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US-12620569-B2 - Quadrupole-mass-filter driving method and quadrupole mass spectrometer

US12620569B2US 12620569 B2US12620569 B2US 12620569B2US-12620569-B2

Abstract

A quadrupole mass filter ( 50 ) has a main-rod section ( 500 ) including rod electrodes arranged around a central axis C and a first pre-rod section ( 501 ) including pre-rod electrodes. Along with an RF voltage having a frequency corresponding to the m/z of an ion, DC voltage is applied to the pre-rod electrodes. The DC voltage and the amplitude of the RF voltage are determined so that a-value and q-value substantially satisfy the conditions that a≠0, (π−βx·π)N={(½)+m}π and βy·π·N={(½)+n}π, where m, n and N are natural numbers, with the X-axis direction connecting the centers of two rod electrodes facing each other across the central axis in a plane perpendicular to the central axis, the Y-axis direction connecting the centers of the other two rod electrodes in the plane, and βx and βy representing β values (0<β<1) related to a secular oscillation of an ion in the X and Y directions, respectively.

Inventors

  • Manabu Ueda
  • Shin Fujita
  • Junichi Taniguchi
  • Shinjiro Fujita
  • Shiro Mizutani

Assignees

  • SHIMADZU CORPORATION

Dates

Publication Date
20260505
Application Date
20231229
Priority Date
20230327

Claims (20)

