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Determination of ion—molecule collision frequencies by Fourier transform ion cyclotron resonance spectroscopy
Volume 62, number 2
CHEMICAL. PHYSICS LElTERS
DETERMLNATION
OF ION---MOLECULE
BY FOURIER-TRANSFORM
1 April1979
COLLZSION FREQUENCSES
ION CYCLOTRON
RESONANCE
SPECTROSCOPY
Grald PARlSOD and Melvin B. COMISAROW Deparrment of Chetnirtry. University of British Columbia. Vancouver. B-C. Calzada i’6T I IV5 Received 7 December 1978
it is shown that nonreactive ion-molecule collision frequencies may be determined &her by analysis of the tmnsient signd resulting from excited ion cyclotron motion or by linewidth measurement of the Fotqier transform of the *ansient
The study of ion-molecule interaction potentials has been one of the important applications of ion cyclotron resonance (ICR) spectroscopy_ The overall procedure is to determine experimental ion-molecule collision frequencies which are then compared with the collision frequencies predicted from an assumed ion-neutral interaction potential and standard kinetic theory. The most common method of measurinS non-reactive ionmolecule colliiion frequencies by ICR is to measure the linewidth of a collisionally broadened spectral line [I-S] although transient ICR methods 19-l l] have also been found to be useful- The determination of nonreztctive ion-molecule collision frequencies by ICR methods had the advantageous feature of inherent mass analysis. Recently, a new method called Fourier transform ion cyclotron resonance (ET ICR) spectroscopy. has been developed [12-211 for conducting 1CR experiments. In the FT ICR method, the cyclotron motion of the sample ions is coherently excited and the transient signal 1303 from that motion is detected and stored in the memory of a digital computer_ Fourier transformation of this transient signal gives the ICR frequency spectrum- For a transient signal which is damped by non-reactive ion-molecule collisions, the analytical form of the transient is [21] F(r) = K cos (or) e-‘E
,
(1)
where K is a constant which depends upon the experimental parameters, w is the cyclotron frequency, t is
time and E is the reduced collision frequency. The reduced collision frequency is the damping coefficient in the equstion of motion of driven. collisionally damped 1CR system [2,3,6] and for an ion-neutral pair in which the ion-induced dipole interaction is dominsnt, is given by .$ = 2.21 xq cW#/rn
,
(7)
xbhere r~ is the ion charge, (Y is the neutral polarizability. p is the ion-neutral reckced mass. and ~71is the ion mass. In the high pressure limit that the FT ICR acquisition time, T, is much greater than the inverse of the reduced collision frequency TS l/t, the magnitude mode line shape [16_lS,21], C(o’). is given by 1211 C(&J’) = --* E[lt(W’-W)2/~2]1~“
(3)
The full width at half height, LL_Q~ _of the high pressure, magnitude mode lineshape is @en by [21] Aw5~~=2&.$_
(4)
Eqs- (1) and (4) provide two methods for determination of the reduced collision frequency. $j_The collision frequency can be determined either by analysis of the exponential envelope of the decaying oscillation ]eq_ (l)] or by linewidth measurement of the spectral peak [eq. (4)1The experiments were performed on a home-built FT ICR spectrometer which has been briefly described 303
Volume 62. number 2
1 Aprit 1979
CHEMICAL PttYSICS LETTERS
elsewhere [32 j_ The vacuum system of the spectrometer was fiBed with CH4 to n pressurein the range 5 X IO-6 to 1X Z04 torr, Pressureswere measuredon rrE&yardAipert ionization gauge which was calibrated against 8 capacitance manometer. Electron impact ionization with a 4 rnspulse of30 eV electrons ionizes the sample to CH: and C@ ions_After a reaction time delay period of 50 ms to &ow the ion-molecule reactions
and 10
to go to completion, the ion motion in the srunpfewas sekctiveIy excited by a 0. I ms, I8 mV/cm rddiofrequency pi.& Itt the ion c_vcfotronfrequency. The sign31 frcm the excited cyriotron motion was then mixed and fihered to form a specrrally extracted analog signltf.This analog signal was digitized at IO0 kHz to form a digital rnnsicnt signaLwhich was stored in the memory of 3 computer_ After applying 3 quench pulse, the cycIe was repeated 10 times to enhance the signal to noise ratio of the transient. Numerical Fourier transform&ion produces the FT ICR frequerxy spccrrunr, Fig- 1 is a plot of the rrvfuced collision frequency, $. for Ci-if ions in CH4 from trmsient ;tnalysisversus the sane colkion frequency from linewidth measurement. Errchpoint in fig. I is the v&e of E from ax& ysis of the emefope of:Jxe transient [eq. (I)1 ptotted
E Wc-~ 1 from hen&h Fig_ I_ Plot oi the reduced collkion fxquency, E.for CH$ ions in C& determined by iast squsns SI& sis of the exponentW emelope of the transient s&at versusthesamec&Son frequency masured by tiewidth zln;llysis[eq. (3) I- The measure-
mentsu’rredetermined01.xthe pressure aqe
ta 5 Y IW5 torr.
