Anal. Chem. 1980,
Table 111. Mean Values of Aromaticity Calculated for Each Method From Six Independent Integral Intensity Measurements for All Delay Times Used sample I I1
I11 Ma
C1
c 2
c 3
c 4
c 5
0.706 0.760 0.769 0.745
0.733 0.755 0.769
0.754 0.763 0.771 0.763
0.699 0.733 0.755 0.729
0.727 0.746 0.791 0.755
0.752
a M = mean value of aromaticity obtained from methods 1-111.
intensities measurements, are below 10% relative. T h e relative error of measurement according to Equation 3 for measured relaxation times and the shortest delay time (1.1s) is maximally 10% and consequently its value has to fall with increasing TD. By using gated decoupling and relaxation reagent, the influence of NOE is eliminated for all carbons and thus the results of aromaticity determination are changed. Which types of carbons are influenced mostly in this manner, is very difficult to say, because of the complex character of the samples. The NOE is considered to be completely suppressed using delay times T DL 9 T,(28) in method 11;thus the mean aromaticity is still influenced with the conditions of measurements used. From the practical point of view, it is possible to accept the correct values of aromaticity in the range *6% relative from the mean value, obtained by each independent method (1-111) using delay times 1-21 s for this type of sample.
ACKNOWLEDGMENT We wish to express our sincere thanks to Dr. P. KubSEek, Department of Physical Chemistry, UJEP Brno, for the
52, 1797-1803
1797
measurement of ESR spectra.
LITERATURE CITED Fischer, P.; Stadelhofer, J. W.; Zander, M. fuel 1978, 57,345. Bartle, K . D.; Martin, T. G.; Williams, D. F. fuel 1975, 54,226. VanderHart, D. L.; Retcofsky, H. L. f u e l 1976, 55, 202. Bartuska. V. J.; Maciel. G. E.; Schaefer, J.; Stejskai, E. 0.Fuel 1977, 56,354. (5) Retcofsky, H. L.; VanderHart, D. L. fuel1978, 57,421. (6) Schweighardt, F. K.; Friedei, R. A . ; Retcofsky, H. L. Appl. Spectrosc. 1976, 30, 291. (7) Schweighardt, F. K.; Retcofsky, H. L.; Friedel, R. A. fuel 1976, 55,313. (8) Cantor, D. M. Anal. Chem. 1978, 50, 1185. (9) Yokono, T.; Miyazawa, K.; Sanada, Y. Fuel 1978, 57, 555. (10) Gavalas, G. P.; Oka, M. Fuel1978, 57, 285. (11) DoGru, R.; Erbatur, G.; Gaines, A. F.: Yiirum, Y.: Icli, S.: Wirthlin, T. fuel 1978, 57, 399. (12) HBjek, M.: Sklenii, V ; Sebor, G.; Lang, I.;Weisser, 0.Anal. Chem. 1978, 50, 773. (13) Thiauit, L.; Mersseman, A. Org. Magn. Reson. 1976, 8, 28. (14) Schoolery, J. N. Progr. Nucl. Magn. Reson. 1977, 77, 79. (15) Dorn, H. C.; Wooton, D. L. Anal. Chem. 1976, 48, 2146. (16) Seshadri, K. S.; Rubedo, R. F.; Jewell, D. M.; Malone. H. P. Fuei1978, 57, 549. (17) Dereppe, J. M.; Moreaux, C.; Castex, H. Fuel 1978, 57, 435. (18) Rectcofsky, H. L.; Friedel, R. A. Fuel, 1976, 55, 363. (19) Freeman, R.; Hill, H. D. W.; Kaptein, R. J . Magn. Reson. 1972, 7,327. (20) Horrocks, W. De W. "NMR of Paramagnetic Molecules", LaMar, G. N., Ed.; Academic Press: New York, 1973; p 429. (21) Sass, M.; Ziessow, D. J . Magn. Res. 1977, 25, 263-76. (22) Knight, S. A. Chemy Ind. 1967, 1920. (23) Yen, T. F. "Chemistry of Asphaltenes in Coal Liquids". Preprint of the University of Southern California, 1977. (24) Leyrla, J. R.; Levy. G. C. "Topics in Carbon-13 NMR Spectroscopy", Levy, G. C., Ed.; Wiley-Interscience: New York, 1974; Vol. I. p 90. (25) Likes, J. "Projecting of Industrial Experiments"; SNTL: Prague, 1968; p 166. (26) System IBM 360, Scientific Subroutine Package, version 111, Russ. transi., Statistika, Moscow, 1974. (27) Tukey, J. W. Biometrics 1949, 5, 232. (28) Harris, R. K.; Newman. R. H. J . Magn. Reson. 1976, 24, 449. (1) (2) (3) (4)
RECEIVED for review February 27, 1.979. Resubmitted May 3, 1980. Accepted May 12, 1980.