  1. 1 . A quadrupole-mass-filter driving method for operating a quadrupole mass filter which includes a main-rod section including four rod electrodes arranged so as to surround a central axis and a first pre-rod section including four rod electrodes arranged at a position on an upstream side of an ion stream from the main-rod section in an extending direction of the central axis, the method comprising: a voltage calculation step for determining a DC voltage Up and an amplitude Vp of an RF voltage with which an a-value and a q-value which are parameters of a Mathieu equation expressing a motion of an ion and have relationships with βx and βy as expressed by equations (1) and (2) substantially satisfy conditions that a≠0, (π−βx·π)N={(½)+m}π and βy·π·N={(½)+n}π, where m, n and N are natural numbers, an X-axis direction is defined as a direction connecting centers of one pair of rod electrodes facing each other across the central axis in a plane perpendicular to the central axis, an Y-axis direction is defined as a direction connecting centers of another pair of rod electrodes in the plane, and βx and βy represent β values (0<β<1) related to a secular oscillation of an ion in the X and Y directions, respectively, with a relationship of Up and Vp with a and q defined by equations (3) and (4); and a voltage application step for applying, to each rod electrode of the main-rod section, a voltage in which a DC voltage according to an m/z of a target ion is superposed on an RF voltage according to the same m/z, as well as applying, to each rod electrode of the first pre-rod electrodes, a voltage in which an RF voltage ±Vp·cos ωt having an amplitude Vp and a frequency equal to a frequency of the RF voltage applied to the main-rod section is superposed on a DC voltage ±Up having a voltage value different from the DC voltage applied to the main-rod section, when an analysis is performed: β x 2 = a + q x 2 ( β x + 2 ) 2 - a - q x 2 ( β x + 4 ) 2 - a - q x 2 ( β x + 6 ) 2 - a - … + q x 2 ( β x - 2 ) 2 - a - q x 2 ( β x - 4 ) 2 - a - q x 2 ( β x - 6 ) 2 - a - … ( 1 ) β y 2 = - a + q y 2 ( β y + 2 ) 2 + a - q y 2 ( β y + 4 ) 2 + a - q y 2 ( β y + 6 ) 2 + a - … + q y 2 ( β y - 2 ) 2 + a - q y 2 ( β y - 4 ) 2 + a - q y 2 ( β y - 6 ) 2 + a - … ( 2 ) a = 8 ⁢ eUp mr 0 2 ⁢ ω 2 ( 3 ) q = 4 ⁢ e ⁢ V ⁢ p mr 0 2 ⁢ ω 2 ( 4 ) where e is a charge of the ion, m is a mass of the ion, r 0 is a distance from the central axis to each rod electrode of the first pre-rod electrode, and ω is an angular frequency of the RF voltage.
  2. 2 . The quadrupole-mass-filter driving method according to claim 1 , wherein N is between 3 and 20, inclusive.
  3. 3 . The quadrupole-mass-filter driving method according to claim 2 , wherein N is between 4 and 10, inclusive.
  4. 4 . The quadrupole-mass-filter driving method according to claim 3 , wherein N is 6.
  5. 5 . The quadrupole-mass-filter driving method according to claim 1 , wherein each of n and m is 1 or 2.
  6. 6 . The quadrupole-mass-filter driving method according to claim 5 , wherein n and m are equal to each other.
  7. 7 . The quadrupole-mass-filter driving method according to claim 1 , wherein βx and βy have a relationship of βx+βy=1.
  8. 8 . The quadrupole-mass-filter driving method according to claim 7 , wherein the voltage calculation step includes determining Up and Vp so that the a-value and the q-value substantially satisfy βx=¾ and βy=¼.
  9. 9 . A quadrupole mass spectrometer comprising: a quadrupole mass filter which includes a main-rod section including four rod electrodes arranged so as to surround a central axis and a first pre-rod section including four rod electrodes arranged so as to surround the central axis at a position on an upstream side of an ion stream from the main-rod section along the central axis; a main voltage application section configured to apply, to each rod electrode of the main-rod section, a voltage in which a DC voltage according to an m/z of an ion is superposed on an RF voltage according to the same m/z, so as to create a quadrupole electric field in the main-rod section; and an auxiliary voltage application section configured to apply, to each rod electrode of the first pre-rod section, a voltage in which an RF voltage ±Vp·cos ωt having the same frequency as the aforementioned RF voltage is superposed on a DC voltage ±Up having a voltage value different from the DC voltage applied to the main-rod section, so as to create a quadrupole electric field in the first pre-rod section, where the DC voltage value Up and the amplitude value Vp of the RF voltage applied by the auxiliary voltage application section are determined so that values of a and q which are parameters of a Mathieu equation expressing a motion of an ion and have relationships with Up and Vp as expressed by equations (3) and (4) as well as relationships with βx and βy as expressed by equations (1) and (2), substantially satisfy conditions that a≠0, (π−βx·π)N={(½)+m}π and βy·π·N={(½)+n}π, where m, n and N are natural numbers, an X-axis direction is defined as a direction connecting centers of one pair of rod electrodes facing each other across the central axis in a plane perpendicular to the central axis, a Y-axis direction is defined as a direction connecting centers of another pair of rod electrodes in the plane, and βx and βy represent β values (0<β<1) related to a secular oscillation of an ion in the X and Y directions, respectively: β x 2 = a + q x 2 ( β x + 2 ) 2 - a - q x 2 ( β x + 4 ) 2 - a - q x 2 ( β x + 6 ) 2 - a - … + q x 2 ( β x - 2 ) 2 - a - q x 2 ( β x - 4 ) 2 - a - q x 2 ( β x - 6 ) 2 - a - … ( 1 ) β y 2 = - a + q y 2 ( β y + 2 ) 2 + a - q y 2 ( β y + 4 ) 2 + a - q y 2 ( β y + 6 ) 2 + a - … + q y 2 ( β y - 2 ) 2 + a - q y 2 ( β y - 4 ) 2 + a - q y 2 ( β y - 6 ) 2 + a - … ( 2 ) a = 8 ⁢ eUp mr 0 2 ⁢ ω 2 ( 3 ) q = 4 ⁢ e ⁢ V ⁢ p mr 0 2 ⁢ ω 2 ( 4 ) where e is a charge of the ion, m is a mass of the ion, r 0 is a distance from the central axis to each rod electrode of the first pre-rod electrode, and ω is an angular frequency of the RF voltage.
  10. 10 . The quadrupole mass spectrometer according to claim 9 , wherein N is between 3 and 20, inclusive.
  11. 11 . The quadrupole mass spectrometer according to claim 10 , wherein N is between 4 and 10, inclusive.
  12. 12 . The quadrupole mass spectrometer according to claim 11 , wherein N is 6.
  13. 13 . The quadrupole mass spectrometer according to claim 9 , wherein each of n and m is 1 or 2.
  14. 14 . The quadrupole mass spectrometer according to claim 13 , wherein n and m are equal to each other.
  15. 15 . The quadrupole mass spectrometer according to claim 9 , wherein βx and βy have a relationship of βx+βy=1.
  16. 16 . The quadrupole mass spectrometer according to claim 15 , wherein the voltages in the auxiliary voltage application section are set so that the a-value and the q-value substantially satisfy βx=¾ and βy=¼.
  17. 17 . The quadrupole mass spectrometer according to claim 9 , wherein: the quadrupole mass filer includes a second pre-rod section including four rod electrodes located further before the first pre-rod section; and the auxiliary voltage application section is further configured to apply an RF voltage having the same frequency as the aforementioned RF voltage, with no DC voltage for creating a quadrupole electric field superposed, to each rod electrode of the second pre-rod section.
  18. 18 . The quadrupole mass spectrometer according to claim 17 , wherein the RF voltage applied to each rod electrode of the second pre-rod section is set so that the q-value satisfies βx=½ and βy=½, where r 0 included in the equation defining this q-value represents a distance from the central axis to each rod electrode of the second pre-rod section.
  19. 19 . The quadrupole mass spectrometer according to claim 17 , wherein the auxiliary voltage application section is further configured to apply DC bias voltages having voltage values different from one another to the first pre-rod section and the second pre-rod section.
  20. 20 . The quadrupole mass spectrometer according to claim 19 , wherein a relationship between the DC bias voltage V B1 applied to each rod electrode of the first pre-rod section and the DC bias voltage V B2 applied to each rod electrode of the second pre-rod section are set so that V B2 /V B1 ={(L2×N1)/(L1×N2)} 2 , where L1 is a length of the rod electrodes of the first pre-rod section, L2 is a length of the rod electrodes of the second pre-rod section, N1 is a number of periods of the RF voltage corresponding to a length of time during which ions pass through the first pre-rod section, and N2 is a number of periods of the RF voltage corresponding to a length of time during which ions pass through the second pre-rod section.

