Anal. Chem. 1997, 69, 3260-3266
Headspace Solid Phase Microextraction. Dynamics and Quantitative Analysis before Reaching a Partition Equilibrium Jiu Ai
US Tobacco Manufacturing Company, Inc., 800 Harrison Street, Nashville, Tennessee 37203
Solid phase microextraction (SPME) has remarkable advantages in headspace chemical analysis over conventional static headspace and purge-and-trap techniques in terms of its ease of use and superior reproducibility. A theoretical treatment of the headspace SPME process is proposed in this report that focuses on the mass transfer at the two interfaces, condensed phase/gas phase and gas phase/SPME polymer. The rate-determining step of the SPME process can be either the analyte evaporation from the condensed phase to its headspace or the analyte diffusion from the SPME polymer film surface into its inner layers. Mass transfer in the gas phase is considered a fast process. The mathematical solution provides an expression that correlates the amount of extracted analyte with its initial concentration in the condensed phase. A directly proportional relationship exists between them in all cases of headspace SPME, and this relationship indicates that SPME quantification is feasible before reaching a partition equilibrium once the SPME conditions and the sampling time are held constant. Experimental extraction-time profiles fit the theoretical predictions. Data plots of the extracted amount vs the initial concentration showed excellent linearity with a sampling time much shorter than that required to reach a partition equilibrium. Solid phase microextraction (SPME), developed by Pawliszyn and co-workers,1,2 has wide applications to volatile and semivolatile organic analysis. It is a convenient and solvent-free method that is especially suitable for headspace sampling. Chemicals in the headspace over a condensed phase are directly extracted and concentrated in the SPME polymer film, which makes this technique advantageous over conventional techniques for headspace analysis.3-5 In recent years, a lot of work on SPME headspace analysis has been reported in the literature. Volatile drug metabolites and toxic materials in human fluids were analyzed using SPME in the headspace over aqueous solutions at elevated temperature.6-10 Headspace analyses of volatile (1) Arthur, C. L.; Pawliszyn, J. Anal. Chem. 1990, 62, 2145-8. (2) Zhang, Z.; Yang, M. J.; Pawliszyn, J. Anal. Chem. 1994, 66, 844A-53A. (3) Zhang, Z.; Pawliszyn, J. J. High Resolut. Chromatogr. 1993, 16, 689-92. (4) MacGillivray, B.; Pawliszyn, J.; Fowlie, P.; Sagara, C. J. Chromatogr. Sci. 1994, 32, 317-22. (5) Zhang, Z.; Pawliszyn, J. J. High Resolut. Chromatogr. 1996, 19, 155-60. (6) Lee, X. P.; Kumazawa, T.; Sato, K.; Suzuki, O. Chromatographia 1996, 42, 135-40. (7) Kumazawa, T.; Lee, X. P.; Tsai, M. C.; Seno, H.; Ishii, A.; Sato, K. Hochudoku 1995, 13, 25-30.
