Molecular collisions cross sections

Based on the molecular collision cross-section, a particle might undergo a collision with another particle in the same cell. In a probabilistic process collision partners are determined and velocity vectors are updated according to the collision cross-section. Typically, simple parametrizations of the cross-section such as the hard-sphere model for monoatomic gases are used. 

C.F. Barnett et al., Atomic and Molecular Collision Cross-Sections of Interest in Controlled Thermonuclear Research, ORNL-3113 (1961) revised In ORNL-3113 (1964). (Oak Ridge National Laboratory, Oak Ridge, Term., USA 1961, 1964)... 

If we employ average values for molecular collision cross sections of about 20 X 10 i cm this reduces to (M in atm) ... 

What is steric repulsion The generic term refers to the space-filling property of atoms and molecules, as manifested in crystal packing densities, molecular collision cross-sections, and other lines of experimental evidence. Indeed, space-filling molecular models are among the most useful tools of the chemistry studenL and atomic radii are among the first properties called to the student s attention to illustrate atomic periodicity trends. 

A second type of gas phase collision is that occurring between the various (heavy) species generated by electron impact reactions, as well as between these species and the unreacted gas-phase molecules (25,2d). Again, dissociation and ionization processes occur, but in addition, recombination and molecular rearrangements are prevalent. Similar rate expressions to that of Equation 2 can be written for these collisions (27). In this case, the concentration of each chemical species, along with the collision cross section, and the species energy distribution function must be known if k is to be calculated. Clearly, much of this information is presently unknown. 

The mean free path X, of a molecule in air can be calculated from the sizes of the molecules involved. The most probable collision partners for a trace molecule (such as CFC-12) in air are molecular nitrogen (N2) and oxygen (02). The trace molecule i is hit whenever its center gets closer to the center of an air molecule than the critical distance, rcrit = r, + rair (Fig. 18.8). Picturing the molecules as spheres, the molecular radius r, can be estimated from the collision cross-section A listed in chemical handbooks such as the Tables of Physical and Chemical Constants (Longman, London, 1973) ... 

Such so-called spin-exchange collisions may be experimentally distinguished only if the experiment involves measurement of differences due to spin interactions. For instance, collision cross-sections for eq. (6-5) might be measured with crossed molecular beams using spin polarizing magnetic fields. 

The molecular collision is the basic mechanism that governs the transport processes in gases. Thus, it is necessary to examine the collision frequency and collision cross section before quantifying the transport coefficients. First consider the probability that a collision occurs between r and r + dr. Denote A. as the mean free path and P(r) as the probability of no collisions within r. Hence, we have... 

The kinetic theory of gases was briefly discussed. It enables the mean or thermal velocity (c) of gas molecules at a given temperature to be obtained and gas flux to be calculated. From the latter, effusion rates, area-related condensation rates and conductances under molecular flow can be determined (see Examples 1.5 and 1.7-1.10). Calculation of collision frequency (obtained from c, n and the collision cross-section of molecules), enables the mean free path (f) of particles to be determined. The easily obtained expression for Ip is a convenient way of stating the variation of / withp (Examples 1.11-1.15). 

The concept of potential-energy surface (or just potentials) is of major importance in spectroscopy and the theoretical study of molecular collisions. It is also essential for the understanding of the macroscopic properties of matter (e.g., thermophysical properties and kinetic rate constants) in terms of structural and dynamical parameters (e.g., molecular geometries and collision cross sections). Its role in the interpretation of recent work in plasmas, lasers, and air pollution, directly or otherwise related to the energy crisis, makes it of even greater value. 

As already noted in the Introduction, such a behavior can be attributed to two contrary effects. For small particles, i.e., particle sizes in the transition and free molecular range, the potential well is not deep whereas the decay length of the potential is greater than the particle size. Therefore, the collisions may be less effective because of the shallow potential well (i.e., the sticking probability may be less than unity), whereas the rate of collisions between the particles may increase because of the increase in the effective collision cross section caused by the increased... 

In a similar way, in the atomic or molecular case, we allow a beam of colliding particles to strike the atoms or molecules that we wish to investigate. A certain number of the particles in the incident beam will pass by without collision, while a certain number will collide and be deflected. We count the fraction colliding, divide this fraction by the number of particles with which they could have collided, and the result is the collision cross section. This can plainly be made the basis of an experimental method of measuring collision cross sections. We start a beam... 

Utilization of both ion and neutral beams for such studies has been reported. Toennies [150] has performed measurements on the inelastic collision cross section for transitions between specified rotational states using a molecular beam apparatus. T1F molecules in the state (J, M) were separated out of a beam traversing an electrostatic four-pole field by virtue of the second-order Stark effect, and were directed into a noble-gas-filled scattering chamber. Molecules which were scattered by less than were then collected in a second four-pole field, and were analyzed for their final rotational state. The beam originated in an effusive oven source and was chopped to obtain a velocity resolution Avjv of about 7 %. The velocity change due to the inelastic encounters was about 0.3 %. Transition probabilities were calculated using time-dependent perturbation theory and the straight-line trajectory approximation. The interaction potential was taken to be purely attractive ... 

We have shown that combining ion mobility spectrometry (IMS) equipment with mass spectrometry (MS) provides a powerful tool to examine the three-dimensional structure of polyatomic ions by measuring collision cross sections of mass identified ions. The technique is particularly useful in conjunction with molecular modeling or electronic structure calculations. Further, we have reviewed applications where the IMS-MS equipment is used to obtain kinetic and thermo chemical data of ions. 

Figure 3.3-15 Typical molecular cross-sections Scoll collision cross-section, Suv, Sm, Sg, cross-section for UV, IR, and Raman spectroscopy.

Moerkerken et al. (1970) applied an RF field to H 2-molecules of a molecular beam passing through a fairly conventional arrangement of A-, B- and C-fields. Molecules in a well-defined rotational state undergo a transition into a state with different Zeeman-effect when they pass through the C-field where the RF field is applied (see Fig. 2). This combination of deflecting fields and spectroscopic techniques permits the production of a beam of preferentially oriented non-polar molecules. The scattering chamber is also shown in Fig. 2 where the beam of selected molecules can be attenuated for determination of the total collision cross section. 

The structure of shock fronts in simple molecular gases such as N2 and O2 has been studied since the 1950 s [1,121]. Kinetic theory provides a powerful framework for analyzing gas-phase shock fronts, and a wealth of data exists to characterize collisional processes in gases. Kinetic theory provides a characteristic length scale to describe the shock front, the mean-free path A, = 2 po, where o is the collision cross-section. For N2 at STP, A. = 65 nm and the average time between collisions is 140 ps. The undisturbed molecules ahead of the shock front are hit by a stream of molecules having a net velocity along the... 

The collision cross-section a is related to effective molecular diameters by a = nd2 so d =, a(ji)112... 

Fig. 13. Electron energy dependence of collision cross section for representative electron impact processes with molecular chlorine. Note threshold energy for endothermic processes (vibrational excitation, ionization, etc.). Qa, Qd, Qe, Qi, Qm. and Qv, correspond to electron attachment (reaction R18 in Table 4), dissociation (R19), electronic excitation (R12), momentum transfer (R20), ionization (R16) and vibrational excitation (not shown in Table 4), respectively. After [44].

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