Collision-free Sampling Research Articles

Imaging-Assisted Single-Photon Doppler-Free Laser Spectroscopy and the Ionization Energy of Metastable Triplet Helium.

Skimmed supersonic beams provide intense, cold, collision-free samples of atoms and molecules and are one of the most widely used tools in atomic and molecular laser spectroscopy. High-resolution optical spectra are typically recorded in a perpendicular arrangement of laser and supersonic beams to minimize Doppler broadening. Typical Doppler widths are nevertheless limited to tens of MHz by the residual transverse-velocity distribution in the gas-expansion cones. We present an imaging method to overcome this limitation that exploits the correlation between the positions of the atoms and molecules in the supersonic expansion and their transverse velocities, and thus their Doppler shifts. With the example of spectra of (1s)(np) ^{3}P_{0-2}←(1s)(2s) ^{3}S_{1} transitions to high Rydberg states of metastable triplet He, we demonstrate the suppression of the residual Doppler broadening and a reduction of the full linewidths at half maximum to only about 1MHz in the UV. Using a retroreflection arrangement for the laser beam and a cross-correlation method, we determine Doppler-free spectra without any signal loss from the selection, by imaging, of atoms within ultranarrow transverse-velocity classes. As an illustration, we determine the ionization energy of triplet metastable He and confirm the significant discrepancy between recent experimental [G. Clausen etal., Phys. Rev. Lett. 127, 093001 (2021)PRLTAO0031-900710.1103/PhysRevLett.127.093001] and high-level theoretical [V. Patkós etal., Phys. Rev. A 103, 042809 (2021)PLRAAN2469-992610.1103/PhysRevA.103.042809] values of this quantity.

Topological trajectory classification with filtrations of simplicial complexes and persistent homology

In this work, we present a sampling-based approach to trajectory classification which enables automated high-level reasoning about topological classes of trajectories. Our approach is applicable to general configuration spaces and relies only on the availability of collision free samples. Unlike previous sampling-based approaches in robotics which use graphs to capture information about the path-connectedness of a configuration space, we construct a multiscale approximation of neighborhoods of the collision free configurations based on filtrations of simplicial complexes. Our approach thereby extracts additional homological information which is essential for a topological trajectory classification. We propose a multiscale classification algorithm for trajectories in configuration spaces of arbitrary dimension and for sets of trajectories starting and ending in two fixed points. Using a cone construction, we then generalize this approach to classify sets of trajectories even when trajectory start and end points are allowed to vary in path-connected subsets. We furthermore show how an augmented filtration of simplicial complexes based on an arbitrary function on the configuration space, such as a costmap, can be defined to incorporate additional constraints. We present an evaluation of our approach in 2-, 3-, 4- and 6-dimensional configuration spaces in simulation and in real-world experiments using a Baxter robot and motion capture data.

Path planning for grasping operations using an adaptive PCA-based sampling method

The planning of collision-free paths for a hand-arm robotic system is a difficult issue due to the large number of degrees of freedom involved and the cluttered environment usually encountered near grasping configurations. To cope with this problem, this paper presents a novel importance sampling method based on the use of principal component analysis (PCA) to enlarge the probability of finding collision-free samples in these difficult regions of the configuration space with low clearance. By using collision-free samples near the goal, PCA is periodically applied in order to obtain a sampling volume near the goal that better covers the free space, improving the efficiency of sampling-based path planning methods. The approach has been tested with success on a hand-arm robotic system composed of a four-finger anthropomorphic mechanical hand (17 joints with 13 independent degrees of freedom) and an industrial robot (6 independent degrees of freedom).

D-Plan: Efficient Collision-Free Path Computation for Part Removal and Disassembly

We present a novel approach to compute a collision-free path for part disassembly simulation and virtual prototyping of part removal. Our algorithm is based on sample-based motion planning that connects collision-free samples in the configuration space using local planning. In order to effectively handle the tight-fitting scenarios, we describe techniques to generate samples in narrow passages and efficient local planning algorithms to connect them with collision-free paths. Our approach is general, makes no assumption about model connectivity or object topology, and can handle polygon soup models that frequently arise in CAD applications. We highlight the performance on many challenging benchmarks including the Alpha puzzle, maintainability of the windscreen wiper motion, and disassembly of a seat from the interior of a car body.

