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An ion cyclotron resonance spectrometer as a gas chromatographic detector. The effect of continuous trapping on performance
73
International Journal of Mass Spectrometry and Ion Processes, 72 (1986) 73-84 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
AN ION CYCLOTRON RESONANCE SPECTROMETER AS A GAS CHROMATOGRAPHIC DETECTOR. THE EFFECT OF CONTINUOUS TRAPPING ON PERFORMANCE
BARBARA
S. LARSEN
Chemistry Department, (Received
**, J. WRONKA
*** and DOUGLAS
P. RIDGE
*
’
University of Delaware, Newark, DE 19716 (U.S.A)
10 March 1986)
ABSTRACT Use of an ion cyclotron resonance (ICR) mass spectrometer in the continuous trapping mode as a detector for a gas chromatograph (GC) is illustrated. The long residence time of the ions in the ion source makes ion/molecule reactions inherent to the technique. These reactions are useful in aiding in the identification of samples eluting from the GC. Furtherthe spectra are pressure-independent. more, under the continuous trapping conditions, Factors governing the mass resolution of the ICR spectrometer and chromatographic resolution of the GC-ICR combination are evaluated. In so doing, a closed-form expression is derived for the residence time of an ion in a trapping ICR cell.
INTRODUCTION
The rapid acquisition of mass spectra inherent in the Fourier transform mass spectrometry (FTMS) technique suggested its application to gas chromatography mass spectrometry (GC-MS). FTMS, however, shares features with ion cyclotron resonance (ICR) mass spectrometry that make it very different from conventional mass spectrometric techniques. The study described below probes the possibility of using some of those features as a basis for a unique and possibly useful approach to GC-MS. The experiments were done with the balanced bridge ICR detector, but could have been done using FT detection had that been available. The analysis eventually applies to any cyclotron resonance-based detection scheme. Preliminary results from the study were available before GC-FTMS experiments were carried out and may have played some modest role in facilitating those
* Based, in part, on ref. 1. ** Present address, DuPont Experimental Station, Wilmington, DE 19898, U.S.A. *** Present address, Chemistry Department, Northeastern University, Boston, MA, U.S.A. + To whom correspondence should be addressed.
01681176/86/$03.50
0 1986 Elsevier Science Publishers
B.V.
74
ultimately successful experiments [2]. For that reason, inclusion of an account of the full study is perhaps appropriate. Furthermore, new theoretical discussion of trapping in the type of cell used in ICR and FTMS is presented. In addition, the approach taken here is an example of a possibly useful kind of analysis of analytical mass spectrometric procedures that may be stimulated by the availability of commercial FTMS instruments. Rather than substituting an FTMS instrument in a conventional application, a new approach is found where a cyclotron resonance-based mass spectrometer performs new functions or performs old functions in completely different ways. An advantage of a conventional electron impact mass spectrometry experiment is that the spectrum is invariant over a wide range of sample pressures. This is particularly useful when the mass spectrometer is used to monitor the effluent from a gas chromatograph. The same spectrum is obtained over the entire GC peak which makes it possible to identify different species eluting at the same retention time. Ion/molecule reactions can occur if the sample pressure is too high. In the conventional GC-MS experiment, ion/molecule reactions are not frequently observed. However, in ICR and FTMS, the long resonance times of the ions makes ion/molecule reactions inherent to the technique. In an earlier paper, we demonstrated that. the non-reactive collisions lead to a change in the ion cyclotron resonance line shape as the sample elutes [2(a)]. It was shown that the shape of the K+ resonance was sufficiently sensitive to collision frequencies that isomers with different dipole moments, and therefore different collision frequencies, could be distinguished. At the same time, it was demonstrated that reactive ion-neutral collisions have a dramatic effect on the mass chromatogram. In fact, using the double resonance technique, isomeric ions could be distinguished based on their characteristic reactivity. The coupling of a capillary GC to an FTMS by Gross and co-workers was the first attempt to acquire the full ICR mass spectrum over the GC peak [3]. The rapid spectrum acquisition capabilities of FTMS made it possible to obtain GC profiles of the eluting compound. To obtain high-resolution capabilities, FTMS requires pressures on the order of 10m7 Torr. Using a jet separator, it was feasible to operate at sufficiently low pressures to obtain a resolution of 8000. Recently, a pulsed-valve FTMS interface to a GC has been described [4]. This is one way to reduce the analyzer pressure further to minimize the problem of ion-neutral collisions. Recently, a differentially pumped tandem FTMS cell has been introduced [5]. This design minimizes the effect of collisions by actually transferring ions to a low pressure cell for analysis. A high level of performance has been demonstrated [5]. In this paper, we will discuss the effects of continuous ion trapping in an ICR detector cell on the mass spectrum of a sample eluting from a GC. We
75
show that, under continuous trapping conditions, the ICR spectrum is independent of pressure even though extensive ion/molecule reactions occur. This suggests that a sample could be identified by simply comparing its spectrum to a standard spectrum even though the spectrum was obtained under conditions of extensive ion/molecule reaction. This is an alternative way of dealing with the effects of ion-neutral collisions in using an ion cyclotron resonance-based mass spectrometer as a GC detector. It should be emphasized that this is not a method to obtain the conventional kind of GC-MS data. It does not give electron impact spectra of the GC eluent as a function of time. Thus, standard libraries would be of no use. It provides a kind of self chemical ionization spectrum that will, in general, be very characteristic of a particular sample. This spectrum will be the same across a sample peak. That is, all parts will increase their intensities in proportion to sample pressure. Thus, the spectral pattern is unchanged across the CC peak. The usual kind of quantitation should, however, be possible. THEORY
