Anal. Chem. 2005, 77, 3053-3059
Automated Multiple Headspace Extraction Procedure: Adsorption Modeling and Determination of Air-to-Water Partition Coefficients A. Brachet, J.-Y. de Saint Laumer, and A. Chaintreau*
Corporate R&D Division, Firmenich SA, 1 Route des Jeunes, 1211 Geneva 8, Switzerland
The present work makes the first attempt to take into account adsorptions in the determination of partition coefficients by modeling the multiple headspace extraction (MHE) process. Modeling a six-step MHE procedure of a homologous series of methyl ketones revealed that their adsorption-desorption on the walls was the rate-limiting step. Moreover, a comparison between experimental and predicted MHE plots shows that only the last MHE points were affected by adsorption phenomena. Using cell materials with the lowest sorptive properties, partition coefficients were then accurately calculated from the first four MHE steps. This kinetic approach supports previous work in which adsorptions were lowered owing to the choice of sampling cell materials. It also justifies some reproducibility limitations of the MHE quantification procedure mentioned in the literature. In a previous work,1 the multiple headspace extraction (MHE) was demonstrated to be a reliable method for the rapid measurement of air-to-water partition coefficients. However, for the most hydrophobic methyl ketones, the determination was influenced by adsorptions on cell materials. Viton O-ring and glass material (even after silanization) significantly adsorbed the most hydrophobic methyl ketones resulting in biased air-to-water partition coefficient values. Adsorptions of nonpolar compounds on glassware and Teflon were previously highlighted by other authors.2-5 Despite their observations, all these materials were still used by many authors for quantification or partition coefficient determination without any correction. Thus, published air-to-water partition coefficients of hydrophobic compounds might be noticeably affected. Two approaches could be considered to overcome biases due to adsorptions: either minimizing them owing to the use of lowadsorbing materials or developing a theoretical model to better approach the theoretical value. In our previous work,1 multiple headspace extractions were performed with a headspace sampling * To whom correspondence should be addressed. E-mail:
[email protected]. (1) Brachet, A.; Chaintreau, A. Anal. Chem. 2005, 77, 3045-3052 (ac0401220). (2) Ackerman, A. H.; Hurtubise, R. J. Talanta 2000, 52, 853-61. (3) Baltussen, E.; Sandra, P.; David, F.; Janssen, H.-G.; Cramers, C. Anal. Chem. 1999, 71, 5213-6. (4) Buttery, R.; Ling, L. C.; Guadagni, D. G. J. Agric. Food Chem. 1969, 17, 385-9. (5) Vaes, W. H. J.; Mayer, P.; Oomen, A. G.; Hermens, J. L. M.; Tolls, J. Anal. Chem. 2000, 72, 639-41. 10.1021/ac040123s CCC: $30.25 Published on Web 04/12/2005
© 2005 American Chemical Society
cell built with constituents exhibiting the lowest sorptive properties (i.e., stainless steel and Teflon). The adsorption of nonpolar volatiles was then dramatically reduced but not fully overcome. As zero-adsorption materials presumably do not exist, theoretical modeling needs to be considered. Theoretical modeling is often used to predict partition coefficients. However, most of the modeling procedures involve a knowledge of physicochemical data, such as saturated vapor pressures, activity coefficients, or solubilities in water.6-8 Moreover, few of them are available in the literature and their measurements are themselves prone to adsorption phenomena. For example, Espinosa Diaz clearly reported the literature discrepancy concerning predicted vapor pressures9 and the partition coefficient values calculated from them. Therefore, modeling from experimental or predicted physicochemical data does not allow an accurate determination of partition coefficients. Inferring partition coefficients directly from the structure of the compound (bond contribution) was recently demonstrated to be the most appropriate model.10 However, this method was only applicable for the prediction of partition coefficients in water at 25 °C. Up to now, no available model is fully satisfactory to predict partition coefficients for a wide range of compounds at any temperature. In contrast to these previous modeling studies, the present work intends to model the MHE procedure itself, to better understand the influence of adsorption on the determination of partition coefficients. To our knowledge, this is the first attempt to take adsorptions into account using only experimental results, without any additional physicochemical data. Moreover, the present model is designed to validate our previous assumption;1 i.e., partition coefficients may be calculated from the first four MHE points when using a cell made of the least sorptive materials. A series of homologous methyl ketones was used as a test mixture with a special emphasis on 2-nonanone because of its significant adsorption on many materials. EXPERIMENTAL SECTION Chemical Products. Methyl ketones from C4 to C9, were purchased from Fluka (Buchs, Switzerland) and Acros (Geel, (6) Amoore, J. E.; Buttery, R. G. Chem. Senses Flavour 1978, 3, 57-71. (7) Fredenslund, A.; Jones, R. L.; Prausnitz, J. M. AIChE J. 1975, 21, 1086. (8) Pierotti, G. J.; Deal, C. H.; Derr, E. L. Ind. Eng. Chem. 1959, 51, 95-105. (9) Espinosa Diaz, M. A.; Guetachew, T.; Landy, P.; Jose, J.; Voilley, A. Fluid Phase Equilib. 1999, 157, 257-70. (10) Voutsas, E. C.; Andreou, C. I.; Theodorou, D. G.; Tassios, D. P. J. Food Sci. 2001, 66, 447-52.