3260 Analytical Chemistry, Vol. 69, No. 16, August 15, 1997
contaminants11 in food, contaminants in groundwater,12-16 and flavors in beverages and food9-11 were accomplished using SPME. Even metal ions in aqueous solution were analyzed as volatile chemicals in headspace after derivatization.17,18 Three phases are involved in a regular headspace SPME process: the condensed phase, the headspace gas phase, and the SPME polymer film. According to the theoretical treatment for the SPME dynamic process proposed by Pawliszyn and coworkers,19,20 mass transfer of an analyte from the condensed phase to its headspace and into the SPME polymer film was described by a single diffusion equation. This second-order partial differential equation cannot be solved with boundary conditions that are realistic for the headspace SPME process. Instead, the finite difference method was used to give numerical solutions to predict the concentration profiles of the analyte.20 An analytical expression that directly correlates the amount of extracted analyte with its initial concentration in the condensed phase is not available. The fundamental work for the dynamic process of headspace SPME still needs to be explored. In the previous study,21 a dynamic model was worked out for the SPME process in a two-phase system (the sample matrix and the SPME polymer). Mass transfer at the only interface was treated with reasonable assumptions to avoid dealing with the second-order diffusion equation. That model predicted the experimental observations and provided the analytical solution to the SPME process in aqueous solution. For headspace SPME, three phases are involved, and there are two interfaces instead of one to be dealt with. The focus is still on the mass transfer at the interfaces. At the gas/polymer interface, Fick’s first law of diffusion is used to describe the mass transfer instead of Fick’s second law of diffusion. At the condensed phase/gas phase (8) Seno, H.; Kumazawa, T.; Ishii, A.; Nishikawa, M.; Watanabe, K.; Hattori, H.; Suzuki, O. Jpn. J. Forensic Toxicol. 1996, 14, 30-4. (9) Lee, X. P.; Kumazawa, T.; Taguchi, T.; Sato, K.; Suzuki, O. Hochudoku 1995, 13, 122-3. (10) Kumazawa, T.; Lee, X. P.; Sato, K.; Seno, H.; Ishii, A.; Suzuki, O. Jpn. J. Forensic Toxicol. 1995, 13, 182-8. (11) Page, B. D.; Lacroix. G. J. Chromatogr. 1993, 648, 199-211. (12) Potter, D. W.; Pawliszyn, J. J. Chromatogr. 1992, 65, 247-55. (13) Wittkamp, B. L.; Tilotta, D. C. Anal. Chem. 1995, 67, 600-5. (14) Langenfeld, J. J.; Hawthorne, S. B.; Miller, D. J. Anal. Chem. 1996, 68, 144-55. (15) Pelusio, F.; Nilsson, T.; Montanarella, L.; Tilio, R.; Larsen, B.; Facchetti, S.; Madsen, J. J. Agric. Food Chem. 1995, 43, 2138-43. (16) Field, J. A.; Nickerson, G.; James, D. J.; Heider, C. J. Agric. Food Chem. 1996, 44, 1768-72. (17) Cai, Y.; Boyona, J. M. J. Chromatogr. A 1995, 696, 113-22. (18) Gorechi, T.; Pawliszyn, J. Anal. Chem. 1996, 68, 3008-14. (19) Louch, D.; Motlagh, S.; Pawliszyn, J. Anal. Chem. 1992, 64, 1187-99. (20) Zhang, Z.; Pawliszyn, J. Anal. Chem. 1993, 65, 1843-52. (21) Ai, J. Anal. Chem. 1997, 69, 1230-6. S0003-2700(97)00024-3 CCC: $14.00
© 1997 American Chemical Society
interface, the analyte evaporation from the condensed phase is considered as driven by the deviation of headspace concentration of the analyte from its equilibrium value. Mass transfer at these two interfaces is correlated according to the principle of balanced mass transfer when a steady-state mass flow is attained. A normal differential equation instead of a second-order partial differential equation is thus derived to describe the dynamic process of headspace SPME. The analytical solution to the equation directly correlates the amount of extracted analyte with its initial concentration in the condensed phase. The model can be used to predict the experimental observations at different extraction conditions. THEORETICAL TREATMENT Dynamic Process of Headspace SPME. During a headspace SPME extraction, there are three phases involved: the condensed phase, its headspace, and the SPME polymer. There should be two interfaces, the condensed/gas interface and the gas/polymer interface. At the gas/polymer interface, the mass transfer is the diffusion of the analyte from gas phase bulk into the SPME polymer film. This process can be described by Fick’s first law of diffusion. For a balanced mass transfer, we have
∂Cg ∂Cf ) -D2 F ) -D1 ∂x ∂x
(1)
