Linear quadrupoles with added hexapole fields

Linear quadrupoles with added hexapole fields are described. The shifts in ion oscillation frequency caused by the addition of a hexapole field are calculated within the effective potential model. Methods to construct linear quadrupoles with added hexapole fields with exact electrode geometries and with round rods are discussed. A quadrupole with added hexapole field can be constructed with round rods by rotating two rods (say the y rods) towards an x rod. Computer simulations are used to investigate the possibility of mass analysis with quadrupoles with added hexapole fields. We find that a quadrupole with an added hexapole field in the range 2-12% can provide mass analysis provided the dc is applied with the correct polarity and value. When a rod set is constructed with round rods, other multipoles in the potential degrade the peak shape, resolution and transmission. The largest of these after the quadrupole and hexapole are a dipole and octopole term. With round rod sets, the peak shape can be improved by using different diameters for the x and y rod pairs to minimize the octopole term in the potential and by injecting ions at the field center where the dipole term is zero. Calculations of the boundaries of the stability diagram for this case show the boundaries move out, relative to those of a pure quadrupole field, but remain sharp.     

Mass selective axial ion ejection from linear quadrupoles with added octopole fields

Mass selective axial ejection of ions from linear quadrupoles with added octopole fields is described. Quadrupoles with 2.0% and 2.6% added octopole fields have been tested and compared with a conventional quadrupole. The effects of trapping ions at different q values, excitation voltage, scan direction, balanced and unbalanced rf voltages on the rods, and dc applied between the rods have been investigated. The highest scan speeds and best resolution are obtained with resonant excitation and ejection at high q (q = 0.8). With axial ejection, the quadrupole with a 2.0% added octopole field provides mass resolution and ejection efficiencies similar to a conventional rod set. Quadrupole, dipole, and simultaneous dipole-dipole excitation between the x and y rod pairs were compared, and no advantage was found with quadrupole or dipole-dipole excitation. The effects of scan speed were investigated and a resolution at half height of about 1600 is possible at scans speed up to 5000 Th/s.     

Mass analysis in islands of stability with linear quadrupoles with added octopole fields

Mass analysis with linear quadrupole mass filters is possible by forming "islands" in the stability diagram with auxiliary quadrupole excitation. In this work, computer simulations are used to calculate stability boundaries, island positions, and peak shapes and ion transmission for mass analysis with linear quadrupole mass filters that have added octopole fields of about 2 to 4%. Rod sets with exact geometries that have quadrupole and octopole fields only in the potential, and round rod sets, with multipoles up to N = 10 (the twenty pole term) included in the calculations, show the same stability boundaries, island positions, and peak shapes. With the DC voltage applied to the rods so that the Mathieu parameter a < 0, conventional mass analysis is possible without the use of an island. With the DC polarity reversed so that a > 0, the resolution and transmission are poor preventing conventional mass analysis. In principle, mass analysis in an island is possible with operation at either of two tips. Provided the correct island tip is chosen for mass analysis, peak shapes comparable to those with a > 0 and no excitation are possible, both with a > 0 and with a < 0. In the latter case, the use of an island of stability allows mass analysis when the added octopole otherwise prevents conventional mass analysis.     

Quadrupole excitation of ions in linear quadrupole ion traps with added octopole fields

Modeling and experimental studies of quadrupole excitation of ions in linear quadrupole traps with added octopole fields are described. An approximate solution to the equations of motion of ions trapped in a quadrupole with added octopole and dodecapole fields, with quadrupole excitation and damping is given. The solutions give the steady-state or stationary amplitudes of oscillation with different excitation frequencies. Trajectory calculations of the oscillation amplitudes are also presented. The calculations show that there can be large changes in the amplitude of ion oscillation with small changes in excitation frequency, on both the low and high-frequency sides of a resonance. Results of experiments with quadrupole excitation of reserpine ions in linear quadrupole traps with 2.0%, 2.6%, and 4.0% added octopole fields are given. It is found that as the excitation frequency is changed, two resonances are generally observed, which are attributed to the motion in the x and y directions. The two resonances can have quite different intensities. Sudden jumps or sharp sided resonances are not observed, although in some cases asymmetric resonances are seen. The calculated frequency differences between the two resonances are in approximate agreement with the experiments.     

