Diffusion-controlled rate constant reactivity

At higher concentrations in solution, the photodimerization of tS has been studied by means of picosecond electronic absorption spectroscopy. The 5i state of tS in benzene at 22°C is quenched with a diffusion-controlled rate constant of 2.03 X lO M s to give a new reactive intermediate exhibiting an absorption maximum at 480 nm. This new species decays unimolecularly with a rate constant of (2.40 0.37) X 10 s. It has tentatively been assigned to either the excimer or a biradicaloid species located at the pericyclic minimum. 

Two Spheres. The steady state diffusion controlled rate constant for two uniformly reactive spheres interacting via a centrosymmetric potential of mean force can be solved numerically and in special cases analytically as given by Eq. 2. For a potential of mean force of zero and no hydrodynamic interaction (NHI), Eq. 2 reduces to the Smoluchowski result (1)... 

Adding viscous cosolvents, e.g., glycerol, to the parenteral formulation will reduce the mean diffusion path of the reactive intermediates and other reactive species. The diffusion-controlled rate constant (kD) of a given chemical reaction is inversely proportional to the viscosity of the formulation (Suppan and Nagwa, 1997) ... 

As expected, the parameters for stabilization and steric effects are positive, in good agreement with the decrease of the fee value with the inaease in both the stabilization and the bulkiness of the aminoxyl radical. It is shown that the major effect is due to the congestion around the aminoxyl moiety ( 90%) with a lower contribution of the stabilization effect ( 10%). The fec,o parameter has a value (2.2 x 10 °M" s" eqn [18]), typical of the diffusion-controlled rate constant that should correspond to the scavenging of alkyl radicals by the hypothetically more reactive dimethylaminoxyl radical. These studies showed that only the four a,a -substituents flanking the aminoxyl function governed the steric hindrance around the radical center. As a consequence, the fee value is independent of the type of nitroxide, provided they have the same substituents and the same stabilization effect. 

Rate constants for the reaction of hydroxyl radicals with different compounds were determined by Haag and Yao (1992) and Chramosta et al. (1993). In the study of Haag and Yao (1992) all hydroxyl radical rate constants were determined using competition kinetics. The measured rate constants demonstrate that OH0 is a relatively nonselective radical towards C-H bonds, but is least reactive with aliphatic polyhalogenated compounds. Olefins and aromatics react with nearly diffusion-controlled rates. Table 4-3 gives some examples comparing direct (kD) and indirect (kR) reaction rate constants of important micropollutants in drinking water. 

The various ways of forming OH were discussed in Chapter 2. It is a very reactive, electrophilic (9 = -0.41 Anbar et al. 1966a) radical, and with most substrates it reacts at close to diffusion-controlled rates (for a compilation of rate constants, see Buxton et al. 1988). It undergoes mainly three types of reactions (1) addition to C-C and C-N double bonds, (2) H-abstraction and (3) ET. Addition and H-abstraction reactions will be discussed below in some detail, because they are relevant for an OH-attack at the nucleobases and at the sugar moiety in DNA. 

The nucleobases and related compounds react with OH at close to diffusion-controlled rates. A compilation of rate constants is given in Table 10.6. In nucleosides and nucleotides, OH attacks mainly at the base moiety, but some H-abstraction also occurs at the sugar moiety (Chap. 3.3). It is recalled that the high reactivity of OH results in a very low OH steady-state concentration, and reactions with substrates, even when present at rather low concentrations, predominate over the their reactions with OH-induced substrate radicals. Thus,... 

An analogous comparison of the reactivity of anions and anionic complexes of Table VI reveals several interesting facts. In this table there are 40 compounds which react with e m at a rate which is more than 70% of the calculated diffusion controlled rate (11 of these compounds have been measured in the present study for the first time). However, only 18 compounds have a values between 0.7 and 1.5 and we consider them to agree reasonably well with the calculated ones. In some cases, the high a values may be because of the fact that they were calculated from the experimental rate constants without correcting for salt effects. These include the following compounds Cr(EDTA)", (6.9) Cr(OX) v3", (6.10) Co(CN)o3", (6.20) Co(CN)5CF, (6.21) Co(CN)5N023", (6.22) Co(N02)63", (6.23) and Co(EDTA)", (6.24). 