Here, F is the mass flow rate, which equals the diffusion rates in the gas phase and the SPME polymer phase for a balanced mass transfer. D1 and D2 are the diffusion coefficients of the analyte in the gas phase and the polymer film phase, respectively. Cg is the concentration of the analyte in the headspace gas phase. Cf is the concentration of the analyte in the SPME polymer film. Let n be the amount of analyte extracted by the SPME polymer film in the unit of moles, and the SPME extraction rate should be related to the mass flow rate as follows:
F)
1 dn A dt
(2)
Here, A is the surface area of the SPME polymer film. Diffusion of a material in the gas phase is much faster than that in the SPME polymer phase. D1 is usually 104-105 times larger than D2. From eq 1, it is obvious that the concentration gradient (∂Cg/∂x) in the gas phase is negligible compared with that in the SPME polymer film. Combining eqs 1 and 2, we have
∂Cf 1 ∂n ) -D2 A ∂t ∂x
(3)
In the polymer phase, the diffusion of the analyte is in a steadystate condition because the diffusion distance is the thickness of the polymer film. Equation 3 can then be written as
1 dn D2 ) (Cf - Cf′) ) m2(Cf - Cf′) A dt δ2
(4)
Here, δ2 is the thickness of the polymer film. Cf is the analyte concentration in the polymer film at the gas/polymer interface, Cf′ is the concentration at inner surface of the polymer film. m2
is the mass transfer coefficient of the analyte in the SPME polymer phase and is equal to D2/δ2. It is a constant for steady-state diffusion. During a headspace SPME sampling, analytes in the gas phase are extracted into the polymer film. The original equilibrium of the analyte between the condensed phase and its headspace gas phase before SPME extraction is broken. Once the analyte concentration in the headspace is depleted due to the SPME absorption, the analyte in the condensed phase will evaporate to the headspace. At the condensed/gas interface, the driving force of net analyte evaporation from the condensed phase is its headspace concentration deviation from the equilibrium value. Let Cg0 be the headspace concentration of the analyte at equilibrium. The driving force of the analyte evaporation is Cg0 - Cg. The evaporation rate is assumed to be proportional to Cg0 - Cg. When a steady-state SPME extraction is attained, the mass flow rate at the condensed/gas interface should be equal to that at the gas/ polymer interface. Thus, the evaporation rate should be equal to the mass flow rate F. We have
1 dn ) k(Cg0 - Cg) A dt
(5)
Here, k is the evaporation rate constant. It is dependent on a lot of factors, such as temperature, surface area, and agitation conditions of the condensed phase. Let Cs be the concentration of the analyte in the condensed phase and K1 the equilibrium partition constant of the analyte between the condensed phase and its headspace. We have
K1 )
Cg0 Cs
(6)
Equation 5 can be rewritten as
1 dn ) k(K1Cs - Cg) A dt
(7)
The above equation, combined with eq 4, can be rewritten as
1 dn ) m2(Cf - Cf′) ) k(K1Cs - Cg) A dt
(8)
Let K2 be the equilibrium partition constant of the analyte between the SPME polymer phase and the headspace gas phase. We then have
Cf ) K2Cg
(9)
It is assumed that the analyte has a linear gradient of concentration in the SPME polymer film. This assumption is common in treating diffusion-controlled mass transfer.22 Then the average concentration of the analyte in the polymer film is approximately (Cf + Cf′)/2. Let Vf be the volume of the polymer film, and the extracted amount n is expressed as follows: (22) Bard, A. J.; Faulkner, L. R. Electrochemical Methods, Fundamentals and Applications; Wiley: New York, 1980.
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n ≈ Vf
Cf + Cf′ 2
(10)
Let C0 be the initial concentration of the analyte in the condensed phase. The analyte in the headspace and the SPME polymer film are originally from the condensed phase. The concentration of the analyte remained in the condensed phase can be expressed as
Cs ) C0 -
n + CgVg Vs
(11)
V is the volume. Subscripts s, g, and f denote the condensed phase, the headspace gas phase, and the SPME polymer phase. Using eqs 8-11 to express K1Cs - Cg in terms of C0 and n, and substituting the result into eq 7, we have
2Am2kK1K2Vs dn ) C dt 2m2K2Vs + kK1Vg + kVg 0 kK1K2Vf + kK1Vg + kVs 2Am2 n (12) 2m2K2VfVs + kK1VfVg + kVfVs Equation 12 is a normal differential equation with two variables, n and t. It can be solved with the following initial condition: when t ) 0, n ) 0.
