Anal. Chem. 1997, 69, 1230-1236
Solid Phase Microextraction for Quantitative Analysis in Nonequilibrium Situations Jiu Ai
US Tobacco Manufacturing Company, Inc., 800 Harrison Street, Nashville, Tennessee 37203
Solid phase microextraction (SPME) is a convenient and efficient extraction method that involves using a thin polymer film coating on a fine silica fiber to adsorb analytes of interests from a sample matrix. A theoretical model is proposed to deal with the dynamic adsorption process of SPME. In this model, mass diffusion from the matrix to the SPME polymer film is considered as the ratedetermining step in reaching an adsorption equilibrium, and a steady-state diffusion is assumed for SPME in an effectively agitated sampling medium. Mathematical treatment of the adsorption process generates an expression that can describe experimental adsorption time profiles of the SPME process. The expression also provides a directly proportional relationship between the amount of analyte adsorbed by the SPME fiber and its initial concentration in the sample matrix. This relationship indicates that SPME quantification is feasible before an adsorption equilibrium is reached, once the agitation condition and the sampling time are held constant. The theoretical model is fitted with experimental data, and there is a very good agreement between them. Data plots of the adsorbed amount vs the initial concentration showed excellent linearity, with a sampling time much shorter than that required for reaching an adsorption equilibrium. Since the beginning of the decade, a new extraction technique called solid phase microextraction (SPME) has been developed by Pawliszyn and co-workers.1,2 This technique has become more and more popular in the analysis of volatile and semivolatile chemicals, as its superiority over conventional extraction methods has been recognized. This technique uses a thin polymer film coating on a fine silica fiber to adsorb chemicals of interest from matrices of analysis such as aqueous solutions or the headspace over condensed phases. After extraction, the polymer-coated silica fiber is put directly into a GC injector, and the chemicals adsorbed on the polymer film are thermally desorbed into the GC column and analyzed. It is an inexpensive, solvent-free, and reliable method that has been applied to both headspace and aqueous sample analysis with excellent sensitivity and good selectivity.2-4 Quantitative analyses of contaminants in groundwater5-8 and (1) Arthur, C. L.; Pawliszyn, J. Anal. Chem. 1990, 62, 2145-2148. (2) Zhang, Z.; Yang, M. J.; Pawliszyn, J. Anal. Chem. 1994, 66, 844A-853A. (3) Arthur, C. L.; Killman, L. M.; Buchholz, K. D.; Pawliszyn, J. Anal. Chem. 1992, 64, 1960-1966. (4) Buchholz, K. D.; Pawliszyn, J. Anal. Chem. 1994, 66, 160-167. (5) Potter, D. W.; Pawliszyn, J. J. Chromatogr. 1992, 65, 247-255. (6) Potter, D. W.; Pawliszyn, J. Environ. Sci. Technol. 1994, 28, 298-305. (7) Wittkamp, B. L.; Tilotta, D. C. Anal. Chem. 1995, 67, 600-605.
