Particles collision theory

This chapter deals with qnantal and semiclassical theory of heavy-particle and electron-atom collisions. Basic and nsefnl fonnnlae for cross sections, rates and associated quantities are presented. A consistent description of the mathematics and vocabnlary of scattering is provided. Topics covered inclnde collisions, rate coefficients, qnantal transition rates and cross sections. Bom cross sections, qnantal potential scattering, collisions between identical particles, qnantal inelastic heavy-particle collisions, electron-atom inelastic collisions, semiclassical inelastic scattering and long-range interactions. 

In chemical kinetics, it is often important to know the proportion of particles with a velocity that exceeds a selected velocity v. According to collision theories of chemical kinetics, particles with a speed in excess of v are energetic enough to react and those with a speed less than v are not. The probability of finding a particle with a speed from 0 to v is the integral of the distribution function over that interval... 

We are concerned with bimolecular reactions between reactants A and B. It is evident that the two reactants must approach each other rather closely on a molecular scale before significant interaction between them can take place. The simplest situation is that of two spherical reactants having radii Ta and tb, reaction being possible only if these two particles collide, which we take to mean that the distance between their centers is equal to the sum of their radii. This is the basis of the hard-sphere collision theory of kinetics. We therefore wish to find the frequency of such bimolecular collisions. For this purpose we consider the relatively simple case of dilute gases. 

Sometimes forms deviating from simple linear relations were used in this early work, particularly the relation of log A to E (31,36), which was derived theoretically (29) but later rejected (37, 38). Otherwise, the quantity log (kM ) was plotted instead of log k, M" being the sum of reciprocal masses of reacting particles according to collision theory (33), and this correction was also later abandoned (34). The two modifications mentioned, in practice, have little influence on the shape of the graph, and the simple plot of E versus log A (or AH versus AS) is now preferred. 

Primary Ionization—(1) In collision theory the ionization produced by the primary particles as contrasted to the "total ionization" which includes the "secondary ionization" produced by delta rays. (2) In counter tubes the total ionization produced by incident radiation without gas amplification. 

Transition state theory complements collision theory. When particles collide with enough energy to react, called the activation energy, Ea, the reactants form a short-lived, high energy activated complex, or transition state, before forming the products. The transition state also could revert back to the reactants. 

Why do factors such as temperature and concentration increase or decrease the rate of a reaction To answer this question, chemists must first answer another question What causes a reaction to occur One obvious answer is that a reaction occurs when two reactant particles collide with one another. This answer is the basis for collision theory In order for a reaction to occur, reacting particles (atoms, molecules, or ions) must collide with one another. 

You can use simple collision theory to begin to understand why factors such as concentration affect reaction rate. If a collision is necessary for a reaction to occur, then it makes sense that the rate of the reaction will increase if there are more collisions per unit time. More reactant particles in a given volume (that is, greater concentration) will increase the number of collisions between the particles per second. Figure 6.7 illustrates this idea. 

A measure of the cross-sectional area swept through by a particle or chemical entity this cross section influences collisions with another molecular or ionic entity. See Collision Theory... 

In the present section we present a theoretical description for the continuum-distorted-wave eikonal-initial-state (CDW-EIS) model. This model is one of the most advanced and complete perturbative theories of heavy particle collisions which has been formulated to date. The reasons for the success of this model particularly in describing ionization at high energies in the MeV/amu range are that ... 

Collision theory proposes that chemical reactions occur as a result of collisions between molecules. Reactions can only happen when particles collide with enough energy. 

Collins and Jameson11 found that for small air bubbles (20 to 100 jzm), varying the particle zeta potential from +30 mV to +60 mV resulted in an order of magnitude change in the observed rate constants for each drop size. Table 9 shows the values of the calculated and observed first-order rate constants for the data of Collins and Jameson obtained when their particles (polystyrene) had the minimum stability (zeta potential + 30 mV). The observed rate constants are much smaller than those calculated from collision theory. Their data indicate that between 1 in 40 to I in 100 collisions results in the particles sticking to bubbles. This is consistent with the particle-collision removal mechanism. 

