High-electric-field asymmetric waveform ion mobility spectrometry optimization method

Abstract

The invention discloses a high-electric-field asymmetric waveform ion mobility spectrometry optimization method, and relates to the field of ions, the high-electric-field asymmetric waveform ion mobility spectrometry optimization method comprises the following steps: S1, simplifying a FAIMS system in a three-dimensional space into a two-dimensional plane, analyzing a migration region in the FAIMS system, and establishing a mathematical model of the migration region; s2, describing an electric field waveform of a migration region by adopting superposition of step signals, and obtaining an expression of an alternating electric field E (t); s3, the step function and the trigonometric function are compounded, and expression of the duty ratio is achieved; compared with the prior art, the method has the beneficial effects that the displacement of the ions in a complete oscillation period is calculated, the structural size of the migration area is optimized according to the ion displacement parameters, the to-be-separated ions are ensured not to leave the migration area in the separation process, the selectivity, resolution and the like of the FAIMS on gas are improved, and the separation performance is improved.

Description

Technical Field

[0001] The present invention relates to the field of ions, and specifically to an optimization method for a high-field asymmetric waveform ion mobility spectrometry. Background Art

[0002] High-field asymmetric waveform ion mobility spectrometry (FAIMS) is a technique for separating and detecting gas-phase ions. FAIMS separates ions by taking advantage of the difference in the mobility of ions in high and low electric fields. By applying an asymmetric waveform electric field, different ions have different trajectories in the electric field, thus achieving separation.

[0003] The core components include an electrode system and a detector. The electrode system usually consists of two parallel electrodes to apply an asymmetric waveform electric field. The detector is used to detect the separated ions, and a mass spectrometer is commonly used. The specific working process is as follows: Ionization in the ionization region: After the sample is ionized, it enters the FAIMS system; Separation in the migration region: The asymmetric waveform electric field separates different ions according to the difference in mobility; Detection in the detection region: The separated ions are captured and analyzed by the detector.

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

[0005] The purpose of the present invention is to provide an optimization method for a high-field asymmetric waveform ion mobility spectrometry to solve the problems raised in the above background art.

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

[0007] An optimization method for a high-field asymmetric waveform ion mobility spectrometry, comprising the following steps:

[0008] Step S1, simplify the FAIMS system in three-dimensional space to a two-dimensional plane, analyze the migration region in the FAIMS system, and establish a mathematical model of the migration region;

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

[0010] Step S3, compound the step function with the trigonometric function to realize the expression of the duty cycle;

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

[0012] Step S5: Based on the calculation formula of the alternating electric field E(t), obtain the electric field E at a determined time, infer the unique mobility K corresponding to the electric field E at the determined time, where the mobility K corresponds to the time t, and obtain the calculation formula K(t) of the mobility K;

[0013] Step S6: According to the calculation formula of the alternating electric field E(t), the calculation formula K(t) of the mobility K, and the gas flow velocity u introduced into the migration region, obtain the displacement of the ions within a complete oscillation period;

[0014] Step S7: Design the size parameters of the migration region according to the ion displacement parameters to ensure that the ions to be separated do not leave the migration region during the separation process.

[0015] As a further solution of the present invention: In step S2, use the superposition of step signals to describe the electric field waveform of the migration region. 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, compound the step function with the trigonometric function, and set the amplitude of g(t) 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. The time occupied above the horizontal axis is t 1 , find the moment t 0 in the figure, so that:

[0022]

[0023] Then t 0 satisfies:

[0024]

[0025] Due to the limitation of the value of 2πf·t 0 , the calculation result must be within the first period, and there is no need to consider the problem of the minimum period. Thus, the unique relationship between t 0 and t 1 is:

[0026]

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

[0028]

[0029] Meanwhile, according to Equation (5), the relationship between the duty cycle D and b can be deduced as:

[0030]

[0031] That is:

[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), the calculation formula of 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 determined time is obtained, and the unique mobility K corresponding to the electric field E at the determined time is deduced. 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, obtain the displacement of the ion in one complete oscillation period in the direction;

[0039] Step S62, according to the gas flow velocity u introduced into the migration region, obtain the displacement of the ion in one complete oscillation period in the direction; and the two directions are orthogonal; through the displacement of the ion in one complete oscillation period and in the two directions, the displacement of the ion in one complete oscillation period is obtained.