1230 Analytical Chemistry, Vol. 69, No. 6, March 15, 1997
flavors in beverages and food9-11 have been accomplished using SPME. An internally cooled SPME technique has been developed by Zhang and Pawliszyn to increase the sensitivity of the analysis.12 In situ derivatization for quantitative fatty acids analysis using SPME has also been addressed by Pan and co-workers.13 To carry out a quantitative analysis, there must be a linearly proportional relationship between the amount of analyte adsorbed by the SPME polymer film and the initial concentration of the analyte in the sample matrix. If n is the number of moles of analyte absorbed by the SPME polymer film and C0 is its initial concentration in the sample matrix, we should have the relation n ∝ C0 for quantitative analysis. During an SPME sampling process, the analyte is partitioned between the polymer phase and the sample matrix phase. If sampling time is long enough, an equilibrium is attained, and the above-mentioned linearly proportional relationship between the adsorbed amount of the SPME polymer film and its initial concentration in the sample matrix is satisfied.1,2 The time needed to reach an adsorption equilibrium during the SPME sampling is dependent on analyte and matrix properties. It ranges from a few minutes to several hours.1,7,8 Once the adsorption equilibrium is reached, the highest sensitivity for an analyte is also attained. If the sensitivity is not the major concern of the analysis, shortening adsorption time becomes the big task. The question is whether it is still feasible to use SPME for quantification and whether there is still a directly proportional relationship between the adsorbed amount and its initial concentration in the sample matrix before an adsorption equilibrium is reached. To seek the relationship between the adsorbed amount and its initial concentration in the matrix in nonequilibrium situations, the dynamic process of the SPME needs to be studied. A theoretical treatment for the dynamic process of SPME was presented by Pawliszyn and co-workers.14,15 Mass diffusion was considered as the rate-determining step that slowed down the process of reaching an adsorption equilibrium. The diffusion equation for the SPME process could not be solved without boundary conditions based on unrealistic assumptions. The analytical solution was obtained only for a perfectly agitated system with an infinite sample volume,14 in which only the diffusion inside the SPME polymer film was considered. For the unagitated (8) Langenfeld, J. J.; Hawthorne, S. B.; Miller, D. J. Anal. Chem. 1996, 68, 144-155. (9) Yang, X.; Pepard, T. J. Agric. Food Chem. 1994, 42, 1925-1930. (10) Coleman, W. M. J. Chromatogr. Sci. 1996, 34, 213-218. (11) Field, J. A.; Nickerson, G.; James, D. D.; Heider, C. J. Agric. Food Chem. 1996, 44, 1768-1772. (12) Zhang, Z.; Pawliszyn, J. Anal. Chem. 1995, 67, 34-43. (13) Pan, L.; Adams, M.; Pawliszyn, J. Anal. Chem. 1995, 67, 4396-4403. (14) Louch, D.; Motlagh, S.; Pawliszyn, J. Anal. Chem. 1992, 64, 1187-1199. (15) Zhang, Z.; Pawliszyn, J. Anal. Chem. 1993, 65, 1843-1852. S0003-2700(96)00954-7 CCC: $14.00
© 1997 American Chemical Society
aqueous solution or the headspace SPME sampling, only numerical solutions were obtained.14,15 Although the theoretical treatment could describe adsorption time profiles of SPME processes, there was no direct analytical expression that connected the amount of analyte adsorbed by the polymer film and its initial concentration in the sample matrix. In this report, a simple dynamic model is presented for the most common SPME case, where the matrix is effectively (not perfectly) agitated to maintain a steady-state diffusion process in the sample matrix. For a steady-state diffusion, the obstacle of solving a diffusion equation (second-order partial differential equation) is avoided. Instead, the analytical solution to the SPME adsorption process is obtained by solving a simple normal differential equation, with diffusion still being the rate-determining step. The analytical solution shows that the adsorbed mass in the SPME polymer film is directly proportional to the initial concentration of the analyte in the sample matrix. It answers the question of feasibility for quantitative analysis in the situation where adsorption equilibrium is not achieved. The model can also describe adsorption time profiles of SPME in both the condensed matrix and the headspace. Experiments were carried out to test the theory. Results are in very good agreement with the theoretical model. THEORETICAL TREATMENT Equilibrium Attained between the SPME Polymer Film and the Sample Matrix Phase. The ideal way to carry out a quantitative analysis applying SPME is to completely transfer an analyte from the sample matrix to the adsorbing polymer film. This is the case of exhaustive extraction and is highly unlikely to occur. In general, what we are seeking is a linearly proportional relationship between the amount of the adsorbed analyte and its initial concentration in the sample matrix. That is, n ∝ C0. When an adsorption equilibrium is reached, the following equation should be valid:
K)
Cf (n/Vf) ) Cs C0 - (n/Vs)
(1)
Here, K is the equilibrium constant, Cf is the concentration of the analyte in the SPME polymer film, Cs is the concentration of the analyte in the sample matrix, n is the amount of the analyte adsorbed by the SPME polymer film in moles, Vf is the volume of the SPME polymer film, C0 is the initial concentration of the analyte in the sample matrix before SPME sampling, and Vs is the volume of the sample matrix. Solving eq 1 for n,
n)
KVfVs C Vs + KVf 0
(2)
The adsorbed amount n is linearly proportional to the initial concentration C0 in eq 2. If the analyte has a very high affinity for the SPME polymer phase, that means K is very large and KVf . Vs, and eq 2 becomes
n ≈ VsC0
This is the situation for exhaustive extraction.
