Encounter-controlled reaction

For bimolecular second-order reactions and for trimolecular reactions, if the reaction rate is very high compared to the rate to bring particles together by diffusion (for gas-phase and liquid-phase reactions), or if diffusion is slow compared to the reaction rate (for homogenous reaction in a glass or mineral), or if the concentrations of the reactants are very low, then the reaction may be limited by diffusion, and is called an encounter-controlled reaction. 

For a fuUy diffusion-controlled (or encounter-controlled) reaction. 

Figure 4.18. Influence of a short-range chemical/cage effect on the efficiency of an irreversible, encounter-controlled reaction at a centrally located reaction center, relative to a purely random process. Plotted is the ratio n) C)/ n) RW) versus system size for a d-dimensional Euclidean lattice of valency v = 2d. The abscissa in the figure is the edge length f overall, the reaction space has N — I sites where N =. The lower curve (A) corresponds...

The versatility of lattice models to describe encounter-controlled reactions in systems of more complicated geometries can be illustrated in two different applications. In this subsection layered diffusion spaces as a model for studying reaction efficiency in clay materials are considered and in the following subsection finite, three-dimensional lattices of different symmetries as a model for processes in zeolites are studied. Now that the separate influences of system size N, dimensionality d (integral and fractal), and valency v have been established, and the relative importance of d = 3 versus surface diffusion (and reduction of dimensionality ) has been quantified, the insights drawn from these studies will be used to unravel effects found in these more structured systems. 

The role of encounter controlled reactions in chemical kinetics has been considered by (a) R.M. Noyes, "progress in Reaction Kinetics," Pergamon Press (1961). (b) North, A.M., ... 

The oxidation of hexacyanoferrate(II) by nitrous acid involves an encounter-controlled reaction between [HFe(CN)6] and the nitrosonium ion. " More conventional nitrosations have also received much attention, as have the use of specific nitrosating agents and the transfer of NO" groups between molecules. The rate constant for the reaction of nitrous acid and methanol (O-nitrosation) is significantly lower than that expected for a diffusion-controlled reaction. Solvent-jump relaxation techniques have been used in the study of the NOCl— 1-butanol reaction in CCI4—HO AC mixtures. 

In all of these reactions the selectivities are remarkable for radical reactions, being characteristic of no-stabilization of transition states by contributions from product structures. Each of these reactions appears to be an encounter-controlled reaction. As an illustration, succinimidyl radical adds to styrene as follows to the double bond twice as rapidly as to the phenyl nucleus. 

D. G. Tmhlar, /. Chem. Educ., 62,104 (1985). Nearly Encounter-Controlled Reactions The... 

After the jump, the particle is taken to have reacted with a given probability if its distance from another particle is within the reaction radius. For fully diffusion-controlled reactions, this probability is unity for partially diffusion-controlled reactions, this reaction probability has to be consistent with the specific rate by a defined procedure. The probability that the particle may have reacted while executing the jump is approximated for binary encounters by a Brownian bridge—that is, it is assumed to be given by exp[—(x — a)(y — a)/D St], where a is the reaction radius, x andy are the interparticle separations before and after the jump, and D is the mutual diffusion coefficient of the reactants. After all... 

Green and Pimblott (1989) have extended the IRT model to partially diffusion-controlled reactions between neutrals. They derive an analytical expression that involves an additional parameter, namely the reaction velocity at encounter. For reactions between charged species, W generally cannot be given analytically but must be obtained numerically. Furthermore, numerical inversion to get t then... 

Alkyl radicals react in solution very rapidly. The rate of their disappearance is limited by the frequency of their encounters. This situation is known as microscopic diffusion control or encounter control, when the measured rate is almost exactly equal to the rate of diffusion [230]. The rate of diffusion-controlled reaction of free radical disappearance is the following (the stoichiometric coefficient of reaction is two [233]) ... 

Diffusion of particles in the polymer matrix occurs much more slowly than in liquids. Since the rate constant of a diffusionally controlled bimolecular reaction depends on the viscosity, the rate constants of such reactions depend on the molecular mobility of a polymer matrix (see monographs [1-4]). These rapid reactions occur in the polymer matrix much more slowly than in the liquid. For example, recombination and disproportionation reactions of free radicals occur rapidly, and their rate is limited by the rate of the reactant encounter. The reaction with sufficient activation energy is not limited by diffusion. Hence, one can expect that the rate constant of such a reaction will be the same in the liquid and solid polymer matrix. Indeed, the process of a bimolecular reaction in the liquid or solid phase occurs in accordance with the following general scheme [4,5] ... 

Smoluchowski, who worked on the rate of coagulation of colloidal particles, was a pioneer in the development of the theory of diffusion-controlled reactions. His theory is based on the assumption that the probability of reaction is equal to 1 when A and B are at the distance of closest approach (Rc) ( absorbing boundary condition ), which corresponds to an infinite value of the intrinsic rate constant kR. The rate constant k for the dissociation of the encounter pair can thus be ignored. As a result of this boundary condition, the concentration of B is equal to zero on the surface of a sphere of radius Rc, and consequently, there is a concentration gradient of B. The rate constant for reaction k (t) can be obtained from the flux of B, in the concentration gradient, through the surface of contact with A. This flux depends on the radial distribution function of B, p(r, t), which is a solution of Fick s equation... 