Linear ion trap with added octopole field component: the property and method

It is well known that superimposition of some positive octopole field will benefit the performance of ion trap mass analyzer. In the radial‐ejection linear ion trap (LIT), adding some octopole field component to the main quadrupole field is usually accomplished by stretching the ejection rod pair. In this study, the effect of octopole potential and some other higher order potential on the performance of LIT mass analyzer is investigated. A simple and effective method, which is to add some octopole component by building a LIT with a pair of rectangular electrodes and a pair of semi‐circular electrodes, is reported. Its properties were studied by numerical simulations and experiments. The results showed that a certain amount of positive octopole component could be produced by simply adjusting the position and width of the rectangular electrodes. A resolution of over 1200 at m/z 609 (~1600 Da/s) was observed in this type of LIT. They also performed tandem mass spectrometry well. The device with optimum geometry for ion ejection from rectangular electrodes provided comparable performance to that for ion ejection from semi‐circular electrodes. This type of LIT design is easy for fabrication and assembly. Copyright © 2015 John Wiley & Sons, Ltd.     

Quadrupole mass filters with octopole fields

The performance of quadrupole mass filters with added octopole fields in the range 2.0-4.0% has been investigated. The added fields are much greater than those normally added to conventional rod sets by mechanical tolerances or construction errors. Quadrupole rod sets with added octopole fields were constructed with round rods by making one pair of rods greater in diameter than the other pair. For positive ions, resolution at half height of only about 200 is possible if the negative direct current (dc) output of the quadrupole power supply is connected to the smaller rods. If the positive dc output of the quadrupole power supply is connected to the smaller rods, the resolution improves dramatically; a resolution at half height of 5800 has been observed with a rod set with 2.6% added octopole field. For negative ions the best resolution is obtained with the polarity of the dc reversed, i.e. with the negative dc applied to the smaller rods. These findings are unexpected in view of the literature that argues that to obtain high mass resolution with quadrupole mass filters, higher order multipoles must be kept as small as possible. Numerical simulations of peak shapes agree qualitatively with experiments. Simulation of the boundaries of the first stability region for positive ions shows that when the positive dc is applied to the smaller rods, the addition of a 2.0% octopole field causes the boundaries to shift slightly but the boundaries are well defined, and the tip of the stability region remains sharp. When the positive dc is applied to the larger rods, the boundaries of the stability region move out and become diffuse. For instruments that require a rod set that can be used both as a linear trap and a mass filter, these rod sets may offer improved trap performance while still being capable of providing conventional mass analysis.     

Ion excitation in a linear quadrupole ion trap with an added octopole field

Modeling of ion motion and experimental investigations of ion excitation in a linear quadrupole trap with a 4% added octopole field are described. The results are compared with those obtained with a conventional round rod set. Motion in the effective potential of the rod set can explain many of the observed phenomena. The frequencies of ion oscillation in the x and y directions shift with amplitude in opposite directions as the amplitudes of oscillation increase. Excitation profiles for ion fragmentation become asymmetric and in some cases show bistable behavior where the amplitude of oscillation suddenly jumps between high and low values with very small changes in excitation frequency. Experiments show these effects. Ions are injected into a linear trap, stored, isolated, excited for MS/MS, and then mass analyzed in a time-of-flight mass analyzer. Frequency shifts between the x and y motions are observed, and in some cases asymmetric excitation profiles and bistable behavior are observed. Higher MS/MS efficiencies are expected when an octopole field is added. MS/MS efficiencies (N(2) collision gas) have been measured for a conventional quadrupole rod set and a linear ion trap with a 4% added octopole field. Efficiencies are chemical compound dependent, but when an octopole field is added, efficiencies can be substantially higher than with a conventional rod set, particularly at pressures of 1.4 x 10(-4) torr or less.     