(3)
In both eqs 2 and 3, a directly proportional relationship exists between the adsorbed amount n and the initial concentration in the sample matrix C0. This relation provides the foundation for the quantitative analysis of the SPME technique as described in the literature.1,2 These two equations were cited in almost all reports in the literature dealing with the SPME technique. Nonequilibrium between the Polymer Film and the Sample Matrix. SPME sampling may not reach an adsorption equilibrium when a shorter sampling time is applied. In this case, eq 2 is not valid. The approach to deal with the dynamic process of SPME is presented in this section. Mass diffusion from the sample matrix to the SPME polymer film and from the surface of the polymer film to its inner layers is considered as the ratedetermining step that slows down the process of reaching an equilibrium.14 If diffusion is the rate-controlling factor, Fick’s first law of diffusion can be expressed as follows for a continuous-flow system at the sample matrix/SPME polymer interface region:
F ) -D1
dCs dCf ) -D2 dx dx
(4)
Here, F is the mass flow rate of the analyte from the sample matrix to the SPME polymer surface, which should be equal to the flow rate from the polymer surface to its inner layers for a balanced mass transfer, D1 is the diffusion coefficient of the analyte in the sample matrix phase, D2 is the diffusion coefficient of the analyte in the polymer phase, and Cs and Cf are concentrations of the analyte in sample matrix and polymer film, respectively. F must be proportional to the SPME adsorption rate of the analyte and can be expressed in the following way:
or
F∝
dn dt
(5)
F)
1 dn A dt
(6)
Equation 4 becomes
∂Cs ∂Cf 1 ∂n ) -D1 ) -D2 A ∂t ∂x ∂x
(7)
where A is the surface area of the SPME polymer film. Here, an assumption is made that a steady-state mass transfer can be established when agitation is applied effectively in the sample matrix (aqueous phase in most cases). In the situation of steady-state diffusion, the diffusion layer can be assumed to be constant. Since the SPME polymer coating is a thin film, the diffusion layer is the film thickness, and a steady-state diffusion is in effect in this phase. Thus, the partial differential equation (eq 7) can be simplified to a normal differential equation:
D2 1 dn D1 ) (C - Cs′) ) (C - Cf′) A dt δ1 s δ2 f
(8)
Here, Cs is the analyte concentration in the bulk of the sample matrix, Cs′ is the surface concentration of the analyte in the sample matrix, δ1 is the diffusion layer thickness in the sample matrix (assumed to be a constant), δ2 is the thickness of the polymer Analytical Chemistry, Vol. 69, No. 6, March 15, 1997
1231
we have
n ) Vf
Cf + Cf′ 2
(13)
Solving eqs 12 and 13 for Cf and Cf′, we have
Cf - Cf′ )
2m1K 2m1KVf + 2m1Vs C n m1 + 2m2K 0 m1VsVf + 2m2KVsVf
(14)
Putting expression 14 back in to eq 8, we have
Figure 1. Interface of polymer-coated silica fiber in contact with an aqueous solution. A steady-state diffusion is assumed when the aqueous solution is effectively agitated. The concentration gradient in the SPME polymer film is assumed to be linear.
