Collision mean free path

Plasma-arc diamond deposition is produced at a higher pressure than in a microwave plasma (0.15 to 1 atm). At such pressure, the average distance traveled by the species between collisions (mean free path) is reduced and, as a result, molecules and ions collide more frequently and heat more readily. 

Thus the parameter S s 1/X, the reciprocal of the average distance to collision (mean free path) or, saying it in another way... 

The average distance that a molecule travels between collisions is its mean free path. At room temperature and atmospheric pressure, the mean free path of a nitrogen molecule with a molecular diameter of 300 pm (four times the covalent radius) is 93 mn, or about 310 molecular diameters. If the nitrogen molecule were the size of a golf baU, it would travel about 40 ft between collisions. Mean free path increases with decreasing pressure. Under conditions of ultrahigh vacuum (10 ° torr), the mean free path of a nitrogen molecule is hundreds of kilometers. 

We are now going to use this distribution fiinction, together with some elementary notions from mechanics and probability theory, to calculate some properties of a dilute gas in equilibrium. We will calculate tire pressure that the gas exerts on the walls of the container as well as the rate of eflfiision of particles from a very small hole in the wall of the container. As a last example, we will calculate the mean free path of a molecule between collisions with other molecules in the gas. 

The average time between collisions is then v and in this time tlie particle will typically travel a distance X, the mean free path, where... 

This is the desired result. It shows that the mean free path is mversely proportional to the density and the collision cross section. This is a physically sensible result, and could have been obtained by dimensional... 

If we wish to know the number of (VpV)-collisions that actually take place in this small time interval, we need to know exactly where each particle is located and then follow the motion of all the particles from time tto time t+ bt. In fact, this is what is done in computer simulated molecular dynamics. We wish to avoid this exact specification of the particle trajectories, and instead carry out a plausible argument for the computation of r To do this, Boltzmann made the following assumption, called the Stosszahlansatz, which we encountered already in the calculation of the mean free path ... 

When Che diameter of the Cube is small compared with molecular mean free path lengths in che gas mixture at Che pressure and temperature of interest, molecule-wall collisions are much more frequent Chan molecule-molecule collisions, and the partial pressure gradient of each species is entirely determined by momentum transfer to Che wall by mechanism (i). As shown by Knudsen [3] it is not difficult to estimate the rate of momentum transfer in this case, and hence deduce the flux relations. 

The Stefan-Maxwell equations have been presented for the case of a gas in the absence of a porous medium. However, in a porous medium whose pores are all wide compared with mean free path lengths it is reasonable to guess that the fluxes will still satisfy relations of the Stefan-Maxwell form since intermolecular collisions still dominate molecule-wall collisions. 

In a cascade process, one incident electron (e ) collides with a neutral atom ((S)) to produce a second electron and an ion ( ). Now there are two electrons and one ion. These two electrons collide with another neutral atom to produce four electrons and three ions. This process continues rapidly and — after about 20 successive sets of collisions — there are millions of electrons and ions. (The mean free path between collisions is very small at atmospheric pressures.) A typical atmospheric-pressure plasma will contain 10 each of electrons and ions per milliliter. Some ions and electrons are lost by recombination to reform neutral atoms, with emission of light. 

In a vacuum (a) and under the effect of a potential difference of V volts between two electrodes (A,B), an ion (mass m and charge ze) will travel in a straight line and reach a velocity v governed by the equation, mv = 2zeV. At atmospheric pressure (b), the motion of the ion is chaotic as it suffers many collisions. There is still a driving force of V volts, but the ions cannot attain the full velocity gained in a vacuum. Instead, the movement (drift) of the ion between the electrodes is described by a new term, the mobility. At low pressures, the ion has a long mean free path between collisions, and these may be sufficient to deflect the ion from its initial trajectory so that it does not reach the electrode B. 

Effusion separator (or effusion enricher). An interface in which carrier gas is preferentially removed from the gas entering the mass spectrometer by effusive flow (e.g., through a porous tube or through a slit). This flow is usually molecular flow, such that the mean free path is much greater than the largest dimension of a traverse section of the channel. The flow characteristics are determined by collisions of the gas molecules with surfaces flow effects from molecular collisions are insignificant. 

Vacuum Flow When gas flows under high vacuum conditions or through very small openings, the continuum hypothesis is no longer appropriate if the channel dimension is not very large compared to the mean free path of the gas. When the mean free path is comparable to the channel dimension, flow is dominated by collisions of molecules with the wall, rather than by colhsions between molecules. An approximate expression based on Brown, et al. J. Appl. Phys., 17, 802-813 [1946]) for the mean free path is... 

The mean free path, which is die average distance a molecule navels between collisions, is... 

The inelastic collision process is characterized by an inelastic mean free path, which is the distance traveled after which only 1/e of the Auger electrons maintain their initial energy. This is very important because only the electrons that escape the sample with their characteristic Auger energy are usefrd in identifying the atoms in... 

Mean free path The average distance travelled by a particle between collisions. In a gas it is inversely proportional to the pressure. 

Static defects scatter elastically the charge carriers. Electrons do not loose memory of the phase contained in their wave function and thus propagate through the sample in a coherent way. By contrast, electron-phonon or electron-electron collisions are inelastic and generally destroy the phase coherence. The resulting inelastic mean free path, Li , which is the distance that an electron travels between two inelastic collisions, is generally equal to the phase coherence length, the distance that an electron travels before its initial phase is destroyed ... 

The assumption that the probability of simultaneous occurrence of two particles, of velocities vt and v2 in a differential space volume around r, is equal to the product of the probabilities of their occurrence individually in this volume, is known as the assumption of molecular chaos. In a dense gas, there would be collisions in rapid succession among particles in any small region of the gas the velocity of any one particle would be expected to become closely related to the velocity of its neighboring particles. These effects of correlation are assumed to be absent in the derivation of the Boltzmann equation since mean free paths in a rarefied gas are of the order of 10 5 cm, particles that interact in a collision have come from quite different regions of gas, and would be expected not to interact again with each other over a time involving many collisions. 

Moreover, since the mean free path is of the order of 100 times the molecular diameter, i.e., the range of force for a collision, collisions involving three or more particles are sufficiently rare to be neglected. This binary collision assumption (as well as the molecular chaos assumption) becomes better as the number density of the gas is decreased. Since these assumptions are increasingly valid as the particles spend a larger percentage of time out of the influence of another particle, one may expect that ideal gas behavior may be closely related to the consequences of the Boltzmann equation. This will be seen to be correct in the results of the approximation schemes used to solve the equation. 

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