Anal. Chem. 1982, 5 4 , 1941-1947
To further characterize the ethylammonium nitrate stationary phase a series d benzene derivatives containing a single functional group were separated by temperature program analysis, Figure 3, This separation could not be performed isothermally as the range of capacity factor values is too high. However, the general trend in retention is clearly discernible with the least polar components of the mixture a t the front of the chroimatogram, components with a large dipole moment toward the center and the strongly hydrogen bonding benzyl alcohol a t the end. A group of compoundhi were found to be difficult to chromatograph on the molten salt stationary p h e . Neither ethyl-, propyl-, or butylamine nor aniline could be eluted from the column at its highest operating temperature of 120 “C. Although pyridine was chromatographable, it had poor peak shape. Phenol and benzaldehyde were not eluted in a reasonable time a t 120 “C. These substances were the most acidic/basic tested and would be expected to be the strongest proton donors/acceptors in hydrogen bonding interactions. Presumably these com~poundsinteract too strongly with ethylammonium nitrate to be eluted within the accessible temperature range of the column. Ethylammonium nitrate is a useful polar stationary phase for gas-liquid chromatography. The columns prepared during this study provided about 75% of the column plate count efficiency of the Carbclwax 20M column for compounds showing normal retention. Except where noted in the text, the test compounds eluted as symmetrical peaks with asymmetry factors of 1.0 f 0.2. Alkanes and alkenes are not re. tained by the organic molten salt and compounds which are strong proton donors oir acceptors cannot be eluted in a convenient time, even at the maximum column operating temperature of 120 “C. Long-term column testing over approximately 5 months has demonstrated that the molten salt
1941
has adequate thermal stability for chromatographic use. The molten salt is also stable to direct aqueous injections. The chromatographic properties of ethylammonium nitrate are sufficiently encouraging to suggest that other organic molten salts should be evaluated as polar reference stationary phases for gas chromatography. A higher maximum operating temperature would be a useful feature.
LITERATURE CITED (1) Balulescu, G. E.; Ilie, V. A. “Stationary Phases in Gas Chromatography”; Pergamon Press: Oxford, 1975. (2) Haken, J. K. J. Chromatogr. Sci. 1971, 9 , 13A. (3) Preston, S.T. J. Chromatogr. Sci. 1970, 8 , 18A. (4) Mann, J. R.; Preston, S. T. J. Chromatogr. Sci. 1973, 7 1 , 216. (5) Rledo, F.; Frltz, D.; Tarjan, G.; Kovats, E. sz. J. Chromatogr. 1976, 726, 63. ( 6 ) Haken, J. K.; Ho, D. K. M. J. Chromatogr. 1977, 742, 203. (7) Poole, C. F.; Butler, H. T.; Agnello, S. A,; Sye, W.-F.; Zlatkis, A,; Holzer, 0. J. Chromatogr. 1981, 217, 39. (8) Frank, H.; Nicholson, G. J.; Bayer, E. J. Chromatogr. Sci. 1977, 75, 174. (9) Saeed, T.; Sandra, P.; Verzele, M. J . Chromatogr. 1979, 786,611. (10) Bednas, M. E.; Russell, D. S.Can. J . Chem. 1958, 3 6 , 1272. (11) GII-Av, E.; Herling, J.; Shabati, J. J . Chromatogr. 1958, 7 , 509. (12) Spencer, S.F. Anal. Chem. 1963, 35, 592. (13) Juvet, R. S.; Wachi, F. M. Anal. Chem. 1960, 32, 290. (14) Tadmor, J. Anal. Chem. 1964, 3 6 , 1565. (15) Sugden, S.; Wllkins, H. J. Chem. SOC. 1929, 1291. (16) Reinsborough, V. C. Rev. Pure Appl. Cbem. 1966, 79, 281. (17) Ubbelohde, A. R. Nature (London) 1973, 244, 487. (18) Ubbelohde, A. R. “The Molten State of Matter: Melting and Crystal Structure”; Wiley: New York, 1978. (19) Evans, D. F.; Chen, S.-H.; Schriver, G. W.; Arnett, E. M. J. Am. Chem. SOC. 1981, 103, 481. (20) Ettre, L. S. Chromatographia 1974, 7 , 261.
RECEIVED for review June 7 , 1982. Accepted July 23, 1982. Work in the authors’ laboratory is supported by the donors of the Petroleum Research Fund, administered by the American Chemical Society, the Camille and Henry Dreyfus Foundation, Michigan Heart Association, and AB Hassle.
