Coating Distribution Coefficients for Solid Phase

Solid phase microextraction (SPME) is a sampling technique that can be used ..... are some peaks which do not appear to follow the trend observed in F...
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Anal. Chem. 1997, 69, 402-408

Estimation of Air/Coating Distribution Coefficients for Solid Phase Microextraction Using Retention Indexes from Linear Temperature-Programmed Capillary Gas Chromatography. Application to the Sampling and Analysis of Total Petroleum Hydrocarbons in Air Perry A. Martos, Angela Saraullo, and Janusz Pawliszyn*

The Guelph-Waterloo Centre for Graduate Work In Chemistry (GWC), Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

The paper describes a method to quantify hydrocarbons in air exclusively on the basis of chromatographic parameters without the need for calibration. A simple technique is presented to estimate distribution coefficients (K) between air and the poly(dimethylsiloxane) solid phase microextraction (SPME) fiber coating using the linear temperature-programmed retention index system (LTPRI). There is a linear relationship (r2 ) 0.99989) between the log K for a series of n-alkanes and LTPRI, thus providing a means by which establishing a K for any peak in a chromatogram is possible given its published or experimentally determined LTPRI. This alternative approach to establishing K values significantly enhances and simplifies the use of SPME for sampling and analyzing air for quantification of compounds without the need for fiber calibration. Analysis of a group of 29 isoparaffinic compounds and a group of 33 aromatic compounds showed excellent agreement between their theoretical air to fiber distribution coefficients based on LTPRI and the experimentally obtained distribution coefficients. In addition, for a very complex mixture of organics such as gasoline, SPME can establish a total petroleum hydrocarbon in air level using LTPRI. This method was carefully evaluated, and the results were essentially identical between standard procedures and the proposed simple procedure described in the paper.

Cair )

Cfiber nfiber 1 ) (at a fixed temperature) K Vfiber K

in eq 1 provides the key to air sampling with SPME PDMS. For example, when sampling an unknown airborne concentration of analyte(s) with SPME, the analytically measured parameter in eq 1 is the nfiber where the Vfiber and K are known. When the sampling temperature is different from the temperature at which K was established, the linear relationship between K and temperature, eq 2, can be used to correct the K value,3 where ∆Hv is the analyte

log K )

[ ( )

∆Hv ∆Hv RT + log 2.303RT γip* 2.303RT*

(1) Zhang, Z.; Yang, M. J.; Pawliszyn, J. Anal. Chem. 1994, 66, 844A-853A. (2) Chai, M.; Pawliszyn, J. Environ. Sci. Technol. 1995, 29, 693-701. (3) Martos, P.; Pawliszyn, J. Anal. Chem., in press. (4) Go´recki, T.; Pawliszyn, J. Anal. Chem. 1995, 67, 3265-3274. (5) MacGillivray, B.; Pawliszyn, J.; Fowlie, P.; Sagara, C. J. Chromatogr. Sci. 1994, 32, 317-322. (6) Pawliszyn, J. Trends Anal. Chem. 1995, 14, 113-122.

402 Analytical Chemistry, Vol. 69, No. 3, February 1, 1997

]

(2)

heat of vaporization, R is the gas constant, T is the sampling temperature, p* and T* are the solute vapor pressure at a known temperature, and γi is the solute activity coefficient. This equation can take the general form as shown in eq 3,3 where a ) ∆Hv/

log K ) a/T + b

(3)

2.303R and b ) [log(RT/γip*) - ∆Hv/2.303RT*]. By substituting eq 3 into eq 1, we get eq 4,3 where we can now establish the Cair

Cair ) Solid phase microextraction (SPME) is a sampling technique that can be used for a number of matrices, including water, headspace, and air.1-6 Air sampling ambient or industrial air with SPME with the liquid-like poly(dimethylsiloxane) (PDMS) can be expressed with eq 1,3 where Cair and Cfiber are the analyte concentrations in the air and fiber, respectively (at equilibrium), K is the partition coefficient, nfiber is the analyte mass loaded on the fiber, and Vfiber is the fiber volume. Knowledge of the K value

(1)

nfiber × 10-(a/T+b) Vf

(4)

for a target analyte given the analyte’s a and b values. Therefore, it can be seen that, if K is known, eq 1 or eq 4 can be readily used to quantify unknown concentrations of target analytes by measuring the nfiber and the sampling temperature. Establishing a K value can be a tedious and time-consuming process, and in those cases where there are unknown compounds of interest or significance present in a chromatogram, SPME could not, until now, be used to provide an estimate of their concentrations. Therefore, a simple yet accurate and universally reproducible approach to establishing K values would be highly desirable with such a system as that described in this paper. It is demonstrated that a general method to establish K values for S0003-2700(96)00633-6 CCC: $14.00

