J. Phys. Chem. 1989, 93. 3021-3025 Up = 0.33 nm/ps
For the same shock as before with y = a / 4 and a shock thickness of 10 nm we have
Us= 1.902 nm/ps respectively. If the length of the dumbbell is taken as 0.5 nm and if it lies at 45' to the shock front, t2 = 0.194 ps, w+ = 0.467 rad/ps, and the net angular velocity after the shock has passed over both masses is w = -0.040 rad/ps The effect of a finite velocity gradient in the shock front can be addressed in the following way. Consider the same diatomic molecule for which angular velocity was calculated in the previous paragraph. But now let it be situated in a velocity gradient 8ula.x < 0; Le., the shock wave is again moving over it from left to right in Figure 14. If we again require that the molecule translates and rotates as a rigid body, we have au cos y ax
au
-wl sin y = 6u = - 6x = -1 ax
3021
0.33 nm/ps w;=-
10 nm
= -0.033 rad/ps
In the above calculations it has been assumed that the molecule was free to rotate, even though the sample is in the liquid state. It is widely believed by those working in the liquid state that this is true, at least at normal densities.33 This tends to be confirmed for CS2 by previous measurements of orientational relaxation time for the CS2molecule in the liquid state, approximately 2 ps.26-34 It may be possible in time to make more realistic calculations on this aspect of the problem. Enough has been said here to make the concept of shock-induced rotation followed by parallel packing plausible and worthy of further consideration. It is hoped that such consideration will be forthcoming from others, if not from the present authors. Registry No. CS2, 75-15-0.
or w
au = -- cot y; y # n x
(33) Tsviotz, L., private communication. (34) Ippen, E. P.; Shank, C. V. Appl. Phys. Lett. 1975, 26, 92.
ax
Effect of Drift Gas on Mobility of Ions Zeev Karpas* and Zvi Berant Physics Department, Nuclear Research Center, Negev, P.O. Box 9001, Beer-Sheva, Israel 84190 (Received: July 27, 1988)
The effects of the drift gas on the mobility of ions were examined. In the generally accepted model, a hard-core potential is used to represent the interaction between the ion and drift gas molecules.'v2 The effects of the drift gas are manifested in the reduced-mass term and in the collision cross-section term. Use of a series of drift gases, namely, helium, nitrogen, air, argon, carbon dioxide, and sulfur hexafluoride, made it possible to distinguish between mass effects and polarizability effects. Thus, it was found that addition of a correction term to the theoretical model improves the agreement with experimental data. This mass-dependent term counterbalances the loss of sensitivity to small changes in ion mass for heavy ions of the reduced-mass term. The lower the mass and polarizability of the drift gas molecules the greater the importance of this correction.
Introduction The theoretical expression for the mobility, K , of ions in an electric field is2 where q = charge of the ion and m = its mass, N = density of the drift gas molecules and M = their mass, k = Boltzmann constant, T = effective temperature in the cell, p = reduced mass of the ion and neutral p mM/(m M), and OD = collision cross section. Under the low-field conditions of the ion mobility spectrometer (IMS), the effective temperature is essentially equal to the cell temperature. As seen in eq 1, the dependence of the mobility of an ion on its mass enters directly through the reduced-mass term, p, and in a more subtle way through the collision cross-section term,2 QD
+
RD =
?rr,2fi(l*')'(T*)
(2)
( I ) Berant, 2.;Karpas, Z. J . A m . Chem. SOC.,in press. (2) (a) Mason, E. A. In Plasma Chromatography; Carr, T. W., Ed.; Plenum Press: New York, 1984; Chapter 2. (b) Revercomb, H. E.; Mason, E. A. Anal. Chem. 1975, 47, 970. (c) Ellis, H. W.; Pai, R. Y.; McDaniel, E. W.; Mason, E. A.; Viehland, L. A. A I . Data Nucl. Data Tables 1976, 17, 177. (d) Ellis, H. W.; McDaniel, E. W.; Albritton, D. L.; Viehland, L. A,; Lin, S. L.; Mason, E. S . A t . Data Nucl. Data Tables 1978, 22, 179. (e) Mason, E. A.; O'Hara, H.; Smith, F. J. J . Phys. E . : A t . Mol. Phys. 1972, 5 , 169.