Mass analysis with islands of stability with linear quadrupoles incorporating higher order multipole fields

Mass analysis with islands of stability has been investigated with three linear quadrupole mass filters: two with 4% added hexapole fields constructed with equal diameter (quadrupole 4A) and unequal diameter (quadrupole 4B) rods, and a conventional round-rod quadrupole that has apparently been slightly damaged. Islands are formed by applying auxiliary quadrupole excitation. With the Mathieu parameter, a < 0, mass analysis with both quadrupoles with hexapole fields operated normally, i.e., without islands, gives only low resolution. A factor of 10 or more increase in resolution is possible with the use of stability islands. With a > 0, when quadrupole 4A is operated normally, peak shapes similar to that of a conventional quadrupole can be obtained at resolutions higher than 850. At lower resolutions, peaks are split. When quadrupole 4B is operated without islands, resolution up to 2000 is possible, but there are low mass tails and structure is formed on the peaks. With mass analysis with an island of stability, both quadrupoles 4A and 4B show peaks free of structure and without tails. Ion transmission is also improved with some operating conditions. With the conventional round-rod quadrupole, mass analysis with islands of stability increases the limiting resolution from 2500 to 4360. At a resolution of 2500, the transmission is increased by about two orders of magnitude. These results show that the use of islands of stability improves mass analysis with quadrupoles with distorted fields, and may, in the future, allow use of quadrupoles constructed with at least some lower mechanical tolerances.     

Quadrupole mass filters with added hexapole fields

Conventional mass analysis has been investigated experimentally with six quadrupole mass filters with added hexapole fields; three with added hexapole fields of 4%, 8% and 12% with equal diameter rods, and three with added hexapole fields of 4%, 8% and 12% with unequal diameter rods to remove an added octopole field. Compared with conventional quadrupoles, these rod sets have very large field distortions. With the positive resolving dc applied to the y rods (Mathieu parameter ) only low resolution (10–100) and low transmission are seen. With the polarity reversed ( ) much higher resolution (≥1000) and transmission are possible. Increasing the magnitude of the added hexapole field decreases the limiting resolution at m/z 609. Removing the added octopole field increases the limiting resolution. In some cases structure is formed on the peaks. For a given scan line slope, U/V _rf , the resolution decreases as the amplitude of the added hexapole field increases. These results are consistent with changes to the stability diagrams, calculated here. With , adding a hexapole field causes the x stability boundary to move outward with all rod sets. With , the boundaries become diffuse and the tip of the stability diagram becomes rounded, limiting the resolution to ca. 10‐100. Where comparisons are possible, experiments show the rod sets with added hexapole fields have transmission 10–300 times less than a conventional quadrupole. Thus these quadrupoles are less useful for mass analysis than conventional quadrupoles. However, it is surprising, given the highly distorted fields, that some of the quadrupoles give resolution of 1000 or more. Copyright © 2010 John Wiley & Sons, Ltd.     

Experimental investigation of mass analysis using an island of stability with a quadrupole with 2.0% added octopole field

We describe experimental investigations of mass analysis using an island of stability with a linear quadrupole with a 2.0% added octopole field. The island is formed by auxiliary quadrupole excitation. The experiments confirm the results of previous computer simulations (Konenkov et al., J. Am. Soc. Mass Spectrom. 2007; 18: 826-834). With the resolving direct current (dc) applied to the quadrupole so that the Mathieu parameter a > 0, conventional mass analysis with applied radio-frequency (rf) and dc and no auxiliary excitation is possible. In this case, use of an island of stability yields similar peak shape and resolution. However, with the polarity of the resolving dc reversed, so that a < 0, only very low resolution can be obtained; the added octopole prevents conventional mass analysis. By using a stability island when a < 0, the resolution is substantially improved. In this case the use of an island allows mass analysis under conditions where the added octopole field severely degrades conventional analysis. The experiments also confirm the position of the island predicted by the simulations.     

