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A new mass spectrograph for the analysis of dissociation fragments
International Journal of Mass Spectrometry and Zon Processes, 91 (1989) 11-17 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
11
A NEW MASS SPECTROGRAPH FOR THE ANALYSIS OF DISSOCIATION FRAGMENTS
H. MATSUDA Institute of Physics, CoIlege of General Education, Osaka University, Toyonaka, Osaka 560 (Japan) (Received
18 April 1988)
ABSTRACT A new type of double focusing mass spectrograph is proposed. It consists of a uniform electric field and a uniform magnetic field. All ions of different masses with approximately equal velocities after collisional activation are focused on a straight focal plane and mass analyzed simultaneously. The double focusing (angle and energy) holds for all masses.
INTRODUCTION
The MS/MS system is a powerful technique to achieve the structural characterization of complex molecules. Here the precursor ions of definite mass are selected by the first mass spectrometer (MS-l), activated by the collision with gas molecules, and dissociated. The fragment ions produced are mass analyzed by the second mass spectrometer (MS-2). As an MS-2, the use of a double focusing instrument is necessary to increase mass resolution [l]. To increase sensitivity, a simultaneous ion detection technique is advantageous [2]. However, a conventional double focusing mass spectrometer consisting of an electric sector and a magnetic sector does not fit the simultaneous ion detection over a wide mass range, because the ions to be analyzed have approximately equal velocity instead of approximately equal energy and the energies of ions of different masses are proportional to their masses. The mass spectrum of the fragment ions is only obtained by linked scanning with E/B constant. A new type of double focusing mass spectrograph is proposed here to overcome the above difficulty. The details are described as follows. ION TRAJECTORY
IN THE UNIFORM
ELECTRIC
FIELD.
Consider the movement of an ion in the x-z plane of a Cartesian coordinate system shown in Fig. 1. The uniform electric field E,, is applied 0168-1176/89/$03.50
0 1989 Elsevier Science Publishers
B.V.
12 virtual
image
Fig. 1. Coordinate system for uniform electric field. Two trajectories corresponding injection angles 0, and (0, + a) are shown.
to the
to the negative direction of the x-axis in the region x > 0. The electric potential is assumed to be zero on the z-axis and in the region x -C0. We calculate the trajectory of an arbitrary ion with mass m, charge e and velocity u = ~(1 + S,), where u. is the velocity of the reference ion. The equations of motion are given by d2x m= -eE, dt2
(1)
d2.z ms=
(2)
o
We assume that the ion is injected at x = z = 0 with an angle (0, + a) with respect to the z-axis, where 0, is the angle of the reference ion. Eq. 1 is solved with respect to t as
(3) From Eq. 2 we have dz dt = const = u,(l + 8,) cos(8, + LX) = u. cos do(1 + 6, - (Ytan 8,) in the first order approximation we obtain t=
’ e,(1 -
uo cos
6, + a tan
(4)
assuming a +C 1, 6,-K 1. Integrating
0,)
Eq. 4
(5)
Substituting Eq. 5 into Eq. 3 and using the relationship = u,(l + 6,) sin(8, + a) =uo sin00(1+6,+acot
0,)
(6)
13
we obtain ci sin 0, cos 0,
- $
tan e,(l - 28” + 2(Xtan t9,)
(7)
where zo =
2mu,2 sin 6, cos 6,
(8) eE0 is the value of the z-coordinate where the reference ion ((Y= 8” = 0) intersects the z-axis again. We assume that the arbitrary ion intersects the z-axis again at z = z,, + AZ. Then, from Eq. 7 we obtain AZ - = 28, + a(cot 0, - tan 0,) (9) ZO
For the well known case of 0, = 45 “, AZ/Z, is independent of 1~. This means that the ion beam is focused on the z-axis and the velocity dispersion at the focus point is given by 2~~8,. For a general case of 0, # 45 O, the focus point is obtained by putting the coefficient of (Yin Eq. 7 to be zero. Then the coordinates of the focus point are given by x -= zo
2 sin 0,1 cos e,(1-2sirlr2B,) 1
Z -=
(10)
2 sin’ e,
z0
If 0, > 45 O, the focus point is in the region x > 0 and the ion beam diverges again after the focus point. Therefore, in the field free region x -C0, ions move as if they started from a virtual image point in a free space. The position of the virtual image point is calculated from the value of dx/dz at X=0 -tan8,-L
co2 e,
01)
It should be noted that Eq. 11 is independent of S U. From Eqs. 11 and 9, the distance I, between the virtual image point and the point z = z. is calculated to be 1, =
z.