0022-3654/89/2093-3021$01.50/0
where Tc) is the dimensionless collision integral that depends on the ion-neutral interaction potential and is a function of the dimensionless temperature, T* = kT/to. Here, eo is the depth of the potential minimum and r,,, its position2 Q('v')'(
€0
= q2ap/ [3(rm - a141
(3)
where apis the polarizability of the neutral molecule and a is a parameter that represents the effectivecore diameter and expresses the separation between the center of mass and center of charge of the ion. The interaction potential for the hard-core 12,4 potential, for a drift gas molecule without a permanent dipole or quadrupole moment, is2 V r ) = (to/2)([(rm - a ) / ( r -
- 3[(rm - a ) / ( r - a)141
(4) In practice it is more convenient to use a reduced core diameter, a* a/rm. The failure of the rigid-sphere and polarization limit models to reproduce experimental mobility data, except for very simple cases, has been noted before2s3and demonstrated previously.' It was shown' that the measured mobility of ions may deviate considerably from the predictions of the model in which a hard(3) Bohringer, H.; Fahey, D. W.; Lindinger, W.; Howorka, F.; Fehsenfeld, F. C. Albritton, D. L. Int. J . Mass Spectrom. Ion Processes 1987, 81, 45.
0 1989 American Chemical Society
3022 The Journal of Physical Chemistry, Vol. 93, No. 8, 1989
Karpas and Berant
TABLE I: Reduced Mobility (cm2/V.s) in Helium, Nitrogen, Air, Argon, Carbon Dioxide, and Sulfur Hexafluoride of the Major Ion Formed in Aliphatic and Aromatic Amines (Assumed To Be the Protonated Molecule)
compound
ion mass
ethylamine n-propylamine trimethylamine n-butylamine diethylamine triethylamine di-n-but ylamine tribut ylamine tri-n-octylamine triisooctylamine tridodecylamine
46 60 60
74 74
102 130 186 354 354 522
pyridine 4-picoline
80 94 94
aniline
2,4-lutidine 2,4,6-collidine 2-ethylaniline quinoline
108
122 I22
130 136
2-isopropy laniline
polarizability of drift gas,4 A'
He NZ Aliphatic Amines 12.1 2.38 10.4 2.18 2.36 10.6 9.09 2.00 9.09 7.58 1.97 6.01 1.66 1.41 4.78 2.83 0.89 3.03 2.08 0.67 Aromatic Amines 10.1 8.87 8.84 7.92 7.13 7.24 7.52
6.73 0.205
core potential is used to represent the interaction between the ion and drift gas molecule.2 While good qualitative reproduction of measured mobility values was obtained with this model, the quantitative agreement over a broad range of ion masses was not as good. It was suggested] that the physical reason underlying the shortcoming of the model, with use of the hard-core potential, was its loss of sensitivity to changes in the mass of the ion for heavy ions. This problem was found to be more severe when helium was used than when air was the drift gas. An empirical correction factor was added to the interaction potential, through an additional parameter in the effective ion radius.] Thus r, = (ro + zm)[l
+ 6(m/M)'/31
(5)
where 6 is a constant representing the relative density of the ion and neutral reactants and is taken as unity,* r, is a constant, and z is the correction factor suggested previously' to increase the sensitivity of the cross section to changes in the ion mass. This greatly improved the agreement between the measured mobilities and the calculated values, for air and especially for he1ium.I In order to test the validity of this modification of the model and in order to distinguish between simple mass effects of the drift gas on the ion mobility and those arising from the interaction potential (through the polarizability and structure of the neutral molecule), different drift gases were used. These gases differ considerably in their mass and polarizability, as shown in Table 1 [taken from ref 41, although they all have no permanent dipole moment. The published data on ion mobilities in gases other than nitrogen or air, obtained from IMS measurements, are surprisingly limited. In a recent compilation of IMS data,5only three references were given to IMS studies in which SF,6 and C027,8were used. There are a number of other work^,^-'^ most notable is that of Kolaitis and L ~ b m a nin, ~which the mobility of several ions in nitrogen, air, argon, P-10 (90% Ar-10% CH,), and CO, are reported. In the present work, the assortment of drift gases was extended to (4) McDaniel, E. W.; Mason, E. A. The Mobility and Dgfusion of Ions
1973. H.;Hill, H. H., Jr. J . Chromatogr. 1986,
in Gases; Wiley-Interscience: New York,
( 5 ) Shumate, C.; St. Louis, R.
