Collision energy, relative

FIGURE 13.28 Whether a reaction takes place when two species collide in the gas phase depends on their relative orientations. In the reaction between a Cl atom and an HI molecule, for example, only those collisions in which the Cl atom approaches the HI molecule from a direction that lies inside the cone indicated here lead to reaction, even though the energy of collisions in other orientations may exceed the activation energy. 

The relative collision energy in a CMB experiment is given by Ec = gv , where g is the reduced mass of the system and vr is the relative velocity. In general... 

Distribution of relative kinetic energies of collision in the direction along the line of molecular centers at different temperatures. 

Since the energy needed for electron ejection is provided by transfer of an electron from the target to the projectile ion, the term transfer ionization (TI)101 has been proposed for this type of process. The energy requirement for TI to be energetically possible without the use of relative collision energy is given by... 

In order to take particle-particle interactions into account, a stability ratio W is included which relates the collision kernel /So to the aggregation kernel /3agg. The stability ratio W depends on the interaction potential aggregation rate without to the rate with interactions additional to the omnipresent van der Waals forces. For Brownian motion as dominant reason for collisions, the stability ratio W can be calculated according to Eq. (6) taken from Fuchs [ 10]. In case of shear as aggregation mechanism, the force dip/dr relative to the friction force should rather be considered instead of the ratio of interaction energy relative to thermal energy. 

In the exact quantum calculation of the dynamics of a reaction on a particular potential-energy surface, it is necessary to solve the Schrodinger equation for the scattering from all occupied internal states of the reagents to all possible internal states of the products as a function of the relative collision energy. This is a multichannel process in that many final product vibrational and rotational states may be populated from a... 

In order for a reaction to occur, the energy of collision must equal or exceed some critical value called the threshold energy. The effective energy is, of course, not the total kinetic energy of the two colliding molecules but is, instead, the kinetic energy corresponding to the component of the relative velocity of the two... 

It is easy to understand a bimolecular reaction on the basis of collision theory. Thus, when two molecules A and B collide their relative kinetic energy exceeds the threshold energy, the collision may result in the breaking of bonds and the formation of new bonds. But how can one account for a unimolecular reaction If we assume that in such a reaction (A — P) the molecule A acquires the necessary activation energy by colliding with another molecule, then the reaction should obey second-order kinetics and not the first-order kinetics which is actually observed in several unimolecular gaseous reactions. A satisfactory theory of these reactions was proposed by F.A. Lindemann in 1922. According to him, a unimolecular reaction... 

The exchange of energy between an oscillator and a simple molecule was first analyzed from a classical viewpoint by I andau and Teller, who showed that, for a very slow collision, the net inelastic transfer is zero. This can be seen intuitively by considering the behavior of an infinitesimal and nearly constant force applied to one atom of a vibrating molecule. On one half cycle when the force and motion are in phase there will be an increase in momentum and kinetic energy of this atom which will be almost precisely compensated in the next half cycle by a decrease in momentum and kinetic energy. Closer analysis shows that the net effect of such a force over a cycle is to slowly accelerate the entire oscillator but not to excite it. The probability of inelastic transfer increases with the hard-ness of the collision. This latter is measured by the ratio of the time of a vibration to the collision time, rtr/rcoii = Vnl Tva, where intermolecular forces/ v is the oscillator frequency, and Vr is the relative collision velocity. 

The relative collision rates can be calculated from the kinetic theory of gases. Both values should strictly include a term to take account of the entropy and energy of viscous flow, which depends, according to the Eyring theory, on the structure of the liquid and on the work required to form a hole in the liquid for the diffusing molecule to move into (see Section III). The rate of collision of gas molecules with a surface, Zs, is given by ... 

---