Velocity Distribution Of Molecules Research Articles

From clusters of moving molecules to continua: Material elements as open systems

We discuss the discrete-to-continuum transition in the description of matter, starting from a cluster of flowing molecules with equal mass and ending up with a non-simple fluid. We account for the fluctuations beyond a local affine approximation of the velocity distribution of molecules within a space window adopted to compute some prominent statistics. The resulting continuum picture accounts for local mass variation in each space window corresponding to a point in the continuum scale. From a statistical viewpoint, every material element is thus considered as a grand-canonical ensemble. So-called C-derivatives account for macroscopic-to-mesoscopic relative motion. When considered for second-rank tensors, they extend Truesdell’s derivative and reduce to Oldroyd’s one when the macroscopic-to-mesoscopic relative motion vanishes. Fluctuations beyond an affine component best approximating the kinetic energy are summarized into a second-rank symmetric tensor whose time variation enters a balance equation governing transfer from velocity fluctuations to heat. Eventually, we discuss essential elements of thermodynamics in the present setting. What emerges is the possibility of a non-Fourier type heat transfer. The results address computational schemes for field representations of sparse phase dynamics, such as granular materials, and the one of bodies with transport of scattered molecules, such as pollutants in fluids or proteins in biological tissues.

Scattering Kernel Kinetic Approach of Small Particles Transport in a Free Molecular Regime in Gaseous Media

We investigated through the scattering kernel kinetic concept the transport of small particles in gaseous media in a free molecular regime. The scattering kernel is generally used to provide gas-surface interaction boundary conditions for Boltzmann kinetic equation in flow problems (Maxwell, Phil. Trans. R. Soc. 170, 231, 1879; Sharipov, 2001). We developed a general expression for the transport force explicitly in terms of the scattering kernel and of gas molecule velocity distribution function. From the general expression, first, we could use the first-order Chapman-Enskog solution for the distribution function of gas molecules f(r, v, t) which shows three types of transportation mechanisms, or forces, such that F = FD+FT+FS. Where FD is the drag force on the particle due to its relative motion in the gas, FT is the thermophoretic force due to a gradient of temperature in the gas, and FS is due to shear forces on the particle. Second, it is possible to use any of the several scattering kernel models published in the literature. The traditional simple reflection kernels, specular, diffuse, and Maxwell, which comprises particular cases of the generalized force, are limited and do not fully describe the real reflection mode of molecule-particle interaction. So, we used the general (Struchtrup, Phys. Fluids. 25, 112001, 2013) reflection kernel model to study the drag force on small particles. The results were compared with available experimental data. We concluded that it is necessary to explicitly include impact velocity and particle surface rugosity effects which are predicted by the Struchtrup reflection kernel thermal activation model of molecule-particle interaction.

Buffer-gas cooling of molecules in the low-density regime: comparison between simulation and experiment

Cryogenic buffer gas cells have been a workhorse for the cooling of molecules in the last few decades. The straightforward sympathetic cooling principle makes them applicable to a huge variety of different species. Notwithstanding this success, detailed simulations of buffer gas cells are rare, and have never been compared to experimental data in the regime of low to intermediate buffer gas densities. Here, we present a numerical approach based on a trajectory analysis, with molecules performing a random walk in the cell due to collisions with a homogeneous buffer gas. This method can reproduce experimental flux and velocity distributions of molecules emerging from the buffer gas cell for varying buffer gas densities. This includes the strong decrease in molecule output from the cell for increasing buffer gas density and the so-called boosting effect, when molecules are accelerated by buffer-gas atoms after leaving the cell. The simulations provide various insights which could substantially improve buffer-gas cell design.

The formula for the resistance force during slow motion of a sphere in an ideal gas

In this article the formula for the resistance force during slow motion of a sphere in an ideal equilibrium gas is discussed, taking into account the velocity distribution of molecules. Using the density function of the velocity distribution of molecules hitting the surface of the body during a certain period of time, an expression for the resistance force is obtained. The resulting expression is compared with the well-known expression in the Stokes law.