..
373. 1.d l..
( 6 ) Carr, T. W. Anal. Chem. 1979, 51, 705. (7) Rokushika, S.; Hatano. H.; Hill, H. H., Jr. AMI. Chem. 1986, 58, 361. (8) Lubman, D. M . Anal. Chem. 1984, 56, 1298. (9) Kolaitis, L.; Lubman, D. M. Anal. Chem. 1986, 58, 1993. ( I O ) Patterson, P. L. J . Chem. Phys. 1970, 53, 696. ( I 1 ) Hagen, D. F. In Plasma Chromatography; Carr, T. W., Ed.; Plenum Press: New York, 1984; Chapter 4. (12) Ellis, H. W.; Pai, R. Y . ;Gatland, I. R.; McDaniel. E. W.: Wernlund. R. F.; Cohen, M. J . J . Chem. Phys. 1976, 64, 3935
1.76
air
Ar
COZ
2.36
2.07 1.77 1.97 1.53 1.67
1.27 1.24
1.77
1.17
1.33 1.24 0.78 0.84
1.03 0.94 0.63 0.68 0.49
2.13 2.33 1.98 2.15 1.95 1.64
1.38 0.88
0.93 0.66 2.21
2.07 2.07 1.95
0.59
2.05 1.90 1.82 1.77
1.82 1.83 1.82 1.72
1.65
1.73
F6
1.32
0.75 0.68 0.75
1.11
0.60
1.22
0.67 0.63 0.54 0.48 0.33 0.34 0.25
1.24 1.20 1.21
1.18 1.14
1.68 1.68
1.12
1.57
1.06
1.64
2.59
1.12
0.67 0.64 0.64 0.6 1 0.59 0.59 0.57 0.55 4.48
include low-mass, low-polarizability helium and high-mass, high-polarizability SF6. Furthermore, the mass range of the ions studied here spans over 1 order of magnitude, as opposed to a factor of 2 or 3 encountered in most other studies.
Section The mobility measurements were carried out with a PhemtoChem 100 ion mobility spectrometer, made by PCP, Inc. The experimental conditions were described in detail previously,I so they are only briefly summarized here. Data acquisition and averaging were performed with Computerscope (made by R C Electronics) hardware and software. The cell temperature, T , was fixed to within 0.5 "C and was maintained close to 200 OC. The ambient atmospheric pressure, P , was about 720 Torr and measured to within 0.1 Torr. The carrier and drift gas flow rates, calibrated with a wet test meter (Precision Scientific), were set at 100 and 500 mL/min, respectively. The electric field strength, E, was 200 V/cm for nitrogen, air, C o 2 , and SF6,and 57 and 80 V/cm for He and Ar, respectively. The reduced mobility, KO,was calculated from Experimental
KO = (d/Et)(273/ T)(P/760) (6) where d is the length of the drift region and t is the measured drift time. The width of the grid gating pulse was set at 0.1 ms for mobility measurements in He, N2, and air, 0.2 ms in C 0 2 and SF6, and 0.5 ms in Ar. Thus, sensitivity was retained, and compensation was made for ion losses arising from long drift times (like in argon). Sample introduction was by insertion of a syringe needle, on which headspace vapors of the sample were adsorbed, into the orifice of the IMS cell. Special care was taken to avoid overloading the instrument. All samples were commercially available and were used without purification. The precision of the reduced mobility measurements was estimated as being better than 1% for measurements in air and better than 2% in the other drift gases. The improved precision in air is due to the use of lutidine (2,4-dimethylpyridine) as a reference compound for the mobility scale,I3 with a reduced mobility of 1.95 cm2/V.s.