film, Cf is the analyte concentration in the polymer film at the surface with the sample matrix, and Cf′ is the analyte concentration in the polymer film in contact with the silica fiber. Figure 1 shows the interface area of the aqueous phase with SPME polymercoated silica fiber and the concentration assignments. At the interface of the polymer film and the sample matrix, it is supposed that a partition equilibrium can be quickly reached for the analyte between the sample matrix and the SPME polymer layer. So, we have
K)
Cf Cs′
(9)
Cf K
(10)
then
Cs′ )
1 dn ) m2(Cf - Cf′) A dt 2m1KVf + 2m1Vs 2m1K C n ) m2 m1 + 2m2K 0 m1VsVf + 2m2KVsVf
(
[
(
n ) 1 - exp -A
)]
2m1m2KVf + 2m1m2Vs m1VsVf + 2m2KVsVf
Equation 16 is the solution to eq 7 with the assumption of a steadystate diffusion in both the sample matrix and the SPME polymer film. It expresses a relation between the amount of analyte adsorbed in the SPME polymer film n and the initial concentration of the analyte in the sample matrix C0 as a function of adsorption time t. In eq 16, the amount of analyte adsorbed in the SPME polymer film, n, is directly proportional to the initial concentration of the analyte in the sample matrix, C0, if the adsorption time, t, is held constant for each sampling. When adsorption time goes to infinity, the exponential term vanishes, and eq 16 becomes eq 2, which means the adsorption equilibrium is reached. Let n0 be the amount of the analyte adsorbed by SPME polymer film at equilibrium. Equation 2 is then written as follows:
(
)
Cr n ) m2 (Cf - Cf′) Vs K
(12)
In the polymer film, a steady-state diffusion is achieved because of a thin and constant diffusion distance. An approximation can be made that a linear concentration gradient of the analyte exists in the polymer film. Then, the average concentration of the analyte in the polymer film is approximately (Cf + Cf′)/2. Then 1232
Analytical Chemistry, Vol. 69, No. 6, March 15, 1997
KVfVs C KVf + Vs 0
(17)
m1m2KVf + m1m2Vs m1VsVf + 2m2KVsVf
(18)
n0 )
Let
m 1 C0 -
KVfVs C KVf + Vs 0 (16)
(11)
Let m1 ) D1/δ1 and m2 ) D2/δ2. m1 and m2 are mass transfer coefficients in the sample matrix and in the SPME polymer, respectively. For a steady-state diffusion process, these two parameters are considered as constant for an effectively agitated matrix. Thus, eq 8 can be rewritten as
(15)
Equation 15 can be solved with the following initial condition (when t ) 0, n ) 0):
and, in the bulk of the sample matrix,
n Cs ) C0 Vs
)
a ) 2A
Equation 16 becomes
or
n ) n0 [1 - exp(-at)]
(19)
n ) 1 - exp(-at) n0
(20)
The parameter a defined in eq 18 is a measure of how fast an adsorption equilibrium can be reached in the SPME process. It is determined by mass transfer coefficients, equilibrium constant, and physical dimensions of the sample matrix and the SPME polymer film. For a constantly agitated system, a is a constant.
The directly proportional relationship between n and C0, which is required for quantitative analysis, is established in the mathematical treatment of the SPME dynamic process. Thus, eq 16 or its simplified version (eq 19) provides the theoretical basis for quantitative analysis using SPME in nonequilibrium cases. The next step is to verify this nonequilibrium model with experimental data. EXPERIMENTAL SECTION The 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. The volume of the polymer film was approximately 5 × 10-5 cm3, and its surface area was about 0.06 cm2. Three chemicals were used in the experiment: 2-phenylethanol, 2-methoxy-4-(2-propenyl)phenol (eugenol), and 2,4-dimethylphenol. 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 these three chemicals was prepared with methanol as the solvent. For the experiments to study adsorption time profiles in the aqueous phase, a small amount of the stock solution was added to distilled water mixed with 10% saturated NaCl solution. Concentrations of the chemicals in the aqueous solution were 0.620 µg/mL for 2-phenylethanol, 0.466 µg/mL for 2,4-dimethylphenol, and 0.679 µg/mL for eugenol. The polyacrylate fiber was inserted directly into the aqueous solution in a 5 mL vial. Either the vial was put in an ultrasonic bath (Model 2210 from Branson, Danbury, CT) for agitation, or the aqueous solution was agitated with a magnetic stirring bar. One milliliter of the solution was put in the vial when it was agitated with ultrasound. Three milliliters of the solution was put in the vial when it was agitated with the magnetic stirring bar. The