Diffusion clock method

Recognizing this, Richard and Jencks, proposed using azide ion as a clock for obtaining absolute reactivities of less stable cations. The basic assumption is that azide ion is reacting at the diffusion limit with the cation. Taking 5 x 10 M s as the second-order rate constant for this reaction, measurement of the selectivity fcaz Nu for the competition between azide ion and a second nucleophile then provides the absolute rate constant since feaz is known. The clock approach has now been applied to a number of cations, with measurements of selectivities by both competition kinetics and common ion inhibition. Other nucleophiles have been employed as the clock. The laser flash photolysis (LFP) experiments to be discussed later have verified the azide clock assumption. Cations with lifetimes in water less than about 100 ps do react with azide ion with a rate constant in the range 5-10x10 M- s-, " which means that rate constants obtained by a clock method can be viewed with reasonable confidence. 

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. 

The reaction of azide ions with carbocations is the basis of the azide clock method for estimating carbocation lifetimes in hydroxylic solvents (lifetime = 1 lkiy where lq, is the first-order rate constant for attack of water on the carbocation) this is analogous to the radical clock technique discussed in Chapter 10. In the present case, a rate-product correlation is assumed for the very rapid competing product-forming steps of SN1 reactions (Scheme 2.24). Because the slow step of an SN1 reaction is formation of a carbocation, typical kinetic data do not provide information about this step. Furthermore, the rate constant for the reaction of azide ion with a carbocation (kaz) is assumed to be diffusion controlled (ca. 5 x 109 M 1 s 1). The rate constant for attack by water can then be obtained from the mole ratio of azide product/solvolysis product, and the molar concentrations of azide (Equation 2.18, equivalent to Equation 2.14) [48]. The reliability of the estimated lifetimes was later... 

Using the D values of the dialkylanilines at 298K and Equation 13.13, the time required for 1-phenylethyl and 1-naphthoxy radicals to move to the locations amenable to combine at the 2- and 4-positions of 1-naphthoxy, ca. 3.1 and 5.0 A, respectively, correspond to ca. 2.4-24 and 6.3-63 ns in unstretched PEG and ca. 24—240 and 63-630 ns in unstretched PE46, depending on the specific diffusion coefficient employed. The times required for formation of the keto intermediates of 2-AN and 4-AN from lb by the radical clock method described above are ca. 3 and 14 ns, respectively, in unstretched or sttetched PEG and ca. 2-3 and 26-33 ns, respectively, in unstretched LDPE. In stretched LDPE, where translocation increases... 

The lifetime of the ionic bicyclobutane is a parameter of prime importance. An attempt was made to estimate this parameter for the thio-derivative using the clocking method . The latter involves competition between two nucleophiles e.g., PhS" and the solvent MeOH. Assuming that the PhS " reacts with carbocations at a diffusion-controlled rate and given the product ratio as a function of concentration, the lifetime of 118 in methanol was calculated to be of the order of 10" seconds . ... 

The rate constants for reaction of Bu3SnH with the primary a-alkoxy radical 24 and the secondary ce-alkoxy radical 29 are in reasonably good agreement. However, one would not expect the primary radical to react less rapidly than the secondary radical. The kinetic ESR method used to calibrate 24 involved a competition method wherein the cyclization reactions competed with diffusion-controlled radical termination reactions, and diffusional rate constants were determined to obtain the absolute rate constants for the clock reactions.88 The LFP calibrations of radical clocks... 

The extension of equilibrium measurements to normally reactive carbocations in solution followed two experimental developments. One was the stoichiometric generation of cations by flash photolysis or radiolysis under conditions that their subsequent reactions could be monitored by rapid recording spectroscopic techniques.3,4,18 20 The second was the identification of nucleophiles reacting with carbocations under diffusion control, which could be used as clocks for competing reactions in analogy with similar measurements of the lifetimes of radicals.21,22 The combination of rate constants for reactions of carbocations determined by these methods with rate constants for their formation in the reverse solvolytic (or other) reactions furnished the desired equilibrium constants. 

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