Results and Discussion It was assumed that the major ion formed under the IMS cell conditions was the protonated parent molecule in all the amines ( I 3) Karpas, Z . Anal. Chem., in press
The Journal of Physical Chemistry, Vol. 93, No. 8, 1989 3023
Effect of Drift Gas on Ion Mobility
-
.
N
E
X
u
Ln
ION MASS ( a m u ) Figure 1. Measured inverse reduced mobility in helium ( O ) , nitrogen (O),argon (+), carbon dioxide (El), and sulfur hexafluoride ( X ) of the
major ion formed in aliphatic amines, as a function of the ion mass. that were investigated here.I3 The measured reduced mobilities in the different drift gases, NZ,Ar, C 0 2 ,and SF6, are listed in Table I. All were corrected for temperature, pressure, and electric field variations according to eq 6. As evident from Table I, in some cases, most notably the small tertiary amines, the measured reduced mobility should be attributed to a fragment ion. For example, trimethylamine in Ar, C 0 2 , and SF6 obviously dissociates to protonated dimethylamine. The reduced mobility of the ions in air1J3and helium] was reported previously and are given here for comparison. There is generally good agreement with the values reported in other s t u d i e ~ . ~ . ' ~ It is convenient to represent the inverse mobility as a function of the ion mass.2 Such a plot for the reduced mobilities of the aliphatic amines in helium, nitrogen, argon, Coz, and SF6 is shown in Figure 1. A number of trends immediately stand out from the data of Table I and Figure 1. First, the reduced mobility of a given ion decreases as the molecular weight of the drift gas increases, Le., horizontally from left to right in Table I and vertically in Figure 1. Second, the heavier the ion, the lower its mobility in a given drift gas. However, neither of these effects exhibits a simple mass dependence. Third, while the polarizability of argon is slightly lower than that of air or NZ,the mobility of a given ion is actually a little lower in argon. In Table I, the data points for a given ion in nitrogen, air, and argon are barely distinguishable from one another. Fourth, the agreement between our measurement of mobility of protonated aromatic amines in COz and those of Lubman9 is quite good. However, the statement that in C 0 2 the mobility is almost independent of ion massg does not hold under the conditions of our experiments, probably due to the much broader range of ion masses examined here. Rokushika et aL7 reported mobility values of protonated methyl esters in COzsimilar to those found here for protonated amines of similar masses. Fifth, although the masses of argon and C 0 2 differ only by lo%, the mobility of a given ion is between 20% and 70%higher in Ar than in C 0 2 . Due to the relatively high polarizability of COz and SF6(see Table I), there is a possibility of their clustering with the core ion, as noted previously for CO$9312and for SF6'0. It was found that clustering in C 0 2 depends strongly on the temperature and pressure of the drift gas. Ellis et a1.I2 showed that in C 0 2 at atmospheric pressure the major reactant negative ion was CO,-(CO2),. At 25 OC the most abundant ions were those in which n = 5-7, but at 150 "C only small clusters with n < 2 were formed. Kolaitis and Lubman, in their IMS/MS study? reported significant clustering of C 0 2with the core ions at 89 "C but could not detect such clusters in the mass spectrometer at elevated temperatures (above 160 "C). Rokushika et al.' demonstrated that as the temperature was raised above 120 O C , the C 0 2clusters were broken sufficiently so that the core ion could influence the mobility. As mentioned above, the mass-mobility correlation (14)
2013.