© 1997 American Chemical Society

compounds of interest utilizes the common retention index system which is used by chromatography experts world-wide. The retention index system is often used to identify analytes on the basis of their retention behavior as related to standard compounds, such as the n-alkanes. This paper shows there is a linear relationship between the log K value and the linear temperatureprogrammed retention index system (LTPRI) (eq 13 in Theory). Therefore, establishing K values with LTPRI provides a simple yet accurate estimation of K values for compounds in a sample as the analytes are chromatographically separated. Also, for very complex mixtures of hydrocarbons, such as in gasoline, each peak from that mixture can be individually quantified on the basis of its K value using the LTPRI approach, and the total can be summed to provide the total petroleum hydrocarbon concentration (see Results and Discussion). This removes the requirement to establish K values for target compounds before air sampling and provides a means by which K values can be accurately estimated to check on K values reported in literature or established experimentally and to afford a means by which to estimate analyte airborne detection limits. Other considerations such as analyte losses to the sampling vessels, the method of preparing a standard gas mixture (statically versus dynamically), technical and capital costs of the analysis, and environmental costs associated with the use of toxic organic compounds provide an incentive to simpler methods of establishing K values. Finally, the method can be extended to column stationary phases which differ from the PDMS phase by making use of the appropriate activity coefficients at infinite dilution. THEORY In chromatography, the chemical potential at equilibrium of an analyte between the mobile phase and the stationary phase is expressed by eq 5,7 where µs ) µ°s + RT ln γ′Cs and µm ) µ°m +

the column, uj is the average linear velocity of the mobile phase in the column, and Vm and Vs are the volumes of the mobile and stationary phases, respectively. The K on the right-hand side of eq 8 was defined in eq 7. The νj is expressed as a ratio of column length L and retention time tr (L/tr) and, if substituted into eq 8, yields eq 9, where tr is the peak retention time and tm is the column

tr )

(

) (

)

Vs Vs L 1+K ) tm 1 + K u j Vm Vm

dead time. By rearranging eq 9, it is obvious that the adjusted retention time (tr′) is directly proportional to the K value. The

Vs tr′ ) tr - tm ) K Vm

(10)

retention index system is frequently used to identify compounds on the basis of their relative retention times. Historically, the Kovats retention index system has been the primary source of this procedure; however, the Kovats retention index system requires isothermal chromatographic conditions, which serves little purpose for complex mixtures of analytes spanning a broad range of boiling points.8 The linear temperature-programmed retention index system (LTPRI) (eq 11) is used quite extensively,2 in place of the Kovats retention index, to establish retention indexes with the assumption that the temperature program is linear and logarithms of the adjusted retention times are replaced by the retention temperatures, as shown in eq 11, where Tr(A) is the analyte retention

LTPRI ) 100 ×

(

)

Tr(A) - Tr(n)

Tr(n+1) - Tr(n)

+ 100n

RT ln γ′′Cm. If γ′ ) 1 and γ′′ ) 1, then eq 6 can be realized,7

µ°s + RT ln γ′Cs ) µ°m + RT ln γ′′Cm

(6)

temperature, Tr(n) is the retention temperature of the n-alkane eluting directly before Tr(A), Tr(n+1) is the retention temperature of the n-alkane eluting directly after Tr(A), and n is the number of carbon atoms for Tr(n). If the increase in temperature is linear, then the retention time is proportional to tr (eq 12), where rT is

Tr ) T0 + tr′rT where R is the gas constant, T is the temperature in K, and Cs and Cm are the solute concentrations in the stationary and mobile phases, which after rearrangement yields eq 7. The time for a

(

)

( )

Cs µ°m - µ°s ∆µ° ) exp ) exp Cm RT RT

(7)

solute to pass completely through the column (the solute retention time, tr) is a function of the time spent between the mobile and stationary phases. Equation 8 describes the rate of migration through the column,7 where νj is the rate of migration through

(

νj ) u j

) (

(11)

(5)

µs ) µm

K)

(9)

) (

CsVs CmVm )u j 1+ CmVm + CsVs CmVm

-1

)u j 1+K

Vs Vm

)

-1

(8) (7) Laub, R. J.; Pecsok, R. L. Physicochemical Applications of Gas Chromatography; John Wiley & Sons: New York, 1978; Chapter 2.

(12)

the temperature program rate and T0 is the initial column temperature. Combining eqs 11 and 12 yields eq 13,8 where tr(A)

LTPRI ) 100 ×

(

tr(A) - tr(n)

)

tr(n+1) - tr(n)

+ 100n

(13)

is the analyte retention time, tr(n) is the retention time of the n-alkane eluting directly before tr(A), tr(n+1) is the retention time of the n-alkane eluting directly after tr(A), and n is the number of carbon atoms for tr(n).2 LTPRI values are easily established with eq 13 or are, alternatively, readily available from a number of published sources.9 There are a number of advantages to the use of LTPRI in favor of using Kovats retention indexes, predomi(8) Paca´kova´, V.; Ladislav, F. Chromatographic Retention Indices; Ellis Horwood Ltd.: Hempsted, England, 1992; pp 21-22. (9) The Sadtler Capillary GC Standard Retention Index Library and Data Base, Sadtler Research Laboratories, Philadelphia, PA.

