GC interface than in a MIMS where the vacuum provides a large partial pressure gradient for rapid mass transfer. For a GC interface, a positive pressure needs to be maintained on the permeate side to facilitate the flow of carrier gas through the column. Consequently, the lag time can be a limiting factor in on-line membrane extraction coupled with gas chromatography. This is also true for those membrane extraction devices used in MIMS where the permeated analytes are pneumatically transported to the MS.10 Pulsed sample introduction has been reported for MIMS16-19 and only recently for GC interface.20,21 This non-steady-state membrane extraction method, which is suitable for the analysis of small-volume individual samples as well as for continuous process stream monitoring, is explored in this paper for on-line GC detection. Since the system does not have to reach steady (16) Soni, M. H.; Callahan, J. H.; McElvany, S. W. Anal. Chem. 1998, 70, 31033113. (17) Soni, M.; Bauser, S.; Amy, J. W.; Wong, P.; Cooks, R. G. Anal. Chem., 1995, 67, 1409-1412. (18) Hayward, M. J.; Kotiaho, T.; Lister, A. K.; Cooks, R. G.; Austin, G. D.; Narayan, R.; Tsao, G. T. Anal. Chem. 1990, 62, 1798-1804. (19) Tsai, G.-J.; Austin, G. D.; Syu, M. J.; Tsao, G. T. Anal. Chem. 1991, 63, 2460-2465. (20) Guo, X.; Mitra, S. Continuous Monitoring of Volatile Organic Compounds in Water Using Pulse Introduction Membrane Extraction. J. Chromatogr. In press. (21) Guo, X.; Mitra, S. Anal. Lett. 1998, 31 (2), 367-379.
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state, the lag time associated with equilibration is eliminated, resulting in a faster instrumentation response. A non-steady-state model is presented here, and parameters that affect lag time and sensitivity have been studied. EXPERIMENTAL SECTION The pulse introduction technique, which is applicable for any membrane extraction application, is shown in Figure 1 for a GC interface. The aqueous sample is introduced as a pulse into the membrane. An eluent stream is used for transporting the sample to the membrane module. A countercurrent gas stream strips the analytes that permeate through. The GC interface is accomplished using a microsorbent trap (referred to as microtrap) which concentrates the organics before injecting into the GC. Similar trapping devices have been used by other investigators.11,14,15 The sample size ranged from 100 µL to 10 mL, depending upon analysis needs. The injection was accomplished by a pneumatically controlled six-port valve (Valco Instruments Co. Inc., Houston, TX). The eluent was HPLC grade high-purity water. A HPLC pump was used as the eluent pump. Typical operation consisted of injecting a sample onto the eluent steam. A few minutes were allowed for the permeation to complete. The permeated analytes were pneumatically transported to the microtrap by a flow of nitrogen. The analytes were concentrated and then desorbed into the GC for analysis. During continuous on-line monitoring,20 the aqueous stream continuously flowed through the sample loop of the valve, and injections were made periodically into the membrane module. A chromatogram was obtained corresponding to each injection.