Analytical Chemistry, Vol. 77, No. 10, May 15, 2005 3053
Belgium). Sylon CT (5% dimethylchlorosilane in toluene) was supplied by Supelco (Bellefonte, PA). All solvents were of analytical grade. Methanol and toluene were obtained from Carlo Erba Reagenti (Rodano, Italy). Deionized water was provided by Seradest (Basel, Switzerland). MHE Procedure. The air sampling was achieved according to the static and trapped headspace technique previously described,11 and recently automated.1 MHE procedures were entirely described in the previous work.1 All methyl ketone solutions were prepared at 8 mg/L. For all MHE experiments, 1 mL of the sample solution was equilibrated for exactly 1 h at 25 °C, while stirring the sample with a magnetic bar. Materials. Tenax (35-60 mesh) was supplied by P. H. Stehelin & Cie AG (Basel, Switzerland). The sampling cell was a 5 cm × 15 cm Pyrex tube (Omnifit, Cambridge, U.K.) or was made in stainless steel. Glass receptors and glass stir bars were made inhouse. All glass pieces were silanized before use with Sylon CT to lessen adsorptions. All the cartridges were conditioned under a nitrogen stream at 250 °C for 12 h before use. Instrument Conditions. Traps were desorbed using a thermal desorber coupled on line with a GC-FID, as described elsewhere.1 Curve Fitting. The equation of the MHE plot was determined by linear regression of the data points using Excel software (Microsoft, Redmond, WA). Coefficients Ai, Bi, and Ci of the model were optimized by means of the Excel solver program. THEORY The present work is designed to derive and then use a theoretical kinetic model, taking into account the adsorptiondesorption kinetics. All symbols used are listed in the Glossary. Kinetic Evidence of Adsorption. Although our previous work has demonstrated that a Viton O-ring and even silanized glass materials adsorbed significantly the most hydrophobic methyl ketones,1 such materials were still used in some measurements to reveal their influence on partition coefficient values. For instance, using a sampling cell made of Pyrex, with a glass receptor, a glass stir bar, and Viton O-ring, one headspace extraction was performed after different equilibration times (1, 15, 60, 360, and 480 min). As illustrated in Figure 1, a maximum concentration in the headspace was observed after 60 min for the most hydrophobic analytes, and then a decrease occurred (Figure 1, and Supporting Information, Figure 1-a). These kinetic plots suggest that a quick release of solutes occurred from the liquid to the headspace (k′1) and then a slow adsorption (k′2) of nonpolar compounds from the headspace to the walls (Clk′1 . Cg k′2). This also suggests that liquid-to-gas and gas-to-wall rate constants were different and that adsorption-desorption of analytes adsorbed on the walls was the rate-limiting step. To ascertain that volatiles were readily adsorbed onto cell materials, volatiles released from the empty cell walls were monitored. A single headspace extraction of the methyl ketone mixture was carried out, and the sampling cell was quickly dismantled to remove the glass receptor containing the sample and the stir bar. They were replaced with new ones and 1 mL of pure water, and the cell was immediately remounted and closed to achieve a four- or five-step MHE. The percentage of the total amount of each solute released from the inner surface of the cell (11) Chaintreau, A.; Grade, A.; Mun ˜oz-Box, R. Anal. Chem. 1995, 67, 3300-4.