DELAIRE - I agree with you. The above-defined "activation-controlled rate constant", which is the expression of the "true" reactivity of species, may depend on distance, but is time-independent. However, the experimental rate constant has generally a contribution due to diffusion (see equation (26) ), and, due to the fact that a time interval is needed to establish steady-state profiles for the local concentrations of reactants, the experimental rate constant is time dependent. 

The reactivity of macromonomers in copolymerizalion is strongly dependent on the particular comonomer-macromonomer pair. Solvent effects and the viscosity of the polymerization medium can also be important. Propagation may become diffusion controlled such that the propagation rate constant and reactivity ratios depend on the molecular weight of the macromonomer and the viscosity or, more accurately, the free volume of the medium. 

The sum of all results is consistent with the formation of both the aryl cation and the aryl radical in the aqueous acid system without copper, and with the dominance of the aryl radical in the presence of copper. The product ratios are also qualitatively consistent with the hypothesis that the reactivity of aryl cations with nucleophiles is close to that of a diffusion-controlled process (see Sec. 8.3), and that aryl radicals have arylation rate constants that are about two orders of magnitude smaller than that for diffusion control (0.4-1.7 X 107 m-1s-1 Kryger et al., 1977 Scaiano and Stewart, 1983). Due to the relatively low yields of these dediazoniations in the pentyl nitrite/benzene systems, no conclusions should be drawn from the results. 

Table 12-2 gives some of Sterba s results for 1-naphthol, resorcinol, 1-methoxy-naphthalene, 3-methoxyphenol and 1,3-dimethoxybenzene. The data in the table show that the 1-naphthoxide ion is 108 times more reactive than the undissociated naphthol, which is 102 times more reactive than 1-methoxynaphthalene. The rate ratios for the monoanion of resorcinol relative to resorcinol, 3-methoxyphenol, and 1,3-dimethoxybenzene are of similar magnitudes. The dissociation of both OH groups of resorcinol gives rise to a rate constant (2.83 X 109 m -1 s-1) which, in our opinion, is probably mixing- or diffusion-controlled (see Sec. 12.9). 

A minor component, if truly minute, can be discounted as the reactive form. To continue with this example, were KCrQ very, very small, then the bimolecular rate constant would need to be impossibly large to compensate. The maximum rate constant of a bimolecular reaction is limited by the encounter frequency of the solutes. In water at 298 K, the limit is 1010 L mol-1 s"1, the diffusion-controlled limit. This value is derived in Section 9.2. For our immediate purposes, we note that one can discount any proposed bimolecular step with a rate constant that would exceed the diffusion-controlled limit. 

Several assumptions were made in order to analyze kinetic data in terms of this expression (2). First it was assumed that k 2 m kj, k2 k 3, and kj/k j k /k ( - If). Second it was assumed that the rate constants were independent of the extent of reaction i.e., that all six functional groups were equally reactive and that the reaction was not diffusion controlled. The concentration of polymer hydroxyl functionality was determined experimentally using infrared spectroscopy as described elsewhere (7). A major unknown is the instantaneous concentration of methanol. Fits to the kinetic data were made with a variety of assumptions concerning the methanol concentration. The best fit was achieved by assuming that the concentration of methanol was initally constant but decreased at a rate proportional to the concentration of residual polymer hydroxy groups towards the end of the reaction. As... 

Reaction of nitric oxide with superoxide is undoubtedly the most important reaction of nitric oxide, resulting in the formation of peroxynitrite, one of the main reactive species in free radical-mediated damaging processes. This reaction is a diffusion-controlled one, with the rate constant (which has been measured by many workers, see, for example, Ref. [41]), of about 2 x 109 1 mol-1 s-1. Goldstein and Czapski [41] also measured the rate constant for Reaction (11) ... 

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