Karasek, F. W.; Kim, S. H.; Rokushika, S. Anal. Chem. 1978, 50,
0
100
200
300
ION MASS
400
500
(amul
Figure 2. Measured inverse mobility in nitrogen of the major ion formed
in aliphatic amines as a function of the ion mass. The curve is calculated according to the hard-core model: a* = 0.2, r, = 2.29 A, and z = 0.0021 A/amu. I
1.6c
Y 0.81
0
100
200
300
LOO
500
I O N MASS i a m u ) Figure 3. Measured inverse mobility in argon of the major ion formed
in aliphatic amines as a function of the ion mass. Conditions for curve calculations: (a) a* = 0.1, ro = 3.01 A, and z = 0.0018 A/amu; (b) a* = 0.2, ro = 2.66 A, and z = 0.0017 (c) a* = 0.3, ro = 2.15 A, and z = 0.0022 A/amu; (d) a* = 0.2, ro = 3.19 A, and z = 0 A/amu.
I
f
I
I
I
I
I
0
100
200
300
LOO
500
I
I
I
A
1.8
600
ION MASS ( a m u ) Figure 4. Measured inverse mobility in C 0 2of the major ion formed in
aliphatic amines as a function of the ion mass. The curve is calculated with the hard-core model: a* = 0.3, r, = 2.60 A, and z = 0.0018 A/amu. observed for the methyl esters7resembles that found in the present work for amines. The possibility of clustering in C 0 2 and SF6 in our measurements cannot be ruled out. However, at the elevated temperature (200 "C) at which our work was carried out, and in view of the observed dependence of the measured mobility on the ion mass (Figure l), and taking into account the findings of the earlier s t u d i e ~ , ~we . ~ Jassume ~ that the effects of clustering of Co2and sF6in the present study were insignificant. Following the treatment of the mobility data in the previous work,l the best fits obtained for the measurements in nitrogen, argon, C 0 2 ,and SF6 are shown in Figures 2-5, respectively. The reduced effective core radius, a*, the constant ro, and the correction factor, z, that gave the best fit were derived empirically from the data. The
The Journal of Physical Chemistry, Vol. 93, No. 8, 1989
3024
Karpas and Berant I
I
I
I
I
He
- 0
.
N
I
3.51
A
6
I
/
2.0[ 1.5 1.01
0
I
I
!
100
200
300
,
LOO
I
500
I
-L
600
ION MASS i a m u ) Figure 5. Measured inverse mobility in sulfur hexafluoride of the major ion formed in aliphatic amines as a function of the ion mass. The curve is calculated with the hard-core model: a* = 0.3, ro = 3.78 A, and z =
co2
I
I
1
2
LO
-E
30
-
20
-
W
I
200
300
ION MASS
LOO
500
iamui
Figure 6. Calculated depth of the minimum of the interaction potential, to [mev], as a function of the ion mass, in helium, nitrogen, argon, COz, and SF,.