[
(
kK1K2Vf + kK1Vg + kVs t n ) 1 - exp -2Am2 2m2K2VfVs + kK1VfVg + kVfVs
)]
×
partition equilibrium can be reached. It is dependent on the mass transfer coefficient, the evaporation rate constant, the partition constants, and the physical dimension of the headspace SPME system. The larger the parameter a, the faster the partition equilibrium can be reached. The directly proportional relationship between n and C0 in eq 13 provides the basis for quantitative analysis before reaching a partition equilibrium. In the above treatment, mass transfers at both condensed/ gas and gas/polymer interfaces were taken into consideration as rate-determining steps. In reality, mass transfer in one of the interfaces may play the major role and become the bottleneck in reaching a partition equilibrium. Diffusion in the SPME Polymer Film as the RateDetermining Step. When diffusion of an analyte from the polymer film surface to its inner layers is a slow process compared to the analyte evaporation from the condensed phase to its headspace, there is always an analyte partition equilibrium between the condensed phase and its headspace. Then we have Cg ) K1Cs. Using this expression along with eqs 9-11 to express Cf - Cf′ in terms of C0 and n and substituting the result into eq (4), we have
K1K2Vs K1K2Vf + K1Vg + Vs dn ) 2Am2 C - 2Am2 n (17) dt K1Vg + Vs 0 K1VfVg + VfVs This equation is solved with the following initial condition: when t ) 0, n ) 0.
[
(
K1K2Vf + K1Vg + Vs t n ) 1 - exp -2Am2 K1VfVg + VfVs
)]
×
K1K2VfVs C (13) K1K2Vf + K1Vg + Vs 0
K1K2VfVs C (18) K1K2Vf + K1Vg + Vs 0
Equation 13 is the analytical solution to the dynamic process of the headspace SPME. This equation directly correlates extracted amount n to the initial concentration C0, and there is a linearly proportional relationship between them. As sampling time t goes to infinity, the exponential term vanishes, and eq 13 becomes
Expression 18 describes the headspace SPME process when the analyte diffusion in the polymer film is the rate-determining step. It can also be written in the form of eq 16. Parameter a of this equation is independent of the evaporation rate constant k:
K1K2VfVs n0 ) C K1K2Vf + K1Vg + Vs 0
(14)
K1K2Vf + K1Vg + Vs a ) 2Am2 K1VfVg + VfVs
(19)
An exponential model like eq 16 was used to describe adsorption of gases on solid surfaces.23 In this study, it is deduced from the dynamic process of mass transfer at the two interfaces for headspace SPME. Parameter a is a measure of how fast a
Equation 18 can also be derived directly from eq 13. When the evaporation rate constant k is very large and m2 is very small, parameter a defined by eq 15 can be simplified to eq 19. Equation 13 then becomes eq 18. Equation 18 applies to the headspace SPME of very volatile chemicals. Organic chemicals become more volatile at elevated temperatures, and this equation may describe headspace SPME when the condensed phase is heated above ambient temperature. Evaporation from the Condensed Phase as the RateDetermining Step. If the evaporation of the analyte from the condensed phase to its headspace becomes the rate-determining step, the mass transfer at the gas/polymer interface is considered a relatively fast process. In this case, a partition equilibrium is quickly reached at the gas/polymer interface, and there is no concentration gradient in the SPME polymer film. Thus, Cf ) Cf′. We have
(23) Matich, A. J.; Rowan, D. D.; Banks, N. H. Anal. Chem. 1996, 68, 4114-8.
n ) CfVf
Equation 14 is the expression for headspace SPME at partition equilibrium and is reported in the literature.20 Let
kK1K2Vf + kK1Vg + kVs a ) 2Am2 2m2K2VfVs + kK1VfVg + kVfVs
(15)
Equation 13 then becomes
n ) [1 - exp(-at)]n0
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Analytical Chemistry, Vol. 69, No. 16, August 15, 1997
(16)
(20)
Using the above expression along with eqs 9 and 11 to express K1Cs - Cg in terms of C0 and n, and substituting the result into eq 7, we have
K1K2Vf + K1Vg + Vs dn ) AkK1C0 - Ak n dt K2VfVs
(21)
This equation is solved with the following initial conditions: when t ) 0, n ) 0.