The membrane contactor was a standard shell-and-tube design that has been described before.4 The water passed through the tube side while the stripping gas flowed countercurrent on the shell side. Membrane module was made of 12, 8.5-cm-long composite membranes of dimension 0.260 mm o.d. × 0.206 mm i.d. (Applied Membrane Technology, Minnetonka, MN). The composite structure comprised 1-µm-thick homogeneous siloxane film as the active layer supported on a layer of microporous polypropylene. The membrane module was constructed by inserting 12 fibers into a 1/4-in.-o.d. tubing. At each end of the tubing, a T-unit (Components & Controls Inc., Carlstadt, NJ) was used to connect the inlet and the outlet for both the nitrogen and the aqueous stream. The connection points of membrane and T-units were sealed with epoxy to separate nitrogen from the aqueous phase. The microtrap was a small-diameter silica-lined tube packed with a small amount of adsorbent. It had low thermal mass and could be heated and cooled rapidly. When the nitrogen stream carrying the organics flowed through the microtrap, the analytes were trapped and concentrated. An electrical current resistively heated the microtrap and the desorption pulse served as an injection for GC analysis. The details of the microtrap and its working principle have been presented elsewhere.22,23 A 15-cmlong, 0.53-mm-i.d. silica-lined tubing (Restek Corp.) packed with Carbotrap C (Supelco, Supelco Park, PA) served as the microtrap. A 7-10 A current was supplied from a 40-V ac power source to heat the microtrap. The duration and the interval between the heat pulses were controlled using a microprocessor-based controller fabricated in-house. A HP 5890 series II GC (Hewlett-Packard Co., Avondale, PA) equipped with a flame ionization detector and a 30-m-long, 0.53-mm-o.d., 0.21-mm-i.d. SE-54 megabore column with 2.4-µm-thick stationary phase was used for GC separation. HP Chemstation 3365 software was used for data acquisition and analysis. RESULTS AND DISCUSSION Theory of Non-Steady-State Pulse Introduction. In pulse introduction membrane extraction (PIME), the membrane receives a sample pulse of a certain duration. The ideal pulse input is an impulse function as shown in Figure 2. Experimentally, this was achieved by injecting the sample onto an eluent stream that transported it to the membrane.19 After the sample permeates through the membrane, a flow of nitrogen can be used to purge/ clean the membrane. This concept has been discussed in previous publications.20,21 Axial mixing between the eluent and the sample distorted and broadened the pulse. This effect was experimentally determined by injecting a 2-mL sample containing toluene and monitoring its concentration at the outlet of the membrane module using a UV detector (Figure 2). It may be assumed that the concentration profile at the membrane surface was similar. The permeation profile is also shown in Figure 2. It was measured by monitoring the permeate concentration every 30 s by making a microtrap injection at that interval. Slow permeation through the boundary layer, and the membrane resulted in a broadened, skewed bell-shaped permeation profile. Figure 2 shows that a 2.5min impulse broadened to 5 min due to the axial mixing, and the (22) Mitra, S.; Yun, C. J Chromatogr. 1993, 648, 415-421. (23) Mitra, S.; Xu, Y. H.; Chen, W.; Lai, A. J. Chromatogr., A 1996, 727, 111118.
Figure 2. Input and permeation profiles in pulse introduction membrane extraction. Permeation profile was obtained using a 2-mL, 31.5 ppb toluene sample, at an eluent flow rate of 1 mL/min. Input profile was obtained using a 2-mL, 4.4 ppm toluene sample.
permeation profile further broadened to 13 min due to slow permeation. This trend is consistent with previously published reports.19 In PIME, permeation never reached steady state. Non-steadystate permeation can be described by Fick’s second law as
δC(x,t)/δt ) -D(δ2C(x,t)/(δx2)
(2)
where C(x,t) is the concentration at position x, at time t. The boundary conditions are as follows: when x ) 0, at t ) 0, concentration C changes from 0 to C0, at t ) 0 to ∆t, C ) C0, at t ) ∆t, C changes from C0 to 0, at t > ∆t, C ) 0, where C0 is the sample concentration on the membrane surface and ∆t is duration of sample pulse. The mathematical solution of eq 2 for the above boundary conditions is24,25
J(t) ) Jss[f(u) - γf(u - (D(∆t)/l2))]
(3)
where J is the permeation rate at time t, D is diffusivity, Jss is the permeation at steady state and equals DC0A/l, A is the membrane surface area, l is membrane thickness, u ) Dt/l2, and C0 ) KC*, where C* is the sample concentration in water, K is the partition coefficient between membrane and water; γ ) 0, for u < D(∆t)/ l2, and represents the ascending part of the curve; γ ) 1, for u > D(∆t)/l2, represents the descending part of curve. ∞
f(u) ) 1 + 2
∑(-1)
n
exp{-n2(π)2u}
(4)
n)1
The reduced permeation rate Jr is defined as J(t)/Jss; thus eq 4 is reduces to (24) Palmai, G.; Olah, K. J. Membr. Sci. 1984, 21, 161-183. (25) Beckman, I. N. In Polymeric gas separation membranes; CRC Press: Boca Raton, FL, 1994.
