Expulsion rate constant

Using a system of rate equations cmistructed from the above mechanism, Aniansson and Wall showed that in a relaxation experiment close to equilibrium, in the linear regime, the relaxation is determined by two relaxation time constants. The first time constant characterizes the fast relaxation associated with a readjustment of the unimer concentration, without a change in the number density of micelles. As shown by Aniansson and Wall, this contribution depends on the expulsion rate constant, the width of the distribution of the micellar population, a, and the fraction of unimers, X. 

Thus, this simple result suggests that the rate of unimer exchange is governed by the expulsion rate constant. We will see later that this approximation is indeed a good assumption when we compare with the proposed models for unimeric expul-sion/insertion. 

Given the central role of the expulsion rate constant for micellar stability, formation, and dissociation, it is essential to determine the physical governing factors and functional form. Aniansson and Wall based their calculations [54] on a general diffusion in an external potential. In this approach, the diffusion coefficient, D(r) is dependent on the position, r, due to the potential V(r). In a sphero-symmetric system, we can imagine that the diffusion of a unimer only depends on the distance, r, from the origin and this problem can be summarized in a Einstein-Smoluchowski type equation ... 

Hence, the most important process for the equilibrium kinetics is the unimer exchange mechanism which, as expected from the Aniansson-WaU scenario, is mainly governed by the expulsion rate constant. In the model of Halperin and Alexander this release of a single unimer from the micelle is pictured to go through two stages ... 

Equivalently, the same scenario can be expressed mathematically in terms of the expulsion rate constant, kF, which gives ... 

It has been tacitally assumed in this discussion that the second-order formation rate constants measure the simple water substitution process. Although this must apply when unidentate ligands replace coordinated water, a composite process could describe the replacement by multidentate ligands. However, consideration of rate constants for successive formation and dissociation processes suggests that the overall rate of complex formation with flexible bidentate (and probably multidentate) ligands such as diamines, dipyridyl, glycine is probably determined by the rate of expulsion of the first water molecule from the metal aqua ion (56, 80, cf. 3 and 84). 

The extent of catalysis depends critically upon the stability of the intermediate 1. If the rate of expulsion of H20 from 1 (rate constant 7c i) is slower than proton transfer to solvent water, the rate of formation of the intermediate (rate constant ki) will be the rate-limiting step and no catalysis will be observed. The rate constant for protonation of the amine nitrogen of 1 by solvent water, 7cHa (HA = H20), depends on the basicity of the nitrogen and is given by kAKw/Ka, where kA represents the rate constant for diffusion-controlled abstraction of a proton by hydroxide ion, with a value of approximately 1010 M-1 s 1, and... 

The rate constant for expulsion of RNH2 to regenerate the reactants, k 1, is between 106 and 109 s-1 and much faster than that for proton transfer to water (B = H20), which is between 10-1 and 102 s 1. When the general base catalyst is a second molecule of amine... 

The kinetics associated with halide expulsion are rapid, and, in order to measure the rate constant associated with the C step, fast rates of convective... 

Reaction in 1,1,2-trichloroethane at 47.5°C follows first-order kinetics with a rate constant of 4.53 x 10 s. The ethalpy and entropy of activation are 99.2 + 2.1 kJ mol and 16.7 4.2 J mol" deg", respectively. From a kinetic study of other NRj derivatives, the rate of this rearrangement is determined mainly by the bulk of the R substituent (smaller R giving a faster rate). This rearrangement proceeds via an intramolecular migration of Cl from the carbene C to the Cr atom, with simultaneous expulsion of a cis CO ligand. Isomerization to the trans isomer occurs subsequently. ... 

Conjugated unsaturated ketones are unreactive to peracids because of the depletion of electronic charge in the olefiinic bond, but epoxyketones are readily prepared by using the nucleophilic hydroperoxide ion (H02"") [284], In simple aliphatic compounds the epoxidation follows kinetics first order with respect to hydroperoxide ion and unsaturated ketone [28s]- According to House [286], the reaction should be represented as a reversible addition of hydroperoxide ion, followed by closure of the epoxide ring in a slow step, with expulsion of hydroxide ion. The over-all rate will be determined both by the equilibrium constant in the first step and by the rate constant for the second. 

The main reaction in MeCN occurs through a base-catalyzed pathway involving formation of a zwitterionic intermediate, equilibrium formation of an anionic intermediate and a rate-limiting proton transfer to base, rate constant kc, followed by a fast leaving-group expulsion. The corresponding reactions in DMSO, however, are found to proceed by both uncatalyzed (via kh) and catalyzed pathways. Similar reactions in benzene show that the Hammett coefficient determined with substituted anilines for the catalyzed path is extremely large (p = —7.7) relative to that for the uncatalyzed path (p = —4.7). The Bronsted fix value (which may, however, be unreliable since the p fa(H20) values are... 

The radical carbonylation of alkyl and aryl radicals and the cyclization of the resulting acyl radicals onto tcrz-butyl sulfides leads to the formation of y-thiolac-tones with expulsion of the tert-butyl radical (Scheme 4-52) [89]. This process is applicable to a range of substituted 4-rerr-butylthiobutyl bromides and iodides giving moderate to excellent yields of the corresponding thiolactones. Using acyl selenide/tin hydride chemistry and competition kinetic methods, the rate constant for the cyclization was determined to be 7.5x10 s at 25 °C [89]. 

Rate constant for unimer insertion from micelle of size P Rate constant for unimer expulsion from micelle of size P... 

Reactions with neutral molecules have been investigated by the flowing afterglow (FA) technique (see [2, 3]) and earlier by ICR spectroscopy. The reaction usually starts with an initial nucleophilic attack of PHg on the neutral, followed by Intramolecular proton transfer and/or expulsion of a neutral fragment [4]. The table on p. 110 lists the rate constants k at 298 K (with an estimated error of 25% for the FA measurements [4]), efficiencies k/k oo (with kADo calculated by the average-dipole-orlentation theory of [5]), products (neutral products were not detected), and branching ratios, k and the branching ratio depend on the total pressure, when adducts are formed. Molecules, for which no reaction could be observed, are listed below the table. 

A kinetic study of the acid-catalysed loss of alkoxide and thiolate ions from alkoxide and thiolate ion adducts, respectively, of benzylidene Meldrum s acid, methoxy-benzylidene Meldrum s acid, and thiomethoxybenzylidene Meldrum s acid has been reported. The reactions appear to be subject to general acid catalysis, although the catalytic effect of buffers is weak and the bulk of the reported data refers to H+ catalysis. a-Carbon protonation and, in some cases, protonation of one of the carbonyl oxygens to form an enol compete with alkoxide or thiolate ion expulsion. This scenario rendered the kinetic analysis more complex but allowed the determination of p/fa values and of proton-transfer rate constants at the a-carbon. In conjunction with the previously reported data on the nucleophilic addition of RO and RS ions to the same Meldmm s acid derivatives, rate constants for nucleophilic addition by the respective neutral alcohols and thiols could also be calculated. ... 

The above theory was extended by Dormidontova ° to larger deviations from equilibrium and as to include the time for the disentanglement of the insoluble block from the micelle core as well as micelle fusion/fission processes. The insoluble (hydrophobic) block in free copolymers is assumed to be in a collapsed state as in Reference 19. The author first derived scaling laws for the energetic barriers to the different processes unimer insertion/expulsion and micelle fusion/fission. The Kramers theory of rate constants in the high viscosity... 

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