spinning rate was set at the medium level. The adsorption times was 1, 2, 5, 10, 20, 40, 80, and 160 min. After each sampling, the aqueous solution was replaced with fresh one. All SPME samplings were carried out at room temperature. For headspace studies, a static headspace device was set up that could isolate the headspace from the aqueous solution. Figure 2 shows the headspace sampling device. The aqueous solution was put in the bottom flask. The three chemicals in the solution distributed to the headspace of the bottom flask and to the top flask through a valve connection. After a certain period of time (more than 15 min), an equilibrium was reached between the headspace of the bottom flask and the top flask. The valve connecting the two flasks was then closed. The SPME polymer fiber was inserted into the top flask for sampling. In this case, chemicals in the top flask gas phase could be adsorbed. The effect of further evaporation of chemicals from the aqueous matrix to the headspace could be neglected. Thus, the sampling was purely between the headspace gas phase and the SPME polymer film. The aqueous solution used for headspace studies was prepared with the same stock solution but 5 times more concentrated than the solution for aqueous phase direct sampling. Ten milliliters of the solution was put in the bottom flask and stirred with a stirring bar. The volume of the top flask, which was the sample matrix volume, was about 14 mL. Five aqueous solutions were also prepared from the stock solution for studying the relation between the adsorbed amount and the initial solution concentration before an adsorption equi-
Figure 2. Device for SPME of headspace sampling. The bottom flask can be isolated from the top flask, and the gas phase in the top flask is involved in the adsorption during the SPME sampling.
librium was reached. The concentrations ranged from 0.2 to about 6 µg/mL. In order to overcome possible fluctuations of SPME and the GC/MS detection, benzo[b]pyridine (quinoline) was used as the internal standard in this case. It was chosen for its close retention in a DB-5-GC column compared with the three chemicals used in this study. A stock solution of quinoline was prepared with dichloromethane as the solvent, and its concentration was 2.0 mg/mL. It was added to the five aqueous solutions to a concentration of 1.0 µg/mL. The SPME sampling time was 10 min for each one of them, agitated with either ultrasonic vibration or magnetic bar stirring. GC/MS was used as the detection device. An HP5890 II GC was interfaced with a Finnigan MAT TSQ700 mass spectrometer. A 30 m × 0.25 mm with 0.25 µm film DB-5 column (J&W Scientific, Folsom, CA) was used as the analysis column. The injection port temperature, which was also the desorption temperature for SPME fiber, was set at 250 °C, and the desorption time was 2 min. The GC split valve was set to open after 2 min of insertion. The GC was programmed to hold at 100 °C for 3 min, then heated to 300 °C at a heating rate of 15 °C/min, and held at 300 °C for 5 min. Full mass scan from 20 to 400 amu was acquired in the electron impact ionization mode. For each of the three chemicals, two ions were selected and integrated. The integrated intensities of the two ions were summarized for the SPME adsorption time profile plots. RESULTS AND DISCUSSION At first, ultrasonic vibration was used for agitation in the SPME experiments. One problem with the ultrasonic vibration was that there was a significant temperature increase after a certain time of sampling. The elevated temperature may affect the adsorptivity of the polymer film. Generally speaking, higher temperature would reduce the adsorptivity of the polymer film in aqueous solutions. Subsequently, a magnetic stirring bar was used for all the agitation. Almost all the published reports dealing with SPME provided some kind of adsorption time profiles for the analytes being Analytical Chemistry, Vol. 69, No. 6, March 15, 1997
1233
Table 1. Parameter a Obtained from the Regression Using Eq 20a
a ) 2A
m1m2KVf + m1m2Vs (min-1) m1VfVs + 2m2KVfVs
compound
concn (µg/mL)
aqueous solution, ultrasonic agitation
aqueous solution, bar agitation
headspace over aqueous solution
2-phenylethanol dimethylphenol eugenol
0.620 0.466 0.679
0.0580 0.0212 0.0204
0.0365 0.0270 0.0280
0.379 0.241 0.161
a The concentration of the aqueous solution for headspace sampling was 5 times higher than that of the aqueous solution for direct SPME sampling.