[
(
K1K2Vf + K1Vg + Vs t K2VfVs
n ) 1 - exp -Ak
)]
×
K1K2VfVs C (22) K1K2Vf + K1Vg + Vs 0 Equation 22 describes the headspace SPME process when the analyte has a slow evaporation rate. Parameter a in this equation is independent from m2, the mass transfer coefficient of the analyte in the SPME polymer phase. It is expressed as follows:
K1K2Vf + K1Vg + Vs K2VfVs
a ) Ak
(23)
Equation 22 can also be derived from eq 13. When the evaporation rate constant k is very small, eq 15 for parameter a becomes eq 23, and eq 13 becomes eq 22. During room temperature SPME headspace measurements, a lot of chemicals have relatively low volatility. Their evaporation rates are very low. Their concentrations in the gas phase are far too small compared with their concentrations in the condensed phase. That means Cg , Cs and C0 ≈ Cs. If the sampling time t is not long, then we have K1Cs - Cg ≈ K1C0, and eq 7 becomes
1 dn ≈ kK1C0 A dt
(24)
This equation is solved with following the initial condition: when t ) 0, n ) 0.
n ) AkK1C0t
(25)
The extracted amount n is not only directly proportional to C0 but also directly proportional to the SPME sampling time t. Equation 25 can also be derived directly from eq 22. If k is very small, and Vg, Vs, and t are not very large, we have
K1K2Vf + K1Vg + Vs t,1 K2VfVs
Ak
(26)
Then the exponential term in eq 22 can be written as
(
)
K1K2Vf + K1Vg + Vs t ≈ K2VfVs
exp -Ak
K1K2Vf + K1Vg + Vs t (27) K2VfVs
1 - Ak
Substituting the above expression into eq 22, we have eq 25.
Analytical solutions to the headspace SPME at different conditions are derived in the above theoretical treatments. Whether a partition equilibrium is reached or not, n is always directly proportional to C0. This directly proportional relationship is the key requirement for quantitative analysis. To verify the theoretical treatment, experiments were carried out for several SPME headspace conditions. EXPERIMENTAL SECTION Solid phase microextraction (SPME) fiber used in this study was purchased from Supelco (Bellefonte, PA). It was a silica fiber coated with an 85 µm film of polyacrylate as described in the previous study.21 Three chemicals used in this study were the same as in the previous study.21 Pure 2-phenylethanol and eugenol were obtained from Aldrich Chemicals (Milwaukee, WI), and 2,4-dimethylphenol was from Eastman Chemicals (Kingston, TN). They were used without further purification. A stock solution of a mixture of the three chemicals was prepared with methanol as the solvent. For all of the SPME measurements, the condensed phase was prepared with this stock solution by adding a small amount of the stock solution to distilled water mixed with 50% saturated NaCl. Two types of containers for the aqueous solution were used. One was a 5 mL vial. The volume of the aqueous solution added to the vial was 1.0 mL. Thus, Vs ) 1.0 mL and Vg ≈ 4 mL. Another container was a 50 mL Erlenmeyer flask. After adding 15 mL of aqueous solution as the condensed phase, the headspace volume Vg was approximately 40 mL. The surface area of the condensed phase in the 50 mL flask was about eight times larger than that in the 5 mL vial. In both containers, magnetic stirring bars were used to agitate the aqueous phase, except for measurements at elevated temperatures. The stirring rate for agitation was set at the medium level. For elevated temperature headspace SPME, the 5 mL vial was put in a Thermolyne dry bath (from Thermolyne Corp., Dubuque, IA), and the temperature was adjusted to 80 °C. The vial was put in the heating bath for 2 min before the SPME sampling in order to reach a thermal equilibrium. The sampling times was from 1 to 80 min for room temperature headspace SPME and from 1 to 40 min for 80 °C headspace SPME. For the headspace SPME in the 5 mL vial, the aqueous solution was replaced with a fresh one after each measurement. In addition, two sets of aqueous solutions were prepared with the stock solution for the purpose of studying the relationship between the extracted amount n and the initial solution