Ion separation in imperfect fields of the quadrupole mass analyser Part III. Transmission and optimal ion injection

Theoretical aspects of ion separation in imperfect fields of the quadrupole mass analyser are applied to simulate transmission using an analytical approach. Mathematical simulation based on the principles of statistical mechanics reveals in analytical form that the region of beam capture, i.e. the transmission, is inversely proportional to the relative value of the mass analyser distortions to the 1.18th power in log scale. Since the beam at the mass analyser exit has a pulsing profile and the ion current is amplitude modulated by the frequency of the alternating component of the field, transmission losses because of a parasitic modulation increase more than tenfold as the resolution and distortion increase. These losses are reduced to a minimum by a heterogeneous standing wave voltage applied to the mass analyser with a linear distribution of amplitude along the ion transit axis. Then, the transmission increases exponentially 10–100-fold depending on the resolution and relative value of the distortions. This procedure has the advantages of the ion injection at zero phase in each cycle of an r.f. field.     

Modeling of ion processes in atmospheric pressure matrix-assisted laser desorption/ionisation

Atmospheric pressure matrix-assisted laser desorption/ionization (AP-MALDI) has proven a convenient and rapid method for ion production in the mass spectrometric analysis of biomolecules. This technique, like other atmospheric pressure ionization methods, suffers from ion loss during ion transmission from the atmosphere into the vacuum of the mass spectrometer. In this work, a simple model describing ion formation and ion motion towards the inlet capillary of the mass spectrometer is described. Both the gas flow and electric field near the MALDI plate were numerically calculated using the boundary element method (BEM). The ions were moving along with the gas flow and drifting in the electric field in accordance with their ion mobility properties. The ion signal dependence on an electric field strength obtained in the proposed model correlates well with experimental results.     

A Method of Computing Accurate 3D Fields of a Quadrupole Mass Filter and Their Use for Prediction of Filter Behavior

A method is described that enables the three-dimensional fields of a simple quadrupole mass filter (QMF) to be determined to a high accuracy. The technique produces accurate field values in the fringe field region as well as in the center of the filter. Using fields obtained typical filter performance is determined and shown to differ from that predicted when fringe fields are ignored. The computed performance shows features obtained experimentally and displays more complex variation with ion mass and other parameters than when fringe fields are ignored.     

Ion trajectory simulation for electrode configurations with arbitrary geometries

A multi-particle ion trajectory simulation program ITSIM 6.0 is described, which is capable of ion trajectory simulations for electrode configurations with arbitrary geometries. The electrode structures are input from a 3D drawing program AutoCAD and the electric field is calculated using a 3D field solver COMSOL. The program CreatePot acts as interface between the field solver and ITSIM 6.0. It converts the calculated electric field into a field array file readable by ITSIM 6.0 and ion trajectories are calculated by solving Newton's equation using Runge-Kutta integration methods. The accuracy of the field calculation is discussed for the ideal quadrupole ion trap in terms of applied mesh density. Electric fields of several different types of devices with 3D geometry are simulated, including ion transport through an ion optical system as a function of pressure. Ion spatial distributions, including the storage of positively charged ions only and simultaneous storage of positively/negatively charged ions in commercial linear ion traps with various geometries, are investigated using different trapping modes. Inelastic collisions and collision induced dissociation modeled using RRKM theory are studied, with emphasis on the fragmentation of n-butylbenzene inside an ideal quadrupole ion trap. The mass spectrum of 1,3-dichlorobenzene is simulated for the rectilinear ion trap device and good agreement is observed between the simulated and the experimental mass spectra. Collisional cooling using helium at different pressures is found to affect mass resolution in the rectilinear ion trap.     

Field distribution in an electrospray ionization source determined by finite element method

Three‐dimensional computer models of electrospray ionization sources were constructed in COMSOL Multiphysics? to solve the static electric fields using finite element methods. The magnitude of the electric field strength for onset of electrospray and optimum signal was calculated under various conditions. The modification of the electric field distribution in the ion source by an atmospheric pressure ion lens was also investigated by plotting the equipotential surfaces, electric field lines and trajectories of charged droplets. Both the calculated and the experimental results demonstrate that the changes in the ion signal detected by the mass spectrometer are attributable to the focusing effect of the ion lens when appropriate voltages are applied on the sprayer and ion lens. The optimum signal was found by setting the sprayer voltage from 3000 to 5000 V while scanning the ion lens voltage. The calculated strengths of the electric field at the sprayer tip for optimum signals are similar although the applied voltages at the sprayer and ion lens are significantly different. Copyright © 2009 John Wiley & Sons, Ltd.     