Characterization of Small Variations in Profiles of Chromatographic E ution Peaks and Effect of Nonlinear ty of Sorption Isotherm Jean-Louis Excoffler, PUain Jaulmes, Claire Vldal-Madjar, and Georges Gulochon * Ecoie Polytechnique, Laboratoire de Chimie An&tlytique Physlque, Route de Saclay, 9 1 128 Palaiseau Cedex, France
A very sensltive method of comparlson between dlfferent peak proflles, the dlstribu2lon function method (DFM), has been used to detect small1 varlatlons In shape of the chromatographlc peaks when the mass of solute Injected Is Increased. A second easy procedure of peak shape comparlson which sets In colncldence the peak maxlma allows a clear dlstlnction between the two possible sources of a nonlinear behavior of the chrornatographlc response, either a nonllnear sorptlon lsotherni or a nonllnear detector response. I n the case of a nonlinear sorptlon Isotherm the method glves the slgn of the curvature of the Isotherm.
Most chromatographic theories which derive exact expressions for the elution profiles (1-4) or which characterize them through the use of the! central statistical moments (5-7) make the fundamental assumption of linear chromatography, in order to achieve reasonable solutions. Unfortunately the isotherm describing the equilibrium of a solute between two
phases is not strictly linear and its curvature at the origin is not zero. The range of concentration in which the isotherm can be replaced by its tangent at the origin depends both on the type of system and on the precision of the measurements. It is thus important when discussing the application of these theoretical models to experimental chromatographic profiles to test the validity of this assumption and to determine to what extent a deviation from linearity does exist. Houghton (8)and Haarhoff et al. (9) have obtained analytical equations of peak profiles by solving the partial differential equations of chromatography when the deviation of the isotherm from linearity is small. These expressions are too complex to be handled in practice and, therefore, De Clerk and Buys (10-13) and Yamaoka and Nakagawa (14) have developed expressions for the statistical moments with a nonlinear distribution isotherm. In principle, the determination of central statistical moments can be easily done by direct integration from the digital data collected by the computer. However, this procedure can lead to large systematic errors with nonsymmetrical peaks as
0003-2700/€l2/0354-1941$01.25/00 1982 American Chemical Soclety
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ANALYTICAL CHEMISTRY, VOL. 54, NO. 12, OCTOBER 1982
shown by Chesler and Cram (15) who studied in detail the effect of integration limits and the density of data points collected. Furthermore statistical errors become important on higher order moments because of the influence of minor fluctuations of base line on the time when integration is ended. In this work, we propose a method which reveals small deviations from linearity of the distribution isotherm in the case of a tailing elution peak when the central statistical moment method is unable to detect any change in peak retention or peak shape. Studying tailing peaks is specially important in chromatography as a better understanding of the causes of this phenomenon can lead to reduction of peak asymmetry and improve peak resolution during analytical separations. The method can be applied to leading peaks as well, however. The comparison of peak shapes by visualization on a graph, when setting the maxima in coincidence has been first described by Oberholtzer and Rogers (16)who studied the elution behavior of methane, ethane, and isobutane on molecular sieves. This procedure, which has not yet been systematically investigated, permits only a qualitative distinction between peak elution shapes. As in all procedures based on the use of the human eye as an analycal instrument, it is very sensitive to subtle changes in pattern but most difficult to use as a quantitative tool. Therefore, the distribution function method (DFM) described by Rix (17,18)shall be used to detect small variations in peak shape when the mass of sample injected into the column is changed. The DMF compares two elution curves or more generally two response profiles without any assumption regarding the characteristics of the input signal or the transfer function or the reason why the two profiles may differ, with the only aim to decide whether these profiles are identical, i.e., differ only by a mere translation and an affinity parallel to the concentration axis (all y's multiplied by the same number), or not. A number characterizing the difference between the two profiles is calculated and compared to a threshold determined by comparing profiles obtained as a response to the same impulse. This method is very sensitive to shape difference but does not tell anything about the reason of this difference. Furthermore, setting in coincidence the maxima of elution peaks and comparing for example those peaks corresponding to the extreme of the range of variation of the parameter investigated (i.e., here those corresponding to the largest and lowest amount injected) permits a clear distinction between the effech of a nonlinearity of the detector response and those of departure from linearity of the distribution isotherm.
