Kinetics considerations

The rate of copolymer formation between two immiscible reactive polymers depends on the interfacial area available for the reaction and the kinetics at the interfaces. For a given 

Equations 6.6 and 6.7 show that in both unentangled and entangled regimes, when the reaction is diffusion controlled, the interfacial rate constant is insensitive to interfacial structure (e.g. interfacial thickness) and dynamics. This is because the rate limiting step is the slow diffusive transport of a reactive chain to within a critical distance of the interface. In the entangled regime, this critical distance is comparable to the radius of gyration of the chain, Rg. Sub-diffusive transport is assumed to be very rapid. 

It should be noted that Eqs. 6.5 to 6.7 are valid only for the initial rate of copolymer formation. As the interfacial reaction proceeds further, the interface is saturated with more and more copolymer chains and the density of A and B reactive chains in the interfacial region, initially at po, will decrease. These will lead to a decrease in the growth rate of the copolymer at the interface, S(t). There are three regimes for cases with dilute concentrations of A and B reactive chains, as shown in Table 6.2 and Fig. 6.4 [16]. 

After an induction period, the interfacial reaction begins. In the early stage of the reaction, corresponding to times satisfying t V the time at which the density of the reactive chains at the interface starts to decay, both depletion of reactive chains at the interface and 

In the intermediate stage of the reaction or t t t the time at which saturation of the interface by copolymer remains negligible, but the interfacial concentrations of A and B reactive chains, pAi(t) and PBj(t), are reduced below their bulk concentrations, PAi(t) = pBi(t) = Po( Ap) - I other words, within this time interval, there is a depletion hole of reactive chains with spatial extension (DcomO - The reaction rate is dominated by the flux of reactive chains to the interface and is independent of the reaction kinetics, kinto- The copol5nner coverage grows as the square root of time 

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The thickness depends on the supercooling, which, in turn, is the result of kinetic considerations. Accordingly, crystal thickness is related to T, but neither have much to do with T . 

The fundamental equilibrium relationships we have discussed in the last sections are undoubtedly satisfied to the extent possible in polymer crystallization, but this possibility is limited by kinetic considerations. To make sense of the latter, both the mechanisms for crystallization and experimental rates of crystallization need to be examined. 

There are two general theories of the stabUity of lyophobic coUoids, or, more precisely, two general mechanisms controlling the dispersion and flocculation of these coUoids. Both theories regard adsorption of dissolved species as a key process in stabilization. However, one theory is based on a consideration of ionic forces near the interface, whereas the other is based on steric forces. The two theories complement each other and are in no sense contradictory. In some systems, one mechanism may be predominant, and in others both mechanisms may operate simultaneously. The fundamental kinetic considerations common to both theories are based on Smoluchowski s classical theory of the coagulation of coUoids. 

Kinetic Considerations. Extensive kinetic and mechanistic studies have been made on the esterification of carboxyHc acids since Berthelot and Saint-GiHes first studied the esterification of acetic acid (18). Although ester hydrolysis is catalyzed by both hydrogen and hydroxide ions (19,20), a base-catalyzed esterification is not known. A number of mechanisms for acid- and base-catalyzed esterification have been proposed (4). One possible mechanism for the bimolecular acid-catalyzed ester hydrolysis and esterification is shown in equation 2 (6). 

The law of mass action, the laws of kinetics, and the laws of distillation all operate simultaneously in a process of this type. Esterification can occur only when the concentrations of the acid and alcohol are in excess of equiUbrium values otherwise, hydrolysis must occur. The equations governing the rate of the reaction and the variation of the rate constant (as a function of such variables as temperature, catalyst strength, and proportion of reactants) describe the kinetics of the Hquid-phase reaction. The usual distillation laws must be modified, since most esterifications are somewhat exothermic and reaction is occurring on each plate. Since these kinetic considerations are superimposed on distillation operations, each plate must be treated separately by successive calculations after the extent of conversion has been deterrnined (see Distillation). 

Monomer molecules, which have a low but finite solubility in water, diffuse through the water and drift into the soap micelles and swell them. The initiator decomposes into free radicals which also find their way into the micelles and activate polymerisation of a chain within the micelle. Chain growth proceeds until a second radical enters the micelle and starts the growth of a second chain. From kinetic considerations it can be shown that two growing radicals can survive in the same micelle for a few thousandths of a second only before mutual termination occurs. The micelles then remain inactive until a third radical enters the micelle, initiating growth of another chain which continues until a fourth radical comes into the micelle. It is thus seen that statistically the micelle is active for half the time, and as a corollary, at any one time half the micelles contain growing chains. 