Description

TECHNICAL FIELD The present invention relates to a quadrupole mass spectrometer employing a quadrupole mass filter as a mass separator, as well as a quadrupole-mass-filter driving method. In the present description, “quadrupole mass spectrometers” include not only a single type of quadrupole mass spectrometer but also other types of devices, such as a triple quadrupole mass spectrometer having two quadrupole mass filters arranged before and after a collision cell, or a quadrupole time-of-flight mass spectrometer having a quadrupole mass filter located before a collision cell and a time-of-flight mass analyzer located after the collision cell. BACKGROUND ART In a single type of quadrupole mass spectrometer, ions originating from a component (compound) contained in a sample are separated from each other by a quadrupole mass filter according to their mass-to-charge ratios (or more strictly, m/z in italic font, although they are referred to as “mass-to-charge ratios” or “m/z” in the present description), and the separated ions are detected by an ion detector. By repeating a mass scan over a predetermined m/z range in the quadrupole mass filter, a mass spectrum showing the relationship between m/z and ion intensity can be repeatedly obtained. A quadrupole mass filter normally has a configuration in which four rod electrodes each of which has a cylindrical outer shape are arranged parallel to each other, being tangential to an inscribed circle of a predetermined radius whose center lies on a linear axis, as well as circumferentially spaced apart from each other at equal angular intervals (90 degrees). One pair of rod electrodes facing each other across the central axis, which is also an ion beam axis, is supplied with a voltage +(U+V cos ωt) in which a radiofrequency voltage (RF voltage) V cos ωt is superposed on a DC voltage U, while the other pair of rod electrodes is supplied with a voltage −(U+V co ωt) in which an RF voltage with the reversed phase, −V cos ωt, is superposed on a DC voltage having the reversed polarity, −U. By setting the voltage value U of the DC voltages and the amplitude value V of the RF voltages at their respective appropriate values according to the m/z while maintaining a specific relationship between them, the mass filter can selectively allow an ion having that m/z to pass through. A disturbance of an electric field occurs around an end portion of the rod electrodes. This disturbance of the electric field causes a decrease in the transmittance of the ions. In order to reduce such a disturbance of the end-edge electric field, it is often the case that a pre-rod section is provided in front of a main-rod section formed by rod electrodes which have the ion-selecting effect. Typically, the pre-rods constituting the pre-rod section are rod electrodes each of which has a cylindrical outer shape having the same diameter as the main-rod electrodes and a shorter length in the direction of the ion beam axis. Since the pre-rod section is required to have the effect of converging ions having a wide range of m/z, it is normally the case that no DC voltage U is applied to the pre-rod electrodes, and an RF voltage having the same frequency as the RF voltage applied to the main-rod electrodes yet being smaller in amplitude is applied to the pre-rod electrodes. CITATION LIST Patent Literature Patent Literature 1: U.S. Pat. No. 8,207,495 B Non Patent Literature Non Patent Literature 1: Shin Fujita, “Elucidation of ion motion in quadrupole mass spectrometer by Bloch function”, International Journal of Modern Physics A, Vol. 34, No. 36, 2019 SUMMARY OF INVENTION Technical Problem In order to further improve the ion transmittance in a quadrupole mass spectrometer, a device described in Patent Literature 1 applies, to the pre-rod electrodes, a DC bias voltage in addition to the RF voltage having the same frequency as that of the main-rod electrodes and changes the voltage value of the DC bias voltage according to the m/z of the ion so as to control the number of times for the oscillation of the ion passing through the pre-rod electrodes. This technique improves the passage efficiency of the ion and enhances the detection sensitivity, independently of the m/z of the ion, as compared to the case where the DC bias voltage is fixed. Meanwhile, in Non Patent Literature 1, one of the present inventors has reported an attempt to theoretically analyze the behavior of ions passing through a quadrupole mass filter, using a complex amplitude. According to the report, when ions are transferred from the auxiliary electric field created by the pre-rod section to which only the RF voltage is applied, to the main electric field created by the main-rod section, only a portion of the ions accepted into the auxiliary electric field can be appropriately transferred to the main electric field in the next section. In other words, this means that a considerable loss of ions occurs when the ions are transferred from the pre-rod s