EXPERIMENTAL SECTION The gas chromatographic instrument used, with its flame ionization detector, process control sampling valve, and precise controls of inlet and outlet pressures and of the temperatures of column, sampling valve, and pressure controllers, has been designed for high-precision measurements and has been described previously (19). The detector outlet pressure (around 1100 mbars) is controlled within *0.3 mbar by a Negretti and Zambra (London UK) valve which works by reference to vacuum and whose temperature is controlled within *0.1 "C around 30 "C. The inlet pressure is controlled by a Texas Instruments pressure controller referenced to the detector pressure (fluctuations N 0.015 mbar in an hour). The carrier gas is high-purity helium; its flow rate is 0.17 mL/s for a 800 mbar pressure drop. The column is kept in a water bath; ik temperature is controlled within 0.01 "C by a microcomputer with a proportional and integral corrector program. Temperature drift is negligible. An automatic rotative sampling valve (Carlo Erba, Milan, Italy) with a 2-pL sample loop allows the injection of gaseous samples of a mixture of methane and cyclohexane vapor diluted in helium. Injection is ordered by the computer. Rotation of the valve shaft switches off a light beam. The pulse generated by a photocell
acts as time origin for the detector signal acquisition. The mass to 5 X of cyclohexane injected is changed ( - 5 X g) by variation of the concentration of the cyclohexane vapor in the gaseous sample (0.07% to 7% (v/v)). Thus, throughout the whole experiment, the gas volume injected (2 pL) is kept constant, so any possible change in the peak shape when the mass of solute injected is increased cannot be ascribed to a mere perturbation of the gas flow rate. The detector response is calibrated by injection of 2 p L of a gaseous calibrated standard (9.3% zk 0.3% CH4in helium prepared by Air Liquide). A better precision is not required for the type of work described here. The chromatographic signal is measured with an amplifier (Keithley 417K) and a digital voltmeter (Solartron ML 1480-3, Schlumberger) with a four decimal point precision. The digitalized data of the chromatogram are collected on-line by a microcomputer (Commodore CBM 30-32) and transferred to a HewlettPackard 21MX30 minicomputer for storage on magnetic tape. The comparison of peak profiles is achieved by a Fortran program on the minicomputer. Goedert and Guiochon (19) have shown that the high-precision instrument used here and which is essentially the same one they described is able to measure retention times, defined as the mass center of the elution peak, with a repeatability of 2 X W4for a 95% confidence interval. They have studied the instrumental contributions to the errors in retention time measurements, which time are: the measurement of time (relative error = 2 X constant of the electronic system (20 ms), effect of gradient and fluctuations of column temperature (relative error = 0.2 x transit through carrier gas volumes outside the column. The extra dead volumes have been measured by Goedert and Guiochon (19) according to a method similar to that described by Kieselbach (20). The upstream dead volume is less than 10 pL and its contribution to the correction on retention time measurement is negligible. The downstream volume is 110 pL. For the present experiment, with a flow rate of 0.17 mL/s, the retention time systematic error is -650 ms. This correction is made. The chromatographic column (2 m X 2.1 mm i.d. stainless steel) is packed with porous glass beads (125-160 pm,DMCS, Corning) coated with squalane. The total amount of the squalane liquid stationary phase in the column is 53 mg (Le., ca. 0.5% (w/w) on the glass beads). The solute studied is cyclohexane (99.99% purity by gas chromatography, Elf, Solaize, France).
RESULTS We have compared the profiles of peaks obtained with increasing sample size, using three different methods of comparison. (1) The Central Statistical Moment Method. Typical concentration profiles, y = f(t), obtained by recording the elution of cyclohexane peak through the column are shown in Figure l a for amounts ranging from 4.3 to 460 ng. These profiles exhibit a marked tailing. The elution peaks are redrawn in Figure l b by setting in coincidence the maxima. A difference in peak shape is observed between the lowest and the largest amount of cyclohexane injected. No trends appear on the value of any of the statistical moments of the elution curve which could parallel this progressive change in peak profile (Table I). In Table I are listed the retention time of peak maximum tM,the mass center of the elution peak M'], the plate heights H obtained from the central statistical moment M z and H' from the peak width 2a at 0.606 height, the specific asymmetry 2, and the specific excess F, which are related to the central statistical moments (Mi, M3, M4)through the relationships H' = La2/tM2
H = LM2/Mll2 Z = L2M3/MrI3
F = L 2M4/ M'14
(1)
The theoretical importance of 2 and F has been shown previously for gas-solid chromatography ( 5 , 6) and for gas-
ANALYTICAL CHEMISTRY, VOL. 54,NO. 12, OCTOBER 1982
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Table I. Characterization of the Elution Peak with Statistical Moments H =LUZ/
t,,
m, ng
s
3 4.5 7.5 10.0 14.5 97 114 233 286 343 458
249.2 249.6 249.1 249.1 249.4 248.8 248.9 250.0
RSD of measrrct
5
250.1 250.7 251.5
x
10-4
t M 2 , cm 0.087 0.082 0.086 0.075 0.074 0.085 0.083 0.086 0.0~6 0.095 0.107 5
x
10-2
‘
3 +
n
I I 2 -
b
Flgure 1. (a) Chromatogram of cyclohexane: column 2 rn long, 2.1 mm i.d.; 0.5% squalane on glass beads; carrier gas helium, flow rate 10 mL/min, temperature 40 O C . (b) Chromatogram with maxima in coincidence: sample size 1 = 4.5 ng; 2 = 97 ng; 3 = 286 ng; 4 = 460 ng.