studied. In Pawliszyn’s study, numerical solution to the diffusion equation gave a theoretical simulation to the adsorption time profiles.14,15 There was no analytical expression given that directly related the adsorbed amount n to adsorption time t. All experimentally obtained adsorption time profiles either in the literature1,7,8,10,11 or in this study have the characteristics which can be described by eq 16, which is an analytical expression relating n and t. In this study, the measured intensities at different adsorption times were first fitted with eq 19, which is a simplified form of eq 16. Since the mass spectrometer does not provide the absolute value of the analyte, a parameter proportional to the equilibrium adsorption n0 was obtained from the regression. Measured intensities were then divided by this parameter. The ratios should be the real n/n0 as described in eq 20. The ratios vs adsorption time were then plotted and fitted with eq 20. The parameter a was obtained from the regression. Figure 3 shows the adsorption time profiles for three chemicals in an aqueous solution agitated by either ultrasonic vibration or magnetic bar stirring. The lines are the regressions using eq 20. The parameter a obtained from the regression is a measure of how fast the adsorption equilibrium can be achieved. It is listed in Table 1 and is in units of min-1. For 2-phenylethanol (Figure 1a), a is larger for the aqueous solution agitated with ultrasound than for the solution agitated with a magnetic stirring bar set at a medium stirring speed. This means that ultrasonic vibration is more effective in helping mass transfer for 2-phenylethanol. For 2,4-dimethylphenol and eugenol, magnetic bar stirring is a little more effective in helping mass transfer (Figure 1b,c). None of the three chemicals reached an adsorption equilibrium within 1 h of sampling. As indicated in the theoretical treatment section, eq 16 provides a linearly proportional relationship between n and C0 in nonequilibrium situations. If the adsorption time and agitation conditions are held constant through the experiment, it is not necessary to reach an adsorption equilibrium for quantitative analysis. Arthur and Pawliszyn obtained linear SPME adsorption responses as functions of aqueous solution concentrations while the sampling time was set at 2 min, which was not long enough to reach an adsorption equilibrium.1 In this study, similar experiments were carried out with the three chemicals mentioned above. Figure 4 shows the plots of the adsorbed amount vs initial concentrations of chemicals in the aqueous solution agitated by the ultrasonic vibration. The adsorbed amount is the relative intensity of the mass spectrometric response of the analyte against that of the internal standard, quinoline. Adsorption time was 10 min, which was much shorter than the time required to reach an 1234 Analytical Chemistry, Vol. 69, No. 6, March 15, 1997
Figure 3. SPME adsorption time profiles of three chemicals in an aqueous solution. b, Agitated with a stirring bar; 9, agitated with ultrasonic vibration. Both solid and dashed lines are regressions using eq 20.
adsorption equilibrium. For all three chemicals, linear regression lines were obtained with excellent linearity. The coefficients of determination (r2) are better than 0.99 in the concentration range from about 0.2 to 6 µg/mL. For the stirring bar agitated system, similar data were obtained. Figure 5 shows the plots of adsorbed amount vs initial concentration of chemicals in aqueous solution agitated by a magnetic stirring bar. Excellent linearity was also observed for the linear regressions of the data. The coefficients of determination (r2) are better than 0.99 for all three chemicals. The results presented in Figures 4 and 5 prove that the adsorbed amount n is linearly proportional to its initial concentra-
Figure 4. Linear regressions of adsorbed amount vs initial concentration of three chemicals in aqueous solutions agitated with the ultrasonic vibration. Adsorption time was set at 10 min. b, 2-Phenylethanol (r2 ) 0.9999); 9, 2,4-dimethylphenol (r2 ) 0.9966); 2, eugenol (r2 ) 0.9952). r2 is the coefficient of determination. The points were averages from two sets of data, and error bars were the range of the data.