The kinetic analysis of ICR spectra in which ions are reacting in a closed magnetic trap has been made by Hunter and McIver [6] and Bartmess and Caldwell [7]. The secondary ions are formed by sequential reactions of primary positive ions formed continuously by 70 eV electron impact. Ions are lost to the system as they diffuse to the walls and are neutralized. This loss by diffusion is treated as a pseudo-first-order reaction. At steady state, relative peak intensities depend only on rate constants for the loss process and for ion/molecule reactions. The intensities of all the peaks should increase with pressure but the relative intensities remain fixed. This is precisely what is required for effective GC-MS analysis. The mass spectrum, i.e. the relative intensities of all the peaks, should be independent of sample pressure to facilitate unambiguous identification of the sample. The absolute peak intensities should increase linearly with sample pressure to facilitate quantitation. Another effect that will contribute to the pressure independence of the continuous trapping spectra is the formation of unreactive ions. In a matter of a few steps, reactive fragment ions react to form ions which are stable to further reaction with the parent neutral. Under these circumstances, the continuous trapped spectrum is likely to have peaks only of the unreactive ions. In a conventional high-pressure or chemical ionization mass spectrometer source, these ions might undergo three-body association reactions with the parent neutral. That is much less likely to occur in the ICR trap because the ion residence time is long and the pressure is low. This suggests
76
that the continuous trapped spectrum of a molecule might be thought of as a second-order spectrum in that all the facile second-order processes go to completion in order to give the observed ion populations. This second-order spectrum depends only on properties of the molecule. It depends on the ions formed by unimolecular decomposition of the excited parent ion (the electron impact spectrum or, perhaps, the “first-order” spectrum). It also depends on the reactivity of the parent molecule with its fragments. The only instrumental requirement is that the spectrum be obtained under reaction times which are long enough for facile bimolecular ion/molecule reactions to go to completion. Use of continuous trapping, however, places limita.%ns on interfacing the ICR with a GC. The limitations are manifested in the GC resolution and the ICR mass resolution. A useful measure of GC resolution for the present purpose is the time, T,,, between two barely resolved peaks. The lifetime of the ions in the trap, 7, must be less than Tpc or the mass chromatogram peaks will be broadened and the GC resolution diminished. On the other hand, the trapping time, 7, limits the mass resolution of the spectrometer. The mass resolution will increase as T increases. Thus, there is a trade off between GC performance and mass spectrometer performance. To work this relationship out explicitly, we note that the trapping time is given approximately by
qB2a2 ln[$$ + l]
7=
8mc2(v,
(1)
Where B is the magnetic field (in Gauss), a is the smallest distance between the cell plates parallel to the magnetic perpendicular field (in cm), m is the mass of the ion (in g), c is the speed of light (in cm s-i), 5 is the momentum transfer collision frequency (in s-l), vr is the trapping voltage (in cgs volts), T is the temperature (in Kelvin), q is the charge on the ion, and k is the Boltzmann constant. [Equation (1) is derived in the Appendix 1.1 The relationship between r and mass resolution is a result of the fact that they both depend on 5. If we take the width of the ICR line at half-height as a measure of mass resolution, R,, then “_+L/@:=
(4
4B 2tmc
(2)
Solving Eq. (2) for t and substituting in Eq. (1) gives I-==
ln[z+l]
This shows that the trapping time, 7, must increase linearly with the required mass resolution. On the other hand, 7 must be significantly less
77
than the separation between GC peaks to assure that the chromatographic resolution is not degraded in the mass chromatogram. The consequences of the theory can be illustrated for a particular set of experimental requirements. Suppose that unit mass resolution is required at m/z 500. If the available magnetic field strength is 10 kG (1 T) then, from Eq. (2) 5 must be approximately 190 s-l. The collision frequency depends on the neutral number density, n, and a rate constant for momentum transfer collisions, t/n. For a typical value of t/n (1.0 X lop9 cm3 s- ‘), a to a pressure of 6.0 x 1O-6 Torr collision frequency of 190 s-l corresponds at 300 K. That would then be the maximum sample pressure consistent with a minimum resolution of 500 at m/z 500. The interface between the GC and the ion cyclotron resonance spectrometer and the pumping efficiency of the vacuum system determines whether that condition can be met. It should be noted that the sample pressure varies throughout a GC run and therefore 5; will vary, so a resolution better than the minimum will generally be obtained. Collisions of the ions with the inevitable background pressure of carrier gas molecules ultimately limits the resolution. This is further discussed below. For a given analysis, there will be a minimum required GC resolution as well as a minimum required mass resolution. What is required is that the trapping time given by Eq. (3) is significantly less than the time between GC peaks. Suppose that the minimum separation between the peaks for a particular analysis is 2 s; then T must be less than 2 s. Suppose, further, that, as in the example above, the mass resolution is 500 and the magnetic field is 10 kG. Typical values of the additional parameters would be ur = 1 V, a = 2.54 cm and 7 = 398 K. Substituting these values into Eq. (3) gives 7 = 0.26 s, which is indeed much less than 2 s. It is important to note that the trapping time will increase as the sample pressure decreases. The last ions formed from a given sample diffuse to the walls of the cell only as a result of collisions with background carrier gas. There will be significant tailing if the carrier gas pressure is very low. A pressure of carrier gas that would give a maximum trapping time of 2 s would decrease the minimum mass resolution by only about 10%. Thus, the presence of some carrier gas is necessary for adequate GC performance and the amount of carrier gas required has a minimal effect on the mass resolution of the ion cyclotron resonance spectrometer. Equations (2) and (3) tell us how performance can be optimized. From Eq. (2), we see that to improve mass resolution we can decrease the collision frequency, 5. Equation (3) shows that to decrease the trapping times and minimize loss of GC resolution without affecting mass resolution, we can increase ur or decrease a. It should be possible to increase mass resolution by an order of magnitude or more without loss of GC performance.
78
The present vacuum resolution is limited pressure independence can be illustrated with
system is not optimized for GC performance. Mass to unit resolution at m/z 200. Nevertheless, the and sample specificity of continuous trapping spectra it.