liquid chromatography (’, 21). The standard deviation of the measurement of each one of these parameters calculated from a series of six injections in the same experimental conditions is also given in Table I. Because of the large relative standard deviations of the measurements of the central statistical moments, no significant change of peak shape with the amount injected can be revealed. A large dispersion of the results exists, in spite of the high signal to noise ratio, which is always larger than 250, and in spite of the high quality of the equipment used. The rapid deterioration of the precision of the measurements with increasing order of the moments is quite impressive, as is the loss of precision when comparing peak maximum to first moment measurements or those of the HETP from peak width or from the second momeint. The significant tailing of the elution peak introduces uncertainities in the computation of the central statistical moments, because of the limits of integration (15)l. The procedure described by Petitclerc and Guiochon (22) has been used to
M’, , s
H = LM21 Z = L2MJ M , ’ , cm M ’ , 3 , cmz
250.8 250.8 250.8 250.7 251.5 249.9 250.0 250.6 250.6 251.1 251.6
0.25 0.17 0.19 0.23
0.18 0.16 0.1 5 0.16 0.19
2.0 2.0 2.5 4.0
ix
0.25
0.60
10-3
5.0 2.5 4.0 5.0 7.0 3.0
0.25 0.17
3.0
F
= L2M4/
cm2 2.0
0.5 1.0 1.5 2.0
0.5 1.o 0.5 0.5 0.5
1.o 0.80
improve the precision in the determination of the central statistical moments: an exponential decay is adjusted by numerical computation on the tail of the peak and the numerical integration is replaced with the exact contribution derived from the parameters of the exponential. Nevertheless a large dispersion exists in the determination of the central statistical moments of the tailing peak studied. In previous work with the same instrument, it was shown (21) that the repeatability of Z and F measurements is around 10% for a symmetrical peak (n-pentane eluted on a column packed with 20% squalane on Chromosorb P), with Z = 0.100 cm2. The specific asymmetry is about 30 times larger for the elution peak of cyclohexane on the column used here. For the same reasons the change of the retention time of the mass center of the peak with the amount injected is hardly significant. A larger standard deviation than the one we would have expected from the instrument specifications (19) is observed, however. More interesting is the change of the retention time of peak maximum tMwith the amount injected. The precision of its measurement is good, with a repeatability of 5 X and a significant increase of tM with the amount injected is observed. It seems, on comparison of the two series of data, that the mass center of the peak changes less, when the sample size is increased by 2 orders of magnitude, than the peak maximum (0.3% instead of 0.9%). The plate height H’, calculated from peak width at 0.606 peak height, shows that the elution profile becomes broader when the mass injected is increased. The plate height H which is related to the central statistical moment is larger by about a factor of 2 than H’ because it includes the effects of peak tailing. Because the central statistical moment method is unable to reveal small deviations in peak shapes, we have to use a more sophisticated approach for peak profile comparisons. (2) The Distribution Function Method. The comparison of the shape of the different profiles of Figure 1 is made after normalized profiles obtained by a change in abscissa and a dilatation of both coordinates. First the times t, and t z , corresponding respectively to the times when the signal reaches 10% of peak maximum on the front side of the peak and 5% of the maximum on its rear side, are calculated. The normalized profile is derived from the elution profile f ( t ) by using a normalized time
o = - t - tl
tz - tl
(2)
and dividing by the peak area between times tl and t2,hence
P(0) =
flO(t2
- tl) + tll
J,tzf ( t ) d t
(3)
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ANALYTICAL CHEMISTRY, VOL. 54, NO. 12, OCTOBER 1982
ov
I
0
2
1
Flgure 2. Comparison of two distribution functions: mass injected 4.5 ng for f , ( ~ ) :460 ng for F2(7),
F1 iz)
0
=
1
Flgure 4. Definition of the function T : (curve 1) I ’ ( F 2 , f , , i ) corresponding to the distribution functions on Figure 2; (curve 2) tangent T corresponding to the largest A value.
For a quantitative estimate of the deviation from linearity of the I? curve, the number A is defined as
2A = 101
101
C [7’(~’~,J’~,i) - ~(F,,F,,~)I~ + iC [ T ( F ~ , F-~~~()J ’ ~ , F , , ~ ) I ~ i=l =l (5)
0 0
Z
1
Flgure 3. Comparison of two distribution functions, mass injected: 4.5 ng for f 1(7), 12.5 ng for F2(7); (curve 1) f , ( T ) = F2(7),(curve 2 )
r(F
l,i).
The integral in eq 3 will be designated below as the total peak area, although the small wings of the peak, eluted before t = tl and after t = tz,respectively, have been neglected. Various calculations have proved this to have a negligible effect on the final results. The distribution function is
T is the normalized time corresponding to the elution of a certain fraction of the total peak area. A l/looth fraction of this area is arbitrarily defined as unity and the 101 corresponding values (100 intervals) of the distribution function calculated by eq 4 are plotted as shown in Figure 2. On this figure, there are 101 points on each curve, including the two corners of the square; the distribution functions F1(7)and FZ(7) have been computed from the peak profiles of Figure 1 corresponding to the lowest and largest sample sizes, respectively (chromatogram 1and 4). The fact that these two curves are significatively different shows that the two profiles are different. The comparison of the two distribution functions is obtained by plotting F2(7)as a function of F,(T).The resulting r curve (curve 2 in Figure 3) is the diagonal line of the diagram if the two distribution functions coincide, as in the case of the peak profiles corresponding to the two lowest sample sizes (4.5 and 12 ng), which are thus identical.