Ion Mobilities and Residence Times under Chemical Ionization Conditions C. W. Polley, Jr., A. J. Illies, and G. G. Meisels" Department of Chemistry, University of Nebraska -Lincoln,
Lincoln, Nebraska 68588
A pulsed chemical ionization (CI)source employing a coaxial electron entrance-ion exit geometry has been used to obtain ion mobility data for various CI reagent ions. Ion mobilities obtained by this method are in good agreement with results obtained by drift tube measurements where comparison is possible. Ion mobility measurements performed at 125-150 O C provide information regarding the residence times of reagent ions under typical CI conditions. Residence times lie in the range 50-150 ps ( E / P = 5 V/(cm torr); T = 150 O C ; ion pathlength = 1.0 cm).
Since the first analytical application of chemical ionization mass spectrometry (CIMS) was reported by Munson and Field in 1966 (I),CIMS has developed into an extremely useful tool in analytical chemistry (2-7). CI spectra are the result of consecutive ion-molecule reactions and are usually kinetically controlled. A simple kinetic analysis (Appendix) shows that the conversion of sample 0003-2700/80/0352-1797$01 .OO/O
molecules to ions can be related to the residence times of reactant ions in the source (tL),the rate constants k , for the reactions of these ions with the sample molecules, and the concentration of sample molecules. [MI, approximated by
where ZToTSis the total intensity of the sample ions and IiR is the intensity of the reactant ion a t m / e = i . Since the CI response is related to sample concentration through the term in the parentheses, one can treat this term as the CI sensitivity for the sample. Knowledge of each component of this term can then be used to estimate sample sensitivities and detection limits for compounds of interest prior to experimentation. Reactant ion intensities can easily be obtained from the background spectrum of the reagent gas. The rate constant and reaction time, however, are not so easily obtained. Studies of exothermic ion-molecule reactions have indicated that the rate constants for these reactions increase with increasing polarizability and increasing dipole moment of the sample molecules. On the basis of these results a number of theories ?2 1980 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 5 2 , NO. 12, OCTOBER 1980
' 3 cm
0
ions are detected with an electron multiplier. Time delays between the electron pulse and the detected ion pulse are converted to pulse heights, and these pulses are sorted on a 400 channel Technical Measurements Corp. pulse-height analyzer to produce an arrival time distribution for the mass preselected ion. The multichannel analyzer is interfaced to a Varian 620/L minicomputer equipped with 16K core storage and a dual floppy disk syst,em. Additional peripherals include an IBM selectric typewriter for input/output (I/O) and a Hewlett-Packard Model 2D-2 x-y recorder used for plotting the arrival time distributions.
RESULTS AND DISCUSSION d
e C Figure 1. Ion source diagram: (a) ion exit plate; (b) drift guard rings; (c) pressure gauge connection; (d) fihment; (e)gas inlet and thermalizing
chamber have been proposed that can be used to predict the required rate constants (8-1 1 ) . The CI source can be viewed as a miniature drift tube under CI conditions. Ion residence times can therefore be calculated from idealized ion drift considerations originally developed by Langevin (12) and summarized by McDaniel (13). However, such calculated residence times can be substantially in error even under idealized drift conditions (13-16). Ion mobilities for a large variety of ions have been measured by using drift tube (13, 17) and flow drift techniques (18), but these measurements are generally performed a t or near room temperature. T h e temperature dependence of the reduced mobilities for a number of ions has been reviewed (13, 16, 17) but t h e data rarely extend beyond 25 "C. Karasek and coworkers have recently reported the variation of reduced mobilities for several reactant ions in the temperature range 20-200 "C by use of plasma chromatography (PC) (19). These measurements were designed to study the cluster ions observed in PC with N2 as the carrier gas and focus primarily on the clustering equilibria. Ion mobilities of several polyatomic ions have been obtained over a temperature range of -200 to +150 " C from measurements of ion cyclotron resonance line widths (20,21). We have recently constructed a pulsed, high-pressure ionization source that employs a colinear geometry and report here on its use for the determination of ion mobilities and residence times under typical chemical ionization conditions.
