Physics of collisions

Flasted J B 964 Physics of Atomic Collisions (London Butterworth)... 

Now let us add the possibility of collisions. Before we proceed, we make the following two assumptions (1) only binary collisions occur, i.e. we rule out situations in which three or more hard-spheres simultaneously come together (which is a physically reasonable assumption provided that the gas is sufficiently dilute), and (2) Boltzman s Stosszahlansatz, or his molecular chaos assumption that the motion of the hard-spheres is effectively pairwise uncorrelated i.e. that the pair-distribution function is the product of individual distribution functions ... 

In its more advanced aspects, kinetic theory is based upon a description of the gas in terms of the probability of a particle having certain values of coordinates and velocity, at a given time. Particle interactions are developed by the ordinary laws of mechanics, and the results of these are averaged over the probability distribution. The probability distribution function that is used for a given macroscopic physical situation is determined by means of an equation, the Boltzmann transport equation, which describes the space, velocity, and time changes of the distribution function in terms of collisions between particles. This equation is usually solved to give the distribution function in terms of certain macroscopic functions thus, the macroscopic conditions imposed upon the gas are taken into account in the probability function description of the microscopic situation. 

Second Derivation of the Boltzmann Equation.—The derivation of the Boltzmann equation given in the first sections of this chapter suffers from the obvious defect that it is in no way connected with the fundamental law of statistical mechanics, i.e., LiouviUe s equation. As discussed in Section 12.6of The Mathematics of Physics and Chemistry, 2nd Ed.,22 the behavior of all systems of particles should be compatible with this equation, and, thus, one should be able to derive the Boltzmann equation from it. This has been avoided in the previous derivation by implicitly making statistical assumptions about the behavior of colliding particles that the number of collisions between particles of velocities v1 and v2 is taken proportional to /(v.i)/(v2) implies that there has been no previous relation between the particles (statistical independence) before collision. As noted previously, in a... 

Higher time moments of Km(0 are negative as well. This is physically accounted for by the anticorrelated nature of successive collisions in a gas [44], A collision from the front is usually followed by a collision from the back (Fig. 1.5). Owing to the opposite direction of collisions the product of the corresponding moments (M(O)M(t)) is negative, and it provides the main contribution to Km for times of order tj. This is a manifestation of the correlated character of the interaction between a molecule and perturbers. 

Lindholm, E., Second International Conference on the Physics of Electronic and Atomic Collisions, p. 177, W. A. Benjamin, New York, 1961. 

This is one of the fastest known reactions and occurs with nearly every collision to produce H3+, which has been seen in diffuse and giant molecular clouds. However, because the rate of reaction is so fast the detection of H2+ is going to be unlikely as it is quickly removed by the chemistry. Once H3+ is formed it quickly protonates a number of species, particularly CO to form HCO+ and also O to form OH+, leading to the other ions containing protons seen in Table 5.1. The construction of networks of possible reactions requires a knowledge of the fundamental chemical physics of molecules and the possible chemistry in the local environment. 

Luding, S., Collisions contacts between two particles, in Physics of Dry Granular Media (H. J. Herrmann, J. P. Hovi, and S. Luding Eds.), p. 1-19. Kluwer Academic Publishers, Dordrecht (1998) Chpt. 5. 

Nowadays it is widely accepted that there should be realized various phases of QCD in temperature (T) - density (ftp,) plane. When we emphasize the low T and high pp region, the subjects are sometimes called physics of high-density QCD. The main purposes in this field should be to figure out the properties of phase transitions and new phases, and to extract their symmetry breaking pattern and low-energy excitation modes there on the basis of QCD. On the other hand, these studies have phenomenological implications on relativistic heavy-ion collisions and compact stars like neutron stars or quark stars. 

Physical state of reactants—When reactants are mixed in the same physical state, the reaction rates should be higher than if they are in different states, because there is a greater chance of collision. Also, gases and liquids tend to react faster than solids because of the increase in surface area. The more chance for collision, the faster the reaction rate. 

The rate of the reaction is related to probability of the reactants meeting in order to react. Therefore, the concentration of the reactants has an effect, because the probability of the reactants meeting is higher in a concentrated solution than in a dilute solution. Similarly, physical parameters such as agitation and temperature, that increase the rate of diffusion and molecular motion and therefore increase the probability of collisions, will also increase the rate of reaction. 

Because the collisions between ions and molecules in the gas phase are governed by physical (ion-dipole, ion-induced dipole) rather than chemical forces, it is possible to calculate rather accurately the collision rate constant (6, 7). We then express the efficiency of the reaction as the fraction of collisions which lead to products. 

Hatano, Y. Dissociation dynamics of superexcited molecules. In The Physics of Electronic and Atomic Collisions, Dube, L.J. Mitchell, J.B.A. McConkey, J.W. Brion, C.E. AIP Press New York, 1995 67 p. 

In this Chapter, we consider the theory of collision-induced absorption by rare gas mixtures. We look at various theoretical efforts and compare theoretical predictions and computations with measured spectra and other experimental facts. The theory of induced absorption is based on quantum mechanics, but in certain cases, the use of classical physics may be justified, or indeed be the only viable choice. The emphasis will be on the computation of induced absorption by non-reactive, small atomic systems in the infrared. Diatomic and triatomic systems show most of the features of collisional absorption without requiring complex theory for their treatment. The theory of induced absorption of small clusters involving molecules will be considered in Chapter 6. 

G. Birnbaum, B. Guillot and S. Bratos, Theory of Collision-induced Line Shapes - Absorption and Light Scattering at Low Densities, in Advances in Chemical Physics, vol. 51, I. Prigogine and S. A. Rice, eds., Wiley, New York, 1982. 

M. Moraldi and L. Frommhold. Second and third virial coefficients of collision-induced absorption and light scattering. J. J. C. Teixeira-Dias, ed., Molecular Liquids New Perspectives in Physics and Chemistry,... 

TJhe aggregation of particles in a colloidal dispersion proceeds in two distinct reaction steps. Particle transport leads to collisions between suspended colloids, and particle destabilization causes permanent contact between particles upon collision. Consequently, the rate of agglomeration is the product of the collision frequency as determined by conditions of the transport and the collision efficiency factor, the fraction of collisions leading to permanent contact, which is determined by conditions of the destabilization step (2). Particle transport occurs either by Brownian motion (perikinetic) or because of velocity gradients in the suspending medium (orthokinetic). Transport is characterized by physical parame-... 

The rate constant kp is given in terms of physical parameters (Boltzmann Constant KB, the absolute temperature T, and the absolute viscosity rj) that characterize these transport conditions. In the case of not completely destabilized colloids, when according to v. Smoluchowski so-called slow coagulation is observed, the rate constant contains in addition the collision efficiency factor, p, the fraction of collisions leading to permanent attachment under perikinetic conditions ... 

The conservation of energy and momentum is the fundamental requirement which determines the behavior of the SE s in metals, semiconductors, and ionic compounds irradiated by particles. Although we shall not deal with the basic physics of elementary collision processes in our context of chemical kinetics, let us briefly summarize some important results of collision dynamics which we need for the further discussion. If a particle of mass mP and (kinetic) energy EP collides with a SE of mass ms in a crystal, the fraction of EP which is transferred in this collision process to the SE is given by... 

J. B. Hasted, Physics of Atomic Collisions, Butterworth, Washington, D < 1964. 

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