Analytical Chemistry, Vol. 69, No. 3, February 1, 1997

403

nantly that the former does not require measurement of tm (which is not necessarily simple to establish) and it does not suffer from problems associated with isothermal chromatography. For example, the Kovats retention index for the same compound often yields different retention index values depending on the temperature chosen, most probably due to peak broadening, thus making it more difficult to accurately determine retention times.10 Of interest is the finding from recent work11 which has demonstrated that solute activity in PDMS is ostensibly identical to the solute activity in the PDMS capillary stationary phase, thus providing a substantiating component to the notion that parameters used in chromatography can be used to describe properties of SPME PDMS. The relationship between the retention volume of a solute and carbon number within a homologous series has long been known (eq 14),7 where Vg is the retention volume, Cn is the carbon

ln Vg(Cn) ) a + bn

(14)

number, and b and a are the slope and y-intercept of the curve (not to be confused with the a and b terms used earlier). The K for a given solute is related to its Vg and the stationary phase density, F (eq 15).7 Substituting eq 15 into eq 14 for Vg, we get

Vg ) K/F

(15)

eq 16. The density of the PDMS stationary phase is approximately

ln

K ) ln K - ln F ) a + bn F

(16)

1, and by observing that 100n is LTPRI, eq 16 can be modified to provide the relationship between K and retention index, as shown in eq 17 (where the a and b terms now include 2.303). Therefore,

log K ) a + b(LTPRI)

(17)

a linear relationship between log K and LTPRI is expected for a homologous series of carbon atoms, thus providing a simple and accurate approach to estimating K values for any compound provided its LTPRI is known, such as from the Sadtler9 references, or its LTPRI can be experimentally determined, such as with eq 13. EXPERIMENTAL SECTION Chemicals and Materials. Chemicals. Certified Alphagaz PIANO isoparaffins calibration standard and Alphagaz PIANO aromatics calibration standard were from Supelco (Mississauga, ON, Canada). Toluene and carbon disulfide were from Caledon Laboratories, Ltd. (Georgetown, ON, Canada). The following n-alkanes, pentane, hexane, heptane, octane, nonane, decane, undecane, dodecane, tridecane, and tetradecane, were from SigmaAldrich (Milwaukee, WI). Materials. For the Varian 3400 CX gas chromatograph, nitrogen, helium, and hydrogen gases were from Praxair (Waterloo, ON, Canada), and compressed air was generated from an air generator from Balston (Mississauga, ON, Canada). For the Hewlett Packard 5890 Series II gas chromatograph, helium, hydrogen, and air were from Canox (Guelph, ON, Canada). SPME devices with 100, 30, and 7 µm PDMS-coated fiber assemblies were from Supelco, as were the 1.0 L gas sampling bulb and 10 µL syringe. (10) Poole, C. F.; Schuette, S. A. Contemporary Practice of Chromatography; Elsevier Science: New York, 1984; p 24. (11) Zhang, Z.; Pawliszyn, J. J. Phys. Chem. 1996, 100, 17648-17654.

