On the Combinatorics of Galois Numbers

We define interval decompositions of the lattice of subspaces of a finite-dimensional vector space. We show that such a decomposition exists if and only if there exists a family of linear forms with certain properties. As applications we prove that all finite-dimensional real vector spaces admit an interval decomposition, while GF (2) n has an interval decomposition if and only if n ≤ 4. On the other hand, we present an interval decomposition of GF (3) 5. This partially answers a question of Faigle [4, 1]

Miniaturized high-performance drift tube ion mobility spectrometer

Developing powerful hand-held drift tube ion mobility spectrometers (IMS) requires small, lightweight drift tubes with high analytical performance. In this work, we present an easy-to-manufacture, miniaturized drift tube ion mobility spectrometer, which is manufactured from polyether ether ketone, stainless steel foils and printed circuit boards. It is possible to operate the drift tube IMS with a radioactive 3H ionization source or a non-radioactive X-ray ionization source with 3 kV acceleration voltage. The drift tube design provides high resolving power of Rp = 63 at a drift length of just 40 mm, 15 mm × 15 mm in cross-section (outer dimensions) and a drift voltage of 2.5 kV. The limits of detection for less than one second of averaging are 40 pptv for dimethyl-methylphosphonate and 30 pptv for methyl salicylate. For demonstration, the miniaturized drift tube IMS is integrated into a stand-alone battery-powered mobile device, including a closed gas-loop, high performance driver electronics and wireless data transmission. In a proof-of-concept study, this device was tested in an international field evaluation exercise to detect the release of a volatile, hazardous substance inside a large entry hall

Novel ion drift tube for high-performance ion mobility spectrometers based on a composite material

Ion mobility spectrometers (IMS) are able to detect pptV-level concentrations of substances in gasses and in liquids within seconds. Due to the continuous increase in analytical performance and reduction of the instrument size, IMS are established nowadays in a variety of analytical field applications. In order to reduce the manufacturing effort and further enhance their widespread use, we have developed a simple manufacturing process for drift tubes based on a composite material. This composite material consists of alternating layers of metal sheets and insulator material, which are connected to each other in a mechanically stable and gastight manner. Furthermore, this approach allows the production of ion drift tubes in just a few steps from a single piece of material, thus reducing the manufacturing costs and efforts. Here, a drift tube ion mobility spectrometer based on such a composite material is presented. Although its outer dimensions are just 15 mm × 15 mm in cross section and 57 mm in length, it has high resolving power of Rp = 62 and detection limits in the pptV-range, demonstrated for ethanol and 1,2,3-trichloropropane. © 2020, The Author(s)

IMS Instrumentation I : Isolated data acquisition for ion mobility spectrometers with grounded ion sources

The drift voltage required for operating ion mobility spectrometers implies high voltage isolation of either the ion source or the detector. Typically, the detector is grounded due to the sensitivity of the small ion currents to interferences and thus higher requirements for signal integrity than the ion source. However, for certain ion sources, such as non-radioactive electron emitters or electrospray ionization sources, or for coupling with other instruments, such as gas or liquid chromatographs, a grounded ion source is beneficial. In this paper, we present an isolated data acquisition interface using a 16 bit, 250 kilosamples per second analog to digital converter and fiber optic transmitters and receivers. All spectra recorded via this new data acquisition interface and with a grounded ion source show the same peak shapes and noise when compared with a grounded detector, allowing additional freedom in design. © 2020, The Author(s)

Resistive High-Voltage Probe with Frequency Compensation by Planar Compensation Electrode Integrated in Printed Circuit Board Design

Resistive voltage dividers tend to have a highly non-linear transfer function as parasitic and stray capacitances exert an increasing influence with increasing frequency. The non-linear transfer function depends on the topology and resistors used and consists of a low-pass filter with an additional high-pass component in the GHz range. Due to the non-linear transfer function the measured signal differs from the original input signal. Here, we present an improved resistive voltage divider with additional compensation capacities to extend the linear bandwidth. With this new concept, the linear bandwidth is improved from 115 kHz to 88 MHz, while maintaining a DC input impedance of 10 MΩ. For high-voltage insulation and easy manufacturing, surface mounted resistors on a printed circuit board with a compensation electrode on the adjacent side are used. The performance of this resistive voltage divider is demonstrated by measuring a series of high-voltage pulses with an amplitude of 2.5 kVpeak-peak. The measured pulse rise time is about 16 ns, corresponding to an average slew-rate of 150 V/ns. Finally, the developed resistive voltage divider is successfully used to measure fast high-voltage transients required for advanced ion mobility spectrometers with integrated collision induced fragmentation

Detection of Chemical Warfare Agents with a Miniaturized High-Performance Drift Tube Ion Mobility Spectrometer Using High-Energetic Photons for Ionization