EXPERIMENTAL
The ICR mass spectrometer used in these studies is of a conventional design consisting of a three-region rectangular cell [8]. The source region is 2.54 cm long with the electron beam traversing the center. The analyzer region is 7.62 cm long and the collector 2.54 cm long. The spectra were obtained using a capacitance bridge detector, described elsewhere [9], which was applied to the analyzer region. The detector in the frequency-swept mode can scan the mass range rapidly enough to observe the spectrum on the oscilloscope or the output of the phase-sensitive detector can be amplified to drive the galvanometer of a Honeywell 1580 visicorder oscillograph [15]. A mass spectrum ranging from 40 to 250 m/z can be acquired in 0.1 s. This scan time is short enough so that the total ion concentration does not change significantly during the scan. Continuous trapping is obtained by reducing the drift voltages in the analyzer to zero and setting the trapping voltage at or above 1 V. In the present experiment, a continuous 70 eV electron beam was used to produce ions except for K+, which was produced by heating a rhenium filament onto which potassium oxide had been melted. The vacuum system is coupled to an HP5830A gas chromatograph [16] containing a 6 ft. x l/8 in. 3% 0V17 packed column. The interface consisted of a l/4 in. heated copper line which is split via a three-way needle valve (Nupro 55.2s~). The ICR is evacuated by a 4 in. diffusion pump. The split valve is adjusted so that the pressure of the helium carrier gas being introduced into the ICR is 1 X lop3 Torr. The pressure measurements were made using a Baratron MKS 90 capacitance manometer [17]. All samples were obtained through commercial sources. RESULTS AND DISCUSSION
Shown in Fig. l(a) is a GC chromatogram of a mixture of n-decane, n-nonane, and n-heptane, The chromatogram represents the response of the thermal conductivity detector. The split valve is located on the outlet of the thermal conductivity detector. The ICR can then be used to obtain spectra of the eluting sample. The ICR spectra of each of the samples obtained in this way are shown in Fig. l(b)-(d). Several features of these spectra are worth noting. They differ markedly from the EI spectra of the sample compounds. The base peak in the conventional EI spectra of all these
79
(a)
Cd) ll-DeC%le
71
57
T
0
1
234
66
Fig. 1. (a) GC separation of a 1: 1: 1 mixture of n-heptane, n-nonane, and n-decane. (b) Mass spectrum of n-heptane. (c) Mass spectrum of n-nonane. (d) Mass spectrum of n-decane.
compounds is at m/z 43. The effective reaction time is so long in the ICR that this and other lower mass ions react with the parent neutral and are not observed. The low mass ions react by a variety of processes including Habstraction or H, abstraction. Reactions of this nature have been extensively studied by Lias and Ausloos [lo] and Field [ll]. The compounds were examined at fixed pressure by admitting small amounts through a leak valve. The split valve was open so that He was present at 10m3 Torr. Double resonance experiments were then performed to identify some of the ion/molecule reactions. Double resonance identified reactions (3)-(7) where M represents the neutral alkane, (M - l)+ the ion formed by loss of H- and (M - 2)+, the ion formed by loss of HZ. A result of these reactions is the distinctive triplet at (M - 2)+, (M - l)‘, and M+ that appears in the ICR spectra of each of the alkanes. This simplifies identification of the parent ion. The spectra were monitored on an oscilloscope as the samples eluted from the GC. Spectra were also recorded with an oscillographic recorder. The scan time was approximately 0.1 s. The spectra disappeared completely between peaks, indicating that, while residence times were long enough for extensive reaction, they were not long enough to diminish the GC resolution. C,Hf
+ M -+ (M - l)+ + C,H,
(3)
C,H;
+M+(M-1)++C4H1,,
(4)
80
(a)
Fig. 2. Mass spectrum of cis-decalin. (a) Beginning of GC peak; sample concentration lo-208 of maximum. (b) Top of GC peak; sample concentration at its maximum.
C,H;
+ M + (M - l)+ + C,H,
C,H,f+M+(M-2)++C,H,
(5) (6)
C,Hsf +M+(M-2)++C4Hr0 (7) The spectra in Figs. 2 and 3 indicate that the continuous trapping spectra do not change as the peak elutes. A mixture of cis- and’ turns-decalin was injected into the GC. The trace in Fig. 2(a) was obtained at the beginning of the cis-decalin GC peak when the sample concentraiton was between 10 and 20% of the maximum concentration. The trace in Fig. 2(b) was obtained at the top of the GC peak where the sample concentration is a maximum. Similar spectra for the truns-decalin peak are shown in Fig. 3. Allowance must be made for the fact that the oscillographic recorder did not feed paper at a completely uniform rate when operating at its fastest scan rate. The relative intensities of the peaks are unchanged. This exemplifies the effects discussed in the introduction that lead to pressure-independent spectra, even in the presence of extensive ion/molecule reactions. The spectra monitored
(a)
Fig. 3. kass spectrum of truns-decalin. (a) Beginning of GC peak; sample concentration lo-208 of maximum. (b) Top of GC peak; sample concentration at its maximum.
81
-
-Am
41 L_
Fig. 4. Mass spectrum
of 39Ki- and 41K+ at 1 X 10m3 T of He. Resolution
= m/Am
= 500.
continuously on the oscilloscope disappeared completely between cis- and truns-decalin GC peaks, which is further indication that the ion residence time is not long enough to impede the GC performance. The mass resolution in the spectra in Figs. 1-3 is much better at 10m3 Torr of He than it would be at that pressure of any other gas. This is because He has a low mass and low polarizability and therefore a low momentum transfer cross-section. The momentum transfer collision frequency is given approximately by
where (Yis the polarizability of the neutral (cm3), p is the reduced mass of the ion neutral pair (g), and n is the neutral number density (molecule cme3). Combining Eq. (8) with Eq. (2) gives
R,=
B 15 7oop
for the collision-limited mass resolution in He where p is the He pressure (Torr). Equation (9) was derived assuming infinite ion mass. The resulting error is less than 10% for masses greater than 20 Dalton. The magnetic field swept spectrum in Fig. 4 illustrates the resolution attainable at pressure of 10e3 Torr of He. The 39K resonance is at 7.8 kG. REFERENCES 1 B.S. Larsen, Ph.D. Dissertation, University of Delaware, 1983. 2 (a) M.T. Nguyen, J. Wronka, S. Starry and D.P. Ridge, Int. J. Mass Spectrom. Ion Phys., 40 (1981) 195. (b) M.T. Nguyen and D.P. Ridge, Paper presented at the 27th Annu. Conf.