Direct Measurement and Theoretical Calculation of the Rate Coefficient for Cl + CH3 in the Range from T = 202−298 K

The rate coefficient has been measured under pseudo-first-order conditions for the Cl+CH3 association reaction at T=202, 250, and 298 K and P=0.3-2.0 Torr helium using the technique of discharge-flow mass spectrometry with low-energy (12-eV) electron-impact ionization and collision-free sampling. Cl and CH3 were generated rapidly and simultaneously by reaction of F with HCl and CH4, respectively. Fluorine atoms were produced by microwave discharge in an approximately 1% mixture of F2 in He. The decay of CH3 was monitored under pseudo-first-order conditions with the Cl-atom concentration in large excess over the CH3 concentration ([Cl]0/[CH3]0=9-67). Small corrections were made for both axial and radial diffusion and minor secondary chemistry. The rate coefficient was found to be in the falloff regime over the range of pressures studied. For example, at T=202 K, the rate coefficient increases from 8.4x10(-12) at P=0.30 Torr He to 1.8x10(-11) at P=2.00 Torr He, both in units of cm3 molecule-1 s-1. A combination of ab initio quantum chemistry, variational transition-state theory, and master-equation simulations was employed in developing a theoretical model for the temperature and pressure dependence of the rate coefficient. Reasonable empirical representations of energy transfer and of the effect of spin-orbit interactions yield a temperature- and pressure-dependent rate coefficient that is in excellent agreement with the present experimental results. The high-pressure limiting rate coefficient from the RRKM calculations is k2=6.0x10(-11) cm3 molecule-1 s-1, independent of temperature in the range from 200 to 300 K.

Study of the Partial Oxidation of Methanol to Formaldehyde on a Polycrystalline Ag Foil

A study of the partial oxidation reaction of methanol to formaldehyde has been carried out on the surface of an oxygen permeable, Ag-membrane. Surface oxygen species are formed on the high vacuum side of the Ag-foil by diffusion of O atoms generated by dissociative adsorption on the high pressure side at temperatures >500 K. Methanol pressures were kept sufficiently low (≤10-5 Torr) to ensure collision free sampling of the products using electron-impact mass spectrometry. Starting with a new Ag-foil, reaction rates were found to increase over time, with maximum rates achieved after activation times of several hours. Activation is accompanied by significant changes in membrane morphology. For a methanol pressure of 1 × 10-6 Torr, the maximum rate of formaldehyde formation is 7 × 1014 mol/s-cm2 at 900 K and only decreases by a factor of 2 as the foil temperature is reduced to 300 K. Reaction at room temperature is attributed to the high diffusion rate of O atoms dissolved in the bulk which maintains the surface oxygen concentration sufficiently high to achieve reaction rates of 5 × 1014 mol/s-cm2 for hours when the methanol pressure is held at 2 × 10-6 Torr. Attempts to titrate all the membrane O atoms through reaction with methanol were unsuccessful, and suggest that the loading must be greater than 1019 O atoms/gram of Ag.

Rate constant and RRKM product study for the reaction between CH3 and C2H3 at T = 298 K

The total rate constant k1 has been determined at P = 1 Torr nominal pressure (He) and at T = 298 K for the vinyl-methyl cross-radical reaction CH3 + C2H3 yields products. The measurements were performed in a discharge flow system coupled with collision-free sampling to a mass spectrometer operated at low electron energies. Vinyl and methyl radicals were generated by the reactions of F with C2H4 and CH4, respectively. The kinetic studies were performed by monitoring the decay of C2H3 with methyl in excess, 6 < |CH3|(sub 0)/|C2H3|(sub 0) < 21. The overall rate coefficient was determined to be k1(298 K) = (1.02 +/- 0.53)x10(exp -10) cubic cm/molecule/s with the quoted uncertainty representing total errors. Numerical modeling was required to correct for secondary vinyl consumption by reactions such as C2H3 + H and C2H3 + C2H3. The present result for k1 at T = 298 K is compared to two previous studies at high pressure (100-300 Torr He) and to a very recent study at low pressure (0.9-3.7 Torr He). Comparison is also made with the rate constant for the similar reaction CH3 + C2H5 and with a value for k1 estimated by the geometric mean rule employing values for k(CH3 + CH3) and k(C2H3 + C2H3). Qualitative product studies at T = 298 K and 200 K indicated formation of C3H6, C2H2, and C2H5 as products of the combination-stabilization, disproportionation, and combination-decomposition channels, respectively, of the CH3 + C2H3 reaction. We also observed the secondary C4H8 product of the subsequent reaction of C3H5 with excess CH3; this observation provides convincing evidence for the combination-decomposition channel yielding C3H5 + H. RRKM calculations with helium as the deactivator support the present and very recent experimental observations that allylic C-H bond rupture is an important path in the combination reaction. The pressure and temperature dependencies of the branching fractions are also predicted.