Computation of dynamic adsorption with adaptive integral,finite difference,and finite element methods

Analysis of diffusion-controlled adsorption and surface tension in one-dimensional planar coordinates with a finite diffusion length and a nonlinear isotherm, such as the Langmuir or Frumkin isotherm, requires numerical solution of the governing equations. This paper presents three numerical methods for solving this problem. First, the often-used integral (I) method with the trapezoidal rule approximation is improved by implementing a technique for error estimation and choosing time-step sizes adaptively. Next, an improved finite difference (FD) method and a new finite element (FE) method are developed. Both methods incorporate (a). an algorithm for generating spatially stretched grids and (b). a predictor-corrector method with adaptive time integration. The analytical solution of the problem for a linear dynamic isotherm (Henry isotherm) is used to validate the numerical solutions. Solutions for the Langmuir and Frumkin isotherms obtained using the I, FD, and FE methods are compared with regard to accuracy and efficiency. The results show that to attain the same accuracy, the FE method is the most efficient of the three methods used.     

pKA in proteins solving the Poisson–Boltzmann equation with finite elements

Knowledge on pK_A values is an eminent factor to understand the function of proteins in living systems. We present a novel approach demonstrating that the finite element (FE) method of solving the linearized Poisson–Boltzmann equation (lPBE) can successfully be used to compute pK_A values in proteins with high accuracy as a possible replacement to finite difference (FD) method. For this purpose, we implemented the software molecular Finite Element Solver (mFES) in the framework of the Karlsberg+ program to compute pK_A values. This work focuses on a comparison between pK_A computations obtained with the well‐established FD method and with the new developed FE method mFES, solving the lPBE using protein crystal structures without conformational changes. Accurate and coarse model systems are set up with mFES using a similar number of unknowns compared with the FD method. Our FE method delivers results for computations of pK_A values and interaction energies of titratable groups, which are comparable in accuracy. We introduce different thermodynamic cycles to evaluate pK_A values and we show for the FE method how different parameters influence the accuracy of computed pK_A values. © 2015 Wiley Periodicals, Inc.     

Effects of the source gap on transmission efficiency of a quadrupole mass spectrometer

Rationale

Recent trends towards miniature and portable quadrupole mass spectrometry (QMS) entail challenges in instrumental sensitivity, which is influenced by 3D fringe field effects on ion transmission in the Quadrupole Mass Filter (QMF). The relationship of these effects with the gap from the ion source to the QMF entrance (source gap) is significant and little explored. We examine transmission characteristics experimentally and use the results to test the predictive accuracy of a recently developed 3D QMF simulation model. The model is then applied to directly investigate optimal transmission m/z ranges across multiple source gaps.

Methods

A portable single filter quadrupole mass spectrometer is used to analyse transmission characteristics across a range of common gases. We use an experimental approach originally proposed by Ehlert, enhanced with a novel method for absolute calibration of the transmission curve. Custom QMF simulation software employs the boundary element method (BEM) to compute accurate 3D electric fields. This is used to study the effects of the source gap on transmission efficiency.

Results

Experimental findings confirm a centrally peaked transmission curve; simulations correctly predict the optimal transmission location (in m/z) and percentage, and extend the experimental trend. We compare several methods for determining fringe field length, demonstrating how the size of the physical source gap influences both the length and the intensity of the fringe field at the QMF entrance. A complex relationship with ion transmission is revealed in which different source gaps promote optimal transmission at differing m/z ranges.

Conclusions

The presented results map the relationship between the source gap and transmission efficiency for the given instrument, using a simulation method transferrable to other setups. This is of importance to miniature and portable quadrupole mass spectrometers design for specific applications, for the first time enabling the source gap to be tailored for optimal transmission in the desired mass range.

     

