Bimolecular reaction, defined

Consider a bimolecular reaction between a substrate and a reagent. Upon each encounter of these two species there is a probability P that reaction will occur. If the solution contains two substrates Sj and S2, each characterized by a probability of reaction P, and P2 with the common reagent, evidently the ratio P2lP is a measure of the selectivity of this process for S2 relative to S,. If the two substrates are not markedly dissimilar, the ratio P2IP1 will be similar to the ratio of rate constants, 2/ 1- Leffler and Grunwald pp define the selectivity as... 

Termination results in the removal of the activated species from the reaction. It involves the bimolecular reaction between the MA and a specific reactive species, D. Depending on the type of polymerization reaction, the reactive species may be a radical or an ion acceptor. The reaction, then, can be defined as Eq. 4.12. 

According to my view, the polymerizations by ionizing radiations at the lowest m are bimolecular reactions, propagated by the species P+ Sv. For these reactions there are no ambiguities, and [P+ Sv] = c, so that k+p is defined by (4.1) and (4.15). The available values, including those calculated in this Section and in Section 5, are collected in Table 5. 

This complex is in equilibrium with the reactants, A and B. The equilibrium product for the bimolecular reaction under consideration is defined by ... 

In particular, it is useful to define the critical point through F(nc) = 0 (the stationary state). Since multicomponent chemical systems often reveal quite complicated types of motion, we restrict ourselves in this preliminary treatment to the stable stationary states, which are approached by the system without oscillations in time. To illustrate this point, we mention the simplest reversible and irreversible bimolecular reactions like A+A —> B, A+B -y B, A + B —> C. The difference of densities rj t) = n(t) — nc can be used as the redefined order parameter 77 (Fig. 1.6). For the bimolecular processes the... 

Chemical processes in condensed media often cannot be reduced to simple mono- and bimolecular reactions simply because chains of reaction take place. Therefore their kinetics is described by a set of ordinary differential equations (2.1.1) which are generally nonlinear due to bimolecular stages. Independent variables n ( ), i = 1,..., s (intermediate reactions products) define a number of equations under study. 

During their diffusive walks, H centres can either approach their own F centres to within the distance r ro and recombine with them in the course of the so-called geminate (monomolecular) reaction or leave them behind in their random walks. Some of these H centres recombine with foreign F centres, thus participating in bimolecular reactions. The rest of the H centres become trapped by impurities, dislocations, or aggregate in the form of immobile dimer H2 centres thus going out of the secondary reactions as shown in Fig. 3.4. In other words, the survival probability of the geminate pairs (F centres) directly defines the defect accumulation efficiency and thus, a material s sensitivity to radiation. 

It is shown below (Chapter 4) that its solution is also important for the bimolecular stage of a reaction defining a stationary recombination profile. The second linearly independent solution of this equation could be expressed through y(r) as... 

The rate constant is defined as the reaction rate per unit volume of the reaction chamber divided by the product of the reactant concentrations. Thus, for a bimolecular reaction... 

According to the Smoluchowski theory of diffusion-controlled bimolecular reactions in solutions, this constant decreases with time from its kinetic value, k0 to a stationary (Markovian) value, which is kD under diffusional control. In the contact approximation it is given by Eq. (3.21), but for remote annihilation with the rate Wrr(r) its behavior is qualitatively the same as far as k(t) is defined by Eq. (3.34)... 

In case of a bimolecular reaction of the type vaA +vbB —> Products, the composition of the feed mixture is an important free parameter. This can be conveniently expressed using a stoichiometric feed ratio X defined as follows ... 

The softness kernels are relevant to the remaining cases of two or more interacting systems. However, they do not by themselves provide sufficient information to constitute a basis for a theory of chemical reactivity. Clearly, the chemical stimulus to one molecule in a bimolecular reaction is provided by the other. That being the case, an eighth issue arises. Both the perturbing system and the responding system have internal dynamics, yet the softness kernel is a static response function. Dynamic reactivities need to be defined. 

A special feature of bimolecular reactions is that a, defined by eq 102 and normally positive, might become negative when reactant A2 is adsorbed much more strongly than reactant Ai and when, additionally, the value of D2P2,s/v2 is very small. For o < 0, the method of Roberts and Satterfield cannot be applied [91],... 

The estimated values of the p s and of the original parameters are shown in Table V. Despite the wide range of initiator and monomer concentrations used, it is not possible to obtain precise estimates of this many parameters from the data. In particular, ps is very poorly defined for this system. Notice that the geometric mean approximation is equivalent to fis = 1 (see Equation 15). For a diffusion-controlled bimolecular reaction the arithmetic mean is appropriate as shown above, and this is reflected in the fact that p3 is significantly less than 1. 

The basis of the rate acceleration by this host is an increased effective molarity within the assembly cavity. This principle has been demonstrated with other supramolecular compounds that possess a defined inner space [27, 28]. This is a powerful but narrow capability of these assemblies, employing size- and shape-complementarity to bring molecules together in the promotion of bimolecular reactions. Importantly, this phenomenon does not depend on perturbation of the potential energy surface to effect the rate accelerations. 

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