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Figure 1. Extracted amount of methyl ketones (C4-C9) obtained after one headspace extraction (GC area units) using a Pyrex cell equipped with Viton O-ring for different equilibration times (1, 15, 60, 360, and 480 min).
was then determined after each equilibration step (typically 1 h) of the MHE. This experiment was repeated using three different sampling cells: the one made of Pyrex and a Viton O-ring (Figure 2a), another made of Pyrex and Teflon O-rings (Figure 2b), and the last made of stainless steel and Teflon O-rings (Figure 2c). Using the Pyrex cell equipped with a Viton O-ring, methyl ketones were highly adsorbed whatever the analyte polarity (Figure 2a). However, more hydrophobic compounds were much more retained on glass walls or O-ring (∼25% of 2-nonanone) than polar ones ( 0 and q > 0, respectively. According to eq 39, β1 < 0 and according to eq 42, β2 < 0 since (p2 - q2) > 0. From eqs 39 and 40, β2 - β1 ) q, and then β2 > β1. As for an infinite equilibration time, the amounts of solute reach their equilibrium values, the limiting conditions were as follows
A3 + B3 + C3 ) ml,0 + mg,0 + ms,0
(43)
since β1 < 0 and β2 < 0 with ml,0, mg,0, and ms,0, the initial solute masses at t ) 0. The combined eqs 36 and 30 with eq 43 give
B3
(
)
k2 k-1 +1+ ) ml,0 + mg,0 + ms,0 k1 k-2
(44)
thus B3 depends on rate constants of both equilibria and on the initial concentration of the solute in the liquid, gas and “wall” phases
k1k-2 B3 ) (ml,0 + mg,0 + ms,0) (45) k-1k-2 + k1k-2 + k1k2 Adding eqs 31 and 32 gives
k1(A1 + A2) + k-2(C1 + C2) ) (k-1 + k2)(B1 + B2) + (β2B2 + β1B1) (46) Initial conditions (at t ) 0) give
A1 + A2 + A3 ) ml,0
(47)
B1 + B2 + B3 ) mg,0
(48)
C1 + C2 + C3 ) ms,0
(49)
Therefore, eq 46 becomes
k1(ml,0 - A3) + k-2(ms,0 - C3) ) (k-1 + k2)(mg,0 - B3) + β2(mg,0 - B3 - B1) + β1B1 (50) thus
B1(β1 - β2) ) - k1A3 - k-2C3 + k2B3 + k-1B3 + B3β2 + k1ml,0 + k-2ms,0 - (β2 + k-1 + k2)mg,0 (51) Equations 51 and 48 can be simplified using eq 24 to express B1
Table 1. Optimized Coefficients for 2-Nonanone after Running the Model Pyrex cell
K1 k1 K2 k2
stainless steel cell
Viton O-ring
Teflon O-ring
Teflon O-ring
2.200 1000 0.532 0.0058
2.306 1000 0.028 0.0004
2.405 1000 0.027 0.0005
and B2 as
B1 ) B2 )
B3β2 + k1ml,0 + k-2ms,0 - (β2 + k-1 + k2)mg,0 (β1 - β2) B3β1 + k1ml,0 + k-2ms,0 - (β1 + k-1 + k2)mg,0 (β2 - β1)
(52)
(53)
RESULTS AND DISCUSSION From the previous equations, K1, k1, K2, and k2 can be optimized to fit experimental data. Masses mg, ml, and ms were first calculated for each MHE step according to the eqs 10-12, respectively. Equilibration time was fixed at 60 min and coefficients A1, A2, A3, B1, B2, B3, C1, C2, C3, β1, and β2 were calculated according to the eqs 28-30, 56, 57, 45, 34-36, 39, and 40, respectively. These latter coefficients were calculated from initial arbitrary values of K1, k1, K2, k2, and ml,0 defined as the initial liquid mass of 2-nonanone expressed as GC peak area. Masses mg, ml, and ms were calculated for both experiments, i.e., MHE with aqueous solution of 2-nonanone and MHE with pure water. Second, all these calculated masses were optimized by changing the coefficients values of K2, k2, K1, k1, and ml,0. Optimization was performed until the lowest residues (defined as the difference between natural logarithms of experimental and predicted areas) were obtained. For example, when using a stainless steel cell, residual error values (except one) were contained within the range of ( 2 SDexp (the experimental standard deviation SDexp of the natural logarithm of the area was calculated from four replications of a one-step MHE procedure). Therefore, experimental values were sufficiently explained by the model, thus allowing the use of predicted MHE plots. Only results for 2-nonanone, i.e., the most adsorbed