N. J. Nilsson. "Learning Machines", McGraw-Hill, New York, N.Y., 1965, p 79. T. L. Isenhour and P. C. Jurs, Anal. Chem., 43, (lo), 20A (1971). W. Spendley, 'G. R.-Hext, and F. R. Himsworth, Technometrlcs, 4, 441 (1962). J. A. Nelder and R. Mead, Compuf. J., 7, 308 (1965). D. M. Olsson and L. S. Nelson, Technometrics, 17, 45 (1975). R. R. Ernst, Rev. Sci. Instrum., 39, 998 (1968). D. E. Long, Anal. Chin?.Acta, 46, 193 (1969). S. N. Deming and S. L. Morgan, Anal. Chem., 48, 1170 (1974). R. Smits. C. Vanroelen, and D. L. Massart, Fresenius' Z.Anal. Chem.. 273, l ( 1 9 7 5 ) . L. Pietrantonio and P. C. Jurs, Pattern Recognition, 4, 391 (1972). R. 0. Duda and P. E. Hart, "Pattern Classification and Scene Analysis", Wiley-lnterscience, New York, N.Y., 1973, p 141. G. S. G. Beveridge and R. S. Schechter, "Optimization: Theory and Practice", McGraw-Hill, New York, N.Y., 1970, p 374. S. N. Deming and S. L. Morgan, Anal. Chem., 45, 278A (1973). R. 0.Duda and P. E. Hart, Ref. 17, p 116.
T. M. Cover and P. E. Hart, l€€€ Trans. lnf. Theory, IT-13, 21 (1967). J. B. Justice and T. L. Isenhour. Anal. Chem., 46, 223 (1974). J. 8.Justice, to be published. R. 0.Duda and P. E. Hart, Ref. 17, p 69. L. E. Wangen, N. N. Frew, and T. L. Isenhour. Anal. Chem., 43, 845 (1971). (26) P. C. Jurs, Anal. Chem., 43, 22 (1971).
(21) (22) (23) (24) (25)
RECEIVEDfor review April 14, 1975. Accepted June 20, 1975. C.L.W. is Visiting Associate Professor, 1974-75 Academic Year, from the University of Nebraska-Lincoln. T.L.I. is an Alfred P. Sloan Fellow, 1971-75. Support of this research through Grant GP-41515X (CLW) and Grant GP-43720 (TLI) by the National Science Foundation is gratefully acknowledged.
Identification of Positive Reactant Ions Observed for Nitrogen Carrier Gas in Plasma Chromatograph Mobility Studies D. 1. Carroll, 1. Dzidic, R. N. Stillwell, and E. C. Horning Institute for Lipid Research, Baylor Colleoe of Medicine, Houston, Texas 77025
A Plasma Chromatograph-mass spectrometer (PC-MS) combined instrument was used to define the ion species responsible for the three major peaks observed in positive ion mobility studies of nitrogen carrier gas at 160 'C and 7 ppm water concentration. These species are: I, NH4+ with about 7 % of NH4+(H20); ii, NO+ with about 10% of NO+(H20); 111, H+(H20)2 and H+(H20)3 In about 7:3 ratio, for ion peaks showing reduced mobilities of 3.00, 2.62, and 2.32 cm2 v-l sec-l, respectively. Literature identifications based upon presumed equivalence of mobility and mass measurements are in error.