稳定图的测定与矩形离子阱质谱性能分析

从理论上讲, 离子阱质谱仪的性能是由阱内电场分布决定的,而电场分布又是由组成离子阱的电极几何结构和离子阱工作电压决定的. 对于矩形离子阱, 即使不考虑其几何结构的偏差, 其阱内的电场分布一般也很复杂. 在矩形离子阱内, 除四极电场外, 还包含多种成分的其他各种高阶场, 它们直接影响离子在阱内的运动轨迹和离子阱质谱的性能. 由于各种电场成分对离子阱内离子运动的影响非常复杂, 还很难从数学上给出精确的解析解, 使得目前从理论上还无法预测高阶场成分对质谱性能的影响. 本工作通过测定不同几何结构的矩形离子阱的稳定图, 从实验上比较了不同场半径, 即不同电场分布条件下的离子阱质谱性能的差别. 实验中, 通过改变离子阱的几何比例结构, 详细测定了不同结构的矩形离子阱的稳定图特征, 并与实验测得的质谱分析结果进行比较. 同时, 我们还详细介绍了矩形离子阱质谱的稳定图的测定方法, 并根据得到的不同情况下的稳定图结构分析了离子阱的质谱性能. 研究结果表明： 可以通过比较试验得到的稳定图结构来判断其离子阱质谱仪的性能如质量分辨能力等. 此外, 实验结果还发现： 对于y方向拉伸结构的矩形离子阱, 其实验绘制得到的是不完整的稳定图. 但根据稳定图边界的特点, 通过采用四极直流电压调制的方法, 可以对y方向拉伸结构的矩形离子阱的性能进行改善, 极大地提高了阱的质量分辨能力.     

Ion Trap Electric Field Characterization Using Slab Coupled Optical Fiber Sensors

This paper presents a method for characterizing electric field profiles of radio frequency (rf) quadrupole ion trap structures using sensors based on slab coupled optical-fiber sensor (SCOS) technology. The all-dielectric and virtually optical fiber-sized SCOS fits within the compact environment required for ion traps and is able to distinguish electric field orientation and amplitude with minimal perturbation. Measurement of the fields offers insight into the functionality of traps, which may not be obtainable solely by performing simulations. The SCOS accurately mapped the well-known field profiles within a commercially available three-dimensional quadrupole ion trap (Paul trap). The results of this test allowed the SCOS to map the more complicated fields within the coaxial ion trap with a high degree of confidence as to the accuracy of the measurement. Figure

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An appreciation of the scientific researches of Dr Peter H. Dawson

Upon the death of Peter H. Dawson in 2015, mass spectrometry lost a major figure. Within the area of radiofrequency quadrupole electric fields applied to mass spectrometry, Dawson stands alongside its pioneers Wolfgang Paul, Nobelist and inventor of the technology, and Wilson Brubaker, who identified and overcame the deleterious effects of fringing electric fields on quadrupole mass filter performance. Seventy‐one of Dawson's 97 scientific publications are concerned with quadrupole mass analysers, ion traps and monopole mass spectrometers. Of especial note are his book and review articles in which he disseminated information on the theoretical fundamentals and practicalities of these systems to a wider audience, thereby having a major impact on the development of this important field of endeavour. The scientific researches of Dr Dawson, and his advice and counsel, influenced to a major degree, and to the better, the research careers, teachings and the lives of the authors of this piece. Their combined researches on quadrupole devices led to the commercialization of the ion trap as a mass spectrometer by which mass spectral information became available at greatly reduced cost. Thus, the advent of commercial ion trapping instruments permitted a greater use of mass spectrometry in both technically advanced countries and those less well advanced. The greatest impact in health services was mass spectrometric analysis of environmental problems, well and stream water, food free of pesticides, etc., and forensic sciences. Our combined indebtedness to Dr Dawson is manifested by this appreciation of his scientific work, the highlighting of his main contributions, and creation of a substantive reference source to his work that can be used by other scientists. A comprehensive list of Dr Dawson's publications, including abstracts or summaries, has been arranged in chronological order of date of submission.     

Analytical performance of a high-pressure radio frequency-only quadrupole collision cell with an axial field applied by using conical rods

The effect on triple-quadrupole performance of applying an axial field, in an rf-only quadrupole collision cell operated at pressures sufficiently high that collisional focusing is operating, has been investigated. The advantages of such cells have been shown previously to include increased transmission and much improved resolution in fragment ion spectra relative to the performance of collision cells operating at lower gas pressures. The disadvantages of high-pressure collision cells all derive from the relatively long transit times for the ions, which can be long relative to characteristic times for scanning the first mass filter (precursor ion selector) or for switching its setting in multiple reaction monitoring (MRM) cycles. The present work describes experiments on a high-pressure cell in which an axial field is created through use of conical rather than cylindrical or hyperbolic rods. In addition, results of computations of the electric fields within such a cell, and of ion trajectories through it, are presented. It is shown that application of axial fields of the order of 0. 1 V/cm can remove all hysteresis effects associated with the long ion transit times, and thus provide excellent performance in quantitation work using MRM, as well as in other scan modes. Furthermore, the advantages of collisional focusing in quadrupole collision cells are shown to be unimpaired by these low axial fields.     

