An optimization method for ion mobility spectrometry with high electric field asymmetric waveform

Abstract

The present invention discloses a method for optimizing a high electric field asymmetric waveform ion migration spectrum. The present invention relates to the field of ions. The method comprises the following steps: step S1, simplifying a three-dimensional FAIMS system into a two-dimensional plane, analyzing the migration zone in the FAIMS system, and establishing a mathematical model of the migration zone; step S2, describing the electric field waveform of the migration zone by superposition of step signals, and obtaining an expression for the alternating electric field E(t); step S3, compounding the step function with a trigonometric function to realize the expression of the duty cycle; compared with the prior art, the present invention has the following beneficial effects: the present invention calculates the displacement of ions within a complete oscillation cycle, and optimizes the structural size of the migration zone according to the ion displacement parameters, thereby ensuring that the ions to be separated do not leave the migration zone during the separation process, improving the selectivity and resolution of FAIMS for gas, and improving the separation performance.

Description

Technical Field

[0001] The present invention relates to the field of ions, and in particular to a method for optimizing ion mobility spectrometry using a high electric field asymmetric waveform. Background Art

[0002] Field Asymmetric Waveform Ion Mobility Spectrometry (FAIMS) is a technique used to separate and detect gas-phase ions. FAIMS exploits the difference in ion mobility between high and low electric fields. By applying an asymmetric waveform electric field, different ions move along different paths within the field, achieving separation.

[0003] Core components include an electrode system and a detector. The electrode system typically consists of two parallel electrodes that apply an asymmetric electric field. The detector, typically a mass spectrometer, detects the separated ions. The detailed working process involves ionization in the ionization zone: ionization of the sample into the FAIMS system; separation in the mobility zone: ionization of the sample using an asymmetric electric field to separate ions based on their mobility; and detection in the detection zone: ionization of the separated ions by the detector for analysis.

[0004] The existing FAIMS ion separation performance is relatively low and needs to be improved. Summary of the Invention

[0005] The object of the present invention is to provide a method for optimizing high electric field asymmetric waveform ion mobility spectrometry to solve the problems raised in the above background technology.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A method for optimizing high electric field asymmetric waveform ion mobility spectrometry, comprising the following steps:

[0008] Step S1, simplifying the three-dimensional FAIMS system into a two-dimensional plane, analyzing the migration zone in the FAIMS system, and establishing a mathematical model of the migration zone;

[0009] Step S2, using the superposition of step signals to describe the electric field waveform of the migration region, and obtaining the expression of the alternating electric field E(t);

[0010] Step S3, compounding the step function with the trigonometric function to express the duty cycle;

[0011] Step S4, obtaining a calculation formula for the alternating electric field E(t) based on the expression of the duty cycle and the expression of the alternating electric field E(t);

[0012] Step S5, based on the calculation formula of the alternating electric field E(t), the electric field E at the determined time is obtained, and a unique mobility K corresponding to the electric field E at the determined time is inferred. The mobility K corresponds to the time t, and the calculation formula K(t) of the mobility K is obtained;

[0013] Step S6, obtaining the displacement of the ions within a complete oscillation cycle based on the calculation formula of the alternating electric field E(t), the calculation formula of the mobility K K(t), and the gas flow rate u introduced into the migration zone;

[0014] Step S7, designing the migration zone size parameters according to the ion displacement parameters to ensure that the ions to be separated do not leave the migration zone during the separation process.

[0015] As a further solution of the present invention: in step S2, the electric field waveform of the migration region is described by superposition of step signals. Let the alternating electric field be E(t), then the expression of E(t) is:

[0016] E(t)=E H ·H(g(t))+E L ·H(-g(t))+0(t) (1);

[0017]

[0018] f is the signal frequency.

[0019] As a further solution of the present invention: in step S3, the step function is combined with the trigonometric function, and the amplitude of g(t) is set to:

[0020] a=1 (4);

[0021] Under this condition, move the sine function graph downward to obtain the g(t) graph, with a period of T and a time t1 above the horizontal axis. Find the time t0 in the graph so that:

[0022]

[0023] Then t0 satisfies:

[0024]

[0025] Due to the limitation of 2πf·t0, the calculation result must be within the first period, and there is no need to consider the minimum period. Therefore, the only relationship between t0 and t1 that can be inferred is:

[0026]

[0027] Let the duty cycle be D, then D satisfies:

[0028]

[0029] At the same time, according to formula (5), the relationship between duty cycle D and b can be inferred as:

