Termination rate coefficient

Center of mass or translational diffusion is believed to be the rate-determining step for small radicals33 and may also be important for larger species. However, other diffusion mechanisms are operative and are required to bring ihe chain ends together and these will often be the major term in the termination rate coefficient for the case of macromolecular species. These include ... 

In dealing with radical-radical termination in bulk, polymerization it is common practice to divide the polymerization timeline into three or more conversion regimes.2 "0 The reason for this is evident from Figure 5.3. Within each regime, expressions for the termination rate coefficient are defined according to the dominant mechanism for chain end diffusion. The usual division is as follows ... 

Table 5.1 Parameters Characterizing Chain Length Dependence of Termination Rate Coefficients in Radical Polymerization of Common Monomers 1...

In order to estimate the dependence of the termination rate constant on conversion, molecular weight and temperature, the following is assumed k- becomes diffusion controlled when the diffusion coefficient for a polymer radical Dp becomes less than or equal to a critical diffusion coefficient D ... 

Table 16.1 presents the inhibition coefficients / and the termination rate constants kn in systems with the cyclic chain termination mechanism with aromatic amines. Naturally, these are apparent rate constants, which characterize primarily the rate-limiting step of the chain termination process. 

Inhibition Coefficients /and Rate Constants k for the Reactions of Peroxyl Radicals with Aromatic Amines in Systems with a Cyclic Mechanism of Chain Termination... 

In many real polymerisation reactions, the kinetic scheme given above will be inadequate. Other reaction steps may have to be included amd the results of chain transfer to polymer are not always easy to describe. There is clear evidence which suggests that the chain termination rate coefficient is reduced in value when the concentration of polymer is high [43, 44]. The quantitative assessment for such changes is still a subject of much research [45, 46]. At very high concentrations, the value of kp may also be reduced [47]. Other physical events may also be important, particularly when the reaction becomes heterogeneous. 

If aU propagation rate coefficients are equal and all termination rate coefficients are equal, we can obtain a simple expression for the chain length distribution, called the Schultz Flory distribution... 

Once least squares values of the /3 s were obtained, it was desirable to extract from them as much information as possible about the original parameters. To do so, we make one further statement concerning the relations between the rate constants for mutual termination of polymeric radicals of different size. It has been shown (2) that termination rates in free radical polymerizations are determined by diffusion rates rather than chemical factors. The relative displacement of two radicals undergoing Brownian motion with diffusion coefficients D and D" also follows the laws of Brownian diffusion with diffusivity D = D -J- D" (11). It... 

Mahabadi and O Driscoll [5] derived the termination rate constant for two flexible polymeric radicals, R and R in solution, based on the chain lengths m and n, intramolecular coefficients of linear expansion aA and aB, and on the excluded volume [9]. 

Like coupling, disproportionation as a reaction of two polymer radicals is second order in free radicals. A contribution of disproportionation to termination thus does not alter the algebraic form of the rate equation 10.25, but the termination rate coefficient klc becomes the sum of two second-order coefficients klc and for coupling and disproportionation, respectively. However, the degree of polymerization, the molecular weight, and the molecular-weight distribution are affected by disproportionation (see Section 10.3.4). 

Termination reactions occur between two relatively large radicals, and termination rates arc limited by the rates at which the radical ends can encounter each other. As a result, kt is a decreasing function of the dimensions of the reacting radical. The segmental diffusion coefficient and the termination rate constant increase as the polymer concentration increases from zero. This initial increase is more pronounced when the molecular weight of the polymer is high and/or when the polymerization is carried out in a medium which is a good solvent for the polymer. For similar reasons, k t is inversely proportional to the viscosity of reaction medium. A model has been proposed that accounts for these variations in k, in low-conversion radical polymerizations [15,16]. 

An important further contribution to the analysis of steady-state reacticm systems has been made by Ugclstad et d. (1967), They have shown how account can be taken of the likely possihillty that radicals that exit from the reaction loci contribute to the stationary concentration of free radicals in the external phase which is available for entry into a reaction loci. For this purpose, it is necessary to distinguish blmolecular mutual termination between radicals that occurs in the reaction loci (i.e., within polymer/ monomer particles) from that which occurs in the external phase. The rate at which the former reaction occurs is characterized by the rate coefficient the rate of the latter reaction by. The total rate of entry of radicals into all loci within unit volume of reaction system is then expressed as the sum of three contributions. The first derives from the rate of formation of new "acquirable radicals within the external phase the second derives from the rate at which acquirable radicals become present in the external phase by the process of exit from the loci the third (which is negative) allows for the fact that radicals can be lost from the external phase by bimolecular mutual termination within the external phase. The resultant equation is... 

Two measurements of the bimolecular termination rate coefficient in the polymerization of ethylene by Ti complexes are available. For (7r-CsH5)2TiCl2/AlMe2Cl a value of 0.5 1 mole sec at 0°C has been reported [111] and for (7r-CsHs)2TiEtCl/AlEtCl2, 0.61 mole sec at0°C [202]. The rate coefficient of decomposition of the latter complex in the absence of ethylene was much lower being 5 x 10 1 mole sec at 20 C [202]. 

As noted by earlier investigators, a correction must be applied to the termination coefficient ktc to allow for the decrease in termination rate caused by the reduction in rates of diffusion of the polymer radicals as conversion and viscosity increase. An empirical correction function was developed to correct ktc for the increased viscosity at higher conversions. 

One of the most striking features of CCT is the exceptionally fast rate at which it takes place. The molecular weight of a polymer can be reduced from tens of thousands to several hundred utilizing concentrations of cobalt catalyst as low as 100—300 ppm or 10 3 mol/L. The efficiency of catalysis can be measured as the ratio between the chain-transfer coefficients of the catalyzed reaction versus the noncatalyzed reaction. The chain-transfer constant to monomer, Cm, in MMA polymerization is believed to be approximately 2 x 10 5.29 The chain-transfer constant to catalyst, Cc, is as high as 103 for porphyrins and 104 for cobaloximes. Hence, improved efficiency of the catalyzed relative to the uncatalyzed reaction, CJCu, is 104/10 5 or 109. This value for the catalyst efficiency is comparable to many enzymatically catalyzed reactions whose efficiencies are in the range of 109—1011.18 The rate of hydrogen atom transfer for cobaloximes, the most active class of CCT catalysts to date, is so high that it is considered to be controlled by diffusion.5-30 32 Indeed, kc in this case is comparable to the termination rate constant.33... 

Termination rate coefficients can be measured using the y-radiolysis relaxation method. This involves initiation using y-radiation, followed by removal of the reaction vessel from the y-source. Conversion during the relaxation period is monitored by dilatometry, and the decay in polymerization rate over time is related to the rate of radical loss. When large particles are used, radical loss is dominated by intraparticle termination, rather than exit into the aqueous phase, and the rate coefficient for termination can be determined from the decay curve. By using multiple insertions and removals, the termination rate coefficient is determined over a wide range of polymer mass fraction (wp). 

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