Modelling the internal field distribution in human erythrocytes exposed to MW radiation

This paper studies the internal electric field distribution in human erythrocytes exposed to MW radiation. For this purpose, an erythrocyte cell model is exposed to linearly polarized electromagnetic (EM) plane waves of frequency 900 MHz and the electric field within the cell is calculated by using a finite element (FE) technique with adaptive meshing. The results obtained show the dependence of the induced electric field distribution on the main modelling parameters, i.e., the electrical properties (permittivity and conductivity) of the membrane and cytoplasm and the orientation of the cell with respect to the applied field. It is found that for certain orientations, the field amplification within the membrane of the erythrocyte shape cell can be higher than the one observed in an equivalent simple spheroidal geometry cell, commonly used in bioelectromagnetism. The present work shows that a better insight of the interaction of electromagnetic fields with basic biological structures is obtained when the most possible realistic cell shape is used.     

Non‐vacuum field desorption ion source implemented under super‐atmospheric pressure

Standard field desorption (FD) ionization is implemented under high vacuum condition. In this paper, non‐vacuum FD is performed under a super‐atmospheric pressure environment using untreated tungsten wires as FD emitter, and the ion source was coupled to a commercial linear ion trap mass spectrometer. The operating pressure of the ion source was 6 bars which was high enough to provide sufficient dielectric strength to the working gas so that the high voltage that was required for FD could be applied to the emitter without occurrence of electrical discharge. Non‐volatile sample deposited on the bare tungsten wire FD emitter was heated by flowing direct current through the emitter. Similar to vacuum FD, the formation of conical protrusion of the liquefied sample layer under the strong electric field was also observed. Using the present ion source, high pressure field‐desorption of polar neutral compounds, organic salts and ionic liquids is demonstrated. Copyright © 2012 John Wiley & Sons, Ltd.     

The high-pressure segmented quadrupole collision cell (HP-SQCC) as an ion molecule reactor

A high-pressure 20-segment quadrupole collision cell (HP-SQCC), which replaces a collision cell in a modified triple-quadrupole mass spectrometer is investigated in this work as an ion-molecule reactor with an inherent heat source. The highest working pressure achievable is 20 mTorr. The 20 quadrupole segments permit superimposition of linear axial electric field over the conventional quadrupole field in the radial direction. The axial and radial fields are employed to control ion temperature. Heat is transferred to the reactants through ion frictional heating. The HP-SQCC utilizes a combination of several physicochemical phenomena and an attempt is made to examine a range of ion-molecule reactions. Due to a sufficiently large number of reactive collisions, the reactor is used to promote sequential exothermic ion-molecule reactions. To characterize the performance of the HP-SQCC, the various ion-molecule reactions between the fragment ions of ferrocene (Cp(2)Fe), cobaltocene (Cp(2)Co) and nitrogen, oxygen, water and carbon monoxide are investigated.     

The coupling effects of hexapole and octopole fields in quadrupole ion traps: a theoretical study

A theoretical method, the harmonic balance method, was introduced to study the coupling effects of hexapole and octopole fields on ion motion in a quadrupole ion trap. Ion motion characteristics, such as ion motion center displacement, ion secular frequency shift, nonlinear resonance curve and buffer gas damping effects, have been studied with the presence of both hexapole and octopole fields. It is found that hexapole fields have bigger impacts on ion motion center displacement, while octopole fields dominate ion secular frequency shift. Furthermore, the nonlinear features originated from hexapole and octopole fields could enhance or cancel each other, which provide us more space in a practical ion trap design process. As an example, an ion trap with improved performance was designed using a specific combination of hexapole and octopole fields. In this ion trap, a hexapole field was used to achieve efficient ion directional ejection, while an octopole field was added to correct the chemical mass shift and resolution degradation introduced by the hexapole field. Copyright © 2013 John Wiley & Sons, Ltd.     

Space Charge Induced Nonlinear Effects in Quadrupole Ion Traps

A theoretical method was proposed in this work to study space charge effects in quadrupole ion traps, including ion trapping, ion motion frequency shift, and nonlinear effects on ion trajectories. The spatial distributions of ion clouds within quadrupole ion traps were first modeled for both 3D and linear ion traps. It is found that the electric field generated by space charge can be expressed as a summation of even-order fields, such as quadrupole field, octopole field, etc. Ion trajectories were then solved using the harmonic balance method. Similar to high-order field effects, space charge will result in an “ocean wave” shape nonlinear resonance curve for an ion under a dipolar excitation. However, the nonlinear resonance curve will be totally shifted to lower frequencies and bend towards ion secular frequency as ion motion amplitude increases, which is just the opposite effect of any even-order field. Based on theoretical derivations, methods to reduce space charge effects were proposed.