Microscopic diffusion control

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]) ... 

The limiting reaction rate achieved by diffusion occurring after mixing solutions containing two or more reactants. This form of control, also called mixing control, is typically more relevant for reactions involving heterogeneous systems (e.g., solid/liquid or liquid/gas). See also Microscopic Diffusion Control... 

MACROSCOPIC DIFFUSION CONTROL MICROSCOPIC DIFFUSION CONTROL Magic acid,... 

MICROSCOPIC DIFFUSION CONTROL MACROSCOPIC DIFFUSION CONTROL MICROSCOPIC REVERSIBILITY CHEMICAL REACTION DETAILED BALANCING, RRINCIRLE OF CHEMICAL KINETICS MICROTUBULE ASSEMBLY KINETICS BIOCHEMICAL SELF-ASSEMBLY ACTIN ASSEMBLY KINETICS HEMOGLOBINS POLYMERIZATION... 

MICROSCOPIC DIFFUSION CONTROL TRANSPORT NUMBER TRAPPING... 

Another type of electrophilic substitution subject to microscopic diffusion control occurs when a highly reactive form of the substrate is produced in a pre-equilibrium step (e.g. by proton loss) and when this form reacts on encounter with the electrophile. The nitration of p-nitroaniline in 90% sulphuric acid appears to be a reaction of this type (Hartshorn and Ridd, 1968), although the short lifetime of the free amine complicates the mechanistic interpretation. The formulation in Scheme 1 fits this type of reaction provided A is taken to represent the protonated amine, X the free amine, and B the nitronium ion. In 90% sulphuric acid, the nitronium ion is the bulk component of the NOJ—HN03 equilibrium mixture. Many of the reactions in this review can be represented by Scheme f with some reservations concerning the lifetime of the intermediate X. 

The term macroscopic diffusion control has been used to describe processes in which the rate of reaction is determined essentially by the rate of mixing of the reactant solutions. The nitration of toluene in sulpholane by the addition of a solution of nitronium fluoroborate in sulpholane appears to fall into this class (Ridd, 1971a). Obviously, if a reaction is subject to microscopic diffusion control when the reactants meet in a homogeneous solution, it must also be subject to macroscopic diffusion control when preformed solutions of the same reactants are mixed. However, the converse is not true. The difficulty of obtaining complete mixing of solutions in very short time intervals implies that a reaction may still be subject to macroscopic diffusion control when the rate coefficient is considerably below that for reaction on encounter. The mathematical treatment and macroscopic diffusion control has been discussed by Rys (Ott and Rys, 1975 Rys, 1976), and has been further developed recently (Rys, 1977 Nabholtz et al, 1977 Nabholtz and Rys, 1977 Bourne et al., 1977). It will not be considered further in this chapter. 

As outlined above (p. 3), a reaction can be subject to microscopic diffusion control only if one of the reactive intermediates is formed from an inactive precursor in the reaction mixture. There are two sets of conditions which have provided evidence for microscopic diffusion control in nitration. One concerns solutions of nitric acid in aqueous mineral acids or organic solvents for, in most of these solutions, the stoicheiometric nitric acid is mainly present as the molecular species in equilibrium with a very small concentration of nitronium ions. A reaction between a substrate and a nitronium ion from this equilibrium concentration can, in principle, be subject to microscopic diffusion control. The other set of conditions is when the substrate is mainly present as the protonated form SH+ but when reaction occurs through a very small concentration of the neutral base S. A reaction between the neutral base and a nitronium ion can then, in principle, be subject to microscopic diffusion control even if the nitronium ions are the bulk component of the HN03/N0 equilibrium. In considering the evidence for microscopic diffusion control it is convenient to consider separately the reactions of those species involved in prototopic equilibria. 

The clearest evidence for microscopic diffusion control in nitration comes from the kinetic studies of Coombes et al. (1968), with low concentrations of nitric acid in 68.3% sulphuric acid as solvent. In this medium, the concentration of nitronium ions is proportional to the concentration of molecular nitric acid as required by (24) and, since the concentration of nitronium ions is very small, the concentration of molecular nitric acid is effectively equal to the stoicheiometric concentration of nitric acid. At a given acidity, the reactions have the kinetic form (25). Nitric acid is written out in full in this equation to show that the rate coefficient is calculated with reference to the stoicheiometric concentration of the acid. This convention assists the comparison of reaction rates over a wide range of acidity. 

The experimental evidence for microscopic diffusion control in chlorination, bromination, and iodination is complicated by the number of possible electrophilic species which may be involved and, with some substrates, by uncertainty over the exact rate-determining stage. The mechanistic picture therefore resembles that for nitrosation rather than that for nitration. As usual,... 

While considering the influence of the encounter rate on chemical reactivity a microscopic and macroscopic diffusion control should be mentioned. In microscopic diffusion control, the reactants exist together in a homogeneous solution and the reaction occurs on every encounter. 

According to Ridd [79] the clearest evidence for microscopic diffusion control in nitration comes from the kinetic studies of Coombes, Moodie and Schofield [80] with low concentration of nitric acid in 68.3% sulphuric acid as a solvent. In this medium the concentration of nitronium ions is proportional to the concentration of molecular nitric acid according to equation (27) ... 

If (hypothetically) a bimolecular reaction in a homogeneous medium occurred instantaneously when two reactant molecular entities made an encounter, the rate of reaction would be an encounter-controlled rate, determined solely by rates of diffusion of reactants. Such a hypothetical fully diffusion-con-trolled rate is also said to correspond to total microscopic diffusion control and represents the asymptotic limit of the rate of reaction as the RATE constant for the chemical conversion of the encounter pair into product (or products) becomes large relative to the rate constant for separation (or dissociation) of the encounter pair. 

Partial microscopic diffusion control is said to operate in a homogeneous reaction when the rates of chemical conversion and of separation are comparable. (The degree of microscopic diffusion control usually cannot be determined with any precision.)... 

See also microscopic diffusion control stopped flow. 

In the detailed description of proton-transfer reactions, especially of rapid proton transfers between electronegative atoms, it should always be specified whether the term is used to refer to the overall process (including the more-or-less ENCOUNTER-CONTROLLED formation of a hydrogen-bonded complex and the separation of the products [see microscopic diffusion control]) or just to the proton-transfer event (including solvent rearrangement) by itself. 

Special effects arise for a solution reaction that is extremely rapid, in which case the rate may depend on the rate with which the reactant molecules diffuse through the solvent. Two effects are to be distinguished, macroscopic diffusion control and microscopic diffusion control. If a rapid bimolecular reaction in solution is initiated by mixing solutions of the two reactants, the observed rate may depend on the rate with which the solutions mix, and one then speaks of mixing control or macroscopic diffusion control. 

This equation has two limiting cases. When chem is much larger than k, the overall rate constant equals and the reaction is fully controlled by diffusion. This may happen in dense liquids or gases at high pressure. The other extreme occurs if / chem in this case there is no effect of the medium on the reaction. In intermediate cases, the reaction is said to be in partial microscopic diffusion control. 

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