1 X 10 -5 tar
3 20 30 40 &SiuE p torr FG. 1- Plot of rhe reduced colikfon frequency. E. for CH$ in a as a function of CH4 pressure_The individual determin;ltionswe= obtzined from linewidth measurement.
against the value of 5 obtained by linewidth measurement [eq. (4)] of the magnitude mode Fourier trimsform of the same transient. it is obvious from fig. 1 that over the pressureranse studied, the value of g obtained from either method is the same. A further conclusion which can be drawn from fig. I is that eqs. (I) and (4) accurately describe the experimental transientand the experimental iinewidth of a high pressuremzgrzirude mode FT ICR lineshape_ Fig. 3showsa plot of the reduced Lwilisionfrequency, & for CH$ in CH4 as 3 fun ofCH, pressure-The second order reduced coifision frequency, @r. determined by leastsquaresanaiysisis(7_9 LO2)X 10--f0cm3 mol-’ S -I which is in agreement with the v&e of Ridge and Beauchamp(9.06 X 10-*O) [4] and the GJ~KCof Bowers and cc>-workers (23.43 X 10--~~) [S] _ The second order reduced collision frequency for CH$ in CHq is predicted to be 7-04 X XO-io if the ion-induced dipole (pofarf~~ti~~) ootentiaf is the onIy interaction potential between CH: and CH4. The collision frequency of this work is hi&x than this value, suggesting that other forces contribute to the over&t interaction potential_The same conclusion was drawn by Ridge and Beau& [4] whoargued that the interaction between CIiz and CH4 can be best modelfed as a I Z-6-4 potenti @J _ Fig- 3 shows s pto t of the reduced collision frequency for CzHz in CH, as a functiqn of neutral pressure-The least squaresvalue of&z for the data of fig_ 3 is (4.7 %0.1) X IO-to cm3 mol’t s-t _ This value is close to the pofarizittion vaiue (4.62 X IO-to) suggest-
Volume 62, number 2
CHEMICAL PHYSICS
1 April 1979
LETTERS
signals obtained
with tuned
ICR
detectors
[I l] _ This
latter method also operates
500
Klo
Fig.- 3. Plot of the reduced cobision frequency, $. for CaH; in CHq 3s 3 function of CR4 pressure. The individual determinations Pere obtained from Iineaidth measurement. the forces other than the polarization force 3re less important for C,Hf in CH, than for CHf in CH,. Ridge and Bauchamp obtained 3 value of 5.39 X lo-I0 for this collision frequency which agrees well with the value of this work. The r3tio of the collision frequencies for CHf and C, Hr from this work is 1.70 which is virtually identical the ratio (I -65) calculated from the data of Ridge and Besuchsmp [4] _ The similarity of this rrttio of coIIision frequencies suggests that smal1 ing that
differences between the coihsion frequencies of this work and those in the literature [4.S] sre due to differences in rtbsolute pressure meztsurement. Of the two methods for messuring 5 by FT ICR spectroscopy, the linewidth measurement is clearly the most convenient and the data of fig. I susests that no further information accrues from rinalysis of the tmnsient. The pressure mnge over which the methods of this work are applicabIz is I--Z orders of magnitude lower than the pressures used for linewidth me3surements with 3 scanning ICR spectrometer and in this respect the method of this work and the method of line shape analysis on 3 sc3nninS ICR spectrometer 3re complementary. However, since ICR resoIution increases as the pressure is lowered [ 171, the FT ICR methods of this work wtll be 3ppIicabIe to systems where poor m;Lss resolution will limit the applicabiiity of convention31 ICR linewidth measurements. An advantageous aspect of the higher pressures used for conventional ICR linewidth measurements is that these higher pressures may be measured directly with 3 ctlpacitance manometer. The method of transient anafysis of this work is identical to analysis of the collisionally damped ICR
