Collision , elastic molecular

Nevertheless, the given momentum flux formula (2.368) is not useful before the unknown average velocity after the collisions v( has been determined. For elastic molecular collisions this velocity can be calculated, in an averaged sense, from the classical momentum conservation law and the definition of the center of mass velocity as elucidated in the following. 

Hard sphere elastic cross sections [o.-] have been obtained from averaged molecular force constant as determined from experimental equation of state and transport property data (t6.77). The 2h.2 value for represents the self-collision elastic cross section for Ne. The mixed,values for vs. Hg, Ar and... 

In the literature the net momentum flux transferred from molecules of type s to molecules of type r has either been expressed in terms of the average diffusion velocity for the different species in the mixture [109] or the average species velocity is used [148]. Both approaches lead to the same relation for the diffusion force and thus the Maxwell-Stefan multicomponent diffusion equations. In this book we derive an approximate formula for the diffusion force in terms of the average velocities of the species in the mixture. The diffusive fluxes are introduced at a later stage by use of the combined flux definitions. Nevertheless, the given momentum flux formula (2.537) is not useful before the unknown average velocity after the collisions v has been determined. For elastic molecular collisions this velocity can be calculated, in... 

The first molecular dynamics simulation of a condensed phase system was performed by Alder and Wainwright in 1957 using a hard-sphere model [Alder and Wainwright 1957]. In this model, the spheres move at constant velocity in straight lines between collisions. All collisions are perfectly elastic and occur when the separation between the centres of... 

Molecular collisions are elastic, which means that although the molecules transfer energy from one to another, as a whole they do not lose kinetic energy when they collide with each other or with the walls of their container. 

Electrons of still lower energy have been called subvibrational (Mozumder and Magee, 1967). These electrons are hot (epithermal) and must still lose energy to become thermal with energy (3/2)kBT — 0.0375 eV at T = 300 K. Subvibrational electrons are characterized not by forbiddenness of intramolecular vibrational excitation, but by their low cross section. Three avenues of energy loss of subvibrational electrons have been considered (1) elastic collision, (2) excitation of rotation (free or hindered), and (3) excitation of inter-molecular vibration (including, in crystals, lattice vibrations). 

Elastic collision, determined by mass ratio, is a very inefficient process. By default, it is the only available mechanism in rare gases. Rotations are not easily excited in nonpolar molecules, especially in the condensed phase. They can be a contributing factor in molecular gases (vide infra). In polar media, rotations are an important degradation mechanism (Frohlich and Platzman, 1953). 

The Chapman-Enskog equation (see Chapman and Cowling, 1970) is semi-empirical because it uses equation (3.11) and adjusts it for errors in the observations of diffusivity in gases. It also includes a parameter, S2, to account for the elasticity of molecular collisions ... 

Stationary) and the other is moving, and if its trajectory crosses the location of the other object, the energy of the moving object is distributed between the two. If the collision is perfectly elastic the energy remains with the moving ball—if it is inelastic some level of energy transfer will take place. We observe very similar type of events at the molecular level when photons collide with atoms or molecules. 

Here t0 is an average vibrational period in a surface potential well having a value of the order of subpicoseconds for a simple molecule, and U() is a depth of the potential, which strongly depends on the type of interaction. For strong interaction, t exceeds 1 s or more, while in the case of no interaction, such as elastic collision, it is less than T(>. If we assume the Lennard-Jones potential for the interaction potential and expand it at the equilibrium position r0, t() is given by relevant molecular parameters as... 

All gas particles have some volume. All gas particles have some degree of interparticle attraction or repulsion. No collision of gas particles is perfectly elastic. But imperfection is no reason to remain unemployed or lonely. Neither is it a reason to abandon the kinetic molecular theory of ideal gases. In this chapter, you re introduced to a wide variety of applications of kinetic theory, which come in the form of the so-called gas laws. ... 

The quantum theory of molecular collisions in external fields described in this chapter is based on the solutions of the time-independent Schrodinger equation. The scattering formalism considered here can be used to calculate the collision properties of molecules in the presence of static electric or magnetic fields as well as in nonresonant AC fields. In the latter case, the time-dependent problem can be reduced to the time-independent one by means of the Floquet theory, discussed in the previous section. We will consider elastic or inelastic but chemically nonreac-tive collisions of molecules in an external field. The extension of the formalism to reactive scattering problems for molecules in external fields has been described in Ref. [12]. 

Estimates of the rotational diffusivity may be made from MD calculations by fitting an exponential function to Legendre polynomials that express the decorrelation of a unit vector that is fixed in the methane coordinate frame (11). The rotational diffusivity was found to increase with concentration (as a result of sorbate-sorbate collisions which act to decorrelate the molecular orientation). The values are of the same order as those for liquid methane and are 2 orders of magnitude larger than those found by Jobic et al. (73) from a quasi-elastic neutron scattering study of methane in NaZSM-5. 

Raman spectra. In a collision between a photon and a molecule, the photon may undergo elastic collision in which the photon loses no energy but changes its direction of travel. Such scattering is known as Rayleigh scattering and forms the basis for a method of molecular mass determination. Sometimes inelastic collisions occur in which both the... 

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