404

Analytical Chemistry, Vol. 69, No. 3, February 1, 1997

Preparation of Analyte Mixtures. A standard mixture of toluene in carbon disulfide (CS2) was prepared by diluting 8660 µg of toluene in 1.00 mL of CS2 in an EPA-approved Teflon-capped vial. The mixture was then thoroughly mixed and serially diluted to 0.866 µg/mL. The resulting calibration curve was used to calculate the mass of analyte loaded on the fiber. A 10.0% w/w standard mixture of n-alkanes comprised of pentane, hexane, heptane, octane, nonane, decane, undecane, dodecane, tridecane, and tetradecane was prepared by adding 1.00 g of each analyte, starting with n-tetradecane, into a Teflon-capped vial. The mixture was then thoroughly mixed and transferred to 1.8 mL Tefloncapped vials leaving no headspace. This mixture was used in a standard gas generation system previously described to determine K values as discussed below.3 The system was allowed to reach steady state at a concentration of 15 µg/L for each n-alkane at 298 K. The concentration of each n-alkane was verified with a standard method (National Institute of Occupational Safety and Health Method 1500).12 SPME with PDMS Sampling of Isoparaffinic and Aromatic Standard Gas Mixtures. A mixture of standard gases was prepared by adding 1.0 µL of neat isoparaffins or aromatics to the 1.0 L gas sampling bulb (with the half-hole septum covered with Teflon tape). All SPME overnight extractions were carried out with a 100 µm PDMS for the isoparaffins and 30 µm PDMS for the aromatics at 298 K. The standard gas generating device could not be used for these standards due to the fact that only 100 µL of each mixture was available for the experiments. Instrumentation and Methods for SPME and Liquid Injections. Establishing K Values for n-Alkanes. A Star software (Varian) computer-controlled Varian 3400 CX gas chromatograph (without electronic pressure control) equipped with a carbon dioxide-cooled septum-equipped programmable injector (SPI) and an 0.8 mm i.d. SPI insert coupled to a precolumn (1 m long, 0.25 mm i.d.) and an SPB-5 column (30 m, 0.25 mm i.d., 1.0 µm film thickness), which was coupled to a flame ionization detector (FID), was used for the research. The injector was maintained at 225 °C for SPME injections and at 45 °C for liquid injections, followed by a temperature increase to 225 °C at 30 °C/min. The column temperature program for SPME and liquid injections was 45 °C for 1.50 min, 30 °C/min to 175 °C, held for 2.67 min, and then 30 °C/min to 240 °C and held for 2.0 min. Helium, the carrier gas, was set to 40 cm/s at 45 °C for both SPME and liquid injections. The detector gas flow rates were set to 300 mL/min for air, 30 mL/min for nitrogen, and 30 mL/min for hydrogen and were all measured daily. Establishing Retention Times for n-Alkanes, Retention Indexes, and K Values for Isoparaffins and Aromatics. All experiments to establish retention indexes and K values for isoparaffins and aromatics used a computer-controlled Hewlett Packard 5890 Series II gas chromatograph equipped with electronic pressure-controlled (EPC) split/splitless injection port (250 °C) coupled to a deactivated fused silica precolumn (1 m, 0.32 mm i.d.) and a Hewlett Packard PONA column (50 m, 0.20 mm i.d., 0.50 µm film thickness), followed by flame ionization detection (FID) (250 °C). A narrow-bore insert (0.75 mm i.d.) was used for all SPME experiments, and a wide-bore glass wool-packed insert was used for all HP 7673A autosampler liquid injections performed to (12) National Institute for Occupational Safety and Health Manual of Analytical Methods, 1994, U.S. Department of Health and Human Services, electronic version.

Table 1. Summary of Retention Times for a Series of n-Alkanes n-alkane

LPTRI

tr (min)

pentane hexane heptane octane nonane decane undecane dodecane tridecane tetradecane

500 600 700 800 900 1000 1100 1200 1300 1400

4.508 6.868 11.948 20.957 33.643 47.924 62.599 76.879 90.501 103.39

Figure 1. log K for PDMS/air as a function of LTPRI for n-alkanes at 25 °C (conditions, see text).

establish the FID response to toluene for a five-point, 4 orders of magnitude calibration. The purge valve was initially set off, and turned on after 1.0 min for both SPME and liquid injections. Helium, the carrier gas, was set to 28 cm/s and was automatically maintained at that velocity with the EPC. The initial column temperature was 35 °C for 0.50 min, ramped to 220 °C at 1 °C/ min, and then held for 8.0 min, for a total run time of 193.5 min. The detector gas flow rates were set to 375 mL/min for air, 30 mL/min for helium (makeup gas), and 20 mL/min for hydrogen and were all measured daily. The instruments were checked daily for calibration using a liquid midpoint calibration standard. Any deviations in area counts greater than 15% required reinjection of that standard. If the deviation was still greater than 15%, the detector response as a function of amount injected was reestablished. In addition, quality of peak shapes, resolution, and retention times were carefully monitored to ensure that all chromatography was within specifications. Analysis of Airborne Gasoline with SPME. Regular unleaded gasoline was purchased and transferred into 4 mL standard amber vials, cleaned according to U.S. EPA protocols and capped with Teflon. This gasoline was injected into a standard gas generating device (described above) and allowed to reach steady state for 4 weeks. Gasoline was injected at a rate of 4 mg/h with an air stream dilution of approximately 200 mL/min, yielding a total volatile organic carbon concentration of 247 ( 10 µg/L 298 K, as determined with NIOSH Method 1501.12 The 100 µm PDMS was chosen to analyze the airborne gasoline mixture due to the anticipated low mass loading of compounds with known small distribution coefficients. The fiber was exposed to the air mixture for 30 min, thus allowing equilibration of all gasoline components. All SPME analyses of this air mixture were carried out using the Hewlett-Packard gas chromatographic setup described above. RESULTS AND DISCUSSION Relationship between log K for n-Alkanes and LTPRI. The equation for the relationship between log K for air/PDMS at 25 °C and the LTPRI for the studied n-alkanes ranging from n-pentane to n-tetradecane (inclusive) is shown in Figure 1. This curve shows the expected relationship as mentioned in the Theory, thus confirming the expected relationship between log K air/coating and LTPRI (eq 17). Table 1 summarizes the retention times for the n-alkanes from n-pentane to n-tetradecane.

Figure 2. Chromatogram of n-alkanes (conditions, see text). The 7 µm PDMS fiber was used to properly determine the retention times for those compounds with large peak widths at half-height.