Temperature Dependence of the Rate Constant for the Reaction HCO + O2 → HO2 + CO at T = 200−398 K

The absolute rate constant for the reaction HCO + O2 has been measured over the temperature range T = 200−398 K in a discharge flow system at a pressure of 1 Torr (He). This study represents the first measurement of this rate constant at temperatures below T = 298 K. The decay of the HCO radical in the presence of excess O2 was followed by collision-free sampling photoionization mass spectrometry. The results were as follows: k1(200 K) = 5.3 ± 0.8, k1(222 K) = 4.8 ± 0.7, k1(250 K) = 4.4 ± 0.6, k1(298 K) = 4.0 ± 0.6, k1(398 K) = 4.5 ± 0.7 in units 10-12 cm3 molecule-1 s-1. Over the range T = 200−298 K, the data suggest a slight negative temperature dependence and may be represented by the Arrhenius expression k1 = (2.2 ± 0.2) × 10-12 exp[(170 ± 22)/T] cm3 molecule-1 s-1. For the related reaction HCO + NO at T = 298 K we measure k2 = (1.3 ± 0.2) × 10-11 cm3 molecule-1 s-1. The results are compared with previous direct measurements of k1 and k2 and with recent theoretical calculations. For the HCO + O2 reac...

The reaction between N(4S) and C2H3: Rate constant and primary reaction channels

The rate constant and the product branching ratios have been determined at T=298 K for the reaction between ground state atomic nitrogen (4S) and the vinyl radical (C2H3) at a nominal pressure of 1 Torr He. The kinetic technique employed was discharge-flow coupled to a collision-free sampling mass spectrometer. The rate constant was determined by monitoring the decay of the vinyl radical in the presence of excess [N], yielding a value for k(N+C2H3) of (7.7±2.9)×10−11 cm3 molecule−1 s−1. Three primary reaction channels have been experimentally observed: N+C2H3→C2H2+NH (1a), C2H2N+H (1b), and C2H3N (1c). The lowest energy isomers of the C2H2N radical and the C2H3N adduct molecule are CH2CN and CH3CN, respectively and their identification as products of the reaction is consistent with experimental results. Contributions from the higher energy isomers CH2NC or cyc-C2H2N in channel (1b) and CH3NC or H2C=C=NH in channel (1c) are not consistent with the experimental results and can be ruled out. Contribution from other higher energy isomers such as the radicals HC–CH=N, HC=C=NH and H2C=C=N in channel (1b) and the adduct species vinyl nitrene and 2H-azirine in channel (1c) cannot be ruled out in the absence of knowledge of heats of formation of the radical species and ionization energies for both the radical and adduct species. The following branching ratios were determined at T=298 K: Γ1a=0.16, Γ1c=0.04. No other potential products were detected. It can therefore be inferred that channel (1b) accounts for most if not all of the remaining products, i.e., Γ1b=0.80. The magnitude of the rate constant and the nature of the observed products for N+C2H3 are compared with those for the reactions N+CH3 and N+C2H5. The formation of the adduct molecule is considered in terms of initial formation of vinyl nitrene or 2H-azirine followed by a series of ring openings, ring closings, and an H atom transfer to yield the lowest energy isomer acetonitrile, CH3CN. The possible role of the N+C2H3 reaction in the atmospheric chemistry of Titan, Neptune, and Triton is briefly considered.

