Diffusion-controlled bimolecular association

Approximate treatment of the many-particle effects in reversible bimolecular reactions has been undertaken in several papers (see for a review [78]) we would like also to note here pioneering studies of Ovchinnikov s group [79-82] and Kang and Redner s paper [83]. The former approach was discussed above in Section 2.1.2.3 where the kinetics of the approach to equilibrium for the simple reaction A B + B (dissociation and association of molecules A) was shown to approach the equilibrium as t 3/2. Note also that in the paper [84] a new elegant quantum-field formalism has been developed for the first time and applied to the diffusion-controlled reactions in the fluctuation regime its results agree completely with the phenomenological estimate (2.1.61). 

Diffusion control and pre-association in nitrosation, nitration, and halogenation, 16, 1 Dimethyl sulphoxide, physical organic chemistry of reactions, in, 14, 133 Diolefin crystals, photodimerization and photopolymerization of, 30, 117 Dipolar aptotic and protic solvents, rates of bimolecular substitution reactions in,... 

Association of oppositely charged ions is diffusion controlled. Theoretical treatment of Debye3345, that takes into account the Coulombic attraction between the ions, leads to the following expression for the bimolecular association constant, ka,... 

Diffusion-Controlled Encounter. Elementary bimolecular reaction mechanisms require diffiisional encovmter before the reaction. If the intrinsic kinetics are fast, and/or the viscosity of the solution is high, diffusion-controlled encounter may occur. In a homogeneous medium, a rate constant /jdiff can be evaluated which reflects the effective bulk-averaged rate constant associated with bimolecular encounters (45). Diffusional bimolecular encounter should be considered in the appropriate context. If Areact is the intrinsic bimolecular rate constant and djff is the differential rate constant defined above, then the observed rate constant for the bimolecular reaction is given by equation (11) (46). The limiting cases of this equation can be readily identified that is when the rate constant is very large, the observed rate constant corresponds to the diffusional rate constant. 

Diffusion controlled rates of bimolecular association reactions are usually around 10 -10 s in agreement with theoretical modelling studies. These... 

Pseudophase models work for several reasons (i) Reactions in association coUoids can be carried out under conditions of dynamic equilibrium. Thus the totality of the interfacial regions of all the aggregates in micelle, microemulsion, or vesicle solutions, and the totalities of their oil and water regions can be modeled as single interfacial, oil, and water reaction volumes of uniform properties with a separate rate constant for the reaction in each volume. Scheme 4. (ii) The requirement of dynamic equilibrium is met because the rate constants for diffusion of ions and molecules in association colloid solutions are near the diffusion-controlled limit. For example, the entrance and exit rate constants in micellar solutions in Table 1 are orders of magnitude faster than the example rate constants for thermal bimolecular reactions in micellar solutions in Table 4. Many additional examples are compiled in reviews. (iii) Measured rate constants for spontaneous reactions and... 

It is worth noting that Scheme 15.6 is equivalent to Scheme 15.7, with fej = fea[M], where is the bimolecular association rate constant (diffusion controlled in most excimer formation reactions) and [M] is the concentration of monomer in the ground state k i is the dissociation rate constant, which is usually denoted k ). 

Bimolecular association rate constant Rate constant for dissociation Rate constant for Dexter energy transfer Rate constant for diffusion-controlled reactions Rate constant for fluorescence... 

This type of bimolecular diffusion-limited reaction is prevalent in various enzyme-substrate encounters. Brownian dynamics simulations are being used to study the encounter rate of an enzyme with a substrate, protein-protein association, and nucleic add-protein association, which are just a few of the many biochemical processes that occur on characteristic time scales of diffusion-controlled systems. This article introduces the theory behind Brownian dynamics simulations and presents representative results from various areas of application. Detailed discussion of Brownian dynamics can be found in several recent papers. " ... 

A reaction whose rate is limited (or controlled) only by the speed with which reactants diffuse to each other. For a ligand binding to a protein, the bimolecular rate constant for diffusion-limited association is around 10 M s. The enzyme acetylcholinesterase has an apparent on-rate constant of 1.6 x 10 M s with its natural cationic substrate acetylcholine, and the on-rate constant of about 6 X 10 with acetylselenoylcholine and about... 

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