[0030]

[0031] Right now:

[0032]

[0033] As a further solution of the present invention: in step S4, based on the expression of the duty cycle and the expression of the alternating electric field E(t), a calculation formula for the alternating electric field E(t) is obtained;

[0034]

[0035] As a further solution of the present invention: in step S5, based on the calculation formula of the alternating electric field E(t), the electric field E at a certain time is obtained, and a unique mobility K corresponding to the electric field E at the certain time is inferred. The mobility K corresponds to the time t, and the calculation formula K(t) of the mobility K is obtained;

[0036]

[0037] As a further solution of the present invention: step S6 includes:

[0038] Step S61: According to the calculation formula of the alternating electric field E(t) and the calculation formula K(t) of the mobility K, the ion mobility in a complete oscillation cycle is obtained. Directional displacement;

[0039] Step S62: According to the gas flow rate u introduced into the migration zone, the ion Directional displacement; and The two directions are orthogonal; the ion passes through a complete oscillation cycle and The displacement in both directions gives the displacement of the ion during one complete oscillation period.

[0040] As a further solution of the present invention: in step S61, the charged ions move along the electric field direction. The following relationship exists between the calculation formula of the alternating electric field E(t) and the calculation formula of the mobility K(t):

[0041]

[0042] The movement of ions in the mobility spectrum is similar to oscillation motion, from which the displacement of ions along the electric field direction within one oscillation period is calculated. The movement of ions in one oscillation cycle is divided into two parts: upward and downward, which are calculated separately:

[0043]

[0044] Arranging formulas (14) and (15) yields the ion in one oscillation period: Directional displacement:

[0045]

[0046] As a further solution of the present invention: in step S62, the ions are The movement in the direction is considered as laminar flow, and the gas flow rate in the migration zone is u. It can be deduced that the ions Speed ​​of movement in direction:

[0047]

[0048] According to formulas (17) and (18), the number of ions in one oscillation period can be calculated. Directional displacement:

[0049]

[0050] According to formulas (16) and (19), the displacement of the ion in a complete oscillation cycle can be obtained as:

[0051]

[0052] And calculate the relationship between the ion displacement deflection angle θ and displacement in a complete oscillation cycle:

[0053]

[0054] As a further solution of the present invention: in step S7, the migration zone size parameters are designed according to the ion displacement parameters so that The ions with the largest directional displacement still cannot leave the migration zone. Assuming the distance between the migration zone plates is d and the plate length is L, then at least the following conditions must be met:

[0055]

[0056] In order to achieve complete ion separation, combined with formula (22), the plate length L must at least meet the following requirements:

[0057]

[0058] As a further solution of the present invention: in step S7, taking into account the influence of the error, the voltage source is allowed to have an error of 5%, and the power supply error is set to Δ%. The mobility of the charged ions is constant below 10000 V / m, and shows a nonlinear change above 10000 V / m. Therefore, it is necessary to constrain the upper limit of the plate length according to the deviation of the mobility of the high-field part. The mobility of different charged ions varies with voltage differently. In order to facilitate distinction, the mobility of the target ions (i.e., the ions not to be removed) is named K 1H (E) and K 1L (E), the deflection angle of the target ion is named α;

[0059] Then the deviation angle of the target ion cannot exceed:

[0060]

[0061] The board length L of the migration zone must meet the following requirements:

[0062]

[0063] Compared with the existing technology, the beneficial effects of the present invention are: the present invention calculates the displacement of ions within a complete oscillation cycle, and optimizes the structural size of the migration zone based on the ion displacement parameters, ensuring that the ions to be separated do not leave the migration zone during the separation process, thereby improving the selectivity and resolution of FAIMS for gas and improving the separation performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 This is a diagram of the working principle of FAIMS.

[0065] Figure 2 This is the electric field waveform in the migration region.

[0066] Figure 3 is the graph of the g(t) function.

[0067] Figure 4 Schematic diagram of the movement of charged ions in the migration zone.

[0068] Figure 5 Schematic diagram of the movement of charged ions in the migration zone and the size of the migration zone when errors are not considered.