82
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Mass Spectrom. Allied Top., Seattle, Washington, June 3-8, 1979. (c) Presented in discussion at NATO Advanced Study Institute on the Kinetics of Ion/Molecule Reactions, LaBauIe, France, August 19-29,1978. E.B. Ledford, R.L. White, S. Ghaderi, C.L. Wilkins and M.L. Gross, Anal Chem., 52 (1980) 2450. T.M. Sack and M.L. Gross, Anal Chem., 55 (1983) 2419. R.B. Cody, J.A. Kissenger, S. Ghaderi, J.L. Amster, F.W. McLafferty and L.B. Brown, Anal. Chim. Acta, 178 (1985) 43. R.L. Hunter and R.T. McIver, Anal. Chem., 51 (1979) 699. J.E. Bartmess and G. Caldwell, Int. J. Mass Spectrom. Ion Phys., 41 (1981) 125. J. Allison and D.P. Ridge, J. Am. Chem. Sot., 101 (1979) 4998. J. Wronka and D.P. Ridge, Rev. Sci. Instrum., 53 (1982) 491. S.G. Lias and P. Ausloos, Ion/Molecule Reactions. Their Role in Radiation Chemistry, American Chemical Society, Washington, DC, 1975, Chap. 6. F.H. Field, in J.L. Franklin (Ed.), Ion Molecule Reactions, Vol. 1, Plenum Press, New York, 1972, pp. 261-314. T.E. Sharp, J.R. Eyler and E. Li, Int. J. Mass Spectrom. Ion Phys., 9 (1972) 421. T.J. Francl, E.K. Fukuda and R.T. McIver, Int. J. Mass Spectrom. Ion Phys., 50 (1983) 151. D.P. Ridge and J.L. Beauchamp, J. Chem. Phys., 64 (1976) 2735. Honeywell, Denver, CO 80217, U.S.A., Model 1580. Hewlett Packard, Avondale, PA 19311, U.S.A., Model HP5830A. MKS Instruments, Burlington, MA 01803, U.S.A., Pressure Head Type 90; Indicator Type 9OM-XR.
APPENDIX
Trapping times have been calculated by Sharp et al. neglecting trapping voltage [12] and more recently by Franc1 et al. including trapping voltage [13]. Although the two treatments give the same dependences on experimental parameters such as cell size and magnetic field strength, they are in substantial quantitative disagreement at zero trapping field. We present here a simple calculation of trapping time in the presence of trapping voltage. It gives explicitly a simple closed-form expression for the residence time of an average ion. Furthermore, it gives good agreement with Franc1 et al. except at very low trapping voltage where it goes to the result of Sharp et al. An ion exposed to an electric field, E, perpendicular to a magnetic field, B, will move in the direction of E with a velocity, ur, given by VT=
CE-5
-
B
WC
where 6 is the momentum transfer collision frequency of the ion with neutral background gas molecules, CO,= qB/mc is the cyclotron frequency of the ion which varies inversely with m/q, the mass-to-charge ratio of the ion, and c is the speed of light [14]. We take the cell to consist of plates
83
arranged in a rectilinear shape with square or rectangular sides. The sides perpendicular to the magnetic field are called trapping plates and are biased positive relative to the remaining plates (“drift”, “receiving”, or “transmitting” plates). The electric field experienced by an ion in the cell is given approximately by EE-
4vrx
(A2)
a2
where VT is the potential difference between the trapping plates and other plates making up the cubic or rectangular cell, a/2 is the shortest distance from the electron beam to a negatively biased plate and [(a/2) - x] is the shortest distance from the ion to one of the negatively biased plates [12,13]. An ion is formed at x = 0 and strikes a plate at x = a/2. Typically, a will be the edge of a cubic cell or the smallest dimension of a cell with rectangular plates. The velocity with which the ion approaches the cell wall obtained by substituting Eq. (A2) into Eq. (Al) is given by vr =
4vrxc5
W)
a2w,B
In addition to this field-induced motion, the ions will spread as a result of diffusion, which we treat as a random walk with step length equal to the radius of the cyclotron orbit. In time, t, this diffusion produces a root mean square displacement towards the cell wall given by (x)
=
(Ly2f c
where u given by diffusion they are given by
(A4
is the average ion speed. At small values of x, where the velocity Eq. (A3) due to the trapping field is near zero, the random walk is the only mechanism by which the ions move away from where formed. The velocity resulting from this random walk motion is
We take the total velocity of motion towards the cell wall, v, to be given by v=v,+v,
(A61
and find the effective trapping time 7 from 7
J
vdt=
0
a2
W)
84 TABLE
1
Comparison ref. 13 Trapping
of the trapping
voltage
time, T, from Eq. (A9) and the half-life,
Ratio of trapping
VI-
r/T,,2
0.0 0.1 0.2 0.3 0.4 0.6 0.8 1.0 1.5 2.0 3.0 10.0
3.21 1.66 1.29 1.12 1.02 0.91 0.85 0.82 0.77 0.76 0.75 0.81
TI,2, from Eq. (34) of
times
Combining Eqs. (A3), (A5), and (A6) with Eq. (A7), integrating and solving for r gives 7=
qB2a2 8mc25Vr
69
ln(g+l)
In deriving Eq. (A8), u has been set at [8kT/7rm]‘/*. In practical units, r is given by 7=
Pw/41’2* T T 1
2.05 X 10-29B2a2
Eq. (A7)
In 30 6298 V/’ + 1 [
WI
where B is the magnetic field in Tesla, a is the edge of a cubic cell or the smallest dimension of a rectangular cell in cm, p is the pressure in Torr, V+ is the voltage difference between the trapping plates and the remaining cell plates in practical volts, p is the reduced mass of the ion and the neutral in g, (Yis the angle averaged polarizability of the neutral in cm3, and T is the temperature in K. The trapping time from Eq. (A9) is compared with the half-lives from Eq. (34) of ref. 13 in Table 1. The numbers agree within 25% for trapping voltages greater than 0.2 eV, which is quite satisfactory considering the simplicity of the model. Equation (A9) gives the time for an average ion to reach the cell wall, which is not precisely the same thing as the time required to reduce the population by half. At voltages below 0.2 eV, r will rise rapidly and disagree with the limiting value from Eq. (34) of ref. 13, but the V; = 0 limit of 7 given by Eq. (A9) agrees with the result of the treatment in ref. 12. At low values of VT, however, loss of ions to the trapping plates becomes important and results of these models will be in error anyway.