[0040] As a further solution of the present invention: in step S61, the velocity of the charged ion along the electric field direction has the following relationship with the calculation formula of the alternating electric field E(t) and the calculation formula K(t) of the mobility K:

[0041]

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

[0043]

[0044] Rearranging formulas (14) and (15) gives the displacement of ions within one oscillation period: Directional displacement:

[0045]

[0046] As a further solution of the present invention: in step S62, the movement of ions in the direction is regarded as laminar flow, and the gas flow rate introduced into the migration region is u. The movement speed of ions in the direction can be deduced:

[0047]

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

[0049]

[0050] According to formulas (16) and (19), the displacement of ions within one complete oscillation period is:

[0051]

[0052] And the relationship between the deflection angle θ of the ion displacement and the displacement within one complete oscillation period is calculated:

[0053]

[0054] As a further solution of the present invention: in step S7, according to the ion displacement parameters, the size parameters of the migration region are designed so that the ions with the maximum displacement in the

[0055]

[0056] direction still cannot leave the migration region. Assuming the plate spacing of the migration region is d and the plate length is L, at least the following conditions need to be satisfied:

[0057]

[0058] As a further solution of the present invention: in step S7, considering the error effect, the voltage source is allowed to have an error of 5%, and the power supply error is set as Δ%. The mobility of charged ions is a constant below 10,000 V / m and shows a non-linear change above 10,000 V / m. Therefore, it is necessary to constrain the upper bound of the plate length according to the deviation of the mobility in the high-field part. The mobility variation laws of different charged ions with voltage are different. For the sake of easy distinction, the mobility of the target ions (i.e., non-ions to be removed) is named as K 1H (E) and K 1L (E), and the deflection angle of the target ions is named as α;

[0059] Then the deflection angle of the target ions shall not exceed:

[0060]

[0061] The plate length L of the migration region needs to satisfy:

[0062]

[0063] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention calculates the displacement of ions within a complete oscillation period, and optimizes the structural dimensions of the migration region according to the ion displacement parameters, ensuring that the ions to be separated do not leave the migration region during the separation process, improving the selectivity, resolution, etc. of FAIMS for gases, and enhancing the separation performance. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0065] Figure 2 is the electric field waveform diagram of the migration region.

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

[0067] Figure 4 is the motion schematic diagram of charged ions in the migration region.

[0068] Figure 5 is the motion and migration region size schematic diagram of charged ions without considering errors.

[0069] Figure 6 is the motion and migration region size schematic diagram of charged ions considering errors. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0070] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a 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 those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0071] An optimization method for a high electric field asymmetric waveform ion mobility spectrometry includes the following steps:

[0072] Step S1: Simplify the FAIMS system in three-dimensional space into a two-dimensional plane, analyze the migration region in the FAIMS system, and establish a mathematical model of the migration region;

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

[0074] Step S3: Compound the step function and the trigonometric function to realize the expression of the duty cycle;

[0075] Step S4: Based on the expression of the duty cycle and the expression of the alternating electric field E(t), obtain the calculation formula of the alternating electric field E(t);

[0076] Step S5: Based on the calculation formula of the alternating electric field E(t), obtain the electric field E at a certain time, infer the unique mobility K corresponding to the electric field E at a certain time, the mobility K corresponds to the time t, and obtain the calculation formula K(t) of the mobility K;

[0077] Step S6: According to the calculation formula of the alternating electric field E(t), the calculation formula K(t) of the mobility K, and the gas flow rate u introduced into the migration region, obtain the displacement of ions within a complete oscillation period;

[0078] Step S7: According to the ion displacement parameters, design the size parameters of the migration region to ensure that the ions to be separated do not leave the migration region during the separation process.