EXPERIMENTAL SECTION Apparatus. The instrument used for these studies is a 60" sector Varian-MAT CH-4 mass spectrometer that has been modified for high-pressure operation. With the exception of the installation of a new ion source, the instrumentation has undergone only minor modifications since it was first described ( 2 2 ) . A schematic diagram of the new colinear ion source, which is described in detail elsewhere (23),is shown in Figure l. The distance from electron entrance (0.04 cm diameter pinhole) to the ion exit slit (0.54 x 0.008 cm) is 2.29 cm. The drift guard rings establish a uniform field over an axial cross section of 25 mm'. Not shown in Figure 1 are two heater wells, two platinum resistance thermometer wells, and two 0.25 cm diameter channels through which a cooling gas can be passed to lower the source temperature if desired. The ion source presently has a temperature range of -100 to +300 "C. Procedure. The reagent gas is introduced into the ion source via a Granville-Phillips metering valve. The pressure in the ion source (0.52.0torr) is measured with a MKS Baratron capacitance manometer. When binary gas mixtures are studied, the minor component is introduced first, its pressure is measured, and then the major gas is introduced through a second leak valve, until a specified total pressure (0.5-1.0 torr) is achieved. The gas is ionized by a 0.1-ps pulse of electrons having an energy of 20 eV. Ions are allowed to drift to the exit slit and are then accelerated by a 2-kV potential. After passing through the magnet,
Mobility Measurements. T h e drift velocity, u d , of ions in gases is related to the applied field strength, E (V/cm), by the relationship Ud
= KE
( 2)
where K is the mobility which is dependent on the pressure ( P )and temperature ( r ) of the neutral gas. I t is customary to express the mobility as a reduced mobility KO,which is the mobility reduced to a standard gas number density'of 2.69 x 1019/cm3. If one further expresses the drift velocity in terms of the measured drift distance, d , and the drift time, t d , one obtains Ud
= d/td = K o ( 7 6 0 E / P ) ( T / 2 7 3 )
(3)
The reduced mobility is directly accessible from ion drift theory and is given by
KO = 3 5 . 9 / ( a p ) ' / 2
(4)
where CY is the polarizability of the neutral in atomic units (0.529 A) and p is the reduced mass of the ion-molecule pair in atomic units. T h e scattering of an ion is determined by both a long-range attractive polarization potential and short-range repulsive forces. At low temperatures, the polarization potential predominates and the reduced mobility may be estimated by eq 4 for the purpose of comparison. The quantity measured in our experiment is an average arrival time which is composed of two components, the average drift time, td, and an analyzer time, t,, which includes the ion transit time through the acceleration and mass analysis regions of the mass spectrometer, as well as small delays in the electron multiplier and electronics. For low field conditions, the calculations of Wannier (24) show that the drift velocity will remain directly proportional to E / P , and eq 3 will hold. The intercept of a plot of average arrival time vs. (E/P)-' yields the flight time through the analyzer, t,. The reduced mobility is readily obtained from the slope. In separate experiments designed to characterize the operation of the colinear source, it was observed that with the use of high-energy electrons as commonly employed in CI experiments, ionizing events could occur throughout the ion source due to penetration of the ionizing electrons (23). This results in an undefined point of ion formation and, hence, an undefined drift distance. In order to keep penetration to a minimum, we employed ionizing energies of 20 eV, sufficient to just produce measurable ion intensities, throughout these experiments. Operating at low energies also ensures that secondary electrons have an energy that is insufficient to cause further ionization. For ions originating from a point source and detected through a slit of width A y and infinite length, the detected ion current is given by (25)
where no is the number of ions, and DT and
DL
are the dif-