Figure 5. Linear regressions of adsorbed amount vs initial concentration of three chemicals in aqueous solutions agitated with a magnetic stirring bar set at a medium stirring rate. Adsorption time was set at 10 min. b, 2-Phenylethanol (r2 ) 0.9997); 9, 2,4dimethylphenol (r2 ) 0.9991); 2, eugenol (r2 ) 0.9992). r2 is the coefficient of determination.
tion in the sample matrix C0, as described by eq 16. Once the agitation conditions and adsorption time are held constant, the SPME quantification is feasible before an adsorption equilibrium is reached. In headspace sampling, a much faster mass transfer than that observed in aqueous solution is expected. Although no agitation is used in the headspace sampling, the convection in the gas phase
Figure 6. SPME adsorption time profiles of three chemicals in the headspace above an aqueous solution. b, 2-Phenylethanol; 9, 2,4dimethylphenol; 2, eugenol. The lines are regressions using eq 20.
is considered good enough to maintain a steady-state diffusion at the SPME polymer surface. In general, the headspace SPME adsorption process actually involves three phases: the aqueous phase, its headspace, and the SPME polymer film. The threephase system made the mathematical treatment complicated.15 To obtain a two-phase system, the device described in Figure 2 was used. Before the SPME sampling, an equilibrium should be attained between the headspace of the bottom flask and the top flask. Then the connection between these two flasks was closed. The SPME polymer fiber was exposed only to the gas phase of the top flask. During the SPME adsorption, the aqueous solution in the bottom flask was not involved in the sampling process. The adsorption time profiles for the three chemicals in the headspace are shown in Figure 6. The lines are the regressions using eq 20. The parameter a for those chemicals is also listed in Table 1. This parameter is about an order of magnitude higher in gas phase/SPME polymer adsorption than in aqueous phase/ SPME polymer adsorption agitated with a stirring bar. a is a complex parameter, as is shown in eq 18. The ratio of the parameter a from gas phase/polymer adsorption, ag, to that from aqueous phase/polymer adsorption, al, can be expressed as follows:
(
)(
)( )( )
KgVf + Vgs m1l + 2m2Kl mg1 Vls ag ) al KlVf + Vls mg1 + 2m2Kg ml1 Vgs
(21)
Here, superscripts l and g indicate the aqueous phase and gas phase, respectively. Since Vf is on the order of 10-5 cm3, a very small value, the first term and the last term in parentheses in the above expression are canceled by approximation. The above expression becomes Analytical Chemistry, Vol. 69, No. 6, March 15, 1997
1235
()
1 + 2m2Kl/ml1 mg1 ag ≈ ≈ al m1g/m1l + 2m2Kg/m1l m1l 2m2Kl/m11
( ) m1g
m1g/m1l + 2m2Kg/m1l m1l
(22)
There is no literature report about the value of K for the chemicals used in this study. We will assume that Kl is about 1000. m1g/ m11 is assumed to be close to the ratio of the diffusion coefficient in the gas phase against that in the aqueous phase. This ratio is in the range of 10 000.16 The ratio m2/m1l is about 1/10, and Kg . Kl; then, g 1 m1 ag < ≈ 10-100 al 100 ml1
(23)
The experimental results (∼10) fall in the range of this estimation.
CONCLUSION The experimental data of SPME adsorbed quantity vs sampling time can be predicted by eq 16, which is derived from a simple adsorption model of SPME based on a diffusion-controlled mass transfer process. This dynamic model indicates that a linearly proportional relationship exists between the adsorbed analyte and its initial concentration in the sample matrix. Experimental data proved this point by showing an excellent linear relationship between the amount of the adsorbed analyte and its initial concentration in the sample matrix before an adsorption equilibrium was attained. This study verifies that SPME quantitative analysis is feasible in nonequilibrium situations once the agitation conditions and adsorption time are held constant. A much shorter sampling time can be used for quantitative analysis if the sensitivity is not the major concern. Received for review September 18, 1996. December 12, 1996.X
Accepted
AC9609541 (16) Savage, P. E.; Gopalan, S.; Mizan, T. I.; Martino, C. J.; Brock, E. E. AIChE J. 1995, 41, 1723-1778.
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Analytical Chemistry, Vol. 69, No. 6, March 15, 1997
X
Abstract published in Advance ACS Abstracts, January 15, 1997.
