Translational diffusion controlled termination

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. 

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. 

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. 

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. 

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). 

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. 

There is no precise method for the measurement of the termination rate. Major difficulties in rate constant determination arise from the diffusion control of this reaction. Termination rate may depend on segmental and translation diffusion (and reaction diffusion) of radical species occurring in an increasingly viscous medium that change with monomer conversion. In other words, because of the decrease of the diffusion coefficient with molecular size, the termination rate coefficient is lower at higher chain lengths. 

Reactions that are bimolecular can be affected by the viscosity of the medium. The translational motions of flexible polymeric chains are accompanied by concomitant segmental rearrangements. Whether this applies to a particular reaction, however, is hard to tell. For instance, two dynamic processes affect reactions, like termination rates, in chain-growth polymerizations. If the termination processes are controlled by translational motion, the rates of the reactions might be expected to vary with the translational diffusion coefhcients of the polymers. Termination reactions, however, are not controlled by diffusions of entire molecules, but only by segmental diffusions within the coiled... 

The main diffusion-controlled parameter in Refs. [52,53,58,76] is the constant rate of chain propagation depending on the translational mobility of the monomer, determined by the function of the free volume of monomer/polymeric solution. It is considered that the chain termination is limited by the chain propagation, even in the middle states of the conversion as a result of the formation of a viscous network system. In this case only one type of diffusion exists, namely a diffusion of the polymer chain propagation, and the coefficient of this diffusion Dp [52] is determined as a function on the bond length I taking into account that all lengths of bonds in the macromolccule are the same ... 

Experimental results, shown in Figure 3.6, are explained as follows by the above-mentioned authors. At the beginning of the reaction, the high increase in viscosity reduces the segmental or translational diffusion of the reactive species and the collision between two radicals is more and more difficult. As a result decreases faster than and increases. Then, the termination mechanism becomes a diffusion-controlled reaction and can be assimilated to a propagation mechanism. From the top of the curve and because of the great decrease in the mobility of species, first propagation and termination constants and then decrease quickly. 

Problem 6.28 The bimolecular chain termination in free-radical polymerization is a diffusion-controlled reaction that can be treated as a three-stage process (North and Reid, 1963 Odian, 1991), described below. Stage 1. Translational diffusion of the centers of gravity of two macroradicals to such close proximity that certain segments of each chain can be considered to be in contact ... 

The onset of the gel effect has been defined in terms of a switch from control of termination by segmental diffusion of polymer radicals to control by translational diffusion. Entanglement of polymer radicals can explain kinetic aspects of the polymerization of methyl methacrylate up to the stage where growth is diffusion controlled. Features of high conversion polymerizations of styrene and benzyl methacrylatehave been explained in terms of diffusion control of termination,... 

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