The early mass spectrometric studies of Shahin ( I ) , employing a corona discharge in air at atmospheric pressure, indicate that H+(H20), ions should be the dominant species in positive ion mobility spectra observed with nitrogen carrier gas in the Plasma Chromatograph. This was confirmed using a Plasma Chromatograph-mass spectrometer (PC-MS) combined instrument a t Franklin GNO Corporation ( 2 ) .The ions NO+ and NO+(H20) were also found to be present ( 3 ) . A recent review ( 4 ) of Plasma Chromatograph applications contained a positive ion mobility spectrum for nitrogen which showed five peaks. These ions were identified, apparently through mass-mobility calculations, as H+(H20), NOf(H20), H+(H20)3, H+(H20)4, and H+(H20)5 ions. This mobility spectrum differed significantly from those previously published which had only three peaks, identified as H+(H20)2, NO+(H20), and H+(H20)3 (5-7). No explanation was given in the review for the absence of H+(H20)2 ions in the mobility spectrum, or for the discrepancy with respect to earlier publications in reporting five reagent peaks rather than three. Serious errors can be made when ion identifications are based on mobility data alone (8).This appears to be true in the case of the identification of the positive ions observed in PC mobility spectra of nitrogen carrier gas. Based upon mass spectrometric data, the identities of the ions responsible for the three major peaks in the mobility spectrum of nitrogen are: first peak: NH4+ together with some 1956
NH4+(H20); second peak: NO+ together with some NO+(H,O); third peak: Hf(H20),, where n = 2 and 3 for the conditions employed in our study. The degree of ion hydration in each instance is dependent upon the temperature and the water concentration.
EXPERIMENTAL Apparatus. A Plasma Chromatograph-mass spectrometer combination which has been described in detail (8) was used in this work. Primary ions are produced in a carrier gas stream by a 63Ni source; these primary ions initiate a sequence of ion molecule reactions which yield reagent ions. When the carrier gas is nitrogen containing a trace of water, the nitrogen ions which are formed initially enter a sequence of reactions terminating in the formation of H+(H20), ions. Ions formed in the source region are introduced into the drift region; they move through nitrogen at atmospheric pressure under the influence of an electric field. The transit times of ions through the drift region are recorded; these are of the order of milliseconds. The signal output of the instrument is ion current as a function of time. The principles of operation are essentially those of electrophoresis in the gas phase. Either one of two shutter grids is used to pulse ions into the drift region (8). The ions drift from either of the shutter grids to the sampling aperture, and are entrained in the gas flow into a mass analyzer. An ion lens focuses the ions from the aperture into the quadrupole rod structure of the mass analyzer. A Channeltron electron multiplier is used as a detector; pulse counting techniques are employed. The data are collected and displayed with the aid of a PDP 8/E minicomputer. Procedures. A mass spectrum was obtained with both shutter grids open, and a drift time chart was recorded using conventional gating techniques. The mass analyzer was then adjusted to respond to a single ion mass only. The arrival time of that ion was then measured from each grid to the detector (see Figure 3). The difference in arrival times was the drift time of the mass-identified ion between the two shutter grids. Using the known grid distances and the drift tube temperature and pressure, the mobility of the mass-identified ion was calculated. An electron impact source was available to obtain spectra for calibration purposes. The experimental conditions are summarized in Table I. The effluent gas from a container of liquid nitrogen was used as a source of both carrier and drift gases; the gas was cleaned and dried prior to use by passage through two cylinders containing Type 13X molecular sieve. Consistent background ion spectra were obtained after baking out the PC-MS under a vacuum of Torr at 200 O C overnight.
ANALYTICAL CHEMISTRY, VOL. 47, NO. 12, OCTOBER 1975
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/I
CSIFT T i M E
Figure 2. Ion mass profiles for nitrogen obtained with a combined Plasma Chromatograph-mass spectrometer
(rrSEC)
Figure 1. Reactant ions formed in a Plasma Chromatograph with nitrogen as the carrier gas Three positive ion peaks were observed, with the drift times and mobilities indicated in Table I. The experimental conditions are indicated in Table I. All ions of the structure H+(H20), drift as an equilibrium mixture (peak Ill) with a drift time that depends upon the average value of n. it is not possible to obtain separate PC peaks for each ion in the series, as claimed earlier (4-7). Peak II contains NO’ and NO’(H20) ions. Peak I contains NH4+ and NH4’(H20) ions