Summation is carried out for the 101 values of the functions defined below, corresponding to the 101 values of T obtained above respectively. r(Fl,Pz,i) is the curve generated when the distribution function F,(T) is plotted as a function of F1(7), while for symmetrical reasons I’(F2pl,i) is the curve obtained when F1(7)is plotted as a function of F z ( ~ )Thus . l?(Fl,F2,i) is the curve in Figure 3 while I’(F2,F1,i) would be its symmetrical by respect to the bisector of the axis of coordinates. T(F,,F2,i) is the tangent to the corresponding curve r such that A is maximum, A is for this tangent the sum of the lengths of the 101 horizontal and vertical segments between the curve I’ and its tangent T corresponding to the different values of i. The use of two terms in the RHS of eq 5 has been chosen to give to A the mathematical properties of a distance: with this definition the distance between r and its tangent T is independent of the order in which we take F , and F,. To obtain T we chose the tangent to I‘ in one point and we calculate the corresponding value of A, the calculation is repeated for all 101 different tangents, and the largest A value obtained is a measurement of the deviation from linearity of the I? function. Figure 4 shows the I‘(F,) function and the tangent function T(F,)corresponding to the maximum value of A. An easier procedure would have been to define the modifications of peak shape from the distance of the I‘ curve to the diagonal line, using a definition of this distance similar to the one used in eq 5. But it is less sensitive to peak alterations than the method selected here which calculates the distances of the tangents to the I? curve. In Figure 5 the value of A thus obtained is plotted as a function of the mass of cyclohexane injected. A significantly progressive change in the shape of the elution peak is observed when the mass injected is increased a hundredfold. This reflects the changes in profile seen on Figure I b but in addition provides a well-defined number to measure these changes. Each point on this figure corresponds to the most significant profile obtained from a series of six identical experiments. This profile is chosen by calculating the 15 different A values obtained by comparing each of the profiles to the others and deriving for each profile the sum of its distances A to the five
252. 250.
-
+
k
248. ,005
n
2500
ANALYTICAL CHEMISTRY, VOL. 54, NO. 12, OCTOBER 1982
1945
v
100.
300.
280.
a
400.
i
/
2000
3 1500
n
Flgure 8. Comparison between two elution profiles with maxima set in coincidence: mas injected 4.5 ng for cp, = f , ( A t ) / h,, 460 ng for cp2 = f,(At)/h,; (curve I ) front of the peaks, (curve 2) tail of the peaks.
1000
5B0.
. 005 Figure 5. (a) Shape distance, A, as a function of the mass of cyclohexane iniected. (b) . , Plot of retention time vs. samDle size.
others. The most significant one is the one for which this sum is the smallest. The standard deviation off these sums gives an idea of the reproducibility of the profiles. It is a few units for the profiles corresponding to small sizes. It becomes larger for large sample sizes since the reproducibility of sample size does not exceed a few pe'rcent. (3) Comparison of Ptaak Shapes with Maxima in Coincidence. In order to decide whether the peak profile changes are caused by a nonlinear sorption isotherm or a nonlinear detector responrae, we compared the elution profiles again using the same method except that now the maxima are set in coincidence (Figure lb). The origin of the time scale is now t,, the retention time of the peak maximum ( A t = t - t,, peak height = h). The profile corresponding to the IoweEit sample size is compared with any of the other elution profileci a ( A t ) = f&)/hz by plotting cpz(At) as a function of cpl(At) (cf. Figure 6). Curve 1 is obtained for At < 0 and curve 2 for At > 0. The fact thist the two curves do not coincide shows that the change in peak profile associated to an increase in sample size is not the same on the front and on the tail of the peak and thus originates mainly from nonlinearity of the sorption isotherm. With a linear sorption isotherm and a nonlinear detector response the front and the rear parts of the elution peak will coincide with the detector response curve ieince the change in peak profile is now only a function of the concentration of solute in the column effluent. An example illustrating nonlinearity of the detector response is given in Figure 7. Methane elution peak observed with a helium detector operated at 150 V has been chosen as a reference. The detector is linear in the concentration range covered by elution of that peak. The nonlinear response is obtained for the same amount injected but with the detector operated at 600 V. Accordingly the actual concentration profiles are identical. Only the detector response is different; the two curves obtained for At positive and negative are almost in coincidence.
Figure 7. Comparison of elution profiles of methane obtained with a helium detector: maxima set in coincidence: mass injected, 0.1 pg; peak 1, helium detector, 150 V; peak 2, helium detector, 600 V.