compound, are presented hereafter. The optimization procedure was performed for the three different sampling cell versions (Pyrex cell with Viton O-ring, and Pyrex or stainless steel cell with Teflon O-ring), and final optimized values of coefficients provided by the theoretical model were reported in Table 1 (see also the Supporting Information, Table 2-a-c). Whatever their initial values, the optimization procedure led to very similar final values of K2, k2, K1, k1, and ml,0. The initial value of k1 ) 1000 remained unchanged after optimization of the model as reaching the air/solution equilibrium was almost instantaneous in comparison with the air/wall equilibrium. In other terms, whatever the accuracy of k1, if it is high, its value does not influence the determination of k2 and k-2. From the model prediction, kinetic plots of mass ratios could be drawn for the most affected sampling system (i.e., Pyrex cell with Viton O-ring). The gas-liquid equilibrium was faster than Analytical Chemistry, Vol. 77, No. 10, May 15, 2005
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Figure 3. Predicted release of 2-nonanone (a) during entire MHE procedure and (b) removed after one step (experiments using Pyrex cell equipped with Viton O-ring). mg/ml, ms/mg, and ms/ml are the ratios of 2-nonanone in the gas phase to that in the liquid phase, on the wall surface to that of the gas phase, and of the wall surface to that in the gas phase, respectively.
Figure 4. Modeling MHE procedure of 2-nonanone when using (a) a Pyrex cell equipped with Viton O-ring, (b) a Pyrex cell equipped with Teflon O-ring, and (c) a stainless steel cell equipped with Teflon O-ring.
the wall-gas equilibrium (Figure 3a), and the desorption of 2nonanone from the cell walls was slow (Figure 3b). Both observations confirm the initial assumption that rates of adsorption and desorption between the headspace and cell walls were different. Figure 4 shows the correlation between predicted and experimental MHE procedures for the three sampling systems. Whatever the sampling system used, calculated values agreed fairly well with experimental values. Moreover, the model fitted well with experimental values of the MHE with pure water (data not presented). Influence of Adsorption on MHE Curve. Because of the satisfactory agreement between experimental and predicted MHE values, prediction of the MHE curve becomes feasible. Choosing a very low K2 value suggests a much slower adsorption of 2nonanone on the walls than its desorption, corresponding to a negligible adsorption. For the three cell versions, the resulting MHE profile and the one obtained experimentally were compared (Figure 4). If adsorption was reversible/fast or negligible, a 3058
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straight line should be obtained whatever the composition of the cell material. Thus, this straight line obtained when minimizing K2, while other coefficients were kept fixed at their optimal values, confirms the previous assumption (see Kinetic Evidence of Adsorption). Moreover, deviation observed between the experimental and the predicted values occurred only for the last MHE points. The more adsorption phenomena occurred, the more important was the deviation, and low polar compounds were less deviated from linearity (data not shown). With a cell made of Pyrex and Viton O-ring, only the first two MHE points fitted approximately the prediction based on a reversible/fast adsorption hypothesis (Figure 4a), while using a Teflon O-ring up to four MHE points remained unaffected by the adsorption reversibility rate (Figure 4b and c). Therefore, the assumption made in the previous work was now demonstrated;1 i.e., a four-step MHE procedure, using a cell made of low adsorptive materials, is sufficient to accurately determine partition coefficients.