International Journal of Mass Spectrometry and Ion Processes, 72 (1986) 73-84 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
AN ION CYCLOTRON RESONANCE SPECTROMETER AS A GAS CHROMATOGRAPHIC DETECTOR. THE EFFECT OF CONTINUOUS TRAPPING ON PERFORMANCE
BARBARA
S. LARSEN
Chemistry Department, (Received
**, J. WRONKA
*** and DOUGLAS
P. RIDGE
*
’
University of Delaware, Newark, DE 19716 (U.S.A)
10 March 1986)
ABSTRACT Use of an ion cyclotron resonance (ICR) mass spectrometer in the continuous trapping mode as a detector for a gas chromatograph (GC) is illustrated. The long residence time of the ions in the ion source makes ion/molecule reactions inherent to the technique. These reactions are useful in aiding in the identification of samples eluting from the GC. Furtherthe spectra are pressure-independent. more, under the continuous trapping conditions, Factors governing the mass resolution of the ICR spectrometer and chromatographic resolution of the GC-ICR combination are evaluated. In so doing, a closed-form expression is derived for the residence time of an ion in a trapping ICR cell.
INTRODUCTION
The rapid acquisition of mass spectra inherent in the Fourier transform mass spectrometry (FTMS) technique suggested its application to gas chromatography mass spectrometry (GC-MS). FTMS, however, shares features with ion cyclotron resonance (ICR) mass spectrometry that make it very different from conventional mass spectrometric techniques. The study described below probes the possibility of using some of those features as a basis for a unique and possibly useful approach to GC-MS. The experiments were done with the balanced bridge ICR detector, but could have been done using FT detection had that been available. The analysis eventually applies to any cyclotron resonance-based detection scheme. Preliminary results from the study were available before GC-FTMS experiments were carried out and may have played some modest role in facilitating those
* Based, in part, on ref. 1. ** Present address, DuPont Experimental Station, Wilmington, DE 19898, U.S.A. *** Present address, Chemistry Department, Northeastern University, Boston, MA, U.S.A. + To whom correspondence should be addressed.
01681176/86/$03.50
0 1986 Elsevier Science Publishers
B.V.
74
ultimately successful experiments [2]. For that reason, inclusion of an account of the full study is perhaps appropriate. Furthermore, new theoretical discussion of trapping in the type of cell used in ICR and FTMS is presented. In addition, the approach taken here is an example of a possibly useful kind of analysis of analytical mass spectrometric procedures that may be stimulated by the availability of commercial FTMS instruments. Rather than substituting an FTMS instrument in a conventional application, a new approach is found where a cyclotron resonance-based mass spectrometer performs new functions or performs old functions in completely different ways. An advantage of a conventional electron impact mass spectrometry experiment is that the spectrum is invariant over a wide range of sample pressures. This is particularly useful when the mass spectrometer is used to monitor the effluent from a gas chromatograph. The same spectrum is obtained over the entire GC peak which makes it possible to identify different species eluting at the same retention time. Ion/molecule reactions can occur if the sample pressure is too high. In the conventional GC-MS experiment, ion/molecule reactions are not frequently observed. However, in ICR and FTMS, the long resonance times of the ions makes ion/molecule reactions inherent to the technique. In an earlier paper, we demonstrated that. the non-reactive collisions lead to a change in the ion cyclotron resonance line shape as the sample elutes [2(a)]. It was shown that the shape of the K+ resonance was sufficiently sensitive to collision frequencies that isomers with different dipole moments, and therefore different collision frequencies, could be distinguished. At the same time, it was demonstrated that reactive ion-neutral collisions have a dramatic effect on the mass chromatogram. In fact, using the double resonance technique, isomeric ions could be distinguished based on their characteristic reactivity. The coupling of a capillary GC to an FTMS by Gross and co-workers was the first attempt to acquire the full ICR mass spectrum over the GC peak [3]. The rapid spectrum acquisition capabilities of FTMS made it possible to obtain GC profiles of the eluting compound. To obtain high-resolution capabilities, FTMS requires pressures on the order of 10m7 Torr. Using a jet separator, it was feasible to operate at sufficiently low pressures to obtain a resolution of 8000. Recently, a pulsed-valve FTMS interface to a GC has been described [4]. This is one way to reduce the analyzer pressure further to minimize the problem of ion-neutral collisions. Recently, a differentially pumped tandem FTMS cell has been introduced [5]. This design minimizes the effect of collisions by actually transferring ions to a low pressure cell for analysis. A high level of performance has been demonstrated [5]. In this paper, we will discuss the effects of continuous ion trapping in an ICR detector cell on the mass spectrum of a sample eluting from a GC. We
75
show that, under continuous trapping conditions, the ICR spectrum is independent of pressure even though extensive ion/molecule reactions occur. This suggests that a sample could be identified by simply comparing its spectrum to a standard spectrum even though the spectrum was obtained under conditions of extensive ion/molecule reaction. This is an alternative way of dealing with the effects of ion-neutral collisions in using an ion cyclotron resonance-based mass spectrometer as a GC detector. It should be emphasized that this is not a method to obtain the conventional kind of GC-MS data. It does not give electron impact spectra of the GC eluent as a function of time. Thus, standard libraries would be of no use. It provides a kind of self chemical ionization spectrum that will, in general, be very characteristic of a particular sample. This spectrum will be the same across a sample peak. That is, all parts will increase their intensities in proportion to sample pressure. Thus, the spectral pattern is unchanged across the CC peak. The usual kind of quantitation should, however, be possible. THEORY