It has been observed that the quenching cross section for the diatomic homonuclear molecules N2, H2, and D2, clearly depends on the laser polarization, although to a lesser extent than the electron-scattering intensities.116 Although, in principle, the same discussion may be applied as in electron scattering and the theory of the measurement102 may be applied adequately, heavy-particle collisions, especially with molecules, bring a number of complications that have to be taken into consideration ... 

The scales involved in such a reactor should be defined in a relative manner. For a chemist, the molecule is at the start and catalyst (particle) at the end of the scales. To reveal the reaction mechanism over a catalyst particle, a sequence of network of elementary reactions" will be needed. Accordingly, on the basis of, for example, the molecular collision theory (Turns, 2000), the "global reaction" can be derived in terms of global rate coefficient and reaction order. Here, the resultant reaction mechanism is termed "global" by chemists, because the use of it for a specific problem is normally a "black box" approach, without knowing exactly the underlying networks or structures of chemical routes from reactants to products. On the other hand, for a chemical reaction engineer, the catalyst (particle) is often the start and the reactor is the end. The reaction free of inner-particle and outer-particle diffusions, that is,... 

It was further developed the following year (22), and was based primarily on the scheme of Priest (12) with an idea from Gardon (9d). The latter suggested that the rate of capture of oligomeric radicals in solution by pre-existing particles, R, should be proportional to the collision cross-section, or tfie square of the radius of the particles, r. This has been called the "collision theory" of radical capture. In 1975 Fitch and Shih measured capture rates in MMA seeded polymerizations and came to the conclusion that R was proportional to the first power of the radius, as would e predicted by Fick s theory of diffusion (23). In his book, K. J. Barrett also pointed out that diffusion must govern the motions of these species in condensed media (10). 

The effect of the collisional force due to the impact of particles should be included when accounting for the motion of a particle except in a very dilute gas-solid flow situation. Basic mechanisms of collision between two particles or between a particle and a solid wall are discussed in Chapter 2. The collisional force between a particle and a group of neighboring particles in a shear suspension is discussed in 5.3.4.3. In a very dense system where particle collisions dominate the flow behavior, collisional forces can be described by using kinetic theory, as detailed in 5.5. The key equations derived in other chapters pertaining to the collisional forces can be summarized in the following. 

Once particles are present in a volume of gas, they collide and agglomerate by different processes. The coagulation process leads to substantial changes in particle size distribution with time. Coagulation may be induced by any mechanism that involves a relative velocity between particles. Such processes include Brownian motion, shearing flow of fluid, turbulent motion, and differential particle motion associated with external force fields. The theory of particle collisions is quite complicated even if each of these mechanisms is isolated and treated separately. 

Attraction of Two Spheres—An expression for the attraction between two or more particles, based on collision theory rather than attraction due to the motion of spheres, may be developed by the methods of dimensional analysis. Let the force of attraction between two particles of diameters d and d2 be F and assume that when the particles are close enough so that the gaseous film enveloping each particle coalesces over a region about the point of contact, then the whole attraction is due to a free surface energy a. If the average surface of contact of the particles is denoted by Sc then... 

Collision theory, as its name might suggest, focuses on the collisions between particles. The collisions must be frequent, and the colliding particles must have sufficient energy to form an activated complex. The transition-state theory focuses on the behavior of the activated complex. According to the transition-state theory, there are three main factors that determine if a reaction will occur ... 

Collision theory proposes that increases in temperature increase reaction rates by increasing the number of collisions that occur between particles and by increasing the kinetic energy that particles possess when they collide. 

Figure 7.9 is a plot of the average particle radius both calculated and measured experimentally by light scattering as a function of reaction time in the reaction zone. The measured values are always about 60% of the calculated values, using collision theory based on 100%... 

---