A growing demand for low-cost gas sensors capable of detecting the smallest amounts of highly toxic substances in air, including chemical warfare agents (CWAs) and toxic industrial chemicals (TICs), has emerged in recent years. Ion mobility spectrometers (IMS) are particularly suitable for this application due to their high sensitivity and fast response times. In view of the preferred mobile use of such devices, miniaturized ion drift tubes are required as the core of IMS-based lightweight, low-cost, hand-held gas detectors. Thus, we evaluate the suitability of a miniaturized ion mobility spectrometer featuring an ion drift tube length of just 40 mm and a high resolving power of Rp= 60 for the detection of various CWAs, such as nerve agents sarin (GB), tabun (GA), soman (GD), and cyclosarin (GF), as well as the blister agent sulfur mustard (HD), the blood agent hydrogen cyanide (AC) and the choking agent chlorine (CL). We report on the limits of detection reaching minimum concentration levels of, for instance, 29 pptvfor sarin (GB) within an averaging time of only 1 s. Furthermore, we investigate the effects of precursors, simulants, and other common interfering substances on false positive alarms

Wireless Low-Power Transfer for Galvanically Isolated High-Voltage Applications

For various applications, such as gate drivers for transistors, wireless chargers for mobile devices and cars, and isolated measurement equipment, an isolated DC power supply for electronic components is required. In this work, a new concept for an isolated power supply with insulation strength of 50 kV and power transmission of up to 60 W to supply measurement equipment with 12 or 24 V is presented. Furthermore, high overall efficiency of 82.5% at 55 W is achieved. Feasibility is demonstrated in a real application powering data acquisition electronics at high reference potential. Our new concept uses a coreless printed circuit board (PCB) transformer (15 cm × 10 cm × 4 cm and a weight of 480 g) designed for maximum efficiency via a coil layout and close proximity of adjacent coils on one PCB while reaching high isolation strength via the PCB material and potted coils. To increase efficiency, we investigated different coil geometries at different frequencies. A low-cost design consisting of two Qi charging coils mounted on one PCB is compared with our integrated PCB transformers manufactured from a four-layer PCB with ferrites applied on the outside. With this new design, high isolation voltages are possible while reaching high transformer efficiency of up to 90%. © 2022 by the authors. Licensee MDPI, Basel, Switzerland

Fast Readout of Split-Ring Resonators Made Simple and Low-Cost for Application in HPLC

Split-ring resonators (SRR) are simple electrical circuits that show a significant shift in resonance frequency even with the smallest changes in split capacitance, and thus in permittivity, electric conductivity, and dielectric losses of the split capacitor’s dielectric. Usually, the resonance frequency is derived from the frequency response, but recording the frequency spectrum takes a certain amount of time. Here, we present a new capillary split-ring resonator CaSRR with fast readout for liquid chromatography (LC), which is capable of accurately detecting very fast changes in split capacity. The proposed method is based on the detection of the transmitted signal at a single frequency that is analyzed by demodulation. The demodulated signal changes its amplitude depending on the shift of the resonance frequency. Our simple low-cost electronics enables an average sampling rate of 42 Hz with 128 averages of the demodulated signal and has a frequency stability of 840 mHz. Thus, a minimum change in permittivity of ∆εr,min = 11.26 × 10−3 can be detected. Finally, a chromatogram of one sugar (glucose) and one sugar alcohol (xylitol) is recorded using the SRR and is compared to a standard refractive index detector. © 2022 by the authors. Licensee MDPI, Basel, Switzerland

Regarding the Influence of Additives and Additional Plasma-Induced Chemical Ionization on Adduct Formation in ESI/IMS/MS

Ion mobility spectrometers (IMS) separate ions based on their ion mobility, which depends mainly on collision cross-section, mass, and charge of the ions. However, the performance is often hampered in electrospray ionization (ESI) by the appearance of multiple ion mobility peaks in the spectrum for the same analyte due to clustering and additional sodium adducts. In this work, we investigate the influence of solvents and buffer additives on the detected ion mobility peaks using ESI. Additionally, we investigate the effects of an additional chemical ionization (CI) induced by plasma ionization on the ions formed by electrospray. For this purpose, we coupled our high-resolution IMS with a resolving power of Rp = 100 to a time-of-flight mass spectrometer. Depending on the analyte and the chosen additives, the ionization process can be influenced during the electrospray process. For the herbicide isoproturon, the addition of 5 mM sodium acetate results in the formation of the sodium adduct [M + Na]+, which is reflected in the ion mobility K0 of 1.22 cm2/(V·s). In contrast, the addition of 5 mM ammonium acetate yields the protonated species [M + H]+ and a correspondingly higher K0 of 1.29 cm2/(V·s). In some cases, as with the herbicide pyrimethanil, the addition of sodium acetate can completely suppress ionizations. By carefully choosing the solvent additive for ESI-IMS or additional CI, the formation of different ion mobility peaks can be observed. This can facilitate the assignment of ions to ion mobility peaks using IMS as a compact, stand-alone instrument, e.g., for on-site analysis