Kinetic Volume Effects

The value of the exponent a obtained in the above-mentioned experiments is in remarkable accord with predictions based on a consideration of excluded kinetic volume effects. Khokhlov51 proposed, that for a slow, chemically controlled, reaction between the ends of long chains a should be 0.16. The value of a was suggested to increase to 0,28 for chain end-mid chain reaction and to 0.43 for midchain-mid chain reaction. The latter provides one possible explanation for the greater exponent for higher acrylates (Table 5.11.32... 

In contrast, the parameters of local motions are very sensitive to the local conformational microstructure of the polymer chain and to the interactions of units located at a large distance apart along the chain contour but close to each other in space (kinetic volume effects). The parameters of local motions also depend on the external viscosity of the solvent and internal viscosity of the polymer chain... 

A series of theoretical studies of the SCV(C)P have been reported [38,40,70-74], which give valuable information on the kinetics, the molecular weights, the MWD, and the DB of the polymers obtained. Table 2 summarizes the calculated MWD and DB of hyperbranched polymers obtained by SCVP and SCVCP under various conditions. All calculations were conducted, assuming an ideal case, no cyclization (i.e., intramolecular reaction of the vinyl group with an active center), no excluded volume effects (i.e., rate constants are independent of the location of the active center or vinyl group in the macromolecule), and no side reactions (e.g., transfer or termination). 

Jenner investigated the kinetic pressure effect on some specific Michael and Henry reactions and found that the observed activation volumes of the Michael reaction between nitromethane and methyl vinyl ketone are largely dependent on the magnitude of the electrostriction effect, which is highest in the lanthanide-catalyzed reaction and lowest in the base-catalyzed version. In the latter case, the reverse reaction is insensitive to pressure.52 Recently, Kobayashi and co-workers reported a highly efficient Lewis-acid-catalyzed asymmetric Michael addition in water.53 A variety of unsaturated carbonyl derivatives gave selective Michael additions with a-nitrocycloalkanones in water, at room temperature without any added catalyst or in a very dilute aqueous solution of potassium carbonate (Eq. 10.24).54... 

It is easy to understand the lower reactivity of non-ionic nucleophiles in micelles as compared with water. Micelles have a lower polarity than water and reactions of non-ionic nucleophiles are typically inhibited by solvents of low polarity. Thus, micelles behave as a submicroscopic solvent which has less ability than water, or a polar organic solvent, to interact with a polar transition state. Micellar medium effects on reaction rate, like kinetic solvent effects, depend on differences in free energy between initial and transition states, and a favorable distribution of reactants from water into a micellar pseudophase means that reactants have a lower free energy in micelles than in water. This factor, of itself, will inhibit reaction, but it may be offset by favorable interactions with the transition state and, for bimolecular reactions, by the concentration of reactants into the small volume of the micellar pseudophase. 

The method of mathematical simulation has many advantages, and is very close to the physical experiment. However the further development of this approach /a consideration of volume effects, reversible reactions and so onj can be rather difficult because it will reau.ire too much computer time, therefore it is expedient to search some simple analytical or semianalytical approximate approaches to the calculation of cross-linking kinetics and conformational properties of cross-linked macromolecules. The results obtained bv the Fonte Carlo calculation can serve as criteria of the accuracy of such approximation. 

Equations (8) and (10) are applicable to stable isotope systems where isotopic fractionation occurs through mass-dependent processes which comprise the majority of cases described in this volume. These relations may also be used to identify mass-independent fractionation processes, as discussed in Chapter 2 (Birck 2004). Mass-dependent fractionation laws other than those given above distinguish equilibrium from kinetic fractionation effects, and these are discussed in detail in Chapters 3 and 6 (Schauble 2004 Yormg and Galy 2004). Note that distinction between different mass-dependent fractionation laws will generally require very... 

Excluded volume effects in cytoplasm, MOLECULAR CROWDING Excluding kinetic reaction mechanisms, HALDANE RELATION EXERGONIC EXOCYTOSIS EXOENZYME EXOERGIC Exo-j8-f ru ctosi d ase,... 

Quantum chemical calculations need not be limited to the description of the structures and properties of stable molecules, that is, molecules which can actually be observed and characterized experimentally. They may as easily be applied to molecules which are highly reactive ( reactive intermediates ) and, even more interesting, to molecules which are not minima on the overall potential energy surface, but rather correspond to species which connect energy minima ( transition states or transition structures ). In the latter case, there are (and there can be) no experimental structure data. Transition states do not exist in the sense that they can be observed let alone characterized. However, the energies of transition states, relative to energies of reactants, may be inferred from experimental reaction rates, and qualitative information about transition-state geometries may be inferred from such quantities as activation entropies and activation volumes as well as kinetic isotope effects. 

Experiments cannot tell us what transition states look like. The fact is that transition states cannot even be detected experimentally let alone characterized, at least not directly. While measured activation energies relate to the energies of transition states above reactants, and while activation entropies and activation volumes, as well as kinetic isotope effects, may be invoked to imply some aspects of transition-state structure, no experiment can actually provide direct information about the detailed geometries and/or other physical properties of transition states. Quite simply, transition states do not exist in terms of a stable population of molecules on which experimental measurements may be made. Experimental activation parameters provide some guide, but tell us little detail about what actually transpires in going from reactants to products. 

Perhaps the biggest oversight physical chemists make when discussing kinetics is the neglect of volume effects. To be sure any chemical engineer who would forget the influence of volume even in a constantly stirred tank reactor would not be long in the profession. The volume alone can affect the rate of the reaction. How many physical chemistry courses, or text books, point that out ... 

In other words, it is assumed here that the particles are surrounded by a isotropic viscous (not viscoelastic) liquid, and is a friction coefficient of the particle in viscous liquid. The second term represents the elastic force due to the nearest Brownian particles along the chain, and the third term is the direct short-ranged interaction (excluded volume effects, see Section 1.5) between all the Brownian particles. The last term represents the random thermal force defined through multiple interparticle interactions. The hydrodynamic interaction and intramolecular friction forces (internal viscosity or kinetic stiffness), which arise when the macromolecular coil is deformed (see Sections 2.2 and 2.4), are omitted here. 

U. Gosele. Thin-film compound formation Kinetics and effects of volume changes / In Alloying (Eds. J.L. Walter, M.R. Jackson, Ch.T. Sims). - Metals Park (Ohio) ASM International, 1988.-P.489-519. 

The diffraction pattern registers the volume effect regarding the distribution of crazing. In principle if the distribution of crazing is random, the measurements of the diffracted laser intensity should yield the kinetic information on the accumulation of crazing. 

Much of what is currently understood about the Cenozoic history, of deep-sea temperature, carbon chemistry, and global ice volume, has been gleaned from the stable isotope ratios of benthic foraminifera. Benthic foraminifera extract carbonate and other ions from seawater to construct their tests. In many species, this is achieved near carbon and oxygen isotopic equilibrium. Kinetic fractionation effects tend to be small and constant (Grossman, 1984, 1987). As a result, shell fi C and strongly covary with the isotopic... 

Details of sulfur isotope geochemistry are presented elsewhere in this volume (see Chapter 7.10) and are only highlighted here as related to paleo-environmental interpretations of finegrained siliciclastic sequences. Formation of sedimentary pyrite initiates with bacterial sulfate reduction (BSR) under conditions of anoxia within the water column or sediment pore fluids. The kinetic isotope effect associated with bacterial sulfate reduction results in hydrogen sulfide (and ultimately pyrite) that is depleted in relative to the ratios of residual sulfate (Goldhaber... 

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