Velocity distribution 592 molecular

Molecular structure, experimental determination of, 324 Molecular velocities, distribution of, 131... 

Highly exothermic chemical reactions can give ions as products. Such reactions are called chemi-ionization reactions. When one or more of the reactants are formed by pulsed photolysis, and the ion product(s) are time-resolved with a mass spectrometer, this comprises a FPTRMS experiment. The ions can be extracted by a biased pair of electrodes, one of which has an aperture through which ions pass to enter a quadrupole mass spectrometer. The time resolution of this experiment is superior to FPTRMS experiments between neutrals, since the ion velocities are set by the electrode bias voltage, and the thermal molecular velocity distribution limitation is no longer a factor. With modest electrode bias voltages, the detection time can be as short as 2 /is. 

The thermodynamic equilibrium of the system was controlled by examining the molecular velocity distribution (MVD) and the first-neighbor distribution. In the case where only a first-neighbor interaction is present, the latter, as will be shown in Section IV, has an analytical expression given by... 

The molecular velocity distribution was monitored by averaging over the total number of time steps and all the particles. It was foimd to reproduce the Maxwell distribution relative to the average temperature of the system (the value of (v y/(v ) - was about 0.01). We wish to point out, however, that the thermalization in the one-dimensional case offered some difficulties, in contrast with the two-dimensional case, where it requires usually only a few hundred time steps. This occurred principally at low densities where the collisions between the particles are mainly binary collisions. In this case, with our starting conditions, the distribution was found to be... 

Therefore, the conceptual ideas of kinetic theory rely on the assumption that the mean flow, transport and thermodynamic properties of a collection of gas molecules can be obtained from the knowledge of their masses, number density, and a probabilistic velocity distribution function. The gas is thus described in terms of the distribution function which contains information of the spatial distributions of molecules, as well as about the molecular velocity distribution, in the system under consideration. 

The standard theories of chemical kinetics are equilibrium theories in which a Maxwell-Boltzmann energy (or momentum or internal coordinate) distribution of reactants is postulated to persist during a reaction. In the collision theory, mainly due to Hinshelwood,7 the number of energetic, reaction producing collisions is calculated under the assumption that the molecular velocity distribution always remains Maxwellian. In the absolute... 

In a molecular gas, collisions represent a mighty mechanism for energy redistribution between available degrees of freedom of the molecules which results in establishing an almost isotropic molecular velocity distribution irrespective of the... 

Moore, S.B., Carr, R.W. (1977) Molecular Velocity Distribution Effects in Kinetic Studies by Time-resolved Mass Spectrometry. Int. J. Mass Spectrom. Ion Phys. 24 161-171. 

Taatjes, C.A. (2007) How Does the Molecular Velocity Distribution Affect Kinetics Measurements by Time-resolved Mass Spectrometry Int. J. Chem. Kinet. 39 565-570. 

Fig. 3.7 Observation of a narrow saturation resonance by use of a single strong coherent traveling wave and a countertraveling weak probe wave, (a) Experimental arrangement. A small part of the intense wave is reflected back through the cell. The attenuation of this weak wave is studied as a function of the laser-field frequency, (b) Molecular velocity distribution, showing velocity groups that interact resonantly with the strong wave and the probe wave, (c) Absorption of probe wave as a function of frequency.

In a series of impressive publications. Maxwell [95-98] provided most of the fundamental concepts constituting the statistical theory recognizing that the molecular motion has a random character. When the molecular motion is random, the absolute molecular velocity cannot be described deterministically in accordance with a physical law so a probabilistic (stochastic) model is required. Therefore, the conceptual ideas of kinetic theory rely on the assumption that the mean flow, transport and thermodynamic properties of a collection of gas molecules can be obtained from the knowledge of their masses, number density, and a probabilistic velocity distribution function. The gas is thus described in terms of the distribution function which contains information of the spatial distributions of molecules, as well as about the molecular velocity distribution, in the system under consideration. An important introductory result was the Maxwellian velocity distribution function heuristically derived for a gas at equilibrium. It is emphasized that a gas at thermodynamic equilibrium contains no macroscopic gradients, so that the fluid properties like velocity, temperature and density are uniform in space and time. When the gas is out of equilibrium non-uniform spatial distributions of the macroscopic quantities occur, thus additional phenomena arise as a result of the molecular motion. The random movement of molecules from one region to another tend to transport with them the macroscopic properties of the region from which they depart. Therefore, at their destination the molecules find themselves out of equilibrium with the properties of the region in which they arrive. At the continuous macroscopic level the net effect... 

Maxwell molecular velocity distribution molecule kinetic energy distribution free fall acceleration vector gyromagnetic ratio, Lande factor vector of magnetic field strength Planck s constant Miller indexes... 

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