in 3 pressure range whic!l is lower than that used for conventional ICR linewidth measurements. The FT ICR method of this work thus has the advant3ge of simuitaneously achieving the hi$rer resolution accruing from lower pressures \vith the convenience of linewidth me.tsurements_ This resenrch W,E supported by the National Research Council of CanadA .md The Resexch CorporationThe software for obtaining the data ~3s written by Mr. Valerio Gr.rsst_
References [i 1 D. Wobschztll, R-A. Tlueg@ and J-R. Graham, J. Chem. Phys.47 (1967) 4091. [2] D. Wobschall. J. Graham 2nd D. Malone, Phys_. Rev. 13 1 (1963) 1565. [31 J-I_. Beauchamp, Ann. Rev. Phys. Chem. 21 (1971) 528. 14 J D P. Ridge and J-L. Beauchamp, J. Chem. Phi s. 64 (1976) 2735. [5] P.P. Dj merski and R C. Dunbar, J. Chem. Phbs. 57 (1977,) 4049. [61 M.B. Comisarow, J_ Chem. Phys. 55 (1971) 205_ [7] SE. Butrill. J. Chem. Phys. 58 (1973) 656. ISI X1-T. Bowers. P-V. Netion, P.R. Eemper snd A.G. Wrzn, Intern_ J. Mass Spectrom. Ion Phys. 25 (1977) 103. [9 J W-T. Huntress, J. Chem. Phqs. 55 (1971) 2146. [lOI R.C. Dunbar, J_ Chem. Phys. 54 (1971) 711. [I 1 ] CA. Lieder_ R-W. Men nnd R-T_ McI\er Jr., J. Chem. Phls56 (1972) 5184. [111 M.B. Comwow, in: Trzxnsform techniques in chemlstr~, ed. P-R_ Grlffiths (Plenum Preks. New York, 1978) chh. IO. 1131 XB. Corn&row. in: Adwxces in mass spectrometry, Vol. 7B. ed. N.R. Daly (He>den. London. 1978) p- 10-Q. 1141 M.B. Corn&row and A G. Marshall, Chem. Phys. Letters 2.5 (1974) 281. [IS 1 M.B. Corn&row and A G. Marshall, Chem. Phqs. Letters 26 (1974) 469. [16] M-B. Comlruow and A.G. Marsh.&, Can_ J. Chem. 52 (1974) 1997. [17I M-B. ComisaroH and A.G. Marshall. J_ Chum. Ph>s_ 61 (1975) 293. [18] M-B. Corn&row and A.G. M~slxdl, J. Chem. Phls. 64 (1976) 110. [19] 11.B. Comisarov,, V. Grass1 and G. Parisod. Chem_ Ph>s. Letters 57 (1978) 413. [20] M-B. Comisarow, J. Chem. Phys. 69 (1978) 4097. [al] M-B. Comkuow, A-G. Marshall and G. Parisod, J. Chem. Phqs.. submitted for publicatron. 1271 M-B. CO~I~UOW. G. P&sod and V. Grassi, Proceedmgs of the 26th Annual Conference on Mass Speetrometry and Allied Topics, St. Louis, MO., May 28-June 2,19?8, paper \\PI?. 305
CHEMICAL. PHYSICS LElTERS
DETERMLNATION
OF ION---MOLECULE
BY FOURIER-TRANSFORM
1 April1979
COLLZSION FREQUENCSES
ION CYCLOTRON
RESONANCE
SPECTROSCOPY
Grald PARlSOD and Melvin B. COMISAROW Deparrment of Chetnirtry. University of British Columbia. Vancouver. B-C. Calzada i’6T I IV5 Received 7 December 1978
it is shown that nonreactive ion-molecule collision frequencies may be determined &her by analysis of the tmnsient signd resulting from excited ion cyclotron motion or by linewidth measurement of the Fotqier transform of the *ansient
The study of ion-molecule interaction potentials has been one of the important applications of ion cyclotron resonance (ICR) spectroscopy_ The overall procedure is to determine experimental ion-molecule collision frequencies which are then compared with the collision frequencies predicted from an assumed ion-neutral interaction potential and standard kinetic theory. The most common method of measurinS non-reactive ionmolecule colliiion frequencies by ICR is to measure the linewidth of a collisionally broadened spectral line [I-S] although transient ICR methods 19-l l] have also been found to be useful- The determination of nonreztctive ion-molecule collision