Ineffective collision

The apparent efficiency of the size reduction operation depends on the type of equipment used. Thus, for instance, a ball mill is rather less efficient than a drop weight type of crusher because of the ineffective collisions that take place in the ball mill. 

It is assumed that the uniform shear field is unperturbed by the presence of the particles and therefore the path of the /-particles is rectilinear. Although Arp and Mason have shown that the curvature of the stream lines around the particles may appear to have a small effect, van de Ven and Mason" have shown that rolling of particles around one another does significantly reduce the collection efficiency of collisions. However, as a simplification each collision is assumed to result in an effective collection, i.e. flocculation with no electrical or hydrodynamic barriers. This simplification can be later adjusted by a collision efficiency factor, 8 < 1.0 to take into account a proportion of ineffective collisions. 

An important condition for chain growth is that the macroradical is sufficiently stable, which means it has to survive a large number of ineffective collisions with monomer or solvent in order to finally react with a monomer molecule. Any possible decomposition or side reaction has to be sufficiently slow so that it will not compete with propagation. 

Effective and ineffective molecular collisions. For a collision to result in reaction, die molecules must be properly oriented. For the... 

From what we know about molecular sizes, we can calculate that a particular CH4 molecule collides with an oxygen molecule about once every one-thousandth of a microsecond (1(M seconds) in a mixture of household gas (methane, formula CH4) and air under normal conditions. This means that every second this methane molecule encounters 10 oxygen molecules Yet the reaction does not proceed noticeably. We can conclude either that most of the collisions are ineffective or that the collision theory is not a good explanation. We shall see that the former is the case—we can understand why most collisions might be ineffective in terms of ideas that are consistent with the collision theory. 

If the sufficient energy (= act) has been provided to the reactants and the reactants have reached at energy level A, i.e. energy of activated complex, the collision between the reactants will result in the formation of activated complex and the activated complex would yield the products. However, if reactants are not having sufficient energy (i.e. they are at energy level B), the collision between the reactants would not result in the formation of activated complex. Therefore, the collision will be ineffective. Thus, only those collisions, in which reactant molecules have sufficient energy (> act) are useful collisions. 

A bimolecular reaction which would proceed with comparable velocity at the same temperature as this reaction would have a heat of activation of about 60,000 calories, as may be inferred from the table on page 96. Now termolecular collisions are about 1,000 times less frequent than bimolecular collisions at atmospheric pressure. Thus if we have a bimolecular reaction and a termolecular reaction with equal heats of activation, the rate of the latter should be at least 1,000 times smaller than that of the former at the same temperature. It will probably be more nearly 10,000 times slower, since a larger proportion of the ternary collisions are likely to be ineffective on account of unfavourable orientation of the molecules during impact. Conversely, if a termolecular reaction and a bimolecular reaction are to take place at equal rates at the same temperature, then the heat of activation of the termolecular reaction would need to be the smaller by an amount AE, such that e ElRT = 1,000 to 10,000. Thus, other things being equal, the heats of activation of termolecular reactions ought to be about 5,000 calories less at the ordinary temperature, and about 15,000 calories less at 1,000° abs., than those of bimolecular reactions. We have also to allow for the diminished duration of collisions at higher temperatures, which we can do by comparison with the nitric oxide oxidation. 

Quinn studied initial rates—i.e., in the absence of reaction products—in a limited pressure range of 60 to 230 Torr. His hypothesis can explain the dependence on initial pressure he observed, but not what is normally defined as first-order behavior, namely, a rate proportional to the reactant concentration or partial pressure in the course of the reaction in the presence of products formed. This is because ethene (and, for that matter, almost any other molecule with the possible exception of H2) can also serve as activating collision partner. Indeed, addition of inerts has been found to boost the rate [35]. Since one mole of ethane produces approximately one mole of ethene, the concentration of potential collision partners is pc=c + pcc = pc°c and remains essentially unchanged, so that there is no effect on the form of the rate equation and the reaction order (for simplicity, this assumes ethene to be as effective a collision partner as is ethane, and H2 to be ineffective.) Nevertheless, textbooks to this day accept Quinn s explanation, if not Rice and Herzfeld s. 

Figure 16-9 Some possible collisions between N2O and NO molecules in the gas phase, (a) A collision that could be effective in producing the reaction, (b, c) Collisions that would be ineffective. The molecules must have the proper orientations relative to one another and have sufficient energy to react.

A similar mechanism has been postulated for the reaction when conducted in the presence of silica gel metallized with silver, gold, platinum, and palladium.10 Collisions of ethylene molecules with oxygen molecules adsorbed and activated by the effective catalyst centers result in reaction. Collisions of oxygen molecules with adsorbed ethylene molecules, however, are ineffective. 

---