[0069] Figure 6 Schematic diagram of the movement of charged ions in the migration zone and the size of the migration zone when errors are taken into account. DETAILED DESCRIPTION

[0070] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0071] A method for optimizing high electric field asymmetric waveform ion mobility spectrometry, comprising the following steps:

[0072] Step S1, simplifying the three-dimensional FAIMS system into a two-dimensional plane, analyzing the migration zone in the FAIMS system, and establishing a mathematical model of the migration zone;

[0073] Step S2, using the superposition of step signals to describe the electric field waveform of the migration region, and obtaining the expression of the alternating electric field E(t);

[0074] Step S3, compounding the step function with the trigonometric function to express the duty cycle;

[0075] Step S4, obtaining a calculation formula for the alternating electric field E(t) based on the expression of the duty cycle and the expression of the alternating electric field E(t);

[0076] Step S5, based on the calculation formula of the alternating electric field E(t), the electric field E at the determined time is obtained, and a unique mobility K corresponding to the electric field E at the determined time is inferred. The mobility K corresponds to the time t, and the calculation formula K(t) of the mobility K is obtained;

[0077] Step S6, obtaining the displacement of the ions within a complete oscillation cycle based on the calculation formula of the alternating electric field E(t), the calculation formula of the mobility K K(t), and the gas flow rate u introduced into the migration zone;

[0078] Step S7, designing the migration zone size parameters according to the ion displacement parameters to ensure that the ions to be separated do not leave the migration zone during the separation process.

[0079] In the specific embodiment, see Figure 1 : In step S1, for the convenience of research, the three-dimensional FAIMS system is simplified into a two-dimensional plane for research, such as Figure 1 The migration zone in the FAIMS system is analyzed and a mathematical model is established. The input of the model includes the electric field intensity U(t), ion mobility K(t), electric field signal frequency f, electric field signal period T, electric field signal duty cycle D, and gas flow rate u. The output is the migration zone length L.

[0080] In this example, see Figure 2 : In step S2, in order to accurately describe Figure 2The electric field waveform of the migration region shown in the figure is described by superposition of step signals. Let the alternating electric field be E(t), then the expression of E(t) is:

[0081] E(t)=E H ·H(g(t))+E L ·H(-g(t))+0(t) (1);

[0082] Here the step function is

[0083] Here the trigonometric function is

[0084] a is the trigonometric function amplitude, f is the signal frequency, is the phase offset, and b is the function offset.

[0085] In this example, see Figure 3 : In step S3, the step function is combined with the trigonometric function to set the amplitude of g(t) to:

[0086] a=1 (4);

[0087] Under this condition, the sine function image is moved downward, as shown in Figure 3 The g(t) image is shown as follows, with a period of T and a time t1 above the horizontal axis. Find the minimum zero point t0 of the positive half axis of the horizontal axis in the figure, so that:

[0088]

[0089] Then t0 satisfies:

[0090]

[0091] Due to the limitation of 2πf·t0, the calculation result must be within the first period, and there is no need to consider the minimum period. Therefore, the only relationship between t0 and t1 that can be inferred is:

[0092]

[0093] Let the duty cycle of the high field asymmetric waveform be D, then D satisfies:

[0094]

[0095] At the same time, according to formula (5), the relationship between duty cycle D and b can be inferred as:

[0096]

[0097] Right now:

[0098]

[0099] In this embodiment: in step S4, based on the expression of the duty cycle and the expression of the alternating electric field E(t), i.e., formulas (1), (4), (5) and (10), a calculation formula for the alternating electric field E(t) is obtained;

[0100]

[0101] Among them E H is the high-side electric field, E L is the low-side electric field.

[0102] In this embodiment, in step S5, although there is a nonlinear relationship between the gas mobility K and the electric field E, a unique mobility K can still be inferred for a given electric field E. Based on the calculation formula of the alternating electric field E(t), the electric field E at a certain time is obtained, and the unique mobility K corresponding to the electric field E at the certain time is inferred. The mobility K is correlated with time t, and the calculation formula K(t) for the mobility K is obtained.

[0103]

[0104] where K H (E) is the particle mobility under high electric field (above 10000 V / m), K L (E) is the particle mobility at low electric field.

[0105] In this embodiment, step S6 includes:

[0106] Step S61: According to the calculation formula of the alternating electric field E(t) and the calculation formula K(t) of the mobility K, the ion mobility in a complete oscillation cycle is obtained. Directional displacement;

[0107] Step S62: According to the gas flow rate u introduced into the migration zone, the ion Directional displacement; and The two directions are orthogonal; the ion passes through a complete oscillation cycle and The displacement in both directions gives the displacement of the ion during one complete oscillation period.