The data in Table 1 were used to establish the LTPRI data shown in Tables 2 and 3, which is discussed below. Additionally, from Table 1, there is a linear relationship between tr and LTPRI (data not shown) for the n-alkanes ranging from octane to tetradecane (r2 ) 0.9996), thus providing agreement with literature findings.10 Figure 2 shows the chromatogram obtained from the SPME sampling of the standard gas mixture of equal concentrations (15 µg/L each) of n-alkanes described above. This figure shows that n-tetradecane has a significantly larger mass loaded on the fiber compared to n-pentane, thus demonstrating the fact K values increase with increasing carbon number. Typical relative standard deviations (RSDs) of retention times for repeat injections yielded no more than 0.30% RSD. The K values for each of the n-alkanes were determined using a 20 L standard gas generating device previously described,3 thus eliminating the problems associated with establishing K values obtained from small sampling vessels such as wall effects and disturbance of the air system during extraction.13 The equation in Figure 1 provides a means to estimate K values for any compound given its published or experimentally determined LTPRI. To verify the relationship in Figure 1, K values directly determined with SPME were compared to LTPRI (eq 13) and estimated K values for a group of 29 isoparaffinic and a group of 33 aromatic compounds (see below). Estimation of K Values from Literature and Experimentally Determined LTPRI and Comparison to Directly Determined K Values with SPME. Using the n-alkane retention times provided in Table 1, LTPRI values for the studied isoparaffinic (13) Potter, D. W.; Pawliszyn, J. J. Chromatogr. 1992, 625, 247-255.

Analytical Chemistry, Vol. 69, No. 3, February 1, 1997

405

Table 2. Summary of Data for the Isoparaffinic Compoundsa

peak

compound

A LTPRI standard

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

3-methylpentane 2,4-dimethylpentane 2,2,3-trimethylbutane 2-methylhexane 2,3-dimethylpentane 2,2-dimethylhexane 2,5-dimethylhexane 2,2,3-trimethylpentane 2,3-dimethylhexane 2-methylheptane 4-methylheptane 3-methylheptane 3-ethylhexane 2,5-dimethylheptane 3,5-dimethylheptane (D) 3,3-dimethylheptane 3,5-dimethylheptane (L) 2,3-dimethylheptane 3,4-dimethylheptane (D) 3,4-dimethylheptane (L) 2-methyloctane 3-methyloctane 3,3-dimethylpentane 2,2-dimethyloctane 3,3-dimethyloctane 2,3-dimethyloctane 2-methylnonane 3-ethyloctane 3-methylnonane

571.1 620.3 624.7 656.9 658.5 717.0 726.9 726.9 754.1 761.1 762.5 768.7 769.7 827.4 827.4 828.6 828.6 846.5 848.3 849.2 856.3 863.4 864.3 920.3 939.3 958.8 968.6 971.3 974.2

B LTPRI lit.

C LTPRI calcd

D tr (min)

E K (LTPRI)

F K (SPME)

G %Er (K)

577.2 624.2 629.0 661.2 662.8 719.3 728.7 729.7 756.7 763.0 764.6 771.0 772.0 837.0

576.8 623.1 628.1 659.6 661.7 717.9 726.9 726.9 754.5 761.0 762.5 769.0 770.1 833.3 833.3 834.6 834.6 853.1 855.0 855.7 862.3 869.6 870.6 917.6 934.4 953.9 964.8 967.9 971.7

6.320 8.042 8.295 9.898 10.00 13.565 14.375 14.375 16.862 17.440 17.579 18.167 18.265 25.177 25.177 25.345 25.345 27.692 27.928 28.025 28.865 29.788 29.919 36.156 38.553 41.345 42.890 43.335 43.878

157 246 258 351 358 616 672 672 877 933 947 1010 1020 1880 1880 1900 1900 2270 2310 2330 2490 2670 2690 4240 4990 6020 6690 6890 7150

159 262 280 387 412 673 587 569 968 993 1060 1090 990 1970 1960 2090 2100 2390 2420 2620 2600 2890 2610 4320 5050 6100 6690 6970 7100

0.94 6.4 8.2 10 15 9.2 -13 15 10 6.4 12 7.9 -2.9 4.8 4.3 10 11 5.3 4.8 12 4.4 8.2 -3.0 1.9 1.2 1.3 0.0 1.2 -0.70

835.4 857.5 864.6 872.2 873.6 918.7 936.0 954.8 965.2 968.4 971.6

a Column descriptions: (A) LTPRI provided with the certified standard. (B) Literature LTPRI.14 (C) Calculated LTPRI using the experimentally obtained retention times (column D) for the individual hydrocarbons. The log K vs LTPRI calibration curve ranged from pentane to decane for the isoparaffins. The slope and y-intercept were 0.00420 and -0.224, respectively. (D) Retention time for the individual isoparaffins. (E) K values as determined by the log K vs LTPRI (column C) relationship. (F) K values determined experimentally using eq 1. (G) Relative error between the K values in columns E and F.