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.     

Dipole excitation of ions in linear radio frequency quadrupole ion traps with added multipole fields

Ion motion with auxiliary dipole excitation and collisional damping in a linear radiofrequency quadrupole ion trap incorporating small amounts of even higher order multipoles is studied analytically. The ion motion is modeled in a pseudopotential that is mostly quadratic with small amounts of higher spatial harmonics. Ion motion along x and y axes is characterized by two uncoupled forced and damped anharmonic oscillator equations. A multiple time scales method is used to solve the equations of motion of ions with a first order perturbation correction. Analytical relations between the oscillation amplitudes at steady state (the stationary amplitudes) and excitation frequency are calculated. The frequency response curves show that in some cases bistable behavior might be obtained, i.e., there are two stable stationary amplitudes for a given excitation frequency.     

Collisional focusing effects in radio frequency quadrupoles

The transmission of ions through a conventional two-dimensional radiofrequency-only (rf) quadrupole has been studied for comparatively high operating pressures between 5 × 10^?4 and 1 × 10^?2 torr. Measurements of signals from mass-resolved analyte ions and total ion currents show that, provided the initial injection ion energy is low (1–30 eV), the ion transmission observed through a small aperture at the exit of the rf quadrupole first increases as the gas pressure increases, reaching a maximum at ? 8 × 10^?3 torr before decreasing at higher pressures. This is in direct contrast to the expectations of classical scattering. This “collisional focusing” appears to be analogous to effects seen in three-dimensional ion traps. The collisional focusing increases with the mass of the ion (not mass-to-charge ratio) for masses up to at least 16,950 u. The collisional focusing of the ions is found to be accompanied by significant losses of axial kinetic energy. A Monte Carlo simulation of the energy loss process is reported that can provide agreement with the observed losses for reasonable collision cross-sections. The results suggest that operation of rf quadrupoles at relatively high pressure may find practical application in sampling ions from high (e.g., atmospheric) pressure ion sources.     

Orientational phases of classical quadrupoles on a triangular net

The classical Monte Carlo (MC) method is used to study the effect of temperature on the ordering of quadrupoles arranged on a triangular net with toroidal boundary conditions. The results are used to discuss the orientational ordering of nitrogen and hydrogen molecules adsorbed on the basal plane of graphite.     

Linear analysis of pattern formation in nematics in oblique magnetic fields

The dynamics of nematic director field reorientation in non-Freedericksz geometries, after a magnetic field H is applied at an oblique angle relatively to the initial homogeneous director n 0 ( H not normal to n 0), is studied considering a magnetic reorientation driven by hydrodynamic instabilities (with backflow). This study is carried out for bounded samples between two parallel plates with planar boundary conditions and with rigid anchoring. Linear stability and wave vector selection analysis predict that, when the angle of the magnetic to the initial director field is increased, for a given magnetic field intensity, two transitions from a homogeneous to a transient distorted director field reorientation can occur: a transition at a first critical angle to an aperiodic distorted director field and a transition at a second critical angle to a periodic distorted director field. It is shown that the periodic mode is cut off at a higher reduced field when the magnetic field acts away from the normal direction.     

Expanded capsules with reversibly added spacers

Glycolurils insert as spacer elements in a capsule to create a new space with enhanced dimensions.     

Linear polymers in nonhomogeneous flow fields. I. Translational diffusion coefficient

The translational diffusion coefficient D, needed in treatments of flow-induced polymer migration phenomena, is studied. Explicit results are reported for bead–spring model macromolecules with two, three, and four beads, respectively. If the number of beads is large, an integral formulation is used. The results obtained show that D depends upon the hydrodynamic interaction parameters h^* and h^*N^1/2. Nondraining behavior of D is predicted irrespective of h if h^* is close to 0.2357. Approximations for D are obtained and the error involved is estimated.     