frequencies by ICR methods had the advantageous feature of inherent mass analysis. Recently, a new method called Fourier transform ion cyclotron resonance (ET ICR) spectroscopy. has been developed [12-211 for conducting 1CR experiments. In the FT ICR method, the cyclotron motion of the sample ions is coherently excited and the transient signal 1303 from that motion is detected and stored in the memory of a digital computer_ Fourier transformation of this transient signal gives the ICR frequency spectrum- For a transient signal which is damped by non-reactive ion-molecule collisions, the analytical form of the transient is [21] F(r) = K cos (or) e-‘E
,
(1)
where K is a constant which depends upon the experimental parameters, w is the cyclotron frequency, t is
time and E is the reduced collision frequency. The reduced collision frequency is the damping coefficient in the equstion of motion of driven. collisionally damped 1CR system [2,3,6] and for an ion-neutral pair in which the ion-induced dipole interaction is dominsnt, is given by .$ = 2.21 xq cW#/rn
,
(7)
xbhere r~ is the ion charge, (Y is the neutral polarizability. p is the ion-neutral reckced mass. and ~71is the ion mass. In the high pressure limit that the FT ICR acquisition time, T, is much greater than the inverse of the reduced collision frequency TS l/t, the magnitude mode line shape [16_lS,21], C(o’). is given by 1211 C(&J’) = --* E[lt(W’-W)2/~2]1~“
(3)
The full width at half height, LL_Q~ _of the high pressure, magnitude mode lineshape is @en by [21] Aw5~~=2&.$_
(4)
Eqs- (1) and (4) provide two methods for determination of the reduced collision frequency. $j_The collision frequency can be determined either by analysis of the exponential envelope of the decaying oscillation ]eq_ (l)] or by linewidth measurement of the spectral peak [eq. (4)1The experiments were performed on a home-built FT ICR spectrometer which has been briefly described 303
Volume 62. number 2
1 Aprit 1979
CHEMICAL PttYSICS LETTERS
elsewhere [32 j_ The vacuum system of the spectrometer was fiBed with CH4 to n pressurein the range 5 X IO-6 to 1X Z04 torr, Pressureswere measuredon rrE&yardAipert ionization gauge which was calibrated against 8 capacitance manometer. Electron impact ionization with a 4 rnspulse of30 eV electrons ionizes the sample to CH: and C@ ions_After a reaction time delay period of 50 ms to &ow the ion-molecule reactions
and 10
to go to completion, the ion motion in the srunpfewas sekctiveIy excited by a 0. I ms, I8 mV/cm rddiofrequency pi.& Itt the ion c_vcfotronfrequency. The sign31 frcm the excited cyriotron motion was then mixed and fihered to form a specrrally extracted analog signltf.This analog signal was digitized at IO0 kHz to form a digital rnnsicnt signaLwhich was stored in the memory of 3 computer_ After applying 3 quench pulse, the cycIe was repeated 10 times to enhance the signal to noise ratio of the transient. Numerical Fourier transform&ion produces the FT ICR frequerxy spccrrunr, Fig- 1 is a plot of the rrvfuced collision frequency, $. for Ci-if ions in CH4 from trmsient ;tnalysisversus the sane colkion frequency from linewidth measurement. Errchpoint in fig. I is the v&e of E from ax& ysis of the emefope of:Jxe transient [eq. (I)1 ptotted
E Wc-~ 1 from hen&h Fig_ I_ Plot oi the reduced collkion fxquency, E.for CH$ ions in C& determined by iast squsns SI& sis of the exponentW emelope of the transient s&at versusthesamec&Son frequency masured by tiewidth zln;llysis[eq. (3) I- The measure-
mentsu’rredetermined01.xthe pressure aqe
ta 5 Y IW5 torr.