[0108] In this example, see Figure 4 In step S61, according to the principle of ion mobility spectrometry, the movement of ions can be divided into and In two orthogonal directions, the charged ions move along the direction of the electric field (i.e. Direction) Speed The following relationship exists between the calculation formula of the alternating electric field E(t) and the calculation formula of the mobility K(t):

[0109]

[0110] like Figure 4 As shown in the figure, the movement of ions in the migration spectrum is similar to oscillation motion, from which the displacement of ions along the electric field direction within one oscillation period is calculated. The movement of ions in one oscillation cycle is divided into two parts: upward and downward. Combined with the duty cycle D proposed above, they are calculated separately:

[0111]

[0112] Arranging formulas (14) and (15) yields the ion in one oscillation period: Directional displacement:

[0113]

[0114] In this embodiment: In step S62, the ions are placed on the horizontal axis. The movement in the direction is considered as laminar flow, and the gas flow rate in the migration zone is u. It can be deduced that the ions Speed ​​of movement in direction:

[0115]

[0116] According to formulas (17) and (18), the number of ions in one oscillation period can be calculated. Directional displacement:

[0117]

[0118] According to formulas (16) and (19), the displacement of the ion in a complete oscillation cycle can be obtained as:

[0119]

[0120] And calculate the relationship between the ion displacement deflection angle θ and displacement in a complete oscillation cycle:

[0121]

[0122] In this example, see Figure 5 In step S7, in order to ensure that the ions to be removed do not leave the migration zone, the migration zone size parameters are designed according to the ion displacement parameters so that The ions with the largest directional displacement still cannot leave the migration zone. Assuming the distance between the migration zone plates is d and the plate length is L, then at least the following conditions must be met:

[0123]

[0124] Where θ is the ion displacement deflection angle, d is the plate spacing, and L is the plate length.

[0125] In order to achieve complete ion separation, combined with formula (22), the plate length L must at least meet the following requirements:

[0126]

[0127] In this example, see Figure 6 : In step S7, considering the error of the plate voltage, it is necessary to correct the plate length and provide an upper limit of the plate length. The voltage source is allowed to have an error of 5%, and the power supply error is set to Δ%. The mobility of charged ions is constant below 10000V / m and shows nonlinear changes above 10000V / m. Therefore, it is necessary to constrain the upper limit of the plate length according to the deviation of the mobility of the high-field part. The mobility of different charged ions varies with voltage differently. In order to facilitate distinction, the mobility of the target ion (i.e., the ion not to be removed) is named K 1H (E) and K 1L (E), the deflection angle of the target ion is named α;

[0128] Then the deviation angle of the target ion cannot exceed:

[0129]

[0130] Where α is the displacement angle of the target ion, Δ% is the power supply error, K 1H (E) is the mobility of the target ion under high electric field, K 1L (E) is the mobility of the target ion under low electric field.

[0131] The board length L of the migration zone must meet the following requirements:

[0132]

[0133] Where Δ% is the power supply error, K 1H (E) is the mobility of the target ion under high electric field, K 1L (E) is the mobility of the target ion under low electric field.

[0134] The present invention calculates the displacement of ions within a complete oscillation cycle and optimizes the structural dimensions of the migration zone based on the ion displacement parameters to ensure that the ions to be separated do not leave the migration zone during the separation process, thereby improving the selectivity and resolution of FAIMS for gases and enhancing separation performance.

[0135] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the present invention. Therefore, the embodiments should be considered in all respects as exemplary and non-restrictive.