RESULTS A N D DISCUSSION PC-MS Instrumental Data. The PC-MS instrument used in this study permits determination of both the mass and the mobility of ions formed in the reaction region. The Plasma Chromatograph alone provides mobility data only. Mobility is a physical property which can not be depended upon for the identification of the ionic species under study (8). Unfortunately, the Plasma Chromatograph alone has been described as a time-of-flight mass spectrometer, which it is not ( 4 , !?). This does not imply that mobility measurements are not useful, but rather that a measurement of mobility is not equivalent to a measurement of mass. The assumed equivalence of mobility and mass measurements in much previous work has led to the view that several ions in equilibrium can not be responsible for a single PC mobility peak. This fundamental concept is examined in this paper; we believe that errors have been made, and will continue to be made, in the interpretation of PC data as long as mobility measurements are implied to be the equivalent of mass measurements. Positive Ion Mobility Spectra. A typical mobility spectrum observed for nitrogen carrier gas at 160 “C is shown in Figure 1. The reduced mobilities for the ion peaks are in agreement with similar data published earlier (5-7). The initial work a t Franklin GNO Corporation with the prototype PC-MS instrument showed that peak I11 in the spectrum contained the ions H+(H20),, and that peak I1 contained NO+ and NO+(HzO). These results were not formally published, but were made available to interested scientists (10).These early unpublished results form the basis of information used in current mobility peak identification. The results obtained with a combined PC-MS instrument, which show that more than one ion species occurs in each of the positive reactant ion mobility peaks, are not generally accepted a t this time by scientists using a PC instrument alone ( 4 - 7 ) . The PC-MS results are explained by suggesting that adiabatic expansion from atmospheric pressure to Torr results in extreme distortion of the mass spectrum due to “stripping” and “clustering” reactions. The PC-MS mass spectrometric data given in this paper are in good agreement with the equilibrium data of Kebarle et al. (11, 12). There is complete agreement in this instance between theory and experimental observations indicating
The upper chart shows PC positive ions present in the drift region, identified by mass spectrometry. The lower chart shows a mass spectrometric analysis of the drift gas obtained with the electron impact source used for calibration purposes. Water and oxygen are the major impurities in cylinder nitrogen and in nitrogen taken as gas from liquid nitrogen. Peaks at m/e 46 and 65 vary in intensity and are believed to be due to unidentified impurities
that a mobility peak can contain mixed ion species differing in degree of hydration. P e a k 111. The relative distribution of H+(H20), cluster ions can be calculated, if the water vapor pressure and the temperature are known, by using the equilibrium data obtained by Kebarle et al. (9, IO). Conversely, if the water cluster ion intensities are measured and the temperature is known, the water vapor pressure can be calculated. A mass spectrum of total ion current a t 160 “c for nitrogen is shown in Figure 2. An electron impact calibration spectrum is also shown for comparison purposes. The major water cluster ions observed by mass spectrometry are H+(H20)2 and H+(H2O)3. In this spectrum, there is no indication of the presence of H30+ and H+(H20)4 ions. The water vapor pressure can be calculated using the relationships PH2O
=
(1)
I n - lKqn-1 where PH?O is the water vapor pressure in Torr, I , is the relative intensity of the H+(H20), cluster, I,-1 is the relative intensity of the H+(H20),-1 cluster, and Kn,,-1 is the equilibrium constant calculated for these species from Table I of reference 11. At 433 K, the value of K3,2 is 88 Torr-l. The calculated water vapor pressure for the intensity ratios shown in Figure 2 is 5 X Torr, corresponding to about 7 ppm of water. Similar calculations can be made to find the expected relative amounts of H30+ and H+(H20)4 ions a t 433 K and the same water concentrations, These calculations show that both of these ions should be present in less than 0.1% in intensity. “Stripping” or “clustering” of ions during the expansion of the gas would be expected to generate these ion species, if an effect of this kind occurs. Their absence in the mass spectrum shows that these effects are of minor consequence.
Table I. Experimental Conditions C a r r i e r gas, N2; Mode A Temperature, -160” Voltage, 3200 V/14 cm Time base, 20 msec Scan time, 5 min. Drift times, msec
?dvlobilih/, c m 2 v - l s e c - l
I
5.5
3.00
I1 III
6.3
2.62 2.32
Peak
7.1
ANALYTICAL CHEMISTRY, VOL. 47, NO. 12, OCTOBER 1975
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ll
Table 11. Water Cluster Ion Mobilities Ion
%*cm 2 v - 1 sec -14
H*(HzO) 2.67 H'(Hz0)z 2.34 H'(HzO), 2.20 H'(H,O), 2.13 H'(HzO), 2.08 a Do2 = 1.000495, D N = ~ 1.000548.