Rate constant and reaction channels for the reaction of atomic nitrogen with the ethyl radical

The absolute rate constant and primary reaction products have been determined at T=298 K for the atom–radical reaction N(4S)+C2H5 in a discharge flow system with collision-free sampling to a mass spectrometer. The rate constant measurements employed low energy electron impact ionization while the product study used dispersed synchrotron radiation as the photoionization source. The rate constant was determined under pseudo-first-order conditions by monitoring the decay of C2H5 or C2D5 as a function of time in the presence of excess N atoms. The result is k=(1.1±0.3)×10−10 cm3 molecule−1 s−1. For the reaction product experiments using photoionization mass spectrometry, products observed at 114 nm (10.9 eV) were CD3, D2CN and C2D4 for the N+C2D5 reaction. The product identification is based on the unambiguous combination of product m/z values, the shift of the m/z peaks observed for the N+C2D5 reaction products with respect to the N+C2H5 reaction products and the photoionization threshold measured for the major products. The observed products are consistent with the occurrence of the reaction channels D2CN+CD3(2a) and C2D4+ND(2c). Formation of C2D4 product via channel (2c) accounts for approximately 65% of the C2D5 reacted. Most, if not all, of the remaining 35% is probably accounted for by channel (2a). These rate constant and product results are compared with those for the N+CH3 reaction as well as other atom+C2H5 reactions. The role of the N+C2H5 reaction in the formation of HCN in the atmospheres of Titan and Neptune is briefly considered. In addition, the appearance energy for the formation of C2D+3 from C2D5 was determined from photoionization threshold measurements, AE0(C2D+3,C2D5)=239.5 kcal mol−1. From this, values are derived for the zero Kelvin heats of formation of C2D+3 (266 kcal mol−1) and C2D3 (71.6 kcal mol−1).

Rate constant for the reaction of N( 4S) with CH 3 AT 298 K

The absolute rate constant for the reaction of N( 4S) with CH 3 has been determined at 298 K in a discharge flow system coupled with collision-free sampling mass spectrometry at low electron energies. The rate constant was determined under pseudo-first-order conditions with [N] > [CH 3]. The result is k 1 = (8.6±2.0) × 10 −11 cm 3 s −1. This is compared to a previous estimated value as well as values of rate constants for other atom + radical reactions.

Rate constant for the reaction SO+BrO→SO2+Br

The rate of the radical–radical reaction SO+BrO→SO2+Br has been determined at 298 K in a discharge flow system near 1 Torr pressure with detection of SO and BrO via collision-free sampling mass spectrometry. The rate constant was determined using two different methods: measuring the decay of SO radicals in the presence of an excess of BrO and measuring the decay of BrO radicals in excess SO. The results from the two methods are in reasonable agreement and the simple mean of the two values gives the recommended rate constant at 298 K, k=(5.7±2.0) ×10−11 cm3 s−1. This represents the first determination of this rate constant and it is consistent with a previously derived lower limit based on SO2 formation. Comparison is made with other radical–radical reactions involving SO or BrO. The reaction SO+BrO→SO2+Br is of interest for models of the upper atmosphere of the Earth and provides a potential coupling between atmospheric sulfur and bromine chemistry.

Kinetic studies of the reaction of the SO radical with NO2 and ClO from 210 to 363 K

The rates of the reactions of the SO radical with NO2 and ClO have been determined in a discharge flow system near 1 Torr pressure with detection of radical and molecular species using collision-free sampling mass spectrometry. The rate constants were determined from the decay of SO radicals in the presence of an excess of NO2 and ClO. The NO2 reaction was studied between 210 and 363 K and found to be temperature invariant: SO+NO2→SO2+NO; k1=(1.37±0.10)×10−11 cm3 s−1. Similarly, the ClO reaction was observed to be independent of temperature in the interval from 248 to 363 K: SO+ClO→SO2+Cl; k2=(3.22±0.48)×10−11 cm3 s−1. Comparison is made with previous studies of these reactions at room temperature and with other radical–radical reactions involving SO or ClO.