The kinetic analysis of ICR spectra in which ions are reacting in a closed magnetic trap has been made by Hunter and McIver [6] and Bartmess and Caldwell [7]. The secondary ions are formed by sequential reactions of primary positive ions formed continuously by 70 eV electron impact. Ions are lost to the system as they diffuse to the walls and are neutralized. This loss by diffusion is treated as a pseudo-first-order reaction. At steady state, relative peak intensities depend only on rate constants for the loss process and for ion/molecule reactions. The intensities of all the peaks should increase with pressure but the relative intensities remain fixed. This is precisely what is required for effective GC-MS analysis. The mass spectrum, i.e. the relative intensities of all the peaks, should be independent of sample pressure to facilitate unambiguous identification of the sample. The absolute peak intensities should increase linearly with sample pressure to facilitate quantitation. Another effect that will contribute to the pressure independence of the continuous trapping spectra is the formation of unreactive ions. In a matter of a few steps, reactive fragment ions react to form ions which are stable to further reaction with the parent neutral. Under these circumstances, the continuous trapped spectrum is likely to have peaks only of the unreactive ions. In a conventional high-pressure or chemical ionization mass spectrometer source, these ions might undergo three-body association reactions with the parent neutral. That is much less likely to occur in the ICR trap because the ion residence time is long and the pressure is low. This suggests
76
that the continuous trapped spectrum of a molecule might be thought of as a second-order spectrum in that all the facile second-order processes go to completion in order to give the observed ion populations. This second-order spectrum depends only on properties of the molecule. It depends on the ions formed by unimolecular decomposition of the excited parent ion (the electron impact spectrum or, perhaps, the “first-order” spectrum). It also depends on the reactivity of the parent molecule with its fragments. The only instrumental requirement is that the spectrum be obtained under reaction times which are long enough for facile bimolecular ion/molecule reactions to go to completion. Use of continuous trapping, however, places limita.%ns on interfacing the ICR with a GC. The limitations are manifested in the GC resolution and the ICR mass resolution. A useful measure of GC resolution for the present purpose is the time, T,,, between two barely resolved peaks. The lifetime of the ions in the trap, 7, must be less than Tpc or the mass chromatogram peaks will be broadened and the GC resolution diminished. On the other hand, the trapping time, 7, limits the mass resolution of the spectrometer. The mass resolution will increase as T increases. Thus, there is a trade off between GC performance and mass spectrometer performance. To work this relationship out explicitly, we note that the trapping time is given approximately by
qB2a2 ln[$$ + l]
7=
8mc2(v,
(1)
Where B is the magnetic field (in Gauss), a is the smallest distance between the cell plates parallel to the magnetic perpendicular field (in cm), m is the mass of the ion (in g), c is the speed of light (in cm s-i), 5 is the momentum transfer collision frequency (in s-l), vr is the trapping voltage (in cgs volts), T is the temperature (in Kelvin), q is the charge on the ion, and k is the Boltzmann constant. [Equation (1) is derived in the Appendix 1.1 The relationship between r and mass resolution is a result of the fact that they both depend on 5. If we take the width of the ICR line at half-height as a measure of mass resolution, R,, then “_+L/@:=
(4
4B 2tmc
(2)
Solving Eq. (2) for t and substituting in Eq. (1) gives I-==
ln[z+l]
This shows that the trapping time, 7, must increase linearly with the required mass resolution. On the other hand, 7 must be significantly less
77
than the separation between GC peaks to assure that the chromatographic resolution is not degraded in the mass chromatogram. The consequences of the theory can be illustrated for a particular set of experimental requirements. Suppose that unit mass resolution is required at m/z 500. If the available magnetic field strength is 10 kG (1 T) then, from Eq. (2) 5 must be approximately 190 s-l. The collision frequency depends on the neutral number density, n, and a rate constant for momentum transfer collisions, t/n. For a typical value of t/n (1.0 X lop9 cm3 s- ‘), a to a pressure of 6.0 x 1O-6 Torr collision frequency of 190 s-l corresponds at 300 K. That would then be the maximum sample pressure consistent with a minimum resolution of 500 at m/z 500. The interface between the GC and the ion cyclotron resonance spectrometer and the pumping efficiency of the vacuum system determines whether that condition can be met. It should be noted that the sample pressure varies throughout a GC run and therefore 5; will vary, so a resolution better than the minimum will generally be obtained. Collisions of the ions with the inevitable background pressure of carrier gas molecules ultimately limits the resolution. This is further discussed below. For a given analysis, there will be a minimum required GC resolution as well as a minimum required mass resolution. What is required is that the trapping time given by Eq. (3) is significantly less than the time between GC peaks. Suppose that the minimum separation between the peaks for a particular analysis is 2 s; then T must be less than 2 s. Suppose, further, that, as in the example above, the mass resolution is 500 and the magnetic field is 10 kG. Typical values of the additional parameters would be ur = 1 V, a = 2.54 cm and 7 = 398 K. Substituting these values into Eq. (3) gives 7 = 0.26 s, which is indeed much less than 2 s. It is important to note that the trapping time will increase as the sample pressure decreases. The last ions formed from a given sample diffuse to the walls of the cell only as a result of collisions with background carrier gas. There will be significant tailing if the carrier gas pressure is very low. A pressure of carrier gas that would give a maximum trapping time of 2 s would decrease the minimum mass resolution by only about 10%. Thus, the presence of some carrier gas is necessary for adequate GC performance and the amount of carrier gas required has a minimal effect on the mass resolution of the ion cyclotron resonance spectrometer. Equations (2) and (3) tell us how performance can be optimized. From Eq. (2), we see that to improve mass resolution we can decrease the collision frequency, 5. Equation (3) shows that to decrease the trapping times and minimize loss of GC resolution without affecting mass resolution, we can increase ur or decrease a. It should be possible to increase mass resolution by an order of magnitude or more without loss of GC performance.
78
The present vacuum resolution is limited pressure independence can be illustrated with
system is not optimized for GC performance. Mass to unit resolution at m/z 200. Nevertheless, the and sample specificity of continuous trapping spectra it.