1
i 1
Figure 3. Charts showing drift times of the ions corresponding to peaks I, 11, and Ill in Figure 1 The times were measured with a computer and mass spectrometer, ensuring the identity of the ions under study. The drift tlmes for H+(H20)* and H+(Hz0)3 ' were identical; both ions drift as a single peak (Ill)
Drift times should be very much longer than the half-life of both forward and reverse hydration reactions, if hydrated cluster ions are to drift as an equilibrium mixture. The reaction rate constant kf for the reaction of H+(H20)2with water to yield H+(HzO)3 is given in reference 12 as 2.3 X cm6 molecule-2 sec-1. The half-life for the forward reaction is then:
(3) where k f is the forward reaction rate constant, k, is the reverse reaction rate constant, and K2,3 is the equilibrium constant in units of cm3 molecule-l. The equilibrium constant calculated from Table I of reference 11 is in terms of Torr-l. This must be converted to the correct units for Equation 3. Substituting these values for K2,3 (2.5 X cm3 molecule-l) and kf (2.3 X cm6 molecule-2 sec-l), a value of 9.3 x 1O-I3 cm3 molecule-' sec-l is found for kr. The half-life of the reverse reaction is therefore: t1/2 = -- 6 X 10-8sec kJNzI 1958
(4)
.In2 "-1 sec-lU
2.69 2.39 2.26 2.19 2.15
The equilibrium time is of the order of lo-' second, from these calculations. The ions drift, during mobility measuresecond. This means that ments, for a total time of 7 x the ion species H+(H20)2 and H+(Hz0)3 are interchanging nearly IO5 times as they drift. Consequently, the observed mobility should be an average value reflecting the composition of the equilibrium mixture of clugtered species. I t is impossible to obtain separate mobility peaks for individual members of the H+(HzO), ion series in PC mobility experiments. The H+(H20), series of ions arises from reaction of N4+ with traces of water in the nitrogen gas. These reactions have been studied in detail (12). The measured (PC-MS combined instrument) drift times for reactant ions of masses 18, 30, and 37 amu are shown in the panels in Figure 3; ions with mass 55 have identical drift times with ions of mass 37. The 37 amu, or H+(H20)2 drift time, and the 55 amu or H+(HzO)3drift time, correspond to the drift time of the slowest and largest ion peak in the positive ion mobility chart. If the mobility of each member of the series H+(HzO), is known, the mobility of the resulting peak can be calculated: Keq = A i K l + AzK2
+ . . . AnK,
(5)
where Keq is the mobility of the equilibrium mixture, and An the fraction of the total current carried by the series member H+(H20), of mobility K,. These mobilities have been measured by Young and Falconer (13)for values of n to 5, under nonequilibrium conditions and at pressures of several Torr in oxygen. These values can be corrected to give values for nitrogen, based upon the Langevin polarization limit expression: K, = C
where [HzO] and [Nz] are the concentrations of water and nitrogen in molecules ~ m - At ~ , 433 K, and with a water Torr, the forward reaction halfvapor pressure of 5 X life is 2 X second. The rate constant for the reverse reaction can be determined from the calculated equilibrium constant and the measured value of kf from the relationship:
s*
m+M, m ( D , - 1)
where K, is the reduced mobility, C is a constant, m is the mass of the ion under study, M , is the mass, and D, is the dielectric constant of a gas x (14). From this equation, the correction from oxygen to nitrogen is:
The values of K Q measured ~ by Young and Falconer (13), along with the calculated values of KN*from Equation 7 are listed in Table 11. The nitrogen values are only slightly different from the oxygen values. From Figure 2, H+(H20)2 comprises 0.7, and H+(HzO)3 0.3, of the total ion current for the series H+(HzO),. Using Equation 5 and the values from Table I1 for Kz and K3, the equilibrium mobility can be calculated: Keq = 0.7 X 2.39 0.3 X 2.26 = 2.35 cm2 sec-l. This value is in agreement with the measured mobility (2.32 cm2 v-l sec-l) for peak I11 obtained in this study. These results also indicate that an increase in water vapor pressure, at a given temperature, should cause a decrease in the mobility of peak 111. This has, in fact, been observed experimentally (10).