(tan8,- cot e,)sin e,
The velocity dispersion D6 at the virtual image point (perpendicular the beam direction) is given from Eqs. 9 and 11 as D6 = 22, sin 0,
(12)
to 03)
14 DOUBLE FOCUSING
CONDITION
A double focusing mass spectrograph can be realized if a magnetic sector field is connected to the uniform electric field. The conditions for double focusing are that the virtual image point coincides with the source point of the magnetic sector and that the velocity dispersion of the magnetic sector when ions have travelled in reverse through the magnetic field is equal to D, given in Eq. 13. The velocity dispersion of a magnetic sector for a reverse ray is given by D,” = r,(l-
cos +) + I,Jsin
+ + (I-
cos $> tan cl]
where r,, +, or, and I,, stand for the radius, deflection angle, incident angle and source length of the magnetic sector, respectively. The values of I, and D, for various I!?,,are given in Table 1. EXAMPLES
OF THE DOUBLE FOCUSING
MASS SPECTROGRAPH
Four different examples are shown in Figs. 2-5. If the exit boundary of the magnetic sector is a straight line through the origin of the electric field
TABLE 1 Values of I, and D, for various values of 0,.
e.(deg.)
L/z0
Da120
45 50 55 60
0 0.2701 0.5963 1
1.4142 1.5321 1.6383 1.7321
Fig. 2. Example of proposed double focusing mass spectrograph. Ion optical parameters are given in column A of Table 2.
15
Fig. 3. Example of proposed double focusing mass spectrograph. given in column B of Table 2.
Ion optical parameters are
Fig. 4. Example of proposed double focusing mass spectrograph. Ion optical parameters are given in column C of Table 2.
Fig. 5. Example of proposed double focusing mass spectrograph. given in column D of Table 2.
Ion optical parameters are
16 TABLE 2 Values of ion optical parameters for proposed double focusing mass spectrographs. A, B, C, D correspond to Figs. 2, 3, 4 and 5, respectively
0, (deg.) h (deg.) e1 (deg.) e2 (deg.) rm/z0 &ll,/zo IIn2/so Ax A,/r, A, As/r,,,
A
B
C
D
45 180 45 45 0.707 0 0 -1 1 - 2.14 -0.34
45 135 45 16 0.828 0 1.161 - 1.983 1.693 - 2.21 - 0.26
50 130 40 31 0.580 0.270 0.562 - 1.265 1.671 - 1.19 - 0.60
55 100 35 24 0.478 0.596 0.939 - 1.207 2.068 -1.40 - 1.63
(injection point) as shown in Figs. 2-5, the focal plane of the magnetic sector for different masses is also a straight line through the origin and the double focusing holds for all masses, because z,, and r, are proportional to m ( u0 is constant), and +,, e1 and e2 are equal for all masses. The trajectories for different masses are completely similar to each other as shown in Figs. 2-5, where three different trajectories are shown. Ion optical parameters are listed in Table 2. A large incident angle to the magnetic field (45-35”) makes it possible to obtain vertical focusing. The values of the ion optical parameters in Table 2 are suitable for practical use. RESOLVING POWER AND MASS SCALE
The resolving power of a mass spectrograph is given by the equation
neglecting aberrations, where A y, A, and s are the mass dispersion, image magnification and source slit width, respectively. The image magnification of the virtual image of the uniform electric field is unity because the parallel shift of the coordinate in the z-direction does not change the ion trajectory. Therefore, the resolving power of the example mass spectrographs shown in Figs. 2-5 can be calculated using the values of the parameters given in Table 2. Assuming r, = 300 mm and s = 0.1 mm, the estimated resolving powers are 3000 (Fig. 2), 2500 (Fig. 3), 3900 (Fig. 4) and 5100 (Fig. 5).
17
The resolving power is proportional to r,,, (or m) for a fixed width of the source slit. This means that if the resolving power at M = 1000 is 2000, then that at M = 100 is 200. This is enough for mass analysis. Since z,, and a, are proportional to m, the mass scale on a focal plane is proportional to the distance from the origin as can be seen from Figs. 2-5. Therefore, the mass scale on a focal plane is exactly linear. This feature is especially advantageous for precise mass calibration. REFERENCES 1 F.W. McLafferty, Act. Chem. Res., 13 (1980) 33. 2 J.S. Cottrell and S. Evans, Anal. Chem., 59 (1987) 1990. 3 H. Matsuda, Mass Spectrosc. Jpn., 12 (1964) 105.