ANALYTICAL CHEMISTRY, VOL. 52, NO. .12, OCTOBER 1980
-
0
20
40
60
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80
ARRIVAL TIME, p s e c Figure 2. Experimental and calculated arrival time distributions for H,+ in H, at (a) 0.25 torr and (b) 1.00 torr
fusion coefficients for transverse and longitudinal motion, respectively (24). At low fields, these become equal and are reduced to the Einstein relation D = DL = DT = K ( h T / e ) where K is in cm2 V-' s-l, k is the Boltzmann constant, and e is the electron charge. Space charge associated with the expanding ion packet may affect drift velocity measurements (26). Expansion transverse to the applied field decreases the ion collection efficiency, and parallel expansion distorts the shape of the arrival time spectra, but this effect should be symmetrical. Agreement of experimental arrival time distributions at low E/P with those calculated by using the drift-diffusion equations appropriate to the geometry of the apparatus employed has been used to support the absence of space charge effects (26). Such a comparison is shown in Figure 2. The dots refer to the experimental arrival time distributions obtained for H3+ in H2 at source pressures of 0.25 and 1.00 torr (E/P= 5.24 V/(cm torr); T = 125 "C; 20-eV electrons). The solid curves represent the profiles calculated with eq 5 using values for ud and K obtained from high-pressure (1.25-1.5 torr) measurements. The experimental profile a t 1.0 torr is somewhat broader than the calculated one, but its distortion is symmetrical. The peak maxima of the two profiles are in excellent agreement, indicating that the electron entrance has the characteristics of a point source a t this pressure and that reliable drift velocity measurements are obtainable. However, the experimental data obtained a t 0.25 torr deviate significantly from the predicted response. This can be attributed to the penetration of the ionizing electrons into the source. Figure 3 shows the variation of the measured drift velocities for H3+ in H2 with increasing E / P a t several H, source pressures. T h e solid line was obtained from measurements a t high source pressures (1.25-1.50 torr). The data at 1.0 torr agree very well with the high-pressure result throughout the entire E/Prange studied. At the lower pressures, the apparent drift velocities at low values of E/Pdeviate from the expected values. At higher E/Pvalues, however, the measured velocities coincide well with the high-pressure results. We believe that the higher extraction potentials required to produce these E/P values retard the electrons and thus reduce electron penetration. Of the gases studied, the data for hydrogen exhibited the most severe effect of electron penetration on the measured drift velocities. These results then established a lower limit for the operating source pressure of about 0.5 torr to obtain reliable measurements. It is possible to operate a t pressures below this limit if measurements at high values of E/Pindicate that eq 3 still holds. The reduced mobilities for several ions measured a t 25 "C are given in Table I. The precision of the measurements is quite good, generally =tl%or better. The accuracy of the determinations is limited to f 5 % by the pressure, tempera-
0
5
E/P,
IO 15 V/crn- torr
Figure 3. Measured drift velocities with increasing values of E l f for H', in H:, (m) 0.25 torr; (0)0.50 torr; (A)1.OO torr. T = 125 "C; 2 0 e V electrons. Lines were drawn by using drift-diffusion theory ___.__
Table I. Comparison of Reduced Mobilities at 2 5 C K O ,crn'/(v s )
polarion He+ He,' Ne+ Ne,+ Ar'
neutral
iza-
this work
lit.a
tionb
He He Ne
10.40 t 0.05c 10.4 i 0.10 21.4 16.7 t 0.17 18.5 15.55 i- 0.14 4.1-4.2 6.93 3.73 t 0.02 6.14 6.00 Ne 5.64 * 0.07 1.4-1.6 2.42 1.35 t 0.01 Ar 1.833 t 0.008 2.10 1.56 t 0.01 Ar,' Ar 0.90-0.96 1.35 Kr' 0.856 t 0.003 Kr 0.58 0.86 Xe" Xe 0.515 i 0.003 1.87 t 0.06 2.81 1.78 i 0.01 N, N,' 2.33 i 0.06 2.43 2.01 t 0.01 N, N,+ 2.32 t 0.02" 3.00 2.21 i 0.03 CH, CH,' 2.68 2.06 c 0.03 2.28 f O.OZd C,H,+ CH, a Unless noted the reduced mobilities are from the compilation by McDaniel and Mason ( I 7). b Calculated from eq 4. 95% confidence limit. Ridge and Beauchamp (27).
