Rate constant radical chain polymerization

Five different types of rate constants are of concern in radical chain polymerization—those for initiation, propagation, termination, chain transfer, and inhibition. The use of polymerization data under steady-state conditions allows the evaluation of only the initiation rate constant kd (or kt for thermal initiation). The ratio kp/k J2 or kp/kl can be obtained from Eq. 3-25, since Rp, Rj, and [M] are measurable. Similarly, the chain-transfer constant k /kp and the inhibition constant kz/kp can be obtained by any one of several methods discussed. However, the evaluation of the individual kp, k ktr, and kz values under steady-state conditions requires the accurate determination of the propagating radical concentration. This would allow the determination of kp from Eq. 3-22 followed by the calculation of kt, kIr, and kz from the ratios kp/ltj2, ktr/kp, and kz/kp. 

Table 3-10 shows the values of the various concentrations, rates, and rate constants involved in the photopolymerization of methacrylamide as well as the range of values that are generally encountered in radical chain polymerizations. For the methacrylamide case, the experimentally determined quantities werei ,-, (Rp)s, [M], [I], kp/ltj1, ts, and kp/kf. All of the other... 

Consider the activation energy for various radical chain polymerizations. For a polymerization initiated by the thermal decomposition of an initiator, the polymerization rate depends on the ratio of three rate constants kp (kj/k,) 2 in accordance with Eq. 3-32. The temperature dependence of this ratio, obtained by combining three separate Arrhenius-type equations, is given by... 

A case classically associated with radical chain polymerization for which a (pseudo)steady state is assumed for the concentration of active centers this condition is attained when the termination rate equals the initiation rate (the free-radical concentration is kept at a very low value due to the high value of the specific rate constant of the termination step). The propagation rate, is very much faster than the termination rate, so that long chains are produced from the beginning of the polymerization. For linear chains, the polydispersity of the polymer fraction varies between 1.5 and 2. 

Kinetic curves of the polymerization of these monomers in the presence of both emulsifiers with their initial concentration close to CMC are shown in Fig. 9. As can be seen the initial polymerization rate, at the same rate of radical formation (the same concentrations of initiator and the same temperature), decreases from MA to BA in accordance with the decrease of the chain propagation rate constant in these monomers (Bagdasar yan, 1966). Subsequently, however, the polymerization rate of the MA becomes much lower than the rate of other monomers, a fact which apparently is associated with the colloid behavior of the system (reduction of the number of polymerization centers as a result of flocculation). 

Although more studies need to be performed to study the scope and generality of this system, the use of amine hydrochloride salts as initiators for controlled NCA polymerizations shows tremendous promise. The concept of fast, reversible deactivation of a reactive species to obtain controlled polymerization is a proven concept in polymer chemistry, and this system can be compared to the persistent radical effect employed in all controlled radical polymerization strategies [34]. Like those systems, the success of this method requires a carefully controlled matching of the polymer chain propagation rate constant, the amine/amine hydrochloride equilibriiun constant, and the forward and reverse exchange rate constants between amine and amine hydrochloride salt. This means it is likely that reaction conditions (e.g. temperature, halide counterion, solvent) will need to be optimized to obtain controlled polymerization for each different NCA monomer, as is the case for most vinyl monomers in controlled radical polymerizations. Within these constraints, it is possible that controlled NCA polymerizations utilizing simple amine hydrochloride initiators can be obtained. 

Table 6.2 shows the general range of values of the various concentrations, rates, and rate constants pertaining to the above kinetic scheme. These values are typical of radical chain polymerizations. 

The second step of initiation [Eq. (8.83)], being slower than the first [Eq. (8.82)], is rate-determining for initiation (unlike in the case of free-radical chain polymerization) and so though the amide ion produced upon chain transfer to ammonia can initiate polymerization it is but only at a rate controlled by the rate constant, ki, for initiation. Therefore, this chain transfer reaction may be considered as a true kinetic-chain termination step and the application of steady-state condition gives Eq. (8.90). 