ANALYTiCAL CHEMISTRY, VOL. 47, NO. 12, OCTOBER 1975
+
P e a k 11. There is no disagreement with respect to the general nature of the ion(s) responsible for the second peak in the mobility spectrum. When a trace amount of NO is added to the carrier gas, the amplitude of the second peak, and the mass 30 peak in the mass spectrum, increases. Equilibrium calculations can also be made for these ions using the data of French, Hills, and Kebarle ( 1 5 ) .The equilibrium constant, a t 433 K, for the reaction: NO+ t H20
+ N2 s NOf(H20) + N2
(8)
can be obtained from Figure 5 of reference 15; the value is 22 Torr-I. Substituting this value, and the water vapor Torr into Equation 1, it is found that pressure of 5 X the ratio of NO+(H20) to NO+ ion intensities should be 0.11. This is approximately the ratio observed experimentally for mass 30 and mass 48 ions (Figure 2). The time required to establish equilibrium conditions can also be calculated; this is about 10-6 second. Under the experimental conditions of this work, the second peak is due mainly to NO+ ions, in equilibrium with approximately 10% NO+(H20) ions. The origin of NO+ and NO+(H20) ions is not known. Several possible mechanisms have been proposed in the literature ( 4 , 8 ) . As shown in Figure 3, these ions have a drift time equivalent to the second peak observed in positive ion mobility spectra. The intensity of the NO+(H20) ion observed in the PC-MS combined instruemnt was too low to permit accurate measurement of its mobility. The assignment of the structure NO+(H20) to a separate mobility peak, however, contradicts the theoretical and experimental observations made for the H+(H:O), peak. There is no justification for an assignment of this kind. P e a k I. Peak I has been described as H+(H20)2, but the mass spectral data shown in Figures 2 and 3 do not allow this assignment; H+(H20)2 is associated with peak 111. It has also been suggested that the mass 18 peak in the spectra may be due to HzO+. The reaction rate constant for the nonreversible production of H 3 0 + from H2O+ has been cm3 measured by Kebarle et al. and found to be 1.8 X mol-’ sec-l (12). The half life of H20+ ions, at 5 X 10-3 Torr water pressure and 433 K, would be only 2.5 x 10-8 second. Even a t lo3 lower water vapor pressure, the H2O+ ion would not be ohservable in a Plasma Chromatograph. The only logical remaining choice for mass 18 is NH4+. We have found experimentally that an ion of mass 18, with a measured mobility equal to that of the fastest mobility peak (peak I), increases in amplitude, both in the mass spectrum, as well as in the mobility spectrum, upon addition of trace amounts of ammonia. Also, upon addition of ammonia, an ion of mass 36 increases in amplitude. We interpret these results as indicating that Peak I is due to NH4+ and NH4+(H20) ions. These ions are presumably derived from reaction of H+(HzO), ions with traces of NH3 present in the carrier gas: H’(H2O)z
+ NH3
+
NH4+ + 2H20
(9)
The rate constant for this reaction has been measured by Fehsenfeld and Ferguson (16) and found to be 2.6 X cm3 mol-’ sec-l. This implies that every collision of an H+(H20)2 ion with an NH3 molecule results in the production of an NH4+ ion. A concentration of only 0.1 ppb of ammonia in the carrier gas would be required to give a peak corresponding to the peak I amplitude shown in Figure 1. Based upon the work of Payzant, Cunningham, and Kebarle (17), equilibrium calculations can also be made in the
series NH4+(H20), (18).The equilibrium constant for the reaction: NH4+ + HzO + Nz NH4+(H20)+ Nz (10) can be obtained from Figure 2 of reference 17. At 433 K, this value is about 14 Torr-l. Using this value, and a water Torr, the calculated ratio of vapor pressure of 5 X NH4+(H20) to NH4+ is 0.07. This is the approximate value of the ratio of mass 36 to mass 18 observed in our work (illustrated in Figure 2). We conclude that the first peak in the mobility spectrum is due to NH4+ ions, in equilibrium with about 7% NH4+(H20) ions. As shown in Figure 3, mass 18 ions have a drift time equivalent to the first mobility peak observed in positive ion mobility charts. A “tail” extends out to the drift time observed for H+(H20)2and H+(H20)3 ions. This would be expected if these ions are being converted during their transit time to NH4+ ions as indicated by reaction 9.
