Apparent unimolecular reaction

Another mechanism has been suggested by Christiansen and Kramers in which activation is by collision and yet there is an apparently unimolecular reaction. It depends upon the possibility that the products of reaction, possessing the energy corresponding to the chemical heat of reaction as well as the original heat of activation, are able immediately to activate fresh molecules of reactant. In this way reaction-chains are set up. The assumption is made that every molecule of product can at once activate by collision a fresh molecule of the reactant. In this way each activated molecule removed from the system by chemical transformation is replaced by a new activated molecule. 

When a molecule is supplied with an amount of energy that exceeds some threshold energy, a unimolecular reaction can take place, that is, a dissociation or an isomerization. We distinguish between a true unimolecular reaction that can be initiated by absorption of electromagnetic radiation (photo-activation) and an apparent unimolecular reaction initiated by bimolecular collisions (thermal activation). For the apparent unimolecular reaction, the time scales for the activation and the subsequent reaction are well separated. When such a separation is possible, for true or apparent unimolecular reactions, the reaction is also referred to as an indirect reaction. We will discuss the following. 

In a true unimolecular reaction, the activation is done by exposing the molecules to electromagnetic radiation, whereas activation is accomplished by inelastic collisions with other molecules in an apparent unimolecular reaction. The condition for the latter process to be unimolecular is that the time scales of the activation process and the chemical reaction are very different, so that the chemical reaction is much slower than the activation process. 

In an apparent unimolecular reaction, the molecule is activated in a bimolecular collision process. In addition, it is assumed that the preparation of the initial metastable state of the molecule can be separated from its unimolecular decay. Thus, the apparent unimolecular reaction can also be classified as an indirect reaction. One writes such an apparent unimolecular reaction in the form... 

Thus, it is clear what is meant by the words apparent unimolecular reaction, since the activation process can be bimolecular. A key point is the separation in time scales between the activation step and the subsequent unimolecular reaction dynamics. This was also a distinctive feature of the indirect photo-activated reactions considered in the previous section. Thus, the theoretical description of these reaction types is very similar photo-activation makes it, in particular, possible to deposit a precise amount of energy according to E = hi/. 

The basic assumption in statistical theories is that the initially prepared state, in an indirect (true or apparent) unimolecular reaction A (E) —> products, prior to reaction has relaxed (via IVR) such that any distribution of the energy E over the internal degrees of freedom occurs with the same probability. This is illustrated in Fig. 7.3.1, where we have shown a constant energy surface in the phase space of a molecule. Note that the assumption is equivalent to the basic equal a priori probabilities postulate of statistical mechanics, for a microcanonical ensemble where every state within a narrow energy range is populated with the same probability. This uniform population of states describes the system regardless of where it is on the potential energy surface associated with the reaction. 

In a true unimolecular reaction, the energized molecules are formed by absorption of electromagnetic radiation see Section 7.2.2. In an apparent unimolecular reaction, the first step is the formation of the energized molecules by collisions with other molecules. We consider in the following subsection the interplay between the formation of energized molecules—by bimolecular collision—and their subsequent reaction. 

The pre-exponential factor of an apparent unimolecular reaction is, roughly, expected to be of the order of a vibrational frequency, i.e., fO13 to 1014 s 1. The pre-exponential factor of a bimolecular reaction is, roughly, related to the collision frequency, i.e., the number of collisions per unit time and per unit volume. 

The general relation between the rate constant of (apparent) unimolecular reactions and the microscopic dynamics is illustrated in Fig. 8.1.1. 

Thus, according to RRKM theory for an apparent unimolecular reaction, Eq. (7.58) gives the (canonical) rate constant for such an elementary reaction ... 

The first successful theory of unimolecular reactions (2.46) was proposed by Lindemann in 1922. He introduced the idea that apparently unimolecular reactions were really the result of the following processes ... 

To calculate rate constants for bimolecular systems, Eqs (7.19) and (7.20) are used. An equivalent theory can be derived for unimolecular reactions. In a unimolecular reaction only one reactant forms a transition state through radiation or in an apparent unimolecular reaction through collision, which results in product generation. Applying similar assumptions as above (classical motion when crossing the barrier, no recrossing events, and thermal equilibrium) leads to the canonical rate constant, given by... 

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