concentration C0 before reaching a partition equilibrium. The concentration range for the first set was from 0.1 to about 10 µg/mL. The second set had a concentration range from 10 to 50 µg/mL. Benzo[b]pyridine (quinoline) was added as the internal standard in both sets but at different concentrations. Quinoline was chosen for its close GC retention in a DB-5 GC column compared with the three chemicals studied here. Based on the measurement of extraction-time profiles, the SPME sampling time was set at 5 min for each one of them. Five minutes was not long enough to reach a partition equilibrium for all the three chemicals. GC/MS was used as the detection device. A HP5890 II GC was interfaced with a Finnigan MAT TSQ700 mass spectrometer. A 30 m × 0.25 mm with 0.25 µm film DB5 column was used as the analysis column. The injection port temperature, which was also the desorption temperature for the SPME fiber, was set at 250 °C, and the desorption time was set at 2 min; the GC split Analytical Chemistry, Vol. 69, No. 16, August 15, 1997
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Figure 1. Extraction-time profiles for three chemicals of headspace SPME over an aqueous solution at room temperature. Vg is about 4 mL, and Vs is 1.0 mL. b, 2-Phenylethanol: C0 ) 10.3 µg/mL and r ) 0.9998. 9, 2,4-dimethylphenol: C0 ) 7.77 µg/mL and r ) 0.9997. 2, Eugenol: C0 ) 11.3 µg/mL and r ) 0.9996. r is the linear correlation coefficient.
valve should open afterward. The GC was programmed to hold at 100 °C for 3 min and then heated to 300 °C at 15 °C/min and hold at 300 °C for 5 min. Helium was used as the carrying gas in GC, and its flow rate was 1.0 mL/min. Full mass scan from 43 to 350 amu was acquired in the electron impact ionization mode (EI ) 70 eV). The ion source temperature was 150 °C, and the manifold temperature was 70 °C. For each of the three chemicals, two ions were selected and integrated. Their integrated intensities were summarized as the SPME extraction intensity. RESULTS AND DISCUSSION In the previous study,21 a two-phase headspace SPME device was used to measure extraction-time profiles for the same three chemicals used in this study. The dynamic process of the twophase system was predicted with an equation in the same form as eq 16 but with different a and n0. Parameter a, which is a measure of how fast a partition equilibrium can be reached, was 0.379 min-1 for 2-phenylethanol, 0.241 min-1 for 2,4-dimethylphenol, and 0.161 min-1 for eugenol. The times needed to reach 90% of the equilibrium value were 6.1 min for 2-phenylethanol, 9.6 min for 2,4-dimethylphenol, and 14.3 min for eugenol. Partition equilibrium was reached in relatively short sampling times for all three chemicals. Although this headspace device provides a way to study the partition of chemicals in the gas/polymer interface without interference from the condensed phase, there are some disadvantages of using this device, such as a relatively low sensitivity and a long equilibrium time between the gas phase of the two flasks. It is not applicable for regular headspace measurements. In a regular headspace SPME, the condensed phase is not isolated from the headspace. Analyte evaporation from the condensed phase to its headspace is part of the SPME extraction process. The extraction-time profiles for room temperature headspace SPME are shown in Figure 1 for the three chemicals in an aqueous solution with relatively high concentrations. The condensed phase (aqueous solution) concentrations were 10.3 µg/ 3264 Analytical Chemistry, Vol. 69, No. 16, August 15, 1997
Figure 2. Extraction-time profiles of headspace SPME over an aqueous solution. (a) 2-Phenylethanol (1.03 µg/mL), (b) 2,4-dimethylphenol (0.78 µg/mL), and (c) eugenol (1.13 µg/mL). b, Room temperature SPME, Vg ) 4 mL and Vs ) 1.0 mL. Solid lines are linear regressions. 9, Room temperature SPME, Vg ) 40 mL and Vs ) 15 mL. Dashed lines are regressions using eq 22. 2, 80 °C SPME, Vg ) 4 mL and Vs ) 1 mL. Dash-dotted lines are regressions using eq 13.