CONCLUSIONS Mass spectrometric data from a PC-MS combined instrument are in good agreement with data reported by Kebarle et al. (11,12, 15, 17) for clustering of NH4+, NO+, and H+(H20) with water. No effects attributable to the sampling aperture or gas expansion, such as “stripping” or “clustering”, are apparent. The mass spectrometric data and equilibrium calculations show that clustered ion species are responsible for the three peaks observed in the positive ion mobility charts of nitrogen carrier gas. The ion species responsible for these peaks, under the conditions used in this work, are: I, NH4+ with about 7% of NH4+(H20); 11, NO+ with about 10% of NO+(H20); 111, H+(H20)2 and H+(H2O)3 in a ratio of about 7:3. The reduced mobilities are 3.00, 2.62, and 2.32 cm2 v-’ sec-’, respectively. Under other conditions, if the water vapor pressure and gas temperature are known, the relative amounts of each member of each series can be calculated. The argument that only a single ion species is responsible for each of the reactant ion peaks shown in Figure 1 is not supported by experimental or theoretical findings. Earlier literature identifications (4-7) are based upon assumed mass and mobility equivalency, and are incorrect. LITERATURE CITED (1) M. M. Shahin, J. Chem. Phys., 45, 2600 (1966). (2) D. I. Carroll, R . F. Wernlund. and M. J. Cohen, U S . Patent 3,630,757, Feb. 1. 1972. (3) F. W. Karasek, M. J. Cohen. and D. 1. Carroll, J. Chromatogr. Sci., 0, 390 (1971). (4) F. W. Karasek, Anal. Chem., 46, 710A (1974). (5) F. W. Karasek and D. W. Denney. Anal. Chem.. 46,633 (1974). (6) F. W. Karasek and D. M. Kane, Anal. Chem., 46, 780 (1974). (7) F. W. Karasek and D. W. Denney, Anal. Chem., 46, 1312 (1974). (8) G. W. Griffin, I. Dzidic. D. I. Carroll, R. N. Stillwell. and E. C. Horning. Anal. Chem., 45, 1204 (1973). (9) R . A. Keller and M. M. Metro, Sep. Purif. Methods, 3, 207 (1974). (10) D. I. Carroll, Franklin GNO Corp., West Palm Beach, Fla., 800 series memoranda 1968-7 1. (11) P. Kebarle. S. K. Searles, A. Zolla. J. Scarborough, and M. Arshadi, J. Am. Chem. SOC.,80,6393 (1967). (12) A. Good, D. A. Durden, and P. Kebarle, J. Chem. Phys., 52, 212 (1970). (13) C. E. Young and W. E. Falconer, J. Chem. Phys., 57, 918 (1972). (14) F. W. McDaniels “Collision Phenomena in Ionized Gases”, John Wiley 8, Sons, New York, N.Y., 1964, p 432. (15) M. A. French, L. P. Hills, and P. Kebarle, Can. J. Chem.,+51, 456 (1973). (16) F. C. Fehsenfeld and E. E. Ferguson, J. Chem. Phys., 50,6272 (1973). (17) J. D. Payzant. A. J. Cunningham. and P. Kebarle, Can. J. Chem., 51, 3242 (1973).
RECEIVEDfor review March 21, 1975. Accepted June 26, 1975. This work was supported by Grant GM-13901 of the National Institute of General Medical Sciences, Grants HL-05435 and HL-17269 of the National Heart and Lung Institute and Grant ($125 of the Robert A. Welch Foundation.
ANALYTICAL CHEMISTRY, VOL. 47, NO. 12, OCTOBER 1975
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