From a thermodynamic and kinetic perspective, there are only three types of membrane transport processes passive diffusion, faeilitated diffusion, and active transport. To be thoroughly appreciated, membrane transport phenomena must be considered in terms of thermodynamics. Some of the important kinetic considerations also will be discussed. 

For all three halates (in the absence of disproportionation) the preferred mode of decomposition depends, again, on both thermodynamic and kinetic considerations. Oxide formation tends to be favoured by the presence of a strongly polarizing cation (e.g. magnesium, transition-metal and lanthanide halates), whereas halide formation is observed for alkali-metal, alkaline- earth and silver halates. 

The effects of concentration, velocity and temperature are complex and it will become evident that these factors can frequently outweigh the thermodynamic and kinetic considerations detailed in Section 1.4. Thus it has been demonstrated in Chapter 1 that an increase in hydrogen ion concentration will raise the redox potential of the aqueous solution with a consequent increase in rate. On the other hand, an increase in the rate of the cathodic process may cause a decrease in rate when the metal shows an active/passive transition. However, in complex environmental situations these considerations do not always apply, particularly when the metals are subjected to certain conditions of high velocity and temperature. 

The main disadvantage of this technique is that it relies on very accurate temperature measurement, particularly near the top of the temperature profile, so that the position of the 5°F point can be established and the tangent accurately constructed. Also, the end of the bed is predicted only from kinetic considerations when, in fact, other factors may be more important. In practice, however, although this introduces some scatter into successive measurements—as does variation in the duty required of the methanator—the technique has proved very satisfactory. 

The following section deals with the crystallization and interconversion of polymorphic forms of polymers, presenting some thermodynamic and kinetic considerations together with a description of some experimental conditions for the occurrence of solid-solid phase transitions. 

Crystallizations and Interconversions of Polymorphic F orms 3.1 Thermodynamic and Kinetic Considerations... 

The complexity of the system consisting of the diazonium ion and the four reaction products shown in Scheme 5-14 is evident. In contrast to the two-step reaction sequence diazonium ion <= (Z)-diazohydroxide <= (Z)-diazoate (Scheme 5-1 in Sec. 5.1), equilibrium measurements alone cannot give unambiguous evidence for the elucidation of the mechanistic pathway from, for example, diazonium ion to ( )-diazoate. Indeed, kinetic considerations show that, depending on the reaction conditions (pH etc.) and the reactivity of a given diazonium ion (substituents, aromatic or heteroaromatic ring), different pathways become dominant. 

In the previous sections, it was shown how thermodynamic and kinetic considerations govern a CVD reaction. In this section, the nature of the deposit, i.e., its microstructure and how it is controlled by the deposition conditions, is examined. 

Thermodynamic, mass transport, and kinetic considerations, which are reviewed in Ch. 2. 

Yarborough, W.A., Thermochemical and Kinetic Considerations in Diamond Growth, Diamond Films and Technology, 1(3) 165-180 (1992)... 

Emerson, S., Cranston, R., and Liss, P. (1979). Redox species in a reducing fjord Equilibrium and kinetic considerations, Deep-Sea Res. 26, 859-878. 

A more sophisticated understanding is linked to an appreciation of the interaction of thermodynamic and kinetic considerations and is likely to be dependent upon the ability to visualise some form of mental model involving molecular collisions and interactions (Gilbert, 2005). This allows the student to see that two reactions are occurring simultaneously ... 

Studies with other glycosidases " " showed, however, that effective inhibition by glycals is not a general phenomenon, and that inhibition does not correlate well with hydration to 2-deoxy-o-hexoses. Based on kinetic considerations, the interaction of glycosidases with D-glycals (A) can be described by the following scheme ... 

Backman, H., Arve, K., Klingstedt, F. et al. (2006) Kinetic considerations of H2 assisted hydrocarbon selective catalytic reduction of NO over Ag/Al203 Kinetic modelling, Appl. Catal. A 304, 86. 

Eigen s theory describes the self-organisation of biological macromolecules on the basis of kinetic considerations and mathematical formulations, which are in turn based on the thermodynamics of irreversible systems. Evolutionary processes are irreversibly linked to the flow of time. Classical thermodynamics alone cannot describe them but must be extended to include irreversible processes, which take account of the arrow of time (see Sect. 9.2). Eigen s theory is based on two vital concepts ... 

Based on kinetics considerations, it was possible to rule out a large number of HxSyOz species, including S atoms, which are known to react rapidly with ozone. The most likely candidate for X is S3 formed in the association of S atoms with S2, a reaction that could occur within the transfer line linking the furnace with the chemiluminescence chamber [120], Watson and Birks (unpublished results,... 

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