mL for 2-phenylethanol, 7.77 µg/mL for 2,4-dimethylphenol, and 11.3 µg/mL for eugenol. The container was a 5 mL vial. In this situation, Cs was relatively large, while Vs and Vg were relatively small. n is linearly proportional to the sampling time t up to 40 min of sampling time. The linear correlation coefficients (r) are better than 0.999 for all three chemicals. This is the situation described by eq 25. As in the previous study,21 it took less than 15 min to reach 90% of the equilibrium value for all the three chemicals if only the headspace gas phase was involved in the SPME process. The straight lines of the extraction-time profiles in the three-phase system indicate that evaporation of the chemicals from the aqueous phase to its headspace is a very slow process. Another aqueous solution was prepared with the stock solution. The concentrations were 1.03 µg/mL for 2-phenylethanol, 0.78 µg/mL for 2,4-dimethylphenol, and 1.13 µg/mL for eugenol. The aqueous solution was stirred with a magnetic stirring bar during the SPME sampling. The extraction-time profiles of headspace SPME over this solution in the 5 mL vial at room temperature are plotted in Figure 2. Once again, the extraction time profiles for the three chemicals are straight lines with linear correlation coefficients (r) better than 0.99 up to 80 min of sampling. The linear regression are plotted as solid lines in Figure 2.
As is shown in the theoretical treatment, eq 25, which describes the above extraction-time profiles, can be derived from eq 22 when the evaporation rate constant k is very small. If a larger container is used, Vg is larger. A larger Vg usually provides a larger evaporation surface area that leads to a larger k. Then, the extraction-time profile should follow not eq 25 but eq 22. The above aqueous solution was put in a 50 mL Erlenmeyer flask. The surface area of the solution was about 8 times larger and the headspace of the flask after being filled with the solution was 10 times larger than those of the 5 mL vial. The aqueous solution was agitated with a magnetic stirring bar to enhance analyte evaporation. The extraction-time profiles at room temperature for the three chemicals are also plotted in Figure 2. Up to 80 min of sampling, the extraction-time profiles are not straight lines anymore but show the shape that can be described by eq 22 as the dashed lines in Figure 2. Parameter a is 0.042 min for 2-phenylethanol, 0.023 min-1 for 2,4-dimethylphenol, and 0.014 min-1 for eugenol. As is predicted, when k and Vg increase, eq 22 instead of eq 25 is applicable to describe the headspace SPME process. At elevated temperatures, chemicals have much higher evaporation rates. Equation 13, or maybe eq 18, should be used to describe the SPME extraction-time profiles during the headspace sampling at elevated temperatures. The extraction-time profiles of headspace SPME over the same aqueous solution at 80 °C are also plotted in Figure 2. The dash-dotted lines in Figure 2 are the regressions of the data predicted with eq 13. Parameter a is 0.137 min-1 for 2-phenylethanol, 0.129 min-1 for 2,4-dimethylphenol, and 0.100 min-1 for eugenol. Compared to room temperature headspace SPME, it took a much shorter time to reach the partition equilibrium. The times needed to reach 90% of the equilibrium value were 16.8 min for 2-phenylethanol, 17.8 min for 2,4-dimethylphenol, and 23 min for eugenol. It is still slower compared with isolated headspace SPME in the previous study.21 This observation confirms that the evaporation of the three chemicals from the aqueous phase to the headspace at room temperature is the rate-determining step during the headspace SPME. Figure 3 combines the extraction-time profiles of eugenol in the isolated two-phase headspace SPME, the three-phase headspace SPME at room temperature, and the three-phase headspace SPME at 80 °C. The two-phase headspace SPME without the condensed phase involvement is still the fastest one to reach a partition equilibrium. The parameter a is 0.161 min-1 for the isolated headspace SPME, 0.100 min-1 for the three-phase headspace SPME at 80 °C, and 0.014 min-1 for the three-phase headspace SPME at room temperature. At room temperature, the evaporation rate-controlled headspace SPME is much slower than the diffusion in the polymer film-controlled headspace SPME to reach the partition equilibrium. In eqs 13, 18, and 22, there is always a directly proportional relationship between n and C0. This directly proportional relationship meets the key requirement for quantitative analysis of headspace SPME whether a partition equilibrium is reached or not. Once the sampling time is held constant, n is linearly proportional to C0. Straight lines are expected when n is plotted against C0. As is shown in Figure 2, partition equilibrium was not reached for all three chemicals within 15 min of sampling at 80 °C. Five minutes of headspace SPME at 80 °C is far short of the time
Figure 3. Extraction-time profiles of headspace SPME of eugenol. b, SPME at room temperature for a gas/polymer two-phase system. The solid line is the curve regression of the data. 9, SPME at 80 °C for a solution/gas/polymer three-phase system. The dashed line is the regression using eq 13. 2, SPME at room temperature for the solution/gas/polymer three-phase system. The dash-dotted line is the regression using eq 22.