1 X 10 -5 tar
3 20 30 40 &SiuE p torr FG. 1- Plot of rhe reduced colikfon frequency. E. for CH$ in a as a function of CH4 pressure_The individual determin;ltionswe= obtzined from linewidth measurement.
against the value of 5 obtained by linewidth measurement [eq. (4)] of the magnitude mode Fourier trimsform of the same transient. it is obvious from fig. 1 that over the pressureranse studied, the value of g obtained from either method is the same. A further conclusion which can be drawn from fig. I is that eqs. (I) and (4) accurately describe the experimental transientand the experimental iinewidth of a high pressuremzgrzirude mode FT ICR lineshape_ Fig. 3showsa plot of the reduced Lwilisionfrequency, & for CH$ in CH4 as 3 fun ofCH, pressure-The second order reduced coifision frequency, @r. determined by leastsquaresanaiysisis(7_9 LO2)X 10--f0cm3 mol-’ S -I which is in agreement with the v&e of Ridge and Beauchamp(9.06 X 10-*O) [4] and the GJ~KCof Bowers and cc>-workers (23.43 X 10--~~) [S] _ The second order reduced collision frequency for CH$ in CHq is predicted to be 7-04 X XO-io if the ion-induced dipole (pofarf~~ti~~) ootentiaf is the onIy interaction potential between CH: and CH4. The collision frequency of this work is hi&x than this value, suggesting that other forces contribute to the over&t interaction potential_The same conclusion was drawn by Ridge and Beau& [4] whoargued that the interaction between CIiz and CH4 can be best modelfed as a I Z-6-4 potenti @J _ Fig- 3 shows s pto t of the reduced collision frequency for CzHz in CH, as a functiqn of neutral pressure-The least squaresvalue of&z for the data of fig_ 3 is (4.7 %0.1) X IO-to cm3 mol’t s-t _ This value is close to the pofarizittion vaiue (4.62 X IO-to) suggest-
Volume 62, number 2
CHEMICAL PHYSICS
1 April 1979
LETTERS
signals obtained
with tuned
ICR
detectors
[I l] _ This
latter method also operates
500
Klo
Fig.- 3. Plot of the reduced cobision frequency, $. for CaH; in CHq 3s 3 function of CR4 pressure. The individual determinations Pere obtained from Iineaidth measurement. the forces other than the polarization force 3re less important for C,Hf in CH, than for CHf in CH,. Ridge and Bauchamp obtained 3 value of 5.39 X lo-I0 for this collision frequency which agrees well with the value of this work. The r3tio of the collision frequencies for CHf and C, Hr from this work is 1.70 which is virtually identical the ratio (I -65) calculated from the data of Ridge and Besuchsmp [4] _ The similarity of this rrttio of coIIision frequencies suggests that smal1 ing that