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∞
Jr ) 1 + 2
∑(-1)
n
exp{-n2(π)2Dt/l2}
when t < ∆t
n)1
(5)
∞
Jr ) 2
∑(-1)
∞
n
exp{-n2(π)2Dt/l2} - 2
n)1
∑(-1)
n
n)1
exp{-n2(π)2D(t - ∆t)/l2}
when t > ∆t (6)
It is seen that the reduced permeation rate is a function of diffusivity, pulse duration (∆t), and membrane thickness. It has been reported that thick membranes reduce permeation and prolong lag time;2 this is consistent with the above equation. Diffusion coefficient is an important parameter in the above equation. Most reported diffusion coefficients26 have been obtained by measuring the permeation of pure vapors across a membrane. These high concentrations tend to swell the polymeric material, which enhances diffusion. Consequently, at trace concentrations, the diffusion coefficients tend to be much lower.27 Furthermore, in pervaporation, where an analyte diffuses from a liquid phase, a depletion layer is formed near the membrane surface due to the high solubility of the organics in the membrane material. This is considered to be the major resistance to mass transfer when thin membranes are used.28,29 To compute an overall diffusion coefficient that includes the boundary layer effects, the following approach was taken. From eqs 5 and 6, it can be seen that the maximum value in the reduced permeation profile is a function of ∆t. At the maximum point, eq 3 can be written as ∞
Jmax ) Jss{2
∑(-1)
n
exp{-n2(π)2Dtmax/l2} -
n)1
∞
2
∑(-1)
n
exp{-n2(π)2D(tmax - ∆t)/l2}} (7)
n)1
where Jmax is the maximum value in the response profile and tmax is the corresponding time when it occurs. These two parameters were determined experimentally. It was observed that the first two terms in the above equation accounted for more than 99% of the total response. By changing the sample size while keeping other conditions the same, ∆t was varied. Corresponding to different ∆t, different tmax and Jmax were obtained. The overall diffusion coefficients were computed from eq 7 using two sets of measurements at two different sample volumes. The overall diffusion coefficient for benzene was found to be 9.0 × 10 -9 cm2/ s. Such a low value indicates the presence of a well-formed boundary layer.28,29 The permeation profile was computed according to eqs 5 and 6 using the overall diffusion coefficient and the first 10 terms in the series expansion. The computed and the experimental results (26) Dennis, W. E.; Larson, W. D. Permeation and Silicone Elastonmers; Dow Chemical Corp., Medical Product Business, Technical Service & Development, Midland, MI, 199X. (27) Petropoulos, J. H. In Polymeric gas separation membranes; CRC Press: Boca Raton, FL, 1994. (28) Raghunath, B.; Hwang, S.-T. J. Membr. Sci. 1992, 65, 147-161. (29) Psaume, R.; Aptel, Ph.; Aurelle, Y.; Mora, J. C.; Bersillon, J. L. J. Membr. Sci. 1988, 36, 373-384.
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Figure 3. Experimental and computed permeation profiles for benzene. A 3-mL, 50 ppb benzene sample at an eluent flow rate of 0.8 mL/min was used in this analysis.