EXPERIMENTAL
The ICR mass spectrometer used in these studies is of a conventional design consisting of a three-region rectangular cell [8]. The source region is 2.54 cm long with the electron beam traversing the center. The analyzer region is 7.62 cm long and the collector 2.54 cm long. The spectra were obtained using a capacitance bridge detector, described elsewhere [9], which was applied to the analyzer region. The detector in the frequency-swept mode can scan the mass range rapidly enough to observe the spectrum on the oscilloscope or the output of the phase-sensitive detector can be amplified to drive the galvanometer of a Honeywell 1580 visicorder oscillograph [15]. A mass spectrum ranging from 40 to 250 m/z can be acquired in 0.1 s. This scan time is short enough so that the total ion concentration does not change significantly during the scan. Continuous trapping is obtained by reducing the drift voltages in the analyzer to zero and setting the trapping voltage at or above 1 V. In the present experiment, a continuous 70 eV electron beam was used to produce ions except for K+, which was produced by heating a rhenium filament onto which potassium oxide had been melted. The vacuum system is coupled to an HP5830A gas chromatograph [16] containing a 6 ft. x l/8 in. 3% 0V17 packed column. The interface consisted of a l/4 in. heated copper line which is split via a three-way needle valve (Nupro 55.2s~). The ICR is evacuated by a 4 in. diffusion pump. The split valve is adjusted so that the pressure of the helium carrier gas being introduced into the ICR is 1 X lop3 Torr. The pressure measurements were made using a Baratron MKS 90 capacitance manometer [17]. All samples were obtained through commercial sources. RESULTS AND DISCUSSION
Shown in Fig. l(a) is a GC chromatogram of a mixture of n-decane, n-nonane, and n-heptane, The chromatogram represents the response of the thermal conductivity detector. The split valve is located on the outlet of the thermal conductivity detector. The ICR can then be used to obtain spectra of the eluting sample. The ICR spectra of each of the samples obtained in this way are shown in Fig. l(b)-(d). Several features of these spectra are worth noting. They differ markedly from the EI spectra of the sample compounds. The base peak in the conventional EI spectra of all these
79
(a)
Cd) ll-DeC%le
71
57
T
0
1
234
66
Fig. 1. (a) GC separation of a 1: 1: 1 mixture of n-heptane, n-nonane, and n-decane. (b) Mass spectrum of n-heptane. (c) Mass spectrum of n-nonane. (d) Mass spectrum of n-decane.
compounds is at m/z 43. The effective reaction time is so long in the ICR that this and other lower mass ions react with the parent neutral and are not observed. The low mass ions react by a variety of processes including Habstraction or H, abstraction. Reactions of this nature have been extensively studied by Lias and Ausloos [lo] and Field [ll]. The compounds were examined at fixed pressure by admitting small amounts through a leak valve. The split valve was open so that He was present at 10m3 Torr. Double resonance experiments were then performed to identify some of the ion/molecule reactions. Double resonance identified reactions (3)-(7) where M represents the neutral alkane, (M - l)+ the ion formed by loss of H- and (M - 2)+, the ion formed by loss of HZ. A result of these reactions is the distinctive triplet at (M - 2)+, (M - l)‘, and M+ that appears in the ICR spectra of each of the alkanes. This simplifies identification of the parent ion. The spectra were monitored on an oscilloscope as the samples eluted from the GC. Spectra were also recorded with an oscillographic recorder. The scan time was approximately 0.1 s. The spectra disappeared completely between peaks, indicating that, while residence times were long enough for extensive reaction, they were not long enough to diminish the GC resolution. C,Hf
+ M -+ (M - l)+ + C,H,
(3)
C,H;
+M+(M-1)++C4H1,,
(4)
80
(a)
Fig. 2. Mass spectrum of cis-decalin. (a) Beginning of GC peak; sample concentration lo-208 of maximum. (b) Top of GC peak; sample concentration at its maximum.
C,H;
+ M + (M - l)+ + C,H,
C,H,f+M+(M-2)++C,H,
(5) (6)
C,Hsf +M+(M-2)++C4Hr0 (7) The spectra in Figs. 2 and 3 indicate that the continuous trapping spectra do not change as the peak elutes. A mixture of cis- and’ turns-decalin was injected into the GC. The trace in Fig. 2(a) was obtained at the beginning of the cis-decalin GC peak when the sample concentraiton was between 10 and 20% of the maximum concentration. The trace in Fig. 2(b) was obtained at the top of the GC peak where the sample concentration is a maximum. Similar spectra for the truns-decalin peak are shown in Fig. 3. Allowance must be made for the fact that the oscillographic recorder did not feed paper at a completely uniform rate when operating at its fastest scan rate. The relative intensities of the peaks are unchanged. This exemplifies the effects discussed in the introduction that lead to pressure-independent spectra, even in the presence of extensive ion/molecule reactions. The spectra monitored
(a)
Fig. 3. kass spectrum of truns-decalin. (a) Beginning of GC peak; sample concentration lo-208 of maximum. (b) Top of GC peak; sample concentration at its maximum.
81
-
-Am
41 L_
Fig. 4. Mass spectrum
of 39Ki- and 41K+ at 1 X 10m3 T of He. Resolution
= m/Am
= 500.
continuously on the oscilloscope disappeared completely between cis- and truns-decalin GC peaks, which is further indication that the ion residence time is not long enough to impede the GC performance. The mass resolution in the spectra in Figs. 1-3 is much better at 10m3 Torr of He than it would be at that pressure of any other gas. This is because He has a low mass and low polarizability and therefore a low momentum transfer cross-section. The momentum transfer collision frequency is given approximately by
where (Yis the polarizability of the neutral (cm3), p is the reduced mass of the ion neutral pair (g), and n is the neutral number density (molecule cme3). Combining Eq. (8) with Eq. (2) gives
R,=
B 15 7oop
for the collision-limited mass resolution in He where p is the He pressure (Torr). Equation (9) was derived assuming infinite ion mass. The resulting error is less than 10% for masses greater than 20 Dalton. The magnetic field swept spectrum in Fig. 4 illustrates the resolution attainable at pressure of 10e3 Torr of He. The 39K resonance is at 7.8 kG. REFERENCES 1 B.S. Larsen, Ph.D. Dissertation, University of Delaware, 1983. 2 (a) M.T. Nguyen, J. Wronka, S. Starry and D.P. Ridge, Int. J. Mass Spectrom. Ion Phys., 40 (1981) 195. (b) M.T. Nguyen and D.P. Ridge, Paper presented at the 27th Annu. Conf.
