Translational diffusion controlled

This form predicts that k approaches zero when either k or k approaches zero. Considering that the beginning of the gel effect is the result of translational diffusion controlled termination (1), it is reasonable to assume that k may become very small if the translational diffusivity of the i-mer approaches zero. However, if i-mer radicals whose k = 0 are mixed with j-mer radicals whose k i 0, it must be realized that there can be termination due to the mobility of the j-mer. Equation (3) would predict no reaction and on this basis the authors do not accept the geometric mixing rule as having general applicability. 

Scheme 1 Three steps involved in bimolecular termination of radicals translational diffusion, segmental diffusion, and chemical activation. Radical termination is always diffusion controlled segmental diffusion controlled at low conversions, and translational diffusion controlled at high conversions. ...

The rate coeffident for termination under translational diffusion control kn), which primarily affects the section where the steep decrease of occurs, may be expressed as fem=ItJo/ >/r (see first term on the r.h.s. of eqn [9]). Although depends on both polymer content and the type of polymer produced, it has turned out in preceding studies on bulk (meth)acrylate and MMA solution polymerizations that rji may be represented by the simplifying expression ... 

The situation is somewhat more complex when using water as the solvent. Data on kt in aqueous solution, however, is scarce and not all effects are fully understood. Studies into kt in polymerization of l-vinylpyrrolidin-2-one in a solution of water, for instance, has revealed that the full mechanism of termination is shifted with increasing content of water (see Figure 1.8) Termination is being enhanced with increasing concentration of water and the transition between segmental and translational diffusion control is shifting simultaneously. 

Radical polymerizations of macromonomers are greatly influenced by the diffusion control effect [44]. Segmental diffusivity and translational diffusivity of the growing chains of macromonomers are strongly affected by the feed concentration and the molecular weight of the macromonomers. Furthermore, there is little difference in the degree of polymerization between macro-... 

As the polymerization reaction proceeds, scosity of the system increases, retarding the translational and/ or segmental diffusion of propagating polymer radicals. Bimolecular termination reactions subsequently become diffusion controlled. A reduction in termination results in an increase in free radical population, thus providing more sites for monomer incorporation. The gel effect is assumed not to affect the propagation rate constant since a macroradical can continue to react with the smaller, more mobile monomer molecule. Thus, an increase in the overall rate of polymerization and average degree of polymerization results. 

When the two monomers are linked by a short flexible chain, intramolecular excimers can be formed. This process is still diffusion-controlled, but in contrast to the preceding case, it is not translational it requires a close approach between the two molecules via internal rotations during the excited-state lifetime. Equations (4.44), (4.45), (4.47) to (4.49) are still valid after replacing k [M] by k because intramolecular excimer formation is independent of the total concentration. Estimation of the local fluidity of a medium can be achieved by means of probes capable of forming intramolecular excimers (see Chapter 8). 

Anticipating the discussion on acetylene polymerization [98], extensively reported in Section IV, a value of n = 0.6 has been found, which implies a linear diffusion-controlled growth where the molecular librational and translational oscillations control the approach of the monomers to the active sites (chain terminations). 

Specific diffusion control The rate constants depend on the size and topology of the molecule the group is bound to i.e., they depend on the translation diffusion coefficient of the species. 

Then, they depend also on the viscosity of the system. Specific diffusion control is characteristic of fast reactions like fluorescence quenching. In polymer formation, specific diffusion control is responsible for the acceleration of chain polymerization due to the retardation of the termination by recombination of two macroradicals (Trommsdorff effect). Step reactions are usually too slow to exhibit a dependence on translational diffusion also, the temperature dependence of their rate constants is of the Arrhenius type. 

If ki and k.i are much larger than kj, the reaction Is controlled by kj. If however, ki and k.i are larger than or comparable to kz, the reaction rate becomes controlled by the translational diffusion determining the probability of collisions which Is typical for specific diffusion control. The latter case Is operative for fast reactions like fluorescence quenching or free-radical chain reactions. The acceleration of free-radical polymerization due to the diffusion-controlled termination by recombination of macroradicals (Trommsdorff effect) can serve as an example. 

That steps involving atomic or molecular motion can be rate determining, even in fluids, is well known through diffusion limited reaction rates and the solvent cage effect. In solids, motion more subtle than translational diffusion can be influential, and cases of rotational diffusion control are familiar [7],... 

D. The chronoamperometric results can also be used to ascertain the number of electrons involved in the formation of benzonitrile from p-chloro-benzonitrile. In order to translate the chronoamperometric data into a meaningful n value, a compound is selected that has a diffusion coefficient very similar to that of p-chlorobenzonitrile and that gives a stable, known product upon electroreduction. Tolunitrile, which satisfies these criteria, is known to be reduced to its radical anion at a diffusion-controlled rate. Since this one-electron process gives a value of 168 pA s1/2- M x cm 2 for it1/2/CA, the corresponding value of 480 pA s1/2 A/ 1 cm-2 for the reduction of p-chlorobenzonitrile to benzonitrile anion radical must represent an overall three-electron process. When we subtract the one electron that is required to reduce benzonitrile to its radical anion from this total, we immediately conclude that two electrons are involved in cleavage of the carbon-chlorine bond in p-chlorobenzonitrile. A scheme that is consistent with these data is described by Equations 21.1 to 21.6. 

The second explanation for the solvent isotope effect arises from the dynamic medium effect . At 25 °C the rotational and translational diffusion of DjO molecules in D20 is some 20% slower than H20 molecules in H20 (Albery, 1975a) the viscosity of D20 is also 20% greater than H20. Hence any reaction which is diffusion controlled will be 20% slower in D20 than in H20. This effect would certainly apply to transition state D in Fig. 3 where in the transition state the leaving group is diffusing away. A similar effect may also apply to the classical SN1 and SN2 transition states, if the rotational diffusion of water molecules to form the solvation shell is part of the motion along the reaction co-ordinate in the transition state. Robertson (Laughton and Robertson, 1959 Heppolette and Robertson, 1961) has indeed correlated solvent isotope effects for both SN1 and SN2 reactions with the relative fluidities of H20 and D20. However, while the correlation shows that this is a possible explanation, it may also be that the temperature variation of the solvent isotope effect and of the relative fluidities just happen to be very similar (see below). 

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