for benzene permeation presented in Figure 3 show reasonably good agreement. The observed differences are attributed to the distortion of the input profile due to axial mixing. Effect of Process Parameters. The sample introduction rate affects the system response by changing ∆t in eqs 5 and 6. According to eq 3, the maximum response in the response profile increases with ∆t until it reaches Jss. A slower flow rate represents a longer ∆t, the corresponding profile takes longer to reach its maximum, and a higher maximum response is obtained. A series of sample inputs and permeation profiles at different flow rates are shown in Figure 4. It was seen that the maximum response and the time at which it occurred both increased when flow rate decreased. Similar results have been reported by Tsai et al.19 for MIMS, although the permeation was faster because the permeate side was exposed to vacuum in the MS. A faster flow rate also increased mixing of sample with the eluent and resulted in a more dispersed sample volume calculated as the product of flow rate and duration of the input profile (Figure 4). For example, for a 2-mL injection at eluent flow rates of 1 and 4 mL/min (corresponding to ∆t of 2 and 0.5 min), the dispersed volumes were found to be 9 and 11 mL, respectively. A more dispersed sample reduces analyte concentration on the membrane surface and, therefore, the concentration gradient for mass transfer. Sample dispersion can be reduced by low instrument void volume and by low flow rates. The lag time in PIME is proportional to the duration of the permeation profile. It is defined as t10-10%, which is the time interval between the points corresponding to 10% of maximum response in the ascending and descending parts in the permeation profile. Faster flow rates reduce lag time. Figure 5 is a plot of lag time as a function of ∆t. Lower flow rates provide higher residence times, higher response, but also higher lag times. Ethylbenzene, a larger molecule, exhibited a longer lag time due to its lower diffusion coefficient. Other factors such as hydrophobicity, polarity, and nature of functional groups may also play a role here. Reported lag times in MIMS19 are almost 1 order of magnitude lower than the present study. At high flow rates, when the residence time in the membrane module is low, the abbreviated time for permeation results in lower extraction efficiency. This is shown in Figure 6. At low flow rates, extraction efficiencies as high as 90% were achieved. The partition
Figure 4. Permeation and input concentration profiles at different flow rates. Permeation profiles were obtained using a 8-mL sample containing 75 ppb toluene. Input profiles were obtained using a 5-mL sample containing 4.4 ppm toluene.
Figure 5. Lag time as a function of sample duration (∆t) on a membrane module at room temperature. ∆t was varied by varying eluent flow rate. Experiments were done with an 8-mL injection using 75 ppb toluene, 67.5 ppb benzene, and 60 ppb ethylbenzene.
Figure 7. Permeation profiles for a 1 ppm toluene sample as a function of injection volume. Membrane temperature was 50 °C, and the sample flow rate was 3.5 mL/min.
Figure 6. Extraction efficiency as a function of residence time. A 5-mL sample containing 48 ppm acetone, 54 ppm benzene, and 56 ppm toluene was used in this analysis. Membrane temperature was 48 °C.
Figure 8. System response during continuous sample introduction. A 52.3 ppb toluene solution flowed continuously at 1 mL/min. Then the sample concentration was dropped to 27.7 ppb for 10 min before being changed back to 52.3 ppb.
coefficient of the analytes in the membrane affects extraction efficiency. The extraction efficiency of acetone was significantly
lower than that of nonpolar benzene and toluene. This is because acetone has strong affinity for water and a low partition coefficient Analytical Chemistry, Vol. 71, No. 20, October 15, 1999
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Figure 9. Chromatogram of an aqueous sample containing different VOC components.