Influence of the noncondensable component on the characteristics of temperature change and the intensity of water droplet evaporation

The removal of vapor molecules from a droplet surface is an important stage of evaporation in a vapor–gas mixture. In this work, with the evaporation of a water droplet in a vapor–gas medium as the example, the influence of the noncondensable component on the intensity of the evaporation process and the characteristics of the temperature change is examined. The heat supplied to an interface is often assumed to be entirely utilized for evaporation, with the formed vapor removed from the evaporation surface through diffusion. However, the diffusion flux develops at a distance of some mean free paths of vapor molecules away from the evaporation surface, that is, in the Knudsen layer. In this layer, because of intermolecular collisions, the molecule–velocity distribution undergoes substantial changes, which are calculated using the methods of physical kinetics. Herein, the system of two Boltzmann kinetic equations for a vapor–gas mixture is used for calculating mass flux density of the evaporating substance near the evaporation surface. The calculation results are then compared with published experimental data.

Arrested relaxation in an isolated molecular ultracold plasma

Spontaneous avalanche to plasma splits the core of an ellipsoidal Rydberg gas of nitric oxide. Ambipolar expansion first quenches the electron temperature of this core plasma. Then, long-range, resonant charge transfer from ballistic ions to frozen Rydberg molecules in the wings of the ellipsoid quenches the centre-of-mass ion/Rydberg molecule velocity distribution. This sequence of steps gives rise to a remarkable mechanics of self-assembly, in which the kinetic energy of initially formed hot electrons and ions drives an observed separation of plasma volumes. These dynamics adiabatically sequester energy in a reservoir of mass transport, starting a process that anneals separating volumes to form an apparent glass of strongly coupled ions and electrons. Short-time electron spectroscopy provides experimental evidence for complete ionization. The long lifetime of this system, particularly its stability with respect to recombination and neutral dissociation, suggests that this transformation affords a robust state of arrested relaxation, far from thermal equilibrium.

Nonequilibrium kinetic boundary condition at the vapor-liquid interface of argon

A boundary condition for the Boltzmann equation (kinetic boundary condition, KBC) at the vapor-liquid interface of argon is constructed with the help of molecular dynamics (MD) simulations. The KBC is examined at a constant liquid temperature of 85 K in a wide range of nonequilibrium states of vapor. The present investigation is an extension of a previous one by Ishiyama, Yano, and Fujikawa [Phys. Rev. Lett. 95, 084504 (2005)] and provides a more complete form of the KBC. The present KBC includes a thermal accommodation coefficient in addition to evaporation and condensation coefficients, and these coefficients are determined in MD simulations uniquely. The thermal accommodation coefficient shows an anisotropic behavior at the interface for molecular velocities normal versus tangential to the interface. It is also found that the evaporation and condensation coefficients are almost constant in a fairly wide range of nonequilibrium states. The thermal accommodation coefficient of the normal velocity component is almost unity, while that of the tangential component shows a decreasing function of the density of vapor incident on the interface, indicating that the tangential velocity distribution of molecules leaving the interface into the vapor phase may deviate from the tangential parts of the Maxwell velocity distribution at the liquid temperature. A mechanism for the deviation of the KBC from the isotropic Maxwell KBC at the liquid temperature is discussed in terms of anisotropic energy relaxation at the interface. The liquid-temperature dependence of the present KBC is also discussed.