and aromatic compounds (eq 13) were calculated. Tables 2 and 3 provide the data pertinent to the isoparaffins and aromatics, respectively. The isoparaffinic compounds ranged in retention indexes from 577.2 to 971.6, and the aromatics from 642.0 to 1247.2. The group of isoparaffins was bracketed by n-pentane to n-decane, inclusive, while the group of aromatics was bracketed by n-hexane to n-dodecane, inclusive. Columns A and B in both tables summarize the LTPRI provided with the standard mixtures and literature LTPRI, respectively. Column C shows the calculated LTPRI (eq 13), based on the analyte retention times shown in column D. It should be noted that, except for a few compounds for which literature values were not readily available, all data in column C agree very well with those in columns A and B and fall within reported ranges.8,10,14 Once the LTPRI values were established for each compound, a K value was estimated using the form of the equation in Figure 1 (see captions for Tables 2 and 3), the results of which are presented in column E. Column F shows the K value, as calculated with eq 1, directly obtained from the exposure of the SPME fiber coated with 100 µm PDMS from a standard gas mixture of the isoparrafins (29 compounds) and with the PDMS fiber coated with 30 µm PDMS from a standard gas mixture of the aromatics (33 compounds). Finally, column G shows the percent relative error (%Er) between columns E and F. The data in column G clearly demonstrate that, except for a few compounds, the %Er values were well below 10%, thus (14) White, C. M.; Hackett, J.; Anderson, R. R.; Kail, S.; Spock, P. S. J. High Resolut. Chromatogr. 1992, 15, 105-120.

406 Analytical Chemistry, Vol. 69, No. 3, February 1, 1997

Figure 3. Chromatogram for the isoparaffins (conditions, see text). (1) 3-methylpentane, (2) 2,4-dimethylpentane, (3) 2,2,3-trimethylbutane, (4) 2-methylhexane, (5) 2,3-dimethylpentane, (6) 2,2-dimethylhexane, (7) 2,5-dimethylhexane, (8) 2,2,3-trimethylpentane, (9) 2,3-dimethylhexane, (10) 2-methylheptane, (11) 4-methylheptane, (12) 3-methylheptane, (13) 3-ethylhexane, (14) 2,5-dimethylheptane, (15) 3,5-dimethylheptane (D), (16) 3,3-dimethylheptane, (17) 3,5-dimethylheptane (L), (18) 2,3-dimethylheptane, (19) 3,4-dimethylheptane (D), (20) 3,4-dimethylheptane (L), (21) 2-methyloctane, (22) 3-methyloctane, (23) 3,3-diethylpentane, (24) 2,2-dimethyloctane, (25) 3,3dimethyloctane, (26) 2,3-dimethyloctane, (27) 2-methylnonane, (28) 3-ethyloctane, and (29) 3-methylnonane.

substantiating the validity of the method to estimate K values for SPME compared to experimentally establishing them. Figures 3 and 4 show the SPME chromatograms for the isoparaffinic and aromatic compound mixtures with the 100 µm PDMS fiber and the 30 µm PDMS fiber, respectively. Both chromatograms show

Table 3. Summary of Data for the Aromatic Compoundsa

peak

compound

A LTPRI standard

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

benzene toluene ethylbenzene m-xylene p-xylene o-xylene ]isopropylbenzene n-propylbenzene 1-methyl-3-ethylbenzene 1-methyl-4-ethylbenzene 1,3,5-trimethylbenzene 1-methyl-2-ethylbenzene isobutylbenzene sec-butylbenzene 1-methyl-3-isopropylbenzene 1-methyl-4-isopropylbenzene 1-methyl-2-isopropylbenzene 1-methyl-3-n-propylbenzene 1,3-dimethyl-5-ethylbenzene 1-methyl-2-n-propylbenzene 1,4-dimethyl-2-ethylbenzene 1,2-dimethyl-4-ethylbenzene 1,3-dimethyl-2-ethylbenzene 1,2-dimethyl-3-ethylbenzene 1,2,4,5-tetramethylbenzene 2-methylbutylbenzene 1-tert-butyl-2-methylbenzene n-pentylbenzene 1-tert-butyl-3,5-dimethylbenzene 1-tert-butyl-4-ethylbenzene 1,3,5-triethylbenzene 1,2,4-triethylbenzene n-hexylbenzene

638.6 747.1 836.1 844.6 845.7 867.9 907.9 942.1 950.4 952.2 964.1 966.4 992.7 994.7 1005.9 1008.6 1022.7 1037.5 1041.3 1052.5 1063 1070.3 1075.7 1088.4 1101.2 1102.1 1117.2 1143.1 1164.0 1169.4 1205.7 1225.2 1247.2

B LTPRI lit.

