Diffusion limit rates

A common feature of biopolymer adsorjition is that its rate is usually one to tliree orders of magnitude smaller than the diffusion-limited rate to a perfect sink ... 

This treatment obviously is oversimplified. At the next level of development, it is necessary to incorporate the intermolecular forces between A and B. ° If A and B are ions of opposite charge, it is found that the diffusion-limited rate constant is about 10 M s . ... 

Equations (4-5) and (4-7) are alternative expressions for the estimation of the diffusion-limited rate constant, but these equations are not equivalent, because Eq. (4-7) includes the assumption that the Stokes-Einstein equation is applicable. Olea and Thomas" measured the kinetics of quenching of pyrene fluorescence in several solvents and also measured diffusion coefficients. The diffusion coefficients did not vary as t) [as predicted by Eq. (4-6)], but roughly as Tf. Thus Eq. (4-7) is not valid, in this system, whereas Eq. (4-5), used with the experimentally measured diffusion coefficients, gave reasonable agreement with measured rate constants. 

Diffusion-limited rate control at high basicity may set in. This is more eommonly seen in a true Br nsted plot. If the rate-determining step is a proton transfer, and if this is diffusion controlled, then variation in base strength will not affect the rate of reaction. Thus, 3 may be zero at high basicity, whereas at low basicity a dependence on pK may be seen. ° Yang and Jencks ° show an example in the nucleophilic attack of aniline on methyl formate catalyzed by oxygen bases. 

We define an effectiveness factor e as the ratio of the diffusion limited rate to the rate in the absence of diffusion limitation ... 

For a soluble enzyme that is not part of a multi-enzyme complex, the fastest rate of enzyme-inhibitor association is determined by the rate of molecular collisions between the two binding partners (i.e., the enzyme and the inhibitor) in solution. The rate of molecular collisions is in turn controlled by the rate of diffusion. The diffusion-limited rate of molecular collisions is dependent on the radii of the two binding molecules and the solution temperature and viscosity (Fersht, 1999) ... 

Schematic representation of reactant concentration profiles in various global rate regimes. I External mass transfer limits rate. II Pore diffusion limits rate. Ill Both mass transfer effects are present. IV Mass transfer has no influence on rate.

We have also measured the rate constant for the association reaction of two Mn(C0)5 radicals generated on photolysis of Mn2(CO)io- With appropriate assumptions regarding the absorption coefficient for Mn(C0)5, the rate constant for this reaction was determined to be (2.7 0.6) x 10 1 mole l s [6,10]. This is compatible with the diffusion limited rate constant for this reaction that has been measured in solution and is within an order of magnitude of a gas kinetic rate constant as would be expected for an essentially unactivated radical-radical association reaction [33a]. 

Xanthylidene also does not react measurably with 02. The lifetime of XA is the same in 02-saturated cyclohexane as it is in solutions which have been deoxygenated. Bearing in mind that triplet carbenes react with 02 at nearly the diffusion limited rate, if 3XA were in rapid equilibrium with XA, then 02 should shorten the apparent lifetime of the singlet by reacting with the triplet. 

Where k 1 and k301 are forward and reverse activation-controlled rate cosntants, kd is the ate constant for the diffusion of the fragments out of the solvent cage, and dif is the bimolecular diffusion-limited rate constant. 

Appendix) and the observed diffusion-limited rate constant 9 -1 -1... 

The hydroxyl radical reacts at nearly a diffusion limited rate (k 1 x 10 s to 5 X 10 s ) with the aromatic amino acids, as well as with me-... 

Hydrated electrons generated by pulse radiolysis reduce nitroprusside at diffusion limited rates to [Fe(CN)s(NO)] , which undergoes unimolecular decay within milliseconds to yield [Fe(CN)4(NO)] , which, in turn, persists for minutes in aqueous solution [89, 90]. 

Nazarov-like cyclization to give the carbozole tautomer 67. The latter undergoes a hydrogen shift and deprotonation to give the observed product. Typically, the isolated yields of carbazole are low because it reacts with nitrenium ion at the diffusion limited rate giving a poorly defined set of oxidized oligomeric products. Maximal yields of carbazole are obtained only when the reaction is carried out under highly dilute conditions. 

One specific embodiment of this approach has been to use the azide (az) clock method (Fig. 13.62). ° Azide ion (N3 ) is a very strong nucleophile (Nu) and is thus assumed to react with most arylnitrenium ions at the diffusion—limited rate. 

Values for kDM obtained in this way are compared in Table IV with the diffusion-limited rate constant kD computed from the relationship10... 

Intraparticle diffusion limits rates in triphase catalysis whenever the reaction is fast enough to prevent attaiment of an equilibrium distribution of reactant throughout the gel catalyst. Numerous experimental parameters affect intraparticle diffusion. If mass transfer is not rate-limiting, particle size effects on observed rates can be attributed entirely to intraparticle diffusion. Polymer % cross-linking (% CL), % ring substitution (% RS), swelling solvent, and the size of reactant molecule all can affect both intrinsic reactivity and intraparticle diffusion. Typical particle size effects on the... 

At higher concentrations, nitrogen dioxide will further react with most organic radicals at near diffusion limited rates to form a nitroderivative (R—NO2). 

Over molecular length scales, the diffusion distances become very short (< 1 nm) so that only very rapid events can be influenced by these short diffusion times. Necessarily, this limits the number of systems to only relatively few, where the rate at which the reactants can approach one another is slow or comparable with the rate at which the reactants react chemically with each other. Some typical systems which have been studied are discussed in Sect. 2. The Smoluchowski [3] theory of reactions in solution, which occur at a rate limited solely by how fast the reactants can approach each other (sufficiently closely to react chemically almost instantaneously) is discussed in Sect. 3. If the chemical reaction is not so rapid, the observed rate of reaction may be influenced by both the rate of approach and the rate of subsequent chemical reaction. Collins and Kimball [4], and later Noyes [5], have extended the Smoluchowski theory (1917) to consider this situation (Sect. 4). In light of these quantitative theoretical models of diffusion-limited rate processes, some of the more recent and careful experiments on diffusion-controlled reactions in solution are considered briefly in Sect. 5. As the Smoluchowski theory... 

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