differences between the coihsion frequencies of this work and those in the literature [4.S] sre due to differences in rtbsolute pressure meztsurement. Of the two methods for messuring 5 by FT ICR spectroscopy, the linewidth measurement is clearly the most convenient and the data of fig. I susests that no further information accrues from rinalysis of the tmnsient. The pressure mnge over which the methods of this work are applicabIz is I--Z orders of magnitude lower than the pressures used for linewidth me3surements with 3 scanning ICR spectrometer and in this respect the method of this work and the method of line shape analysis on 3 sc3nninS ICR spectrometer 3re complementary. However, since ICR resoIution increases as the pressure is lowered [ 171, the FT ICR methods of this work wtll be 3ppIicabIe to systems where poor m;Lss resolution will limit the applicabiiity of convention31 ICR linewidth measurements. An advantageous aspect of the higher pressures used for conventional ICR linewidth measurements is that these higher pressures may be measured directly with 3 ctlpacitance manometer. The method of transient anafysis of this work is identical to analysis of the collisionally damped ICR
in 3 pressure range whic!l is lower than that used for conventional ICR linewidth measurements. The FT ICR method of this work thus has the advant3ge of simuitaneously achieving the hi$rer resolution accruing from lower pressures \vith the convenience of linewidth me.tsurements_ This resenrch W,E supported by the National Research Council of CanadA .md The Resexch CorporationThe software for obtaining the data ~3s written by Mr. Valerio Gr.rsst_
References [i 1 D. Wobschztll, R-A. Tlueg@ and J-R. Graham, J. Chem. Phys.47 (1967) 4091. [2] D. Wobschall. J. Graham 2nd D. Malone, Phys_. Rev. 13 1 (1963) 1565. [31 J-I_. Beauchamp, Ann. Rev. Phys. Chem. 21 (1971) 528. 14 J D P. Ridge and J-L. Beauchamp, J. Chem. Phi s. 64 (1976) 2735. [5] P.P. Dj merski and R C. Dunbar, J. Chem. Phbs. 57 (1977,) 4049. [61 M.B. Comisarow, J_ Chem. Phys. 55 (1971) 205_ [7] SE. Butrill. J. Chem. Phys. 58 (1973) 656. ISI X1-T. Bowers. P-V. Netion, P.R. Eemper snd A.G. Wrzn, Intern_ J. Mass Spectrom. Ion Phys. 25 (1977) 103. [9 J W-T. Huntress, J. Chem. Phqs. 55 (1971) 2146. [lOI R.C. Dunbar, J_ Chem. Phys. 54 (1971) 711. [I 1 ] CA. Lieder_ R-W. Men nnd R-T_ McI\er Jr., J. Chem. Phls56 (1972) 5184. [111 M.B. Comwow, in: Trzxnsform techniques in chemlstr~, ed. P-R_ Grlffiths (Plenum Preks. New York, 1978) chh. IO. 1131 XB. Corn&row. in: Adwxces in mass spectrometry, Vol. 7B. ed. N.R. Daly (He>den. London. 1978) p- 10-Q. 1141 M.B. Corn&row and A G. Marshall, Chem. Phys. Letters 2.5 (1974) 281. [IS 1 M.B. Corn&row and A G. Marshall, Chem. Phqs. Letters 26 (1974) 469. [16] M-B. Comlruow and A.G. Marsh.&, Can_ J. Chem. 52 (1974) 1997. [17I M-B. ComisaroH and A.G. Marshall. J_ Chum. Ph>s_ 61 (1975) 293. [18] M-B. Corn&row and A.G. M~slxdl, J. Chem. Phls. 64 (1976) 110. [19] 11.B. Comisarov,, V. Grass1 and G. Parisod. Chem_ Ph>s. Letters 57 (1978) 413. [20] M-B. Comisarow, J. Chem. Phys. 69 (1978) 4097. [al] M-B. Comkuow, A-G. Marshall and G. Parisod, J. Chem. Phqs.. submitted for publicatron. 1271 M-B. CO~I~UOW. G. P&sod and V. Grassi, Proceedmgs of the 26th Annual Conference on Mass Speetrometry and Allied Topics, St. Louis, MO., May 28-June 2,19?8, paper \\PI?. 305