ture, and average arrival time measurements. The literature values cited are from the compilation of McDaniel and Mason (17)and were obtained by conventional drift tube and stationary afterglow techniques. For Ne+, Ar+, and Kr+ several values were reported. These are represented by the ranges shown and provide an estimate of f 5 % for the accuracy of these measurements. The mobilities of several ions in CH4 were obtained from measurements of the collision broadening of ion cyclotron resonance lines of the ions ( 2 7 ) . This is not an established technique for obtaining ion mobilities. However, the excellent agreement of the H3+mobility in H2 of 11.03 f 0.14 cm2/(V s ) compared with the drift tube value of 11.1 f 0.5 cm2/(V s) (28) leads one to assume that the values for CH5+and C2H,+ are reliable. The discrepancies between the values of this work and literature values generally range from about 5 to 10%; that is, they are within the combined error limits of the two methods. The discrepancies for the Ar2+and N4+reduced mobilities are significantly larger: 15 and 14%, respectively. The drift velocities for N4+in N2 as a function of E/P were obtained at several pressures from 0.5 to 1.0 torr (Figure 4). For each
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ANALYTICAL CHEMISTRY, VOL. 52, NO. 12, OCTOBER
1980 _______
Table 11. Reduced Mobilities and Ion Residence Times for a Variety of Common CI Reagent Gas Ions ion He+ He2+ Ar' Ai,+ N2+ N,+ H,+
neutral
T," C
He He Ar Ar
150 150 150 150
N2
125
125 125 150 150 150 125 7 25 125
N2
HZ
CH,+ C2H5+ C,H,+ t-C,H,+ N 0'
CH, CH, CH, i-C,Hlo NO NZ H2O Ar
K O ,c m 2 / ( vs ) 9.07 t 17.12 i 1.34 i 1.77 5 1.72 i 2.21 t
7 , U P S
0.03c (21.4)d 0.06 (18.5) 0.01 (2.42)
10 130
0.01 ( 2 . 1 0 ) 0.01 (2.81)
100 99
0.02 (2.43)
77 15 65 64 220 100 61 120 58 130 150
11.06 i 0.06 (14.2)
19
N,b
3.1 1.2 7.1 4.0 6.3 3.6 2.8 5.2 4.0 3.6 10.2 6.2 3.8 9.2 4.4 10.2 8.6 7.3
2.61 i 0.02 (3.00) 2.64 i 0.02 (2.68) 2.52 t 0.05 (2.54) 0.782 t 0.003 (0.90) 1.67 + 0.01 (2.74) 2.77 * 0 . 0 1 (2.76) NO+ 150 1 . 4 4 'r 0.10 (3.63) H,O+ H ,O+ 150 2.92 i 0.03 (3.02) NH,' 3 " 150 1.29 i 0.04 (3.12) "3 150 1.12 i 0.01 (2.73) 150 NH,+NH "3 150 1.11 'r 0.01 (2.56) 14 NH,+2NH, NH,+ He 150 1 2 . 0 t 3.5 (16.7) 14 1.1 NH,+NH He 150 7.7 i 2.0 (16.0) 22 1.3 a Calculated residence time assuming E = 5 V/cm, P = 1 . 0 torr. T = 423 K , and ion drift distance = 1 cm. Number of collisions the ion experiences with methyl stearate during its residence time in the source. 95% confidence limit. Values in parentheses are the polarization limits calculated by using eq 4. _____
3.5
are given in Table 11. Ions studied in their parent gas were analyzed as discussed earlier. The reduced mobility KO,- of an ion which drifts through a binary mixture of gases A and B with mole fractions XA and XB follows Blanc's law (29)
A
I/
0.5tf 0
5
10
15
20
25
E I P , ~ / c r n -torr Figure 4. Measured drift velocities with increasing values of E I P for N,+ in H,: (W) 0.5 torr; (A)0.6 torr; ( 0 )0.8 torr; ( + ) 1 .O torr: T = 25 OC; 20-eV electrons pressure, the drift velocities remained a linear function of E / P over the range of values studied. At the higher E / P values, where the spread in velocities is more apparent, the data suggest that limiting values of the drift velocities are being approached. Similar results were obtained with measurements of Ar2+drift velocities. For Ar2+,the measured KOat 0.8 torr was 1.35 f 0.01 cm2/(V s) as compared to a value of 1.56 f 0.01 obtained a t 1.6 torr. We believe that the values we report for these ions represent lower limits; under our conditions they are not formed within a distance negligible compared to the total drift distance. Drift velocities measured by using a single drift length are often in error by 15% because they do not permit the elimination of end effects (26). The agreement of our results with those obtained in variable length drift tubes is good, indicating that end effects do not cause major difficulties in our source. T h e reduced mobilities obtained under typical chemical ionization conditions for a variety of common reagent gas ions