The determination of the various rate constants (ki, kp, kt, kts, ktr) for cationic chain polymerization is much more difficult than in radical chain polymerization (or in anionic chain polymerization). It is convenient to use Rp data from experiments under steady-state conditions, since the concentration of propagating species is not required. The Rp data from non-steady-state conditions can be used, but only when the concentration of the propagating species is known. For example, the value of kp is obtained directly from Eq. (8.143) from a determination of the polymerization rate when [M J is known. The literature contains too many instances where [M" "] is taken equal to the concentration of the initiator, [IB], in order to determine kp from measured Rp. (For two-component initiator-coinitiator systems, [M" ] is taken to be the initiator concentration [IB] when the coinitiator is in excess or the coinitiator concentration [L] when the initiator is in excess.) Such an assumption holds only if Ri > Rp and the initiator is active, i.e., efficiency is 100%. Using this assumption without experimental verification may thus lead to erroneous results. 

Radical polymerization, including the question of the dependence of chain termination rate constant on the length of the macroradical chain, the possibility for continuous radical polymerization to be achieved through the complexing and stabilization of free radicals and of catalytic chain transfer in radical polymerization. 

It was recently shown12) that in radical polymerization the chain termination rate constant is observed to decrease with the introduction of a polyfunctional complex-ing agent into the system. An especially sharp decrease of the termination rate, up to the formation, under certain conditions, of living radical polymerization centers, was noted in the methyl methacrylate-orthophosphoric acid system. 

A radical chain polymerization is started when the initiator begins to decompose according to Eq. (6.3) and the concentration of radicals in the system, [M ], increases from zero. The rate of termination or disappearance of radicals, being proportional to [M ]- [cf. Eqs. (6.17)-(6.19)], is thus zero in the beginning and increases with time, till at some stage it equals the rate of radical generation. The concentration of radicals in the system then becomes essentially constant (or steady ), as radicals are formed and destroyed at equal rates. This condition, described as steady-state assumption or steady-state approximation , can thus be described by the following two equations ... 

Table 6.4 Some Values of Propagation Rate Constant, kp, and Termination Rate Constant, kt, and Activation Energies in Radical Chain Polymerization...

The MWD is the same as the instantaneous MWD in a batch reactor at the same temperature, initiation rate and conversion (for linear chains). In a batch polymerization, since monomer/radical concentrations and rate constants for termination may vary significantly with conversion, the cumulative MWD would be broader than in a comparable HCSTR. 

In Ref. [77] the dependence of the chain propagation rate constant and the initiation efficiency upon the volumetric concentration of polymer via the processes of radical polymerization in the late conversion states was considered. With the aim of describing such functions, the models of the cell effect and a side cell effect have been used. 

A Smith-Ewart case 1 behavior in 1) can be observed during emulsion polymerization of monomers with a high chain-transfer rate constant such as vinyl chloride because the monomer radicals have a high tendency to escape from the particles. Especially for vinyl chloride emulsion polsunerization, Ugelstad and Hansen (113) derived the following equation 18 to calculate n, which predicts dependence, h a... 

Most commercially available polymers are made by radical initiators. Polymerization can be initiated by all types of radical sources, such as peroxides [386,387], persulfates [388,389], azo compounds [390-392], redox systems [393-394], UV light [395-396], x- [397] or y-radiation [398], electro- [399] or mechanochemically [400]. The radical polymerization shows a strong dependence on temperature, pH, monomer concentration, polymerization medium [392,401], and activators [392]. Water leads to the protonation of the macroradical, which in turn leads to an increase in the reactivity. This is reflected in high values of the chain growth rate constant and therefore the high molecular weight [402] (Figure 3). 

Karaputadze, T. M., Kurilova, A. I., Topchiev, D. A., Kabanov, V. A. (1972). Mechanism of the effect of pH and ionic strength on the chain propagation rate constant during radical polymerization of methacrylic and acrylic acids in aqueous solutions. Vysokomolekulyarnye Soedineniya, Seriya B Kratkie Soobshcheniya, 14, 323-325. 

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