11
A NEW MASS SPECTROGRAPH FOR THE ANALYSIS OF DISSOCIATION FRAGMENTS
H. MATSUDA Institute of Physics, CoIlege of General Education, Osaka University, Toyonaka, Osaka 560 (Japan) (Received
18 April 1988)
ABSTRACT A new type of double focusing mass spectrograph is proposed. It consists of a uniform electric field and a uniform magnetic field. All ions of different masses with approximately equal velocities after collisional activation are focused on a straight focal plane and mass analyzed simultaneously. The double focusing (angle and energy) holds for all masses.
INTRODUCTION
The MS/MS system is a powerful technique to achieve the structural characterization of complex molecules. Here the precursor ions of definite mass are selected by the first mass spectrometer (MS-l), activated by the collision with gas molecules, and dissociated. The fragment ions produced are mass analyzed by the second mass spectrometer (MS-2). As an MS-2, the use of a double focusing instrument is necessary to increase mass resolution [l]. To increase sensitivity, a simultaneous ion detection technique is advantageous [2]. However, a conventional double focusing mass spectrometer consisting of an electric sector and a magnetic sector does not fit the simultaneous ion detection over a wide mass range, because the ions to be analyzed have approximately equal velocity instead of approximately equal energy and the energies of ions of different masses are proportional to their masses. The mass spectrum of the fragment ions is only obtained by linked scanning with E/B constant. A new type of double focusing mass spectrograph is proposed here to overcome the above difficulty. The details are described as follows. ION TRAJECTORY
IN THE UNIFORM
ELECTRIC
FIELD.
Consider the movement of an ion in the x-z plane of a Cartesian coordinate system shown in Fig. 1. The uniform electric field E,, is applied 0168-1176/89/$03.50
0 1989 Elsevier Science Publishers
B.V.
12 virtual
image
Fig. 1. Coordinate system for uniform electric field. Two trajectories corresponding injection angles 0, and (0, + a) are shown.
to the
to the negative direction of the x-axis in the region x > 0. The electric potential is assumed to be zero on the z-axis and in the region x -C0. We calculate the trajectory of an arbitrary ion with mass m, charge e and velocity u = ~(1 + S,), where u. is the velocity of the reference ion. The equations of motion are given by d2x m= -eE, dt2
(1)
d2.z ms=
(2)
o
We assume that the ion is injected at x = z = 0 with an angle (0, + a) with respect to the z-axis, where 0, is the angle of the reference ion. Eq. 1 is solved with respect to t as
(3) From Eq. 2 we have dz dt = const = u,(l + 8,) cos(8, + LX) = u. cos do(1 + 6, - (Ytan 8,) in the first order approximation we obtain t=
’ e,(1 -
uo cos
6, + a tan
(4)
assuming a +C 1, 6,-K 1. Integrating
0,)
Eq. 4
(5)
Substituting Eq. 5 into Eq. 3 and using the relationship = u,(l + 6,) sin(8, + a) =uo sin00(1+6,+acot
0,)
(6)
13
we obtain ci sin 0, cos 0,
- $
tan e,(l - 28” + 2(Xtan t9,)
(7)
where zo =
2mu,2 sin 6, cos 6,
(8) eE0 is the value of the z-coordinate where the reference ion ((Y= 8” = 0) intersects the z-axis again. We assume that the arbitrary ion intersects the z-axis again at z = z,, + AZ. Then, from Eq. 7 we obtain AZ - = 28, + a(cot 0, - tan 0,) (9) ZO
For the well known case of 0, = 45 “, AZ/Z, is independent of 1~. This means that the ion beam is focused on the z-axis and the velocity dispersion at the focus point is given by 2~~8,. For a general case of 0, # 45 O, the focus point is obtained by putting the coefficient of (Yin Eq. 7 to be zero. Then the coordinates of the focus point are given by x -= zo
2 sin 0,1 cos e,(1-2sirlr2B,) 1
Z -=
(10)
2 sin’ e,
z0
If 0, > 45 O, the focus point is in the region x > 0 and the ion beam diverges again after the focus point. Therefore, in the field free region x -C0, ions move as if they started from a virtual image point in a free space. The position of the virtual image point is calculated from the value of dx/dz at X=0 -tan8,-L
co2 e,
01)
It should be noted that Eq. 11 is independent of S U. From Eqs. 11 and 9, the distance I, between the virtual image point and the point z = z. is calculated to be 1, =
z.