DISCUSSION The variations of peak shape with the amount of sample injected revealed by the distribution function method are probably caused by a nonlinear sorption isotherm, as shown by the procedure which sets in coincidence the peak maxima. If the isotherm is nonlinear, the two curves corresponding to the two edges of the peak (cf. Figure 6) will be different whether the detector is linear or not, so a nonlinear detector cannot be ruled out by this simple test, whenever the isotherm is nonlinear. There are easy ways to test the detector independently, however, for example, by using a column which does not retain the compound under study like an empty glass tube. The case when the detector response lags behind the variation of concentration because of chemical kinetics reason is not taken into account in this discussion. It seems to be more than rare in current chromatography. Changes in peak shape with increasing amount injected are not caused in this work by instrumental constributions since
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ANALYTICAL CHEMISTRY, VOL. 54, NO. 12, OCTOBER 1982
the gaseous volume of sample (2 fiL) has been kept constant while the concentration of cyclohexane vapor is increased, as described in the Experimental Section. The sample volume is small compared to the column gas volume. Yamaoka and Nakagawa (23) have studied the effect of increasing sample injection on elution peak profile and found that extra-column effects can produce significant modifications of peak profiles as estimated from the lower statistical moments when a 2-pL liquid sample is injected, but these effects are not significant in the range 10 times lower. The range of sample size studied by these authors, however, is lo3times larger than the largest amount considered in the present work and as only dilute vapor samples have been injected into the column, the change in peak profiles cannot arise from extra-column effects. The concentration of solute in the gaseous phase at peak maximum can be calculated through the relation (24)
(7) where m is the amount injected, N the number of theoretical plates of the column, and VRo the retention volume. With N = 2500 (cf. Table I, H' = L / N ) and VR0 = 29 cm3, the range of concentration of solute in the gas phase investigated is 3 X lo-' to 3 X g/cm3 at peak maximum and corresponds to a mole fraction range in the gaseous phase X, of 0.8 X 10" to 0.8 X The sorption effect which is the change of gas flow rate caused by the sorption of the solute molecule in the stationary phase is of the same order of magnitude as X, (25) and is thus negligible for the system studied here. Anyway, in the present range of mole fraction in the gaseous phase (lo4 to the modifications of peak shapes cannot be explained by the sorption effect which would produce a steeper leading edge and a larger tailing one with increasing solute concentrations, an effect which is the reverse of what is being observed. The mole fraction of solute in the stationary phase XL is related to the concentration of.solute in the liquid phase c L through the relationship
where mL, V,, and ML are, respectively, the mass, the volume, and the molecular weight of stationary phase in the column. The partition coefficient K , defined in chromatography as the ratio of the concentrations of solute in the gas phase, cg, and in the liquid phase, cL, at equilibrium is related to the retention volume VRo (26) V," = VG KVL = V G (+~ k') (9) One can deduce the mole fraction XL combining eq 8 and 9
+
where VG is the gas hold up of the column. With V G = 3.6 cm3, mL = 53 mg, and ML = 422 g the range of mole fraction in the liquid phase studied X L corresponding to the concentration at peak maximum is 6 X to 6 X Thus the plots of Figure 6 reveal a curvature of the distribution isotherm at 40 "C when the elution profile corresponding to a maximum mole fraction in the liquid phase XL = 6 X loT2is compared to the one observed with XL = 6 X 10-4. Moreover the curve 1in Figure 6 obtained by comparison of the front edges of the two peaks (At < 0) generates a curve located above the diagonal which shows that the peak of larger injected mass whose function is plotted on the ordinates presents a broader front edge than the other. For the rear edges the opposite situation prevails, i.e., the corresponding
+
curve lies below the diagonal. Therefore the distribution isotherm exhibits a positive curvature because of a decrease of the skew ratio with increasing amounts injected (27). These results are in agreement with what could be expected from solution thermodynamics. The small differences in peak shapes cannot, however, be revealed from the study of the central statistical moments or from the change of the retention time tR with increasing amounts injected as shown in Figure 5b, where tR,defined as the abscissa of the mass center of the elution peak, is plotted vs. sample size. Although there is a deviation from horizontal, the result is hardly significant. Large dispersions in the determination of the moments exist in spite of a high signal to noise ratio. This is because of the significant tailing of the elution peak which introduces uncertainities in the computation of the central statistical moments, more exactly in the time to end the integration. On the opposite, when moments are calculated between times tl and t 2 defined above as the limits of peak profile comparisons, they are quite reproducible, but the variation of M2, S, and E with sample size is negligible. Because the precision in the measurement of the retention time of peak maximum is better (Table I), a significant increase of t,, is observed with increasing amounts injected, which indicates a positive curvature of the sorption isotherm (28), in agreement with the conclusions derived from the peak shape comparison method.