충격파 내에서 형성되는 아르곤 기체의 운동 에너지 분포와 속도 분포에 대한 비평형 분자동역학 모의실험 연구

A series of nonequilibrium molecular dynamics(NEMD) simulations are performed to investigate the kinetic energy and velocity distributions of molecules in shock waves. In the simulations, argon molecules are used as a medium gas through which shock waves are propagating. The kinetic energy distribution profiles reveals that as a strong shock wave whose Mach number is 27.1 is applied, 39.6% of argon molecules inside the shock wave have larger kinetic energy than molecular ionization energy. This indicates that an application of a strong shock wave to argon gas can give rise to an intense light. The velocity distribution profiles in z direction along which shock waves propagate clearly represent two Maxwell-Boltzmann distributions of molecular velocities in two equilibrium regions and one bimodal velocity distribution profile that is attributed to a nonequilibrium region. The peak appearing in the directional temperature in z direction is discussed on a basis of the bimodal velocity distribution in the nonequilibrium region.

A short pulse (7 μs FWHM) and high repetition rate (dc-5kHz) cantilever piezovalve for pulsed atomic and molecular beams

In this paper we report on the design and operation of a novel piezovalve for the production of short pulsed atomic or molecular beams. The high speed valve operates on the principle of a cantilever piezo. The only moving part, besides the cantilever piezo itself, is a very small O-ring that forms the vacuum seal. The valve can operate continuous (dc) and in pulsed mode with the same drive electronics. Pulsed operation has been tested at repetition frequencies up to 5 kHz. The static deflection of the cantilever, as mounted in the valve body, was measured as a function of driving field strength with a confocal microscope. The deflection and high speed dynamical response of the cantilever can be easily changed and optimized for a particular nozzle diameter or repetition rate by a simple adjustment of the free cantilever length. Pulsed molecular beams with a full width at half maximum pulse width as low as 7 micros have been measured at a position 10 cm downstream of the nozzle exit. This represents a gas pulse with a length of only 10 mm making it well matched to for instance experiments using laser beams. Such a short pulse with 6 bar backing pressure behind a 150 microm nozzle releases about 10(16) particles/pulse and the beam brightness was estimated to be 4x10(22) particles/(s str). The short pulses of the cantilever piezovalve result in a much reduced gas load in the vacuum system. We demonstrate operation of the pulsed valve with skimmer in a single vacuum chamber pumped by a 520 l/s turbomolecular pump maintaining a pressure of 5x10(-6) Torr, which is an excellent vacuum to have the strong and cold skimmed molecular beam interact with laser beams only 10 cm downstream of the nozzle to do velocity map slice imaging with a microchannel-plate imaging detector in a single chamber. The piezovalve produces cold and narrow (Delta v/v=2%-3%) velocity distributions of molecules seeded in helium or neon at modest backing pressures of only 6 bar. The low gas load of the cantilever valve makes it possible to design very compact single chamber molecular beam machines with high quality cold and intense supersonic beams. The high speed cantilever piezovalve may find broad applicability in experiments where short and strong gas pulses are needed with only modest pumping, the effective use of (expensive) samples, or the production of cold atomic and molecular beams.

Thermodynamics / turbulence analogy modelling dissipating molecular gas flows for high Knudsen numbers

AbstractModelling micro channel flows momentum and heat diffusion / convection are recent parameters modelling the molecule velocity distribution. Macroscopic models describe velocity and energy / enthalpie with integrals of mass increments. Using microscopic models motion and forces of a molecular flow have to be computed by models of physical properties, whose are described by statistical power moments of the molecule velocity. Therefore dilute flows have to be investigated in small channels with a mean free path length of molecules higher than the channel width of the the micro channel itself (λ0≥H0). Modelling this process by a continuous flow the boundary conditions have to be modified (e.g. [6]). The present model uses the statistical approximation of the molecule velocity distribution to simulate the behaviour of this discrete flow with a weighted averaged molecule velocity ∼ξi, its standard deviation σ and the characterisic molecule collision rate z. The number density N per volume V near one position is used for the weighting factor averaging method describing the mean molecule velocity. The present model is validated computing Poiseuille and Couette flows with different Knudsen numbers. Showing the advantages of the present model the simulation results are compared with simulation results of the wall–distance depending diffusivity model of Lockerby and Reese [4] and BGK results of a Lattice–Boltzmann simulation. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Velocity distribution of organic molecules emitted from effusion cells measured by time-of-flight technique

Velocity distribution of the molecules emitted from effusion cells commonly used in molecular beam epitaxy was measured by using time-of-flight technique. The result for organic molecular phthalocyanine can be fitted by a shifted Maxwellian distribution. The effects of the temperature and the aspect ratios of the sources are discussed.