on the membrane. In general, increasing the residence time either by having a low flow rate or by having a longer membrane module can increase the extraction efficiency. Sample size was an important variable since a larger sample generated a higher detector response and increased sensitivity. However, at a given flow rate a larger sample increased ∆t and, consequently, lag time. Typical response profiles from different injection volumes are shown in Figure 7. For low-concentration samples, a large volume may however be necessary to achieve low detection limits. For high-concentration samples, smaller injection volumes shorten lag time. Generally speaking, in PIME there is a trade-off between sensitivity and lag time. Factors such as larger sample volume and lower flow rate that enhance sensitivity tend to increase lag time. These parameters need to be adjusted on the basis of the analysis requisite. Much of the work in this study was performed with low-concentration samples, and injection volumes were between 100 µL and 10 mL. Equilibration Time in Membrane Extraction. As seen from the above discussion, the lag time is a significant issue in PIMEGC, where the stripping gas at a positive pressure serves as the carrier stream. Steady state is not reached instantly due to slow mass transfer. The time required to reach equilibrium was determined as follows. A sample containing 52.3 ppb toluene was continuously introduced into the membrane at a flow rate of 1 mL/min. For a period of 10 min, the concentration was dropped to 27 ppb, after which the concentration was changed back to the original level. The system response is presented in Figure 8. The response lagged behind, such that, even 50 min after switching back the concentration, the response did not reach its original value. Part of this lag time may be attributed to internal volume of tubing and fittings and axial mixing with the eluent. An estimated 10 min is attributed to these factors; the equilibration time was still 40 min or more. The objective of this experiment was not to determine the exact equilibration time, which varies 4592
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with flow rate, but to demonstrate the long time required to reach equilibrium. These results are in line with other published data on time required to reach steady state during pervaporation.30,31 In a continuous introduction technique, any measurement made before reaching steady-state does not represent the actual concentration. On the other hand, no steady state assumption is made in PIME. Each injection truly represents the sample concentration. The only requirement here is the elimination of carryover from the previous sample. This is equivalent to reducing the lag time and can be achieved by injecting a smaller sample volume and/or by gas purging the membrane after sample has passed through.20,21 Analytical Performance. In the pulse introduction approach, individual samples are injected one at a time, and continuous monitoring is easily done by making a series of injections by an automated injection valve.20 Combination of membrane extraction with a microsorbent trap results in simple instrumentation for online extraction/analysis of organics in an aqueous matrix. A typical chromatogram for an aqueous sample containing different volatile organic components is shown in Figure 9. The relative standard deviations (RSDs) obtained by seven replicated analyses of a 5-mL sample were 1.3, 1.6, and 1.6% for benzene, toluene, and 1,1,trichlororethane, respectively. This shows good precision of the pulse introduction technique. A linear relationship between system response and concentration was observed at different flow rates and sample sizes. Figure 10 shows typical calibration curves for several common organics. The method detection limits for an 8-mL injection at an eluent flow rate of 2.5 mL/min were 0.0012, 0.0063, and 0.010 ppb for benzene, toluene, and 1,1,1-chloroethane, respectively. The detection limit for ethylbenzene was found to (30) Yang, D.; Majumdar, S.; Kovenklioglu, S.; Sirkar, K. K. J. Membr. Sci. 1995, 103, 195-210. (31) Das, A.; Abon-Nemah, I.; Chandra, S.; Sirkar, K. K. Membrane modified stripping process for removing VOCs in composite hollow fiber modules. J. Membr. Sci. In press.
CONCLUSION A pulse introduction method for on-line membrane extraction was explored. A mathematical model was developed for predicting the permeation process. Process parameters that effect sensitivity and lag time were studied. It was found that there was a trade-off between sensitivity and lag time. Larger sample volumes and lower flow rates that enhanced sensitivity also increased lag times. These parameters need to be adjusted on the basis of the analytical requisite. ACKNOWLEDGMENT Figure 10. Calibration cures of several organic compounds. Sample volume was 5 mL at an eluent flow rate of 1 mL/min. The membrane module temperature was 42 °C.
Financial support from NSF Industry/University Hazardous Substance Management Research Center at the New Jersey Institute of Technology is acknowledged. The authors are also grateful to Dr. Kamalesh K. Sirkar for his valuable input.
be 0.045 ppb at an eluent flow rate of 1.2 mL/min and 8-mL injection volume. The method detection limits (MDLs) were computed on the basis of a standard EPA procedure.32 One should note that the MDL depends on operating parameters such as membrane module design, residence time, and sample volume.
Received for review November 10, 1998. Accepted July 15, 1999.
(32) 40 Code Fed. Regist. 1994, part 136, appendix B.
AC981226B
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