C LTPRI calcd

D tr (min)

E K LTPRI

F K SPME

G %Er (K)

642.0 749.0 844.7 853.4 854.8

640.7 746.5 841.7 850.2 851.3 872.3 907.2 935.4 943.2 945.1 958.0 959.9 991.3 994.1 1005.2 1008.1 1020.4 1034.5 1041.9 1048.9 1059.6 1067.1 1072.1 1085.8 1097.9 1100.7 1113.4 1140.9 1163.6 1165.9 1207.6 1223.2 1245.2

8.934 16.141 26.244 27.321 27.460 30.126 34.670 38.700 39.816 40.087 41.920 42.199 46.682 47.053 48.689 49.109 50.917 53.659 54.070 55.100 56.675 57.768 58.504 60.510 62.285 62.697 64.509 68.443 71.675 72.015 77.925 80.090 83.132

296 815 2020 2190 2220 2710 3780 4960 5340 5440 6150 6260 8450 8680 9660 9920 11200 12800 13700 14700 16200 17400 18300 20900 23400 24000 27100 35300 43900 44900 66800 77600 95700

301 818 2070 2090 2500 2900 3880 5040 4750 6230 6480 6580 8360 8590 10100 10200 12000 13200 15000 14900 15900 17400 18100 20000 24700 24100 26200 34500 45600 43700 67300 75600 90100

1.7 0.39 2.5 -4.6 13 7.0 2.6 1.6 -11 15 5.4 5.1 -1.1 -1.0 4.6 2.8 7.1 3.1 9.5 1.4 -1.9 0.0 -1.1 -4.3 5.6 0.42 -3.3 -2.3 3.9 2.7 0.75 -2.58 -5.9

909.6 938.2 946.9 948.9 954.7 963.7 996.8 1007.8 1010.9 1023.9 1037.8 1044.2 1052.7 1063.1 1070.7 1076.4 1090.0 1101.8 1104.8 1144.3 1165.0 1207.9 1226.1 1247.2

a Column descriptions: (A) LTPRI provided with the certified standard. (B) Literature LTPRI.14 (C) Calculated LTPRI using the experimentally obtained retention times (column D) for the individual hydrocarbons. The log K vs LTPRI calibration curve ranged from hexane to dodecane for the aromatics. (D) Retention time for the individual aromatics. The slope and y-intercept were 0.00415 and -0.1875, respectively. (E) K values as determined by the log K vs LTPRI (column C) relationship. (F) K values determined experimentally using eq 1. (G) Relative error between the K values in columns E and F. Note: for n-hexylbenzene, the K value was adjusted upward by 1.3% to compensate for the extraction of this compound.

by peak height that there is increasing mass loaded on the fiber with increasing retention time, similar to the phenomenon presented in Figure 2. It should be noted that there are some peaks which do not appear to follow the trend observed in Figure 2 because the standard gas mixtures for the isoparrafins and aromatics were not made up of equal amounts of each analyte; however, the same trend as in Figure 2 was observed when the peak areas for the isoparrafins and aromatics were normalized for amount of analyte in the mixture. There is an error of approximately 3% in the K value for a window of (3 LTPRI units, which can be considered insignificant. With the methods previously described3 and presented in this paper, air concentrations of any analyte can be established at any temperature without experimentally calibrating the fiber. Conversely, we can verify directly determined K values using this approach, thus providing a measure of the accuracy of the experimental K value. Finally, other homologous series can be studied using this method, thus further extending this fundamental relationship. Estimating SPME Detection Limits with K. Knowledge of detection limits for Cair with SPME PDMS without experimentation can provide for better experimental design and illuminate potential limitations to the analysis of previously unstudied compounds. Replacing the nfiber in eq 1 with the instrumental limit of detection (LOD), say, for GC/FID, yields eq 18.

Figure 4. Chromatogram for aromatics (conditions, see text). (1) benzene, (2) toluene, (3) ethylbenzene, (4) m-xylene, (5) p-xylene, (6) o-xylene, (7) isopropylbenzene, (8) n-propylbenzene, (9) 1-methyl3-ethylbenzene, (10) 1-methyl-4-ethylbenzene, (11) 1,3,5-trimethylbenzene, (12) 1-methyl-2-ethylbenzene, (13) isobutylbenzene, (14) sec-butylbenzene, (15) 1-methyl-3-isopropylbenzene, (16) 1-methyl4-isopropylbenzene, (17) 1-methyl-2-isopropylbenzene, (18) 1-methyl3-n-propylbenzene, (19) 1,3-dimethyl-5-ethylbenzene, (20) 1-methyl2-n-propylbenzene, (21) 1,4-dimethyl-2-ethylbenzene, (22) 1,2dimethyl-4-ethylbenzene, (23) 1,3-dimethyl-2-ethylbenzene, (24) 1,2dimethyl-3-ethylbenzene, (25) 1,2,4,5-tetramethylbenzene, (26) 2-methyl-n-butyl-benzene, (27) 1-tert-butyl-2-methylbenzene, (28) n-pentylbenzene, (29) 1-tert-butyl-3,5-dimethylbenzene, (30) 1-tertbutyl-4-ethylbenzene, (31) 1,3,5-triethylbenzene, (32) 1,2,4-triethylbenzene, and (33) n-hexylbenzene.