CONCLUSION This work shows that the method of shape comparison using distribution functions (17,18) is a very powerful tool to reveal shape alterations which would remain unapparent from moment analysis or by any other technique previously used. The same method also permits a very sensitive comparison between an experimental and a theoretical profile. The direct comparison of peak shape by setting in coincidence the maxima allows an easy decision regarding the origin of the nonlinearity of the response of the system, whether it is due to a nonlinear sorption isotherm or to a nonlinear detector response. This last method indicates also the sign of the curvature of the sorption isotherm. It might even be possible to relate the A vs. sample size plot (cf. figure 5 ) to the curvature of the isotherm at the origin. The choice of the limits for peak comparison tl and t 2 introduces some amount of arbritrariness in the procedure, although the area neglected is small. This choice permits the valid comparison between the profiles of the central part of the peaks. If one is interested in the tailing part as happens sometimes, the integration limits can be widened, for example, by selecting for t 2 the time when the signal is 1% of the peak maximum, provided that the signal to noise ratio is still at least 3 at this level. We can keep the same definition for tl in the comparison of global peak profiles or wait until the signal has decreased to 50% of the maximum after the maximum has been eluted (comparison of tail profiles). LITERATURE CITED (1) Giddings, J. C. "Dynamics of Chromatography,Part I.: Principles and Theory"; Marcel Dekker: New York, 1965. (2) Giddings, J. C.; Eyring, H. J. Phys. Chem. 1955, 59, 416. (3) McQuarrie, D. A. J. Chem. Phys. 1963, 3 8 , 437. (4) Villermaux, J. J . Chromatogr. Sci. 1974, 72, 822. (5) Kucera, E. J . Chromatogr. 1965, 19,237. (6) Grubner, 0.Adv. Chromatogr. 1968, 6 , 173. (7) Grushka, E. J. Phys. Chem. 1972, 76,2566. (8) Houghton, G. J. Phys. Chem. 1963, 67,84. (9) Haarhoff, P. C.; Vanderlinde, H. J. Anal. Chem. 1966, 3 8 , 573. (IO) De Clerk, K.; Buys, T. S. J. Chromatogr. 1972, 67,1. (11) Buys, T. S.; De Clerk, K. J. Chromatogr. 1972, 67, 13. (12) Buys, T. S.; De Clerk, K. Sep. Sci. 1972, 7 ,543. (13) De Clerk, K.; Buys, T. S. J. Chromatogr. 1973, 8 4 , 1. (14) Yamaoka, K.; Nakagawa, T. J. Phys. Chem. 1975, 79,522. Yamaoka, K.; Nakagawa, T. J. Chromatogr. 1975, 103, 221. (15) Cheder, S.N.; Cram, S.P. Anal. Chem. 1971, 43, 1922.
Anal. Chem. 1982, 5 4 , 1947-1951 (16) (17) (18) (19) (20) (21) 122) i23j (24) (25)
Oberhoitzer, J. E.; Rogers, L. B. Anal. Chem. 1969, 4 1 , 1590. Rix, H. These d'Etat e6 !Sciences, IMAN, Universit6 de Nice. Rix, H. J . Chromatogr. '1981, 204, 163. Goedert, M.; Gulochon, (2. Anal. Chem. 1973, 45. 1188. Kleseibach, R. Anal. Chem. 1963, 35, 1342. Vidai-Madjar, C.; Guiochnn, G. J . Chromatogr. 1977, 142, 61. Petltclerc. T.: Guiochon. G. J. Chromatour. Sci. 1976. 14. 531. Yamaoka, K.; Nakagawa, T. Anal. Che6. 1975, 4 7 , 2050. Guiochon, G. J. Chromntogr. 1964, 1 4 , 378. Conder, J. R.; Purneii, J. H. Trans. faraday Soc. 1966, 6 4 , 3100.
1947
(26) Keuiemans, A. I . M. "Gas Chromatography"; Reinhold: New York, 1957. (27) Conder, J. R. Chromatographia 1974, 7 , 387. (28) Ladurelli, A. These d'Etat es Sciences, Universit6 de Paris VI, Paris, 1978.
RECEIVED for review October 19, 1981. Resubmitted March 31, 1982. Accepted June 25, 1982.