results for nitrogen (Figure 2) resemble those obtained previously for air.' Thus, the best fit in nitrogen was obtained for a* = 0.2, ro = 2.29 A, and z = 0.0021 A/amu, compared with 0.2, 2.34 A, and 0.0021 A/amu, respectively, in air. In argon changing a* from 0.1 to 0.3 with z = 0.0018, 0.0017, and 0.0022 A/amu (Figure 3, curves a-c, respectively) had only a small effect on the fit, similar to what was seen in helium,' while taking a* = 0.2, z = 0, and ro = 3.19 A gave a poor fit with experimental data for ions above mass 200 amu (curve d, Fi ure 3). In C 0 2 ,taking a* = 0.3, ro = 2.60 A, and z = 0.0018 /amu gave a good fit, as seen in Figure 4. In SF6, a good fit with the experimental measurements over the entire ion mass range was obtained by taking a* = 0.3, ro = 3.78 A, and z = 0.0020 h;/amu. From these results and those reported for helium and air,1 some trends are evident. In helium and argon, there appears to be little difference between the curves calculated with a* values between 0.1 and 0.3 and the appropriate ro and z values. In air and nitrogen, taking a* = 0.2 gave the best fit, while in co2and SF6 a larger value of 0.3 was needed to obtain a good fit. This may be a result of the higher polarizability of COz and SF6, which reflects the effect of the higher dipole moment induced in the drift gas molecule in displacing the center of charge from the center of mass of the ion. Thus, this could represent a manifestation of the induced dipole-ion interaction. The importance of the added correction factor (eq 5 ) diminishes as the molecular weight of the drift gas increases. This is not reflected in the magnitude of this factor, which is around 0.002 A/amu for all these drift gases, but rather in the deviation of the calculated curves from the experimental points. On the basis of the empirically derived optimal parameters, a*, ro, and z, the collisional cross section, RD (eq 2), the depth of the minimum in the ion-neutral interaction potential, to (eq 3), and its position, r, (eq 5 ) , can be calculated as a function of the ion mass.
i
22
I
I
I
I
-
L L 0
10
100
20
I
50
0
18
16
14
Figure 7. Interaction potential, V ( r ) ,of protonated tridodecylamine in helium and SF, as a function of the ion-neutral separation distance, r.
lL 1
12
10
r (A")
0.0020 A/amu.
0
1
1
100
I
200
I
300
I
LOO
I
500
I 600
ION MASS ( a m u i Fieure 8. Calculated oosition of the minimum of the interaction Dotential, rm [A], as a function of the ion mass, in helium, nitrogen, argon,
-
co2, and SF6.
Some trends in the strength of the interaction, represented by and shown in Figure 6, are noteworthy. The value of eo decreases as the ion mass increases in all the drift gases and, for a given ion, as the polarizability of the drift gas decreases. However, for a given ion in nitrogen, air, and argon, Q is nearly indistinguishable. In helium, to decreases rapidly with increasing ion mass, so that for heavy ions the interaction potential is very weak. In contrast, in SF,, the decrease of to with ion mass is relatively slower, so that while eo is 18 times larger in SF6 than in H e for an ion of mass 46 amu, it is 130 times larger for an ion of 522 amu. To illustrate this point, the dependence of the interaction potential, V(r) (eq 4), of this latter ion on the ion-neutral separation distance in helium and SF6,is shown in Figure 7. While the position of the minimum ( 1 2.24 A in SF6 and 15.09 A in helium) in both curves is close, the depth of the curve in s F 6 is, as mentioned above, 2 orders of magnitude larger than in helium. Figure 8 depicts the dependence of the calculated r, on the ion mass (eq 5) in the different drift gases. Once again, nitrogen, air, and argon are essentially indistinguishable from each other. In helium, there is an almost linear increase in r, with the ion mass, while in SF6 the increase is initially gradual and becomes even more shallow at high ion masses. This is due to the inclusion of the correction factor in the calculation of r,. As a result, for ethylamine, r, in helium is about two-thirds that of SF6,while, for tridodecylamine, rm in helium is actually 23% larger. In general, the dependence of r, on the type of drift gas decreases as the ion mass increases. This is probably an indication that the size of the drift gas molecule plays an important role in determining the position of the potential minimum for light ions. As the ion mass and size increase, r, depends more on the strength of the interaction (therefore on the neutral's polarizability) and less on the geometrical size of the neutral molecule. Therefore, the curve for helium crosses the curves for the heavier drift gases when the ion mass becomes larger than about 200 amu (Figure 8). The collision cross sections, shown in Figure 9, increase with the ion mass in all drift gases and, once again, are almost the same for nitrogen, air, and argon. The absolute increments of the cross to
J . Phys. Chem. 1989, 93, 3025-3029
-
250
-
-'E
200
-