Analytical Chemistry, Vol. 69, No. 3, February 1, 1997

407

Figure 5. Chromatogram of airborne gasoline obtained with 100 µm PDMS fiber (conditions, see text).

Cair(LOD) )

nfiber(LOD) 1 (at a fixed temperature) Vfiber K

(18)

In this approach, the LOD for SPME is limited by the instrument detection limit for the specific target analyte. The equation indicates that, as K increases, the Cair(LOD) will decrease correspondingly because the instrument detection limit is relatively constant for compounds of similar chemical properties, such as the hydrocarbons (with FID). This provides an additional substantive requirement to the estimation of K values from the LTPRI system. Analysis of Airborne Gasoline with SPME and Comparison to Active Sampling with Charcoal Tubes for a TPH Value. An airborne mixture of gasoline sampled with a PDMS fiber coating and analyzed by GC/FID is shown in Figure 5. The K value for each peak in this chromatogram was determined on the basis of its LTPRI, along with the equation in Figure 1. The amount on the fiber for each peak was determined with the peak’s area count (based on a toluene equivalent assuming constant response factor for each peak). The air concentration (eq 4) for that peak and all of the other peak concentrations were summed, providing a total petroleum hydrocarbon (TPH) in air concentration of 262 ( 13 µg/L at 25 °C, compared to the airborne TPH value of 247 ( 10 µg/L obtained by air sampling with charcoal tubes. This small difference is easily explained by considering the interference presented by the desorbing eluant (carbon disulfide) for charcoal tubes in the analysis of total organics and/ or the errors associated in determining LTPRI from the complex gasoline chromatogram (Figure 5). These results indicate an extremely promising use of SPME for air sampling. The analyst needs only to calibrate the FID and acquire the air sample with SPME at a fixed temperature (assuming an equal response factor for all organic compounds). In addition, due to the fact that K values are very large for compounds greater than n-decane, those compounds with retention times after n-decane contribute very little to the overall value of airborne TPH from gasoline vapor (see eq 18). Thus, a retention time cutoff can be implemented, if required, to simply quantification; however, those compounds with K values larger than n-decane should not be considered less significant than compounds with K values smaller than n-decane. Finally, a faster ramp rate can be used to reduce analysis time without significant error to the overall result, which would allow an increase in sample throughput without compromising the overall accuracy of the analysis. 408

Analytical Chemistry, Vol. 69, No. 3, February 1, 1997

CONCLUSIONS LTPRI can be applied to establish partition coefficients for airborne analytes to SPME fibers coated with PDMS, based on the linear relationship between log K and LTPRI for a homologous series of compounds such as the n-alkanes. Recent work has indicated that there is a direct correlation between SPME fiber coatings and gas chromatographic capillary columns,11 thus further enhancing the validity of using LTPRI from chromatography for SPME. A number of advantages can be realized with this application, predominantly the significance to better experimental design, a way to estimate airborne analyte detection limits given K and Cair (eq 18), obviating the necessity for the analyst to experimentally determine K values, and the possibility of using this system for other fiber phases and other homologous series. Very complex mixtures of unknown airborne organics could not be quantified, until now, by SPME due to the fact that the K values for each of the peaks were difficult or impossible to determine, especially if no standard was available. Using the method presented herein, the unknown compound’s LTPRI can be used to establish its K for SPME. Once the K value is known for that compound, its air concentration can be determined and summed with all the other components from the mixture, providing a TPH in air. In addition, the analysis of air samples for airborne TPH using SPME can be simplified with the use of a postrun macro which could calculate each peak’s LTPRI and the corresponding K, convert the peak areas to mass loaded on the fiber, calculate the air concentration for that peak on the basis of eq 4, and sum up all individual peak concentrations, thus providing airborne TPH concentration. There is an excellent agreement between the results obtained by sampling and analysis of an air stream containing gasoline with SPME fiber coated with PDMS and charcoal tube samples, which proves the method described can be used for quantitation of individual compounds, known or unknown (provided the latter have similar response factors). A prescreen of the air sample in question with GC/mass spectrometry can provide information whether halogenated organics or other substituted organics are present. If the air sample is predominantly non-halogenated, then GC/FID can be safely used for the quantification. In cases where the solutes and the stationary phase differ significantly with respect to the chemical character of the calibration retention index standard (e.g., n-alkanes on polar phases), other homologous series instead of the n-alkanes should be used. For example, appropriate methyl esters of linear saturated fatty acids can be used as the standard for the determination of methyl esters of unsaturated fatty acids.8 ACKNOWLEDGMENT The authors sincerely thank Michael Hoffbauer of LEX Scientific Inc., Guelph, ON, Canada, for the use of laboratory facilities and gas chromatographic equipment. The authors also thank Dr. Tadeusz Go´recki for discussions. This work was financially supported by NSERC, Supelco, and Varian. Received for review June 25, 1996. Accepted October 31, 1996.X AC960633P X

Abstract published in Advance ACS Abstracts, December 15, 1996.