There are two anhydride linkages in ATP, but nucleophilic attack in the enzyme-controlled reaction usually occurs on the terminal P=0 (hydrolysis of ATP to ADP), and only occasionally do we encounter attack on the central P=0 (hydrolysis of ATP to adenosine monophosphate, AMP). Both reactions yield the same amount of energy, AG—34 kJmoD This is not surprising, since in each case the same type of bond is being hydrolysed. The further hydrolysis of AMP to adenosine breaks an ester linkage and would liberate only a fraction of the energy, AG — 9 kJmol and this reaction is not biochemically important. 

A reaction velocity equal to the rate of encounter of reacting molecular entities (also known as diffusion-con-trolled rate). For a bimolecular reaction in aqueous solutions at 25°C, the corresponding second-order rate constant for the encounter-controlled rate is typically about 10 ° M s See Diffusion Control for Bimolecular Collisions in Solution... 

ENCOUNTER-CONTROLLED RATE DIFFUSION-LIMITED REACTION CHEMICAL KINETICS DIFFUSION OF LIGAND TO RECEPTOR DIFFUSION OF MOLECULES INTO A PORE... 

STEREOCHEMICAL TERMINOLOGY, lUPAC RECOMMENDATIONS ENANTIOSELECTIVE REACTION ASYMMETRIC INDUCTION ENCOUNTER COMPLEX ENCOUNTER-CONTROLLED RATE DIFFUSION CONTROL FOR BIMOLECULAR COLLISIONS ENDERGONIC PROCESS ENDO-a (or j8)-N-ACETYLGALACTOSAMI-NIDASE... 

ENCOUNTER-CONTROLLED RATE SECOND-ORDER REACTiON CHEMICAL KINETICS ORDER OF REACTION NOYES EQUATION MOLECULARITY AUTOCATALYSIS FIRST-ORDER REACTION... 

If, upon encounter, the reaction rate is much slower than the rate to bring the species together, then the reaction is not controlled by encounter. If the two rates are comparable, then the reaction is partially controlled by encounter (or diffusion). 

Diffusion-Controlled Reactions. Chemical reactions without Transition States (or energy barriers), the rates of which are determined by the speed in which molecules encounter each other and how likely these encounters are to lead to reaction. 

Let us first consider a very fast reaction between uncharged nonpolar reactants in solution. In this case, the rate is controlled by the number of encounters. Once A and B diffuse into the same solvent cage, they will react hence the rate of these diffusion-controlled reactions is determined by how fast A and B diffuse together in solution. 

Starting with Fick s first law, one can calculate for a solution of two reactants A and B the frequency of A-B encounters, which is in effect the reaction rate constant for diffusion-controlled reactions. This is given by the following, in units of L mol 1 s-1 ... 

Aryl radical additions to anions are generally very fast, with many reactions occurring at or near the diffusion limit. For example, competition studies involving mixtures of nucleophiles competing for the phenyl radical showed that the relative reactivities were within a factor of 10, suggesting encounter control,and absolute rate constants for additions of cyanophenyl and 1-naphthyl radicals to thiophenox-ide, diethyl phosphite anion, and the enolate of acetone are within an order of magnitude of the diffusional rate constant. ... 

On the assumptions that the triplet TMB biradical 37 is the reactive intermediate and that its reaction with O2 occurs at the encounter-controlled rate, the authors estimated that the triplet is more stable than the singlet by at least 4-5 kcal/mol, or more if the diffusion-limited trapping rate assumed is actually lower. 

It is interesting to note that eqn. (190) is reminiscent of the steady-state Collins and Kimball rate coefficient [4] [eqn. (27)] with kact replaced by kacig R) and 4ttRD by eqn. (189). Equation (190) for the rate coefficient is significantly less than the Smoluchowski rate coefficient on two counts hydrodynamics repulsion and rate of encounter pair reaction. Had experimental studies shown that a measured rate coefficient was within a factor of two of the Smoluchowski rate coefficient, it would be tempting to invoke partial diffusion control of the reaction rate. The reduction of rate due to hydrodynamic repulsion should be included first and then the effect of moderately slow reaction rates between encounter pairs. 

Similar considerations apply to the role of spin equilibria in electron transfer reactions. For many years spin state restrictions were invoked to account for the slow electron exchange between diamagnetic, low-spin cobalt(III) and paramagnetic, high-spin cobalt(II) complexes. This explanation is now clearly incorrect. The rates of spin state interconversions are too rapid to be competitive with bimolecular encounters, except at the limit of diffusion-controlled reactions with molar concentrations of reagents. In other words, a spin equilibrium with a... 

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