where M = (KO,AB)-'- (K0,BI-l and KO,AB and KO,Bare the reduced mobilities of the ion in the pure gases A and B, respectively. Deviations from Blanc's law occur when a change in the nature of the ion accompanies a change in the composition of the mixture. A Blanc's law plot for the mobility of NO+ in mixtures of NO and N2 is in excellent agreement with results obtained for pure NO; the value for NO+ in pure N2 given in Table I1 was obtained from a least-squares fit of the experimental results to eq 7 . The results obtained with mixtures that were less than 1% NO in N2 (total pressure = 1.00 torr) are significantly higher than the least-squares line. These deviations were not unexpected, however, since the time delay of NO' formation and the drift of the precursor ion contribute substantially to the total drift time. The NO/N2 system was investigated since dilute mixtures of NO in N2have been used in conventional CI mass spectrometers to provide a significant enhancement of M+ ions for many compounds (30,31). A 10% NO in N2 mixture is frequently employed. The reduced mobility for NO+ in this mixture was found to be 2.59 f 0.01 cm2/(V s). Small amounts of H 2 0 have been added to He or Ar (32, 33) to produce mixed charge exchange and proton transfer reagent gases. The rare gas ions react by dissociative charge exchange to provide fragmentation, and the H30+ion reacts to produce (M + H)+or (M + H,O)+ ions. The experimental results follow Blanc's law a t the higher H 2 0 concentrations and show dramatic evidence for the effect of the formation reactions on average drift velocities in mixtures containing less than 1%H 2 0 (PHZ0 = 0.01 torr) (Figure 5 ) . It was not possible to obtain a reduced mobility for H 3 0 + in pure H20that would relate to the mixture results. At source pressures required to overcome electron penetration in these experiments, formation of the H30+(H20), cluster ions is dominant. A dynamic equilibrium results in which the entity on which the charge resides is increasing and decreasing in mass rapidly. Consequently, the arrival time distributions of the cluster ions reflect an average or effective mobility for
ANALYTICAL CHEMISTRY, VOL. 52, NO. 12, OCTOBER 1980 ncn
"'""t
I
1801
"I
4.0
0.301
I
I
I
1
1
2
4
6
8
10
% H20
I
12
Figure 5. Variation of the reciprocal reduced mobility of H30+ in mixtures of H20 with Ar
all ions in the realm of association reactions. Distributions depend on composition and therefore on pressure. The value for the reduced mobility of H 3 0 +in pure H 2 0 given in Table I1 was determined from a least-squares analysis of the data. Since this value depends on a long extrapolation, its accuracy is very questionable, perhaps no better than f 5 0 % . Finally, we have investigated ions in ammonia, used extensively as a CI reagent. NH4+is a weak protonating agent and it is possible to obtain (M + H)' and (M + NH4)+ions to characterize polyhydroxy compounds such as sugars (34-36). The reagent gas spectrum of ammonia is characterized by the sole presence of cluster ions, NH4+(NH3),, very similar to water. T h e drift velocities for NH4+, NH4+NH3, and NH,+(NH3), in NH3 as a function of E / P are shown in Figure 6. At the higher pressure the three cluster ions have the same effective mobility indicating that they are participating in a dynamic equilibrium. At PNHB = 0.25 torr, these ions