[0079] In a specific embodiment, please refer to Figure 1 : In step S1, for the convenience of research, the FAIMS system in three-dimensional space is simplified into a two-dimensional plane for research, as Figure 1 shown. Analyze the migration region in the FAIMS system and establish a mathematical model for it. The inputs of this model include the electric field strength 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, and the output is the migration region length L.

[0080] In this embodiment, please refer to Figure 2 : In step S2, in order to accurately describe as Figure 2The electric field waveform in the migration region shown is described by the 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 amplitude of the trigonometric function, f is the signal frequency, is the phase offset, and b is the function offset.

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

[0086] a = 1 (4);

[0087] Under this condition, the sine function graph is moved downward, as Figure 3 shown to obtain the g(t) graph, with a period of T and the time occupied above the horizontal axis being t 1 , find the minimum zero point t 0 on the positive half-axis of the horizontal axis in the figure, so that:

[0088]

[0089] Then t 0 satisfies:

[0090]

[0091] Due to the limitation of the value of 2πf·t 0 , the calculation result must be within the first period, and the problem of the minimum period does not need to be considered. Thus, the only relationship between t 0 and t 1 can be inferred as:

[0092]

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

[0094]

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

[0096]

[0097] That is:

[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), namely formulas (1), (4), (5), and (10), the calculation formula of the alternating electric field E(t) is obtained;

[0100]

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

[0102] In this embodiment: In step S5, although there is a non-linear relationship between the gas mobility K and the electric field E, for a given electric field E, a unique mobility K can still be inferred. Based on the calculation formula of the alternating electric field E(t), the electric field E at a determined time is obtained, and the 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 of the mobility K(t) is obtained;

[0103]

[0104] where K H (E) is the particle mobility at a high electric field (above 10000 V / m), and K L (E) is the particle mobility at a 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 of the mobility K(t), obtain the displacement of the ion in one complete oscillation period in the direction;

[0107] Step S62, according to the gas flow rate u introduced into the migration region, obtain the displacement of the ion in one complete oscillation period in the direction; and the two directions are orthogonal; through the displacements of the ion in one complete oscillation period and in the two directions, obtain the displacement of the ion in one complete oscillation period.

[0108] In this embodiment, please refer to Figure 4 : In step S61, according to the principle of ion mobility spectrometry, the movement of ions can be divided into and Two orthogonal directions. The velocity of the charged ions along the electric field direction (i.e., direction) There is the following relationship between the calculation formula of the alternating electric field E(t) and the calculation formula of the mobility K, K(t):

[0109]

[0110] As Figure 4 shown, the movement of ions in the migration spectrum is similar to oscillatory motion. From this, the displacement of ions along the electric field direction within an oscillation period is calculated The movement of ions within an oscillation period is divided into two parts: upward and downward. Combining with the duty cycle D proposed above, the calculations are as follows respectively:

[0111]

[0112] Rearranging formulas (14) and (15) gives the displacement of ions within an oscillation period direction:

[0113]

[0114] In this embodiment: In step S62, the movement of ions in the horizontal axis direction is regarded as laminar flow. The gas flow velocity in the migration region is u. It can be deduced that the movement velocity of ions in the direction:

[0115]

[0116] According to formulas (17) and (18), the displacement of ions within an oscillation period direction can be calculated:

[0117]

[0118] According to formulas (16) and (19), the displacement of ions within a complete oscillation period is:

[0119]

[0120] And the relationship between the displacement deflection angle θ of ions within a complete oscillation period and the displacement is calculated:

[0121]

