Propagation rate constant, determination

The chain propagation rate constant, determined from the known monomer consumption values and the concentration of active centers, is (2.8 0.4) x 10 2 1 mol-1 s . 

In general, carbocationic homopolymerization is characterized by low activation enthalpy, low concentration of active species (10 -10 mol/dm ), high propagation rate constants (10 -10 dm /mol/sec), and short lifetime of the car-benium ion (94). Table 4 lists propagation rate constants determined in bulk carbocationic polymerization of various monomers initiated by y-radiation, electron pulse, or field ionization techniques. 

It is necessary to note the limitation of the approach to the study of the polymerization mechanism, based on a formal comparison of the catalytic activity with the average oxidation degree of transition metal ions in the catalyst. The change of the activity induced by some factor (the catalyst composition, the method of catalyst treatment, etc.) was often assumed to be determined only by the change of the number of active centers. Meanwhile, the activity (A) of the heterogeneous polymerization catalyst depends not only on the surface concentration of the propagation centers (N), but also on the specific activity of one center (propagation rate constant, Kp) and on the effective catalyst surface (Sen) as well ... 

By quenching the polymerization with C1402 or Cl40 the determination of the number of propagation rate constants was found to be also possible for the two-component catalytic system TiCl2 + AlEt2Cl 158, 159). In contrast to alcohols, carbon dioxide and carbon monoxide under polymerization conditions react only with titanium-carbon active bonds and do not react with inactive aluminum-polymer bonds. 

The kinetics of many copolymerizations have now been examined with absolute (overall) propagation rate constants being determined by the rotating sector, PLP or FSR methods. A similar situation as pertains for the MMA-S... 

The correct explanation of the peculiar behaviour of the butadiene-styrene system was provided by O Driscoll and Kuntz 144). As stated previously, under conditions of these experiments butadiene is indeed more reactive than styrene, whether towards lithium polystyrene or polybutadiene, contrary to a naive expectation. This was verified by Ells and Morton 1451 and by Worsfold 146,147) who determined the respective cross-propagation rate constants. It is germane to stress here that the coordination of the monomers with Li4, assumed to be the cause for this gradation of reactivities, takes place in the transition state of the addition and should be distinguished from the formation of an intermediate complex. The formation of a complex ... 

Since these electrochemical problems are of dominant importance for the interpretation of the kinetic results and the evaluation of the propagation rate-constants, we must explore them before we can discuss determination of rate-constants and their significance. 

A similar technique was used almost simultaneously by Penczek [18, 19] for the polymerisation of bis-chloromethyl oxetan (BCMO) by (i-Bu)3A/-H20 in chlorobenzene. In this system, too, there is termination by reaction of growing centres with polymer, but initiation is slow and the equations are correspondingly more complicated. The authors believe that their value of the propagation rate-constant refers to ion-pairs and is thus k"v, and we see no reason to disagree with their view they also determined k and kt. 

In this review there is for the first time a comparative discussion of the three propagating species the unpaired cation, the paired cation and the ester formed from the monomer and an acidic initiator. The relative kinetic importance of these three under different conditions of temperature and of solvent polarity are discussed qualitatively and by means of a three-term rate-equation. From these considerations are derived the optimum conditions for achieving a monoeidic system with the aim of obtaining kinetically simple reactions. It is also emphasised that an initiation reaction that is fast compared to the propagation, and the chemistry of which is known and simple, is essential for the unambiguous determination of propagation rate constants. 

The present author wanted to determine the propagation rate-constant, kp, for the cationic polymerisation of various alkenes (this term here includes vinyl ethers, VE) under such conditions that the interpretation of the measurements should be as unambiguous as possible. If there are no complications from the complexation of the propagating species with constituents of the reaction mixture, the rate of such polymerisations is given generally by equation (1) ... 

The initiation and propagation rate constants for the degradation of the 4-vinylpyridine copolymers obtained at several temperatures may be used to determine both the activation... 

Auguste S, Edwards HGM, Johnson AF et al. (1996) Anionic polymerization of styrene and butadiene initiated by n-butyllithium in ethylbenzene determination of the propagation rate constants using Raman spectroscopy and gel permeation chromatography. Polymer 37 3665-3673... 

In all but one of these studies the apparent rate constants of propagation were determined. The observed apparent propagation rate constant (kSPP) is a summ of products of rate constants on various forms of active centers (e.g. free ions, ion-pairs, aggregates) and their fractions in the polymerizing mixture... 

Propagation rate constants on macroions (kp) and on macroion-pairs (k ) were determined from the dependence of on the fraction of macroions (degree of dissociation a). For systems with only macroions and macroion-pairs participating in equilibrium eqn (3) simplifies to ... 

The frequency of the transfer reactions (4 a) and (4 b) depends on the competition between substrate (polymer) and monomer for the radicals present in the solution, i.e. on the competition between growth and transfer. This competition is usually characterized by a transfer constant which is equal to the ratio of the transfer rate constant to the propagation rate constant, and which can be determined by measurements of the degree of polymerization at various concentration ratios of transfer agent... 

Equation (31) allows the determination of the ratio of propagation rate constants k3/k2 by correlation of the experimental results obtained in copolymerization using equimolar ratios of monomers with the results obtained at non-equimolar monomer ratio and excess of anhydride (an excess of epoxide should not be used because of homopolymerization of the monomers at high degree of conversion). A value of k3,/k2 equal to 0.2 0.1 was found for the system 2-hydroxy-4-(2,3-epoxypropoxy) benzophenone-phthalic anhydride in nitrobenzene initiated by hexadecyltrimethyl-ammonium bromide 56). 

Much remains to be done in this new field. Absolute propagation rate constants need to be determined for those captodative olefins which yield high polymers. No data on ceiling temperatures of captodative olefins have yet been reported. Such data for olefins with substituents with systematically varying steric requirements would be of great interest. 

The overall rate of autoxidation of a substrate is determined not only by the propagation rate constant, kp, but also by the termination rate constant, kt, as given in Eq. (7). Table IV lists approximate rate constants for various peroxy radical terminations. Examination of Table IV reveals that the lower rates of autoxidation for primary and secondary hydrocarbons compared to tertiary... 

The preceding discussion has led us to the conclusion that the surface is the only locus of polymerization which needs to be considered in the heterogeneous polymerization of acrylonitrile. Radicals arrive at the surface at a rate determined by the decomposition of the initiator and efficiency of initiation. Propagation occurs on the surface at a rate determined by the activity of monomer at the surface. By analogy with emulsion polymerization, where monomer diffuses into the particles rapidly enough to maintain near equilibrium activity (14), we assume that the activity of the monomer adsorbed on the particle surface is approximately equal to the mole fraction in solution. The propagation rate constant is presumably influenced somewhat by the presence of the solid surface. 

The stereochemistry of addition to a free centre is mostly determined by interactions between the monomer and active centre during approach to the transition state. In simple cases, represented by equations (34) and (35) only the two primary components will interact, and Bernoulli statistics with a single probability parameter Pm will predominate. For Pm = 0.5, the propagation rate constants of isotactic and syndiotactic growth, kpj and k, will differ... 

Williams et al. studied the radiation-initiated cationic polymerization of styrene. By conductivity measurements they were able to determine very small amounts of ions and thus directly determine the propagation rate constant [381] under otherwise comparable conditions, k+ is about 30times larger than k. ... 

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