八极杆碰撞/反应池-ICP-MS测定纯铜中的磷

利用ORS-ICP-MS测定纯铜中的磷. 对ICP-MS测定条件进行了最佳化的选择, 利用动态反应池技术(ORS)和在线内标加入技术, 可降低基体干扰, 提高灵敏度. 分析方法的检出限为0.33 ng/mL, 加标回收率为94%～97%.     

Linear polymers in nonhomogeneous flow fields. II. The cross-stream migration velocity

The cross-stream migration velocity v _⊥ is that part of the velocity of a particle which has no component in the direction of the undistrubed flow. In order to obtain v _⊥ for bead–spring model macromolecules, it is necessary to compute the trace of the matrix product \documentclass{article}\pagestyle{empty}\begin{document}$ \underline \ell \cdot \underline {{\rm \hat C}} $\end{document}, where \documentclass{article}\pagestyle{empty}\begin{document}$ \underline \ell $\end{document} denotes the migration matrix and \documentclass{article}\pagestyle{empty}\begin{document}$ \underline {{\rm \hat C}} $\end{document} is the modified Kramer's matrix. In this paper this is done via an eigenvalue calculation, where the eigenvalues are estimated by using the Rouse eigenfunctions. The results are then checked against the few known exact results and excellent agreement is found. It turns out that v _⊥ depends on the third power of the molecular weight for free-draining polymers. The dependence upon molecular weight becomes weaker with increasing hydrodynamic interaction until, in the nondraining limit, v _⊥ ∝ M^2.5. A simple yet accurate formula for v _⊥ is proposed. In conjunction with the results for D (of Part I), purely rotational flow fields are shown to be characterized by a single parameter, the particle Peclet number Pe. Up to a constant of order one (actually a function of the hydrodynamic interaction parameters h^* and h, which can vary only between 0.8 and 2.057), Pe depends only upon D, the mean-square equilibrium extension R, and q₀, the magnitude of the maximum shear rate for the flow.     

Characterization of fluorocarbon-in-water emulsions with added triglyceride

Fluorocarbon-in-water emulsions are being explored clinically as synthetic oxygen carriers in general surgery. Stabilizing fluorocarbon emulsions against coarsening is critical in maintaining the biocompatibility of the formulation following intravenous administration. It has been purported that the addition of a small percentage of long-chain triglyceride results in stabilization of fluorocarbon emulsions via formation of a three-phase emulsion. In a three-phase emulsion, the triglyceride forms a layer around the dispersed fluorocarbon, thereby improving the adhesion of the phospholipid surfactant to the dispersed phase. In the present study, we examined the effect of triglyceride addition on the physicochemical characteristics of the resulting complex dispersion. In particular, we examined the particle composition and stability of the dispersed particles using a method which first fractionates (classifies) the different particles prior to sizing (i.e., sedimentation field-flow fractionation). It was determined that the addition of a long-chain triglyceride (soybean oil) results in oil demixing and two distinct populations of emulsion droplets. The presence of the two types of emulsion droplets is not observed via light scattering techniques, since the triglyceride droplets dominate the scattering due to a large difference in the refractive index between the particles and the medium as compared to fluorocarbon droplets. The growth of the fractionated fluorocarbon emulsion droplets was followed over time, and it was found that there was no difference in growth rates with and without added triglyceride. In contrast, addition of medium-chain-triglyceride (MCT) oils results in a single population of emulsion droplets (i.e., a three-phase emulsion). These emulsions are not stable to droplet coalescence, however, as significant penetration of MCT into the phospholipid lipid interfacial layer results in a negative increment in the monolayer spontaneous curvature, thereby favoring water-in-oil emulsions and resulting in destabilization of the emulsion to the effects of terminal heat sterilization or mechanical stress.