Elementary reactions of the SF radical. Part 1.—Rate constants for the reactions F + OCS → SF + CO and SF + SF → SF2+ S

Elementary reactions involving ground-state SF(X2Π) radicals have been studied at 295 K in a discharge-flow system near 1 Torr‡ using mass-spectrometric detection with collision-free sampling. SF radicals were generated by the reaction of F(2PJ) atoms with OCS: F + COS [graphic omitted] SF + CO (1). Rate constants are reported for reaction (1) as well as for the bimolecular disproportionation of SF SF + SF [graphic omitted] SF2+ S (2a)k1=(1.81 ± 0.16)× 10–11; k2a=(2.52 ± 0.19)× 10–11 cm3 s–1(1σ).

Kinetic studies of diatomic free radicals using mass spectrometry. Part 4.—The Br + OClO and BrO + ClO reactions

In a kinetic study of the reaction of ground state Br 2P bromine atoms with chlorine dioxide, it has proved possible to determine not only the rate constant k–1a for the primary reaction, but also the rate constants k1a, k1b, for the various reactions of ClO with BrO radicals via different channels (1a) and (1b). The rate constants (cm3 molecule–1 s–1 at 298 K; error = 1.5σ) were as follows: [graphic omitted] The reaction kinetics were studied in a flow system using collision-free sampling of free radicals and stable molecules to a mass spectrometer. The thermochemistry and reaction kinetics of the XO + XO reactions (X = Cl, Br) are discussed. The ClO + ClO, BrO + BrO and BrO + ClO reactions are all thought to occur via related free radical channels, XO + XO ⇌ X + XOO. In addition, the ClO + ClO and BrO + ClO reactions occur through a similar and parallel channel, XO + XO ⇌ X + OXO.

Kinetic studies for diatomic free radicals using mass spectrometry. Part 3.—Elementary reactions involving BrO X2Π radicals

Elementary reactions involving BrO X2Π radicals have been studied at 298 K in a discharge-flow system linked to a mass spectrometer with collision-free sampling. Detection of BrO was made directly by means of the BrO+ ion current, calibrated in terms of absolute BrO concentrations using the rapid reaction (1), NO + BrO [graphic omitted] NO2+Br.(1) Rate constants at 298 K (cm3 molecule–1 s–1) are reported for the second order decay reaction (2), BrO + BrO [graphic omitted] 2 Br + O2(2) as well as for reaction (1): k1=(2.2 ± 0.4)× 10–11; k2=(6.4 ± 1.3)× 10–12 cm3 molecule s–1. In addition, the rate constant k3 for reaction of Br 2P3/2 atoms with O3(3), has been determined at 298 K: Br + O3 [graghic omitted] BrO + O2(3), k3=(1.2 ± 0.2)× 10–12 cm3 molecule–1 s–1.

The performance of a molecular beam mass-spectrometer sampling system

The salient features of the construction of a four-aperture molecular beam mass-spectrometer used for the collision-free sampling of unstable species are reported, together with detailed studies of the performance of the system. Five modifications of the aperture system, designed for sampling under various condition e.g. from a discharge at pressures near 0.1 mm Hg, or from flames at atmospheric pressure are considered. Performance studies indicated that, of the molecules ionised, more than 75% had arrived at the ionisation point from the first aperture without collision. The main source of molecules which had experienced wall or gas-phase collisions during sampling was the stationary pressure of sample gas in the ion-source compartment, which contributed 20% to the mass spectrum. The background sample gas in the first collimating chamber may also make a significant contribution to the mass spectrum. Scattering of the molecular beam in the first and second chambers resulted in some loss of beam intensity with some aperture systems and sampling conditions.

Theory and application of molecular beam techniques for the design of collision-free sampling systems

Theory and application of molecular beam techniques for the design of collision-free sampling systems

4. Theory and application of molecular beam techniques for the design of collision-free sampling systems: C. W. Nutt and A. J. Biddlestone, Trans. Faraday Soc., 58 (7), July 1962, 1363–1387

4. Theory and application of molecular beam techniques for the design of collision-free sampling systems: C. W. Nutt and A. J. Biddlestone, Trans. Faraday Soc., 58 (7), July 1962, 1363–1387

Theory and application of molecular-beam techniques for the design of collision-free sampling systems. Part 3.—Knocking-on collisions in the collimating chambers

Theory and application of molecular-beam techniques for the design of collision-free sampling systems. Part 3.—Knocking-on collisions in the collimating chambers