no longer have the same measured mobility indicating that equilibrium did not exist throughout the entire drift length. T h e reduced mobilities for NH4+NH3and NH4+(NH3), reported in Table I1 are based on measurements obtained a t PNHB = 0.50 torr. These values are equal as previously mentioned. T h e value for NH4+ is from measurements a t PNHB = 0.25 torr. This value differs by only 16% from the equilibrium value obtained at the higher pressure. The mobility of NH4+and NH4+NH3in NH3/He mixtures has also been studied. The ammonia pressure in the source ranged from 0.05 to 0.40 torr for the NH4+measurements and from 0.20 to 1.00 torr for the KH4+NH3measurements. The reduced mobilities for these ions in pure helium (Table 11) were again obtained from a least-squares analysis of the Blanc's law data. T h e precision of these values is not very good. In the ammonia/helium system, the reduced mobilities of the ions vary by an order of magnitude with mixture composition. The reciprocal reduced mobilities at low percentages of ammonia are small, and small deviations in these measurements result in large confidence limits for the extrapolated (KO)-' and hence the reduced mobility. As mentioned in the introductory section, there is frequently a discrepancy between the observed drift properties and the idealized drift properties predicted by eq 4, particularly for ions moving in their parent gas where resonant charge transfer may occur. For thermal energies the rate constant for this process may be much larger than that calculated in the polarization limit. Charge transfer may dominate all other elastic scattering processes except at very low energies (temperatures) where polarization scattering finally limits the transport process. This causes the mobility to decrease smoothly with increasing temperature, from its polarization limit to the values dictated by the charge-transfer process.
Figure 6. Measured drift velocities with increasing value of E l P for cluster ton in NH, at 150 OC: (W) NH,;' ( 0 )NH,+NH3; (A)NH,f(NH3)2. P = 0.25 torr for solid symbols and P = 0.50 torr for open symbols
Such effects are evident in the results of this study, where the reduced mobilities of He+, Ar+, N2+,and NO+ in their parent gases are 40-60% of the polarization limits a t typical CI temperatures. When resonant charge transfer is not possible, as is the case with NO+ in Nz, the experimental reduced mobility is in very good agreement with the polarization limit. Furthermore, comparison of the results in Tables I and I1 for He+ reveals that the temperature dependence of the mobilities is still pronounced in the range 25-150 "C.The mobilities of Ar+ and Nz+ on the other hand are nearly independent of temperature in this range. Ion transfer is another process by which charge passes easily from a n ion to a neutral. Drift tube studies of the reduced mobilities of H3+in H2( 3 7 , s )and HeZ+in He (39,401 indicate that the effects of ion transfer are analagous to charge transfer; that is, the measured mobilities are lower than the polarization limits. However, this effect is not :is pronounced as with charge transfer. At CI temperatures, the reduced mobilities of He2+,CH5+, and t-C4H9+in their parent gases are only 10-20% lower than the polarization limits. Unlike the temperature dependence of ions involved in a charge-transfer process, the reduced mobilities of ions undergoing an ion transfer initially decrease with temperature, go through a minimum, and then increase with increasing temperature as indicated by the limited data given in Tables I and 11. T h e reduced mobilities of H 3 0 + and NH4' are about 40% of the polarization limit, but this can almost certainly be ascribed to the influence of clustering equilibria.