(tan8,- cot e,)sin e,
The velocity dispersion D6 at the virtual image point (perpendicular the beam direction) is given from Eqs. 9 and 11 as D6 = 22, sin 0,
(12)
to 03)
14 DOUBLE FOCUSING
CONDITION
A double focusing mass spectrograph can be realized if a magnetic sector field is connected to the uniform electric field. The conditions for double focusing are that the virtual image point coincides with the source point of the magnetic sector and that the velocity dispersion of the magnetic sector when ions have travelled in reverse through the magnetic field is equal to D, given in Eq. 13. The velocity dispersion of a magnetic sector for a reverse ray is given by D,” = r,(l-
cos +) + I,Jsin
+ + (I-
cos $> tan cl]
where r,, +, or, and I,, stand for the radius, deflection angle, incident angle and source length of the magnetic sector, respectively. The values of I, and D, for various I!?,,are given in Table 1. EXAMPLES
OF THE DOUBLE FOCUSING
MASS SPECTROGRAPH
Four different examples are shown in Figs. 2-5. If the exit boundary of the magnetic sector is a straight line through the origin of the electric field
TABLE 1 Values of I, and D, for various values of 0,.
e.(deg.)
L/z0
Da120
45 50 55 60
0 0.2701 0.5963 1
1.4142 1.5321 1.6383 1.7321
Fig. 2. Example of proposed double focusing mass spectrograph. Ion optical parameters are given in column A of Table 2.
15
Fig. 3. Example of proposed double focusing mass spectrograph. given in column B of Table 2.
Ion optical parameters are
Fig. 4. Example of proposed double focusing mass spectrograph. Ion optical parameters are given in column C of Table 2.
Fig. 5. Example of proposed double focusing mass spectrograph. given in column D of Table 2.
Ion optical parameters are
16 TABLE 2 Values of ion optical parameters for proposed double focusing mass spectrographs. A, B, C, D correspond to Figs. 2, 3, 4 and 5, respectively
0, (deg.) h (deg.) e1 (deg.) e2 (deg.) rm/z0 &ll,/zo IIn2/so Ax A,/r, A, As/r,,,
A
B
C
D
45 180 45 45 0.707 0 0 -1 1 - 2.14 -0.34
45 135 45 16 0.828 0 1.161 - 1.983 1.693 - 2.21 - 0.26
50 130 40 31 0.580 0.270 0.562 - 1.265 1.671 - 1.19 - 0.60
55 100 35 24 0.478 0.596 0.939 - 1.207 2.068 -1.40 - 1.63
(injection point) as shown in Figs. 2-5, the focal plane of the magnetic sector for different masses is also a straight line through the origin and the double focusing holds for all masses, because z,, and r, are proportional to m ( u0 is constant), and +,, e1 and e2 are equal for all masses. The trajectories for different masses are completely similar to each other as shown in Figs. 2-5, where three different trajectories are shown. Ion optical parameters are listed in Table 2. A large incident angle to the magnetic field (45-35”) makes it possible to obtain vertical focusing. The values of the ion optical parameters in Table 2 are suitable for practical use. RESOLVING POWER AND MASS SCALE
The resolving power of a mass spectrograph is given by the equation
neglecting aberrations, where A y, A, and s are the mass dispersion, image magnification and source slit width, respectively. The image magnification of the virtual image of the uniform electric field is unity because the parallel shift of the coordinate in the z-direction does not change the ion trajectory. Therefore, the resolving power of the example mass spectrographs shown in Figs. 2-5 can be calculated using the values of the parameters given in Table 2. Assuming r, = 300 mm and s = 0.1 mm, the estimated resolving powers are 3000 (Fig. 2), 2500 (Fig. 3), 3900 (Fig. 4) and 5100 (Fig. 5).
17
The resolving power is proportional to r,,, (or m) for a fixed width of the source slit. This means that if the resolving power at M = 1000 is 2000, then that at M = 100 is 200. This is enough for mass analysis. Since z,, and a, are proportional to m, the mass scale on a focal plane is proportional to the distance from the origin as can be seen from Figs. 2-5. Therefore, the mass scale on a focal plane is exactly linear. This feature is especially advantageous for precise mass calibration. REFERENCES 1 F.W. McLafferty, Act. Chem. Res., 13 (1980) 33. 2 J.S. Cottrell and S. Evans, Anal. Chem., 59 (1987) 1990. 3 H. Matsuda, Mass Spectrosc. Jpn., 12 (1964) 105.