[0136] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A method for optimizing high electric field asymmetric waveform ion mobility spectrometry, characterized in that: The high electric field asymmetric waveform ion mobility spectrometry optimization method comprises the following steps: Step S1, simplifying the three-dimensional FAIMS system into a two-dimensional plane, analyzing the migration zone in the FAIMS system, and establishing a mathematical model of the migration zone; Step S2, using the superposition of step signals to describe the electric field waveform of the migration region, and obtaining the expression of the alternating electric field E(t); Step S3, compounding the step function with the trigonometric function to express the duty cycle; Step S4, obtaining a calculation formula for the alternating electric field E(t) based on the expression of the duty cycle and the expression of the alternating electric field E(t); Step S5, based on the calculation formula of the alternating electric field E(t), the electric field E at the determined time is obtained, and a unique mobility K corresponding to the electric field E at the determined time is inferred. The mobility K corresponds to the time t, and the calculation formula K(t) of the mobility K is obtained; Step S6, obtaining the displacement of the ions within a complete oscillation cycle based on the calculation formula of the alternating electric field E(t), the calculation formula of the mobility K K(t), and the gas flow rate u introduced into the migration zone; Step S7, designing the migration zone size parameters according to the ion displacement parameters to ensure that the ions to be separated do not leave the migration zone during the separation process; Step S6 includes: Step S61: According to the calculation formula of the alternating electric field E(t) and the calculation formula K(t) of the mobility K, the ion mobility in a complete oscillation cycle is obtained. Directional displacement; Step S62: According to the gas flow rate u introduced into the migration zone, the ion Directional displacement; and The two directions are orthogonal; the ion passes through a complete oscillation cycle and The displacement in two directions gives the displacement of the ion during one complete oscillation period; In step S61, the charged ions move along the electric field. The following relationship exists between the calculation formula of the alternating electric field E(t) and the calculation formula of the mobility K(t): The movement of ions in the mobility spectrum is similar to oscillation motion, from which the displacement of ions along the electric field direction within one oscillation period is calculated. The movement of ions in one oscillation cycle is divided into two parts: upward and downward, which are calculated separately: Arranging formulas (14) and (15) yields the ion in one oscillation period: Directional displacement: In step S62, the ions are The movement in the direction is considered as laminar flow, and the gas flow rate in the migration zone is u. It can be deduced that the ions in Speed ​​of movement in direction: According to formulas (17) and (18), the ion Directional displacement: According to formulas (16) and (19), the displacement of the ion in a complete oscillation cycle can be obtained as: And calculate the relationship between the ion displacement deflection angle θ and displacement in a complete oscillation cycle:

2. The high electric field asymmetric waveform ion mobility spectrometry optimization method according to claim 1, characterized in that: In step S2, the electric field waveform of the migration region is described by superposition of step signals. Let the alternating electric field be E(t), then the expression of E(t) is: E(t)=E H ·H(g(t))+E L ·H(-g(t))+0(t) (1); f is the signal frequency.

3. The high electric field asymmetric waveform ion mobility spectrometry optimization method according to claim 2, characterized in that: In step S3, the step function is combined with the trigonometric function to set the amplitude of g(t) to: a＝1 (4)； Under this condition, move the sine function graph downward to obtain the g(t) graph, with a period of T and a time t1 above the horizontal axis. Find the time t0 in the graph so that: Then t0 satisfies: Due to the limitation of 2πf·t0, the calculation result must be within the first period, and there is no need to consider the minimum period. Therefore, the only relationship between t0 and t1 that can be inferred is: Let the duty cycle be D, then D satisfies: At the same time, according to formula (5), the relationship between duty cycle D and b can be inferred as: Right now:

4. The high electric field asymmetric waveform ion mobility spectrometry optimization method according to claim 3, characterized in that: In step S4, a calculation formula for the alternating electric field E(t) is obtained based on the expression of the duty cycle and the expression of the alternating electric field E(t); 5. The high electric field asymmetric waveform ion mobility spectrometry optimization method according to claim 1, characterized in that: In step S5, based on the calculation formula of the alternating electric field E(t), the electric field E at a certain time is obtained, and a unique mobility K corresponding to the electric field E at the certain time is inferred. The mobility K corresponds to the time t, and the calculation formula K(t) of the mobility K is obtained; 6. The high electric field asymmetric waveform ion mobility spectrometry optimization method according to any one of claims 1 to 5, characterized in that: In step S7, the migration zone size parameters are designed according to the ion displacement parameters so that The ions with the largest directional displacement still cannot leave the migration zone. Assuming the distance between the migration zone plates is d and the plate length is L, then at least the following conditions must be met: In order to achieve complete ion separation, combined with formula (22), the plate length L must at least meet the following requirements:

7. The high electric field asymmetric waveform ion mobility spectrometry optimization method according to claim 6, characterized in that: In step S7, considering the influence of error, the voltage source is allowed to have a 5% error, and the power supply error is set to Δ%. The mobility of charged ions is constant below 10000 V / m, and shows nonlinear changes above 10000 V / m. Therefore, it is necessary to constrain the upper limit of the plate length according to the deviation of the mobility in the high field part. The mobility of different charged ions varies with voltage in different ways. In order to facilitate distinction, the mobility of the target ion is named K 1H (E) and K 1L (E), the deflection angle of the target ion is named α; Then the deviation angle of the target ion cannot exceed: The board length L of the migration zone must meet the following requirements:

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