reveals how adsorptions affect MHE curves and allows one to deduce the true value of partition coefficients. The comparison model experiments show that, using cell materials with the lowest sorptive properties, a four-step MHE procedure allows an accurate determination of partition coefficients for the most hydrophobic methyl ketones. These results lead to questions concerning the accuracy of published data for nonpolar compounds, as adsorptions have not been considered up to now. ACKNOWLEDGMENT The authors are grateful to Dr. R. L. Snowden for reviewing the manuscript. SUPPORTING INFORMATION AVAILABLE Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org. Figure 5. Air-to-water partition coefficients for six homologous series of methyl ketones at 25 °C as a function of the carbon chain length (experimental values from this work and predicted values from the literature). Table 2. Air-to-Water Partition Coefficient of 2-Nonanone at 25 °C Pyrex cell
stainless steel cell
Viton O-ring Teflon O-ring Teflon O-ring predicted MHE (kgl ) K1Vl/Vg) experimental MHE N)4 N)2
0.0088
0.0092
0.0096
0.0054 0.0079
0.0096 0.0093
0.0097 0.0112
Comparison with Predicted Literature Values. Based on the previous observations, air-to-water partition coefficients were calculated from the first two points and the first four points of MHE experiments performed in a Pyrex and a stainless steel cell, respectively. Partition coefficients were also calculated from the model taking adsorptions into account. Values obtained from the theoretical model were very close to the MHE experimental values (Table 2), knowing that experimental standard deviation of 2-nonanone partition coefficient was 3.4 × 10-4 (see Table 2 of the first paper1). Moreover, the use of a sampling cell with the lowest sorptive material remains crucial to ensure a satisfactory accuracy of coefficients as it requires a sufficient number of experimental data points. Figure 5 shows the air-to-water partition coefficients of methyl ketones, predicted from literature models and from the mean value of four replications of the present model (using a four-step MHE, the stainless steel cell and Teflon O-rings). A great discrepancy was observed for the most hydrophobic compounds. However, our experimental values agree fairly well with predicted values using the bond contribution (BC) model, i.e., a model based on compound structure and that does not require any physicochemical data. This observation agrees with a recent work10 that recommends the BC model as the best one for the prediction of partition coefficients at 25 °C. CONCLUSION For the first time, the present study proposes a theoretical model based on solute mass balance and headspace equilibrium, which takes into account the adsorption of analytes into the sampling cell during the MHE process. The model release plot
GLOSSARY Vg volume of the gas phase (mL) Vl volume of the liquid phase (mL) pseudovolume of the glass walls (mL) Vs mg mass of the solute in the gas phase at equilibrium (g) ml mass of the solute in the liquid phase at equilibrium (g) mass of the solute adsorbed on the glass walls at ms equilibrium (g) Cg concentration of the solute in the gas phase at equilibrium (g/mL) Cl concentration of the solute in the liquid phase at equilibrium (g/mL) Cs a concentration of the solute adsorbed on the glass walls at equilibrium (g/mL) k′1, k1
rate constants controlling the transfer of the solute from the liquid to the gas phases in mL s-1 and s-1, respectively
k′-1, k-1 rate constant controlling the transfer of the solute from the gas to the liquid phases in mL s-1 and s-1, respectively K1
ratio of rate constants, in s-1, controlling the gas-liquid transfer of the solute (unitless)
kgl
equilibrium constant gas-liquid or air-to-water partition coefficient (unitless)
k′2, k2
rate constant controlling the transfer of the solute from the gas phase to the glass wall in mL s-1 and s-1, respectively rate constant controlling the transfer of the solute from the glass wall to the gas phase in mL s-1 and s-1, respectively ratio of rate constants, in s-1, controlling the gas-wall transfer of the solute (unitless) equilibrium constant wall-gas or wall-to-air partition coefficient (unitless) number of experimental MHE points used in the calculation.
k′-2, k-2
K2 ksg N a
For consistency reasons between units, Cs was considered as a concentration in a volume.
Received for review July 6, 2004. Accepted February 9, 2005. AC040123S Analytical Chemistry, Vol. 77, No. 10, May 15, 2005
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