Determination of Trace Levels of Nitrosamines in Air by Gas Chrornatography/Low-Resolution Mass Spectrometry Richard S. Marano," Wllliam S. Updegrove, and Ronald C. Machen Ford Motor Company, Analytical Sciences Department, Engineering & Research Sra ff, Dearborn, Michigan 48 12 1
The selective determlnatlon of volatile nltrosamlnes In alr was demonstrated wlth gas chromatography/low-resolutlon mass spectrometry (GC/MS). Hn accepted sampllng method uslng ThermoSorWN cartridges was used. These cartridges were preeiuted to remove interferlng compounds prior to standard nitrosamine elution and selective Ion monrltorlng (SIM) MS detection. Enhanced sensltlvlty was achleved by use of a commercla! concentrator whlch permltted the lntroductlon of 40 pL of eluant onto fused silica capillary and packed columns. Estimated from recovery studies, detectlon iimlts were In the 0.1-0.2 pg/m3 range for seven volatile nitrosamines. The method was applied to the analysls off alr in tire storage areas. N-MitrosodimethyWamlne In the 0.1-0.3 pg/m3 range and N-nltroeomorphoilne (NMOR) In the 0.3-12 pg/m3 range were determined by both QC/MS and the QC/thermal energy analyzer (7'EA). Cartridges not preeiuted tended to yield lower TEA values by a factor of 2-3. A suppressive TEA Interference is suggested.,
The occurrence and determination of N-nitrosamines has received a great deal of attention in recent years (1). These suspected carcinogens have been found in a number of ambient environments and consumer products (2-4). The necessity of determining these compounds at low levels, in complex matrices has resulted in a number of analytical schemes (5-8). Usually, the final analysis has been done with a chemiluminescence based detector (TEA, Thermo Electron Corp., Waltlham, MA) combined with gas or liquid chromatography. This method of detection has proven to be both sensitive and selective. However, interferences have been noted (9-11). Gas chromatographylmass spectrometry (GC/MS) has been the main method of confirmation (12-14). In many instances, it has been necessary to use high-resolution MS to achieve unambiguous confirmation of TEA results (13-15). This paper describes a GC/low-resolution MS method for the selective determination of volatile nitrosamines a t low concentrations in air.
EXPERIMENTAL SECTION Materials,, Methanol (MleOH) and dichloromethane (DCM) were distilled in glass (Burdick and Jackson Inc., Muskegon, MI). Tenax GC (60/80 mesh, Applied Science, State College, PA) was cleaned by heating to 300 "C under a 100 cm3/min flow of carrier grade helium for 4 h. Standards were supplied by the Analytical
Services Laboratory of Thermo Electron Corp. The four-component standard contained N-nitrosodimethylamine (NDMA), N-nitrosodiethylamine (NDEA), N-nitrosodi-n-butylamine (NDBA) and N-nitrosomorpholine (NMOR) each at 25 yg/mL in ethanol. The seven-component standard included Nnitrosodi-n-propylamine (NDPA), N-nitrosopiperidine (NPIP), and N-nitrosopyrrolidine (NPYR) in addition to the four above each at 10 yg/mL in ethanol. Caution: Nitrosamines should be handled with extreme care. Safe procedures have been described elsewhere ( I ) . Apparatus and Operating Conditions. Two Unacon Series 780 (Envirochem Inc., Kemblesville, PA) trapping-concentrators were used. The design and operation of this instrument have been described elsewhere (116). Trap 1 and trap 2 were glass 81/8 in. long X 1/4 in. 0.d. with internal volumes of 2.5 cm3 and 0.1 cm3, respectively. Each was packed with selective adsorbents as supplied by Envirochem Inc. This dual trapping system has been shown to be an efficient means of concentration and solvent removal in a number of similar complex analyses (16). This is the first known application of such a system to nitrosamine determination. The concentration cycle parameters for each Unacon were identical and are given below in Samples and Analysis. One concentrator was connected to a Unacon 780B GC containing a 50 m X 0.2 mm i.d. Carbowax 20M fused silica capillary column (Hewlett-Packwd, Part No. 19091-60150). The column was initially held at 50 "C for 2 min and then programmed at 4 "C/min at 230 "C. Tho helium carrier was flow controlled at a linear velocity of 30 cm/s. After the helium exited the GC oven, the column was heat traced (230 "C) directly into the ion source of a VG Micromass 16F mass spectrometer (VG LTD. Sussex, England). The MS was scanned from 25 to 300 amu once every second, under standard electron impact conditions (70 eV). Data were collected and analyzed with a Finnigan (INCOS) 4000 data system (method A). The other Unacon was interfaced to a Hewlett-Packard 5992B GC-MS-calculatorsystem equipped with a single 9885 floppy disk system. A 2 m X 2 mm 1i.d. glass column packed with Ultrabond 20M (80/100 mesh, Ultra Scientific Inc., Hope, RI) was used. It was held initially at 70 "C for 1min and then programmed at 10 "C/min to 230 "C. The Unacon transfer line and 5992 injection port were maintained at 230 "C. The helium carrier flow was 20 cm3/min. The GC/MS iinterface was a standard Hewlett-Packard supplied jet separator. Data were acquired and analyzed with Hewlett-Packard floppy disk software (Part No. 05992-10017) (method B). This software was used each day to tune the MS automatically as well as to optimize the optics for maximum throughput sensitivity in the region of 100 amu. When obtaining complete spectra, the quadrapole MS was scanned from 25 to 200 amu at 380 amu/s. Most of the actual nitrosamine quantitation was done by using selected ion monitoring (SIM). Three ions of interest were monitored under instrument software control. The
0003-2700/~l2/0354-1947$01.25/0 0 1982 American Chemical Society