State-Selective Angular and Velocity Distributions of Associatively Desorbing CuF Molecules Determined by CCD Imaging

The present contribution focuses on a new method of determining state-selective angular and velocity distributions of molecules desorbing from surfaces. It is based on the Doppler-resolved CCD imaging technique, i.e., exciting the molecules with an actively stabilized ring dye laser and imaging the fluorescence by a CCD camera. To analyze the two-dimensional images, a closed form mathematical procedure is used. The technique is applied to associatively desorbing CuF molecules in the reaction of molecular fluorine with copper surfaces. For all rovibrational CuF product levels investigated, the desorbing molecules exhibit a cosn θ, n = 1, distribution. Assuming that the velocity distributions of the desorbing CuF molecules are Maxwellian, the fitted translational temperatures are equal to the surface temperature within the error limits, proving an indirect reaction mechanism in agreement with previously determined internal state distributions [Bracker, A.; Jakob, P.; Näher, U.; Rüdiger, M.; Sugawara, K.; Wanner, J. Can. J. Chem. 1994, 72 (J. C. Polanyi Special Issue), 643].

Velocity distributions of molecules ejected in laser ablation

Based on the results of molecular dynamics simulations, we propose an analytical expression for the velocity distributions of molecules ejected in laser ablation. The Maxwell-Boltzmann distribution on a stream velocity, commonly used to describe the measured velocity distributions, is modified to account for a range of stream velocities in the ejected plume. The proposed distribution function provides a consistent description of the axial and radial velocity distributions. The function has two parameters that are independent of the desorption angle and have clear physical meaning, namely, the temperature of the plume and the maximum stream velocity or velocity of the plume propagation.

Problem of distribution moments in statistical physics

The statistical possibilities of studying intrasystem processes in multielement systems are determined by solving the problem of the moments of distributions specified in mathematical and physical formulations. The characteristic properties of the distributions can be revealed by analyzing the simple and product moments (integer, fractional, and functional) and the relationships between them. The proposed method of complex analysis of experimental data and theoretical calculations is illustrated using the examples of the Maxwellian velocity distribution of molecules, the Planck radiation spectral power distribution, and the size distribution of microscopic particles in a disperse-hardened alloy.

Light induced nonequilibrium effects in gases

AbstractIt is possible to disturb the equilibrium velocity distribution of molecules in a gas by absorption of narrow band laser light. This leads to light induced transport phenomena. We report on experiments, where we have measured the pressure difference caused by light induced viscous flow and where we have separated the two nuclear spin modifications of CH3F with the help of light induced drift.

Vibrational effects in the dissociation and scattering of hydrogen at a Cu(111) surface

We have determined dissociative chemisorption probabilities for D 2 on Cu(111) as a function of translational energy and angle of incidence for molecules in specific vibrational states. We find that the translational energy required for dissociation is reduced with increasing vibrational energy, falling from ≈0.6 eV for D 2(v=0) to ≈0.4 and 0.2 eV for molecules in v=1 and v=2 states, respectively. These results were obtained by combining molecular beam measurements of absolute adsorption probabilities with studies of the velocity distributions of molecules desorbed from the surface in specific quantum states. The observations indicate that vibrational and translational energy are strongly coupled by the potential energy surface for this system. This conclusion is supported by quantum-state-resolved scattering experiments that reveal direct vibrational excitation in collisions of H 2 and D 2 with a Cu(111) surface. The threshold for excitation of v=0 to v=1 is found to be similar for both molecules, and slightly higher than that for dissociation.

