Reaction rate, diffusion controlled

In these circumstances a decision must be made which of two (or more) kinet-ically equivalent rate terms should be included in the rate equation and the kinetic scheme (It will seldom be justified to include both terms, certainly not on kinetic grounds.) A useful procedure is to evaluate the rate constant using both of the kinetically equivalent forms. Now if one of these constants (for a second-order reaction) is greater than about 10 ° M s-, the corresponding rate term can be rejected. This criterion is based on the theoretical estimate of a diffusion-controlled reaction rate (this is described in Chapter 4). It is not physically reasonable that a chemical rate constant can be larger than the diffusion rate limit. 

However, there is another operative timescale in solution. This is that timescale for reaction with other photolytically generated species or with added reactants. This reaction cannot take place faster than the diffusion-limited reaction rate which is concentration dependent (59). Typical diffusion-controlled reaction rate constants are 109-1010 dm3 mol"1 second-1. By comparison, a typical gas-kinetic rate con-... 

AGst for BA, XA and DMFL are limits based on unobserved reactions for the other carbenes AGST is calculated by assuming a diffusion controlled reaction rate for the singlet carbene with methyl alcohol. All kinetic parameters refer to room temperature k Sitzmann and Eisenthal, 1983... 

Solids, by Carslaw and Jaeger, a book that has become a bible for electro-chemists studying diffusion-controlled reaction rates. 

This is obviously incorrect as, on chemical grounds, the o-Ps and p-Ps reaction rate constants cannot be different the statistical spin substate factor should not appear in the rate at which the reaction occurs but rather, as in reaction XI, in the yield of the products of the reaction. Formally, reaction schemes XI and XII lead to exactly the same type of kinetic equations to describe the PALS parameters, particularly, A,3. However, if one wishes to compare the experimentally determined k with some theoretical expression such as the diffusion-controlled reaction rate constant, reaction XII will lead to a value of k which is 4 times lower than that yielded by reaction XI if o-... 

Table 4.4 Comparison between experimental Ps reaction rate constants (k ) and diffusion-controlled reaction rate constants calculated from eq. (18) by using either the bubble (kDd, Rb) or the free Ps (kD, RPs = 0.053 nm) radius, (a), unpublished results (b), [82] (c) [61] (d), [84], ox = oxidation sp = spin conversion bs = bound-state formation. The rate constants are in M W. NDMA N-dimethylacetamide 0-NO2 ...

We have already mentioned that Dorfman and collaborators have developed a versatile technique to observe ort-lived carbenium ions in solution generated by dissociative pulse radiolysis. This novel approach to the characterisation of transient species has also allowed this schod to measure the rate constants of many electrophilic reactions between carbenium ions (the benzylium ion in particular) and various nucleophiles. In the first paper of the series Jones and Dorfman reported the rate constants of the benzylium ion reaction with methanol, ethanol, the bromide and the iodide ions in ethylene chloride at 24 C. Values of about 5 x 10 sec were obtained for the halide ions and of around 10 sec for the alcohols. Later studies confirmed that the reaction of halide ions vrith benzylium, diphenyl-methylium and triphenylmethylium ions is at the limit of diffusion control. Reaction rate constants of these three carbenium ions with amines and alcdiols were also reported in the same paper. More recently, these studies have been extended to include cyclopropylphenylmetiiylium ion as electrophile, ammonia as nucleophile and methylene chloride and trichloroethane as solvents These results are extremely... 

Richter PH, Eigen M. Diffusion controlled reaction rates in spheroidal geometry. Application to repressor operator association and membrane repressor enzymes. Biophys. Chem. 1974 2 255-263. 

A wide variety of molecules act as collisional quenchers. Molecular oxygen is one such quencher, possessing diffusion-controlled reaction rates (see Section 14.2.4). In the presence of a quenching agent, the lifetime (x) of a reactive intermediate is inversely proportional to the collisional quenching constant (Kq) and the concentration of the quencher, [Q], when the quenching reaction is diffusion controlled (Lakowicz, 1983) ... 

Dependence of the intermacromolecular diffusion-controlled reaction rate constant for polystyrene samples of varying degree of polymerization and in several solvents... 

Stage II. This is the stage when intermicellar exchange takes place by fusion-fission. For well-defined dispersed droplets the exchange rate coefficient is approximately of the order of 10 -10" lower than the diffusion controlled reaction rate. 

Stable free radicals are frequently employed as inhibitors (436,437). The most commonly used species are nitroxides, eg, 2,2,6,6-tetramethylpiperidine-l-oxyl (TEMPO) 18. They are far too stable to be able to initiate polymerization, but they are reactive enough to imdergo reaction with other free radicals (438). Nitroxides are very efficient inhibitors, being capable of producing induction periods when present in concentrations of less than 10 mol L" Nitroxides, such as TEMPO, react with carbon-centered radicals at close to diffusion controlled reaction rates (439-441). The stoichiometry between the number of the chains... 

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

For spherical particles, diffusion-controlled reaction rates are given by Equation (18.25). Diffusion control implies that reactions are fast. Other reactions involve additional rate-limiting steps that occur after the reacting molecules have come into contact with the sphere. Diffusion control defines an upper limit on the speed of reactions. Any other kind of process must be slower than the diffusion-controlled process because the reaction must take additional time to complete after contact. Association rates are often expressed in terms of a rate coefficient ka defined by 1(a) = -kaC, where... 

The brief outline given in this section will serve as an introduction to the next chapter, which deals with the phenomena of diffusion-controlled reaction rates. 

The Mathematical Theory of Diffusion and Diffusion-Controlled Reaction Rates... 

Figure 33 Concentration-gradient treatment of diffusion-controlled reaction rate. Stages in the reaction A + B -A -H B (see text). Solvent molecules are not shown (see Figure 2.5, Section 2.5).

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