Figure 4. Headspace SPME over aqueous solutions at 80 °C. Extracted amount n is plotted against the initial concentration in aqueous solutions, C0. The sampling time was 5 min, which is shorter than the time required to each a partition equilibrium. b, 2-Phenylethanol (r ) 1.0000); 9, 2,4-dimethylphenol (r ) 1.0000); and 2, eugenol (r ) 0.9998). r is the linear correlation coefficient.
required to reach a partition equilibrium. Headspace SPME was carried out over a series of aqueous solutions with concentrations ranging from 0.103 to 10.3 µg/mL for 2-phenylethanol, from 0.078 to 7.78 µg/mL for 2,4-dimethylphenol, and from 0.104 to 10.4 µg/ mL for eugenol. The amount of extracted chemicals n was measured for each solution with different initial concentrations C0. Figure 4 shows the plots of the data. Straight lines are obtained as predicted. Linear correlation coefficients (r) are better than 0.999 for all three chemicals. The linearly proportional relationship between n and C0 further verifies the theoretical model. Headspace SPME quantification is feasible before reachAnalytical Chemistry, Vol. 69, No. 16, August 15, 1997
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ing a partition equilibrium once the sampling time t is held constant. Room temperature headspace SPME was carried out for another series of more concentrated aqueous solutions with concentrations ranging from 10.3 to 51.7 mg/mL for 2-phenylethanol, from 7.77 to 38.8 mg/mL for 2,4-dimethylphenol, and from 11.3 to 56.6 mg/mL for eugenol. The container was the 5 mL vial, and the sampling time was 5 min. The n vs C0 plots also showed straight lines. The linear correlation coefficients (r) are better than 0.999 for all three chemicals. At the least, this nonequilibrium quantification has a dynamic range of about 3 orders of magnitude. At both room temperature and the elevated temperature, a quantitative relationship between n and C0 is maintained before reaching the partition equilibrium. For chemicals with relatively low volatility, it takes a long time to reach a partition equilibrium during the headspace SPME. Quantitative measurements before reaching the equilibrium will save a lot of experimental time. CONCLUSION Headspace SPME involves three phases that form two interfaces. The mass transfers at these two interfaces can both be
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the rate-determining steps in the dynamic process of SPME. Based on treatments to the mass transfer at the two interfaces, theoretical solutions were derived for the headspace SPME. For 2-phenylethanol, 2,4-dimethylphenol, and eugenol in aqueous solution at room temperature, the rate-determining step was the evaporation of the chemicals from the solution to its headspace. Upon raising the solution temperature, mass transfer at the condensed/gas interface increases very fast. The rate-determining process exists at both the condensed/gas interface and the gas/ polymer interface. An excellent quantitative relationship between n and C0 makes headspace SPME feasible for quantitative analysis before reaching a partition equilibrium.
Received for review January 7, 1997. Accepted May 22, 1997.X AC970024X
X
Abstract published in Advance ACS Abstracts, July 1, 1997.