Dynamics of the desorption of D2 and H2 from Cu(111)

We have determined rotational and vibrational distributions for D2 and H2 desorbed from Cu(111) and have determined velocity distributions of the desorbed molecules for a wide range of vibrational and rotational states. The quantum state populations display strong deviations from a Boltzmann distribution, and the velocity distributions are highly supersonic with properties that depend strongly on quantum state. Molecules desorbed at 925 K were detected in a state-specific manner using laser ionization. Velocity distributions were obtained by measuring the flight times of D+2 ions in a field-free region. Vibrational populations of D2(v=1), D2(v=2), and H2(v=1) were found to be a factor of 20, 79, and 18 above that expected for equilibration at 925 K, respectively, relative to v=0 populations. Boltzmann plots of the rotational state distributions display distinct curvature, particularly for molecules in the ground vibrational state. H2 and D2 molecules in the ground vibrational state have mean kinetic energies of ∼0.6 eV for molecules in low rotational states. This energy was found to increase slightly with increasing J at low J, pass through a maximum at a rotational energy of ∼0.15 eV, and then fall as rotational energy is further increased. H2(v=1), D2(v=1), and D2(v=2) molecules have mean energies of ∼0.30, 0.45, and 0.25 eV, respectively. In each of these cases, the mean energy also varies significantly with rotational state. The velocity distributions of molecules in v=0 have a speed ratio of ∼0.35, which decreases with both increasing rotational and vibrational energy. Results are discussed in terms of a simple dynamical picture of desorption via an anisotropic potential energy barrier.

Interaction dynamics of hydrogen at a Cu(111) surface

We have used molecular beam and laser detection techniques to study the dynamics of adsorption and desorption of H 2 and D 2 at a Cu(111) surface. We have determined the adsorption probability for beams with kinetic energies up to 0.83 eV, vibrational temperatures up to 2300 K, and incidence angles from 0° to 60°. A detailed analysis of these data yields adsorption probability functions for molecules in individual vibrational states. We have also studied the internal state distribution of molecules scattered from the surface. These measurements provide state-resolved information on both adsorption and vibrational excitation. The adsorption and scattering studies have been complemented by studies of desorption dynamics, including preliminary measurements of the velocity distributions of molecules desorbed in specific quantum states. The desorption data are interpreted via the principle of detailed balance to give information on the temperature dependence of the adsorption probability functions. The vibrational dependence of the desorption velocity distributions reproduces trends predicted from the adsorption measurements.

Kinetics of heat transfer to a spherical particle from a rarefied plasma. 3. Maxwellian ion approximation

The authors describe the kinetics of heat transfer to a spherical particle from a rarefied plasma with a Maxwellian velocity distribution of molecules, electrons, and ions. 5 refs., 3 figs.

State specific velocity distribution of hydrogen isotopes desorbing from Pd(100)

Velocity distributions of recombinatively desorbing hydrogen molecules and their isotopic variants HD and D 2 have been determined with internal state selection using resonantly enhanced (VUV + UV) two-photon ionization spectroscopy. In the experiments the surface temperature of the permeation source is kept constant at various temperatures between 440 and 770 K. The velocity distributions of molecules desorbed from a clean Pd(100) surface are found to be Maxwell-Boltzmann like, but an isotope effect of the average kinetic energy is observed. The kinetic energy of hydrogen molecules agrees with that expected for molecules in thermal equilibrium with the surface. For deuterium molecules the average kinetic energy 〈 E kin〉 is about 10–30 meV higher than expected for molecules in a thermal equilibrium at T s . Within the experimental error bars no significant dependence of the average kinetic energies on the rovibrational states is detected. Preadsorption of sulfur leads to a non-Maxwell-Boltzmann velocity distribution with a significantly enhanced average kinetic energy.