Ion Residence Times and Chemical Ionization Sensitivities. With the reduced mobilities listed in Table 11, one can estimate ion residence times for a given set of CI source conditions by use of eq 3. T h e residence times given in the fifth column of Table I1 were calculated by assuming an electric field strength, E = 5 V/cm, reagent gas pressure, P = 1.0 torr, source temperature, T = 150 "C, and an ion drift distance, d = 1.0 cm. These times represent average values of residence time distributions whose spreads are dependent on the diffusion properties of the ions. They can, nevertheless, provide an estimate of the maximum ion-molecule reaction time that is possible with a given set of source conditions. It is important to note here that ion residence times are based on ion drift distances. With a CI ion source employing the conventional orthogonal electron entrance-ion exit configuration, most of the ions are not produced coaxial with the
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ANALYTICAL CHEMISTRY, VOL. 52,
NO. 12, OCTOBER 1980
ion exit slit in the z direction. Rather, they are formed close to the electron entrance and then diffuse a t right angles to the direction of the repeller field in order to be collected (25). The distance from the plane of the electron beam to the ion exit must, therefore, be considered as a minimum distance that the ions could drift. The residence times listed in Table I1 therefore represent a lower limit for the residence times of ions in sources that employ such a geometry. One may be tempted to treat these reaction times as relative sensitivities. However, this approach is not correct since the actual extent of conversion or sensitivity is dependent on the reaction rate constant as well as the reaction time. A better approach considers the number of collisions the ion experiences with the sample during its residence time, N,= k,tM, where k , is the collision rate constant. For large sample molecules the influence of the sample's dipole moment on the collision rate constant will be small compared to the effect of polarizability, and the collision rate constant can therefore be estimated by the following simple expression (8) k, = 2
~
e
m
(8)
T h e final column in Table I1 lists the number of collisions between the various reactants ions and methyl stearate sample molecules a t a partial pressure of 0.001 torr under the ion source conditions listed earlier. These collision numbers vary by less than a factor of 2, suggesting that in general the CI sensitivity for a given compound will be independent of the reagent gas employed if the ion-molecule reaction rate constant is of the same magnitude as the collision rate constant. For a series of polyamines, similar sensitivities were indeed observed by using CH4, N2,and i-C4HI0as the reagent gases (40). Similarly, the same sensitivities were observed for the CI spectra of valerophenone whether CHI or C H 4 / H 2 0was used as the reagent gas (41). The reduced sensitivities in 10% NO/N2 mixtures vs. isobutane as reagent gases (31) may be the result of other effects. The results for NH4+in He indicate a disadvantage of using He or Hz as the major component of a mixed reagent gas. In the case where the major component of the reagent gas has a polarizability that is much smaller than that of the minor component, the mobilities are increased and the residence times are decreased. This change results in a significant decrease in the overall sensitivity. In a case such as GC/CIMS in which a major component of the reagent gas mixture is the carrier gas, it therefore seems advisable to use N2 or CH4, which have much larger polarizabilities than He or HS, as the carrier gas. If that is not possible because of constraints imposed by GC analysis or the GC/MS interface, the ratio of a suitable reagent gas to carrier gas concentrations in the source should be maximized.
APPENDIX Under the conditions of the CI experiment, we can consider the following generalized model.
P+ + G
-
R+
+N
(All
kh
P+ + M
R+ + M
ka f
k -+
products
(A21
CS,+(+ ...)
(A31
In these equations G is the reagent gas, M is the compound t o be analyzed, P+ is an ion formed by direct ionization of the reagent gas, R+ is a reactant ion, and SI+ is a sample ion with m / e = i. In these experiments the ionic concentrations are much less than the concentrations of the neutral reactants. Therefore, these reactions can be treated as quasi first order and
If the ratio of sample gas molecules to reagent gas molecules is kept small, then k,[G] >> kb[M], since the rate constants should be within a factor of 2 of each other. The rate of reaction A2 is negligible in comparison with A1 and [P+I
[l - exp(-(k,[G] Similarly, k,[G] [R']
N
(A5)
[P+I0 ex~{-ka[GItl
-
k[Ml)tll (A6)
>> k[M] and [P+],[l - exp(-k,[G]tj] exp(-k[M]t) (A7)
Until a sample is introduced, [MI = 0 and [R+] = [P+lO[1- exp{-k,[G]t)] = [ R + ] M = ~ (A8) [R+]M=,is the concentration of the reactant ion in the reagent gas spectrum. Substituting A8 into A7 results in the following expression [R+l = [R+]M=,exp{-h[M]tJ
(A91
In terms of sample ionization d(C[Si+l)/dt = k [ M l [ R + l ~ ,expl-k[Mlt] ~ (A101
SI+ = [R+]M=o[l- exp(-k[M]t)]
(All)
If the extent of conversion is kept small (k[M]t
