Bimolecular termination rate constants

It is known that observing in radical polymerization processes change of chains bimolecular termination rate constant kt (reaction is controlled by diffusion) is often connected with the change of reaction solution viscosity [4, 5] which is naturally increased by the accumulation of reaction product in system - polymer. And then the contribution of viscosity factor is significant and that is why the reduction of rate constant of chains bimolecular termination kt is observed first of all. Fiowever, for a number of monomers it is necessary to consider the factor of influence of initial reaction solution viscosity on polymerization parameters. 

The obtained data (namely the non-linearity of change of Vp on [M]) may be explained by the fact that due to comparatively high values of r rei of initial solutions of monomer salts (at [M] > 1 mole l1) the constant of chains bimolecular termination rate kt even at conditions of very small conversions is turned to be sensitive to the viscosity of initial reaction solutions and consequently to monomer concentration. Mentioned change of values of relative viscosity with the rise of initial monomer concentration should lead to symbatic reduction of constant kt and thus to mentioned non-linear increase of polymerization initial rate. The suggested explanation may be checked experimentally. If we assume that in the studied system the constant kt is naturally depended on monomer solution viscosity then in accordance with North s conceptions [4, 5] we should take that k0 rf1. Then polymerization rate may be calculated by equation 1... 

They were able to observe that inereased styrene eoneentrations reduces the polymerization rates of both methaerylate and styrene due to an inerease in the termination rate and due to flie stability of the styryl radical. Raising styrene concentrations also inereases the final methacrylate conversion, but the final styrene conversion decreases because styrene plasticizes the network, allowing methacrylate conversion to rise at higher styrene concentrations. The final concentration of radicals is reduced at higher styrene concentrations, because of an increase in the bimolecular termination rate for networks with low cross-link densities. The proportion of styryl radicals trapped in the vitrified matrix was found to be markedly higher flian the proportion predicted from the ratio of styrene monomer in the feed resin or from the copolymerization rate constants... 

Two types of functions in the models for the description of the polymerization processes at moderate and high conversions have been described in the literature [47-53, 57-61, 63, 70-75]. For example, in Ref. [63] until the depth of conversion 7-0,6, the kinetics of the polymerization process are described by a change of the bimolecular chain termination rate constant parameters of the propagation and initiation efficiency are assumed to be constant values. Decreasing the chain termination constant rate via especial empirical dependence has been introduced for values of F > 0,6. Decreasing the chain termination constant rate for F < 0,6 is determined via the coefficients of the translational and segmental diffusion of the macroradicals ... 

From equation (4.49) we obtain k = 6nr DJ for the bimolecular chain termination rate constant. By estimation of the diffusion coefficient of a macroradical in a range of three orders of magnitude (from the diffusion coefficient in the liquid phase to the diffusion coefficient in the solid phase) Di=10 -10" m s" we find A ,=5x(10 -10 ) m moP. s". In the liquid monomeric phase the value tv, in accordance with the literature, is estimated to be in the range / .=10 -10 m moP s . Comparison of the obtained estimations does not confirm this, but at the same time does not exclude the possibility of the diffusion control on the rate of bimolecular chain termination in the liquid monomeric phase. Simultaneously, the values k and ka from Table 4.3 are 6-7 orders of magnitude smaller than kx and convincingly confirm that they do not present the bimolecular chain termination in the interface layer. That is why the question about the diffusion controls on /t,i and ka should be discussed in another way. 

The weak gel-effect, which is exhibited as a linear section of the kinetic curve up to the autoacceleration stage, is caused by partial diffusion control on the rate of bimolecular chain termination. Thus, we present the chain termination rate constant Jt,v in the following... 

In the absence of antioxidants, radicals terminate according to bimolecular processes (steps 4, 5 and 6). At relatively low temperature, close to ambient temperature, the corresponding termination rate constants classify in the following order (Gillen et al., 1995) ... 

Kinetic results were consistent with a bimolecular termination reaction whereas reaction products and mechanisms were something of a mystery. At that time it was known that the termination rate constant for autoxidation of cumene ( ) is about three orders of magnitude smaller than the termination rate constant for autoxidation of tetralin (7.). It was, however, generally accepted that the tennination rate constants for tertiary ( ) and secondary (9 ) alkylperoxy radicals are insensitive to the structure of the hydrocarbon residue in the radical. 

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. 

A characteristic reaction of free radicals is the bimolecular self-reaction which, in many cases, proceeds at the diffusion-controlled limit or close to it, although the reversible coupling of free radicals in solution to yield diamagnetic dimers has been found to be a common feature of several classes of relatively stable organic radicals. Unfortunatly, only the rate constants for self-termination of (CH3)jCSO (6 x 10 M s at 173 K) and (CH3CH2)2NS0 (1.1 X 10 M s at 163K) have been measured up to date by kinetic ESR spectroscopy and consequently not many mechanistic conclusions can be reached. 

Here,i j is the initiation rate, is the rate constant for the bimolecular termination, and K is the equilibrium constant From Eq. (64), the polymerization rate Rp is represented as... 

It can be observed that the initial rate of polymerization decreases and the autoacceleration peak is suppressed as the TED concentration is increased. The TED molecules generate dithiocarbamyl (DTC) radicals upon initiation. As a result, termination may occur by carbon-carbon combination which leads to a dead polymer and by carbon-DTC radical reaction which produces a reinitiatable ( living ) polymer. The cross-termination of carbon-DTC radicals occurs early in the reaction (with the carbon-carbon radical termination), and this feature is observed by the suppression of the initial rate of polymerization. As the conversion increases, the viscosity of the system poses mass transfer limitations to the bimolecular termination of carbon radicals. As has been observed in Figure 3, this effect results in a decrease in the ktCC. However, as the DTC radicals are small and mobile, the crosstermination does not become diffusion limited, i.e., the kinetic constant for termination of carbon-DTC radicals, ktCS, does not decrease. Therefore, the crosstermination becomes the dominant reaction pathway. This leads to a suppression of the autoacceleration peak as the carbon-DTC radical termination limits the carbon radical concentration to a low value, thus limiting the rate of polymerization. This observation is in accordance with results of previous studies (10) with XDT and TED, where it was found that when there was an excess of DTC radicals, the carbon radical concentration was lower and the cross-termination reaction was the dominant termination pathway. 

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