82
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Mass Spectrom. Allied Top., Seattle, Washington, June 3-8, 1979. (c) Presented in discussion at NATO Advanced Study Institute on the Kinetics of Ion/Molecule Reactions, LaBauIe, France, August 19-29,1978. E.B. Ledford, R.L. White, S. Ghaderi, C.L. Wilkins and M.L. Gross, Anal Chem., 52 (1980) 2450. T.M. Sack and M.L. Gross, Anal Chem., 55 (1983) 2419. R.B. Cody, J.A. Kissenger, S. Ghaderi, J.L. Amster, F.W. McLafferty and L.B. Brown, Anal. Chim. Acta, 178 (1985) 43. R.L. Hunter and R.T. McIver, Anal. Chem., 51 (1979) 699. J.E. Bartmess and G. Caldwell, Int. J. Mass Spectrom. Ion Phys., 41 (1981) 125. J. Allison and D.P. Ridge, J. Am. Chem. Sot., 101 (1979) 4998. J. Wronka and D.P. Ridge, Rev. Sci. Instrum., 53 (1982) 491. S.G. Lias and P. Ausloos, Ion/Molecule Reactions. Their Role in Radiation Chemistry, American Chemical Society, Washington, DC, 1975, Chap. 6. F.H. Field, in J.L. Franklin (Ed.), Ion Molecule Reactions, Vol. 1, Plenum Press, New York, 1972, pp. 261-314. T.E. Sharp, J.R. Eyler and E. Li, Int. J. Mass Spectrom. Ion Phys., 9 (1972) 421. T.J. Francl, E.K. Fukuda and R.T. McIver, Int. J. Mass Spectrom. Ion Phys., 50 (1983) 151. D.P. Ridge and J.L. Beauchamp, J. Chem. Phys., 64 (1976) 2735. Honeywell, Denver, CO 80217, U.S.A., Model 1580. Hewlett Packard, Avondale, PA 19311, U.S.A., Model HP5830A. MKS Instruments, Burlington, MA 01803, U.S.A., Pressure Head Type 90; Indicator Type 9OM-XR.
APPENDIX
Trapping times have been calculated by Sharp et al. neglecting trapping voltage [12] and more recently by Franc1 et al. including trapping voltage [13]. Although the two treatments give the same dependences on experimental parameters such as cell size and magnetic field strength, they are in substantial quantitative disagreement at zero trapping field. We present here a simple calculation of trapping time in the presence of trapping voltage. It gives explicitly a simple closed-form expression for the residence time of an average ion. Furthermore, it gives good agreement with Franc1 et al. except at very low trapping voltage where it goes to the result of Sharp et al. An ion exposed to an electric field, E, perpendicular to a magnetic field, B, will move in the direction of E with a velocity, ur, given by VT=
CE-5
-
B
WC
where 6 is the momentum transfer collision frequency of the ion with neutral background gas molecules, CO,= qB/mc is the cyclotron frequency of the ion which varies inversely with m/q, the mass-to-charge ratio of the ion, and c is the speed of light [14]. We take the cell to consist of plates
83
arranged in a rectilinear shape with square or rectangular sides. The sides perpendicular to the magnetic field are called trapping plates and are biased positive relative to the remaining plates (“drift”, “receiving”, or “transmitting” plates). The electric field experienced by an ion in the cell is given approximately by EE-
4vrx
(A2)
a2
where VT is the potential difference between the trapping plates and other plates making up the cubic or rectangular cell, a/2 is the shortest distance from the electron beam to a negatively biased plate and [(a/2) - x] is the shortest distance from the ion to one of the negatively biased plates [12,13]. An ion is formed at x = 0 and strikes a plate at x = a/2. Typically, a will be the edge of a cubic cell or the smallest dimension of a cell with rectangular plates. The velocity with which the ion approaches the cell wall obtained by substituting Eq. (A2) into Eq. (Al) is given by vr =
4vrxc5
W)
a2w,B
In addition to this field-induced motion, the ions will spread as a result of diffusion, which we treat as a random walk with step length equal to the radius of the cyclotron orbit. In time, t, this diffusion produces a root mean square displacement towards the cell wall given by (x)
=
(Ly2f c
where u given by diffusion they are given by
(A4
is the average ion speed. At small values of x, where the velocity Eq. (A3) due to the trapping field is near zero, the random walk is the only mechanism by which the ions move away from where formed. The velocity resulting from this random walk motion is
We take the total velocity of motion towards the cell wall, v, to be given by v=v,+v,
(A61
and find the effective trapping time 7 from 7
J
vdt=
0
a2
W)
84 TABLE
1
Comparison ref. 13 Trapping
of the trapping
voltage
time, T, from Eq. (A9) and the half-life,
Ratio of trapping
VI-
r/T,,2
0.0 0.1 0.2 0.3 0.4 0.6 0.8 1.0 1.5 2.0 3.0 10.0
3.21 1.66 1.29 1.12 1.02 0.91 0.85 0.82 0.77 0.76 0.75 0.81
TI,2, from Eq. (34) of
times
Combining Eqs. (A3), (A5), and (A6) with Eq. (A7), integrating and solving for r gives 7=
qB2a2 8mc25Vr
69
ln(g+l)
In deriving Eq. (A8), u has been set at [8kT/7rm]‘/*. In practical units, r is given by 7=
Pw/41’2* T T 1
2.05 X 10-29B2a2
Eq. (A7)
In 30 6298 V/’ + 1 [
WI
where B is the magnetic field in Tesla, a is the edge of a cubic cell or the smallest dimension of a rectangular cell in cm, p is the pressure in Torr, V+ is the voltage difference between the trapping plates and the remaining cell plates in practical volts, p is the reduced mass of the ion and the neutral in g, (Yis the angle averaged polarizability of the neutral in cm3, and T is the temperature in K. The trapping time from Eq. (A9) is compared with the half-lives from Eq. (34) of ref. 13 in Table 1. The numbers agree within 25% for trapping voltages greater than 0.2 eV, which is quite satisfactory considering the simplicity of the model. Equation (A9) gives the time for an average ion to reach the cell wall, which is not precisely the same thing as the time required to reduce the population by half. At voltages below 0.2 eV, r will rise rapidly and disagree with the limiting value from Eq. (34) of ref. 13, but the V; = 0 limit of 7 given by Eq. (A9) agrees with the result of the treatment in ref. 12. At low values of VT, however, loss of ions to the trapping plates becomes important and results of these models will be in error anyway.