[0122] In this embodiment, please refer to Figure 5 : In step S7, in order to ensure that the ions to be removed do not leave the migration region, according to the ion displacement parameters, the size parameters of the migration region are designed so that The ions with the largest directional displacement still cannot leave the migration region. Assuming the plate spacing of the migration region is d and the plate length is L, the following conditions must be satisfied at least:

[0123]

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

[0125] To achieve complete separation of ions, combining with formula (22), the plate length L must satisfy at least:

[0126]

[0127] In this embodiment, please refer to Figure 6 : In step S7, considering the error of the plate voltage, it is necessary to correct the plate length and provide the upper bound of the plate length. The voltage source is allowed to have an error of 5%. Let the power supply error be Δ%. The mobility of the charged ions is a constant below 10,000 V / m and shows a non-linear change above 10,000 V / m. Therefore, it is necessary to constrain the upper bound of the plate length according to the deviation of the mobility in the high-field part. The mobility change laws of different charged ions with voltage are different. For the sake of easy distinction, the mobility of the target ions (i.e., non-ions to be removed) is named K 1H (E) and K 1L (E), and the deflection angle of the target ions is named α;

[0128] Then the deflection angle of the target ions cannot exceed:

[0129]

[0130] where α is the displacement deflection angle of the target ions, Δ% is the power supply error, K 1H (E) is the mobility of the target ions in the high electric field, and K 1L (E) is the mobility of the target ions in the low electric field.

[0131] The plate length L of the migration region must satisfy:

[0132]

[0133] where Δ% is the power supply error, K 1H (E) is the mobility of the target ions in the high electric field, and K 1L (E) is the mobility of the target ions in the low electric field.

[0134] The present invention calculates the displacement of ions in a complete oscillation period, and optimizes the structural dimensions of the migration region according to the ion displacement parameters, so as to ensure that the ions to be separated do not leave the migration region during the separation process, improve the selectivity and resolution of FAIMS for gases, etc., and improve the separation performance.

[0135] It is obvious to those skilled in the art that the present invention is not limited to the details of the above-mentioned exemplary embodiments, and the present invention can be implemented in other specific forms without departing from the spirit or basic characteristics of the present invention. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-restrictive.

[0136] In addition, it should be understood that although this specification is described according to embodiments, not every embodiment only contains an independent technical solution. This narrative manner of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments 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 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; Step S6, obtaining the displacement of the ions in a complete oscillation cycle according to the calculation formula of the alternating electric field E(t), the calculation formula K(t) of the mobility K, 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.

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 compounded with the trigonometric function, and the amplitude of g(t) is set 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, based on the expression of the duty cycle and the expression of the alternating electric field E(t), a calculation formula of the alternating electric field E(t) is obtained; 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 the 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 claim 1, characterized in that: Step S6 includes: Step S61, according to the calculation formula of alternating electric field E(t) and the calculation formula K(t) of 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 ions pass through in one complete oscillation cycle and The displacement in both directions gives the displacement of the ion during one complete oscillation period.

7. The high electric field asymmetric waveform ion mobility spectrometry optimization method according to claim 6, characterized in that: In step S61, the charged ions move along the electric field. There is the following relationship 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, from which the displacement of ions along the electric field direction within one oscillation period is calculated. The movement of ions in one oscillation period is divided into two parts: upward and downward, which are calculated separately: Arranging equations (14) and (15) yields the ion in one oscillation period: Direction displacement:

8. The high electric field asymmetric waveform ion mobility spectrometry optimization method according to claim 7, characterized in that: 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: According to formulas (17) and (18), the ion mass in one oscillation period can be calculated Direction 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:

9. The high electric field asymmetric waveform ion mobility spectrometry optimization method according to any one of claims 1 to 8, 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 satisfy:

10. The high electric field asymmetric waveform ion mobility spectrometry optimization method according to claim 9, characterized in that: In step S7, considering the influence of error, the voltage source is allowed to have an error of 5%, and the power source 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 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; Then the deviation angle of the target ion cannot exceed: The length L of the migration zone must meet the following requirements:

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