Rate coefficients for free-radical polymerization

Beuermann, S., Buback, M., Davis, T.P., et al., 1997. Critically evaluated rate coefficients for free-radical polymerization 2. Propagation rate coefficients for methyl methacrylate. Macromol. Chem. Phys. 198 (5), 1545-1560. 

Projea No. 2004-034-1-400 Critically evaluated propagation rate coefficients for free-radical polymerization of water-soluble monomers polymerized in the aqueous phase Projea No. 2009-050-1-400 Critically evaluated rate coefficients associated with initiation of radical polymerization... 

Boodhoo, K.V.K. 1999. Spinning Disc Reactor for Polymerization of Styrene. Chemical and Process Engineering. Newcastle upon Tyne, University of Newcastie, Buback, M.E.A., 1995. Critically Evaluated Rate Coefficients for Free-radical Polymerization. I Propagation Rate Coefficient for Styrene. Macromol. Chem. Phys. 196 3267-3280. 

Asua JM, Beuermann S, Buback M, CastignoUes P, Charleux B, Gilbert RG, Hutchinson RA, Leiza JR, Nikitin AN, Vairon JP, van Herk AM. Critically evaluated rate coefficients for free-radical polymerization, 5. Propagation rate coefficient for butyl acrylate. Macromol Chem Phys 2004 205 2151-2160. 

Bamer-Kowollik C, Buback M, Egorov M, Fukuda T, Goto A, Olaj OF, Russell GT, Vana P, Yamada B, Zetterlund PB. Critically evaluated termination rate coefficients for free-radical polymerization experimental methods. Prog Polym Sci 2005 30 605-643. 

The use of quantum chemistry to obtain the individual rate coefficients of a free-radical polymerization process frees them from errors due to kinetic model-based assumptions. However, this approach introduces a new source of error in the model predictions the quantum chemical calculations themselves. As is well known, as there are no simple analytical solutions to a many-electron Schrodinger equation, numerical approximations are required. While accurate methods exist, they are generally very computationally intensive and their computational cost typically scales exponentially with the size of the system under study. The apphcation of quantum chemical methods to radical polymerization processes necessarily involves a compromise in which small model systems are used to mimic the reactions of their polymeric counterparts so that high levels of theory may be used. This is then balanced by the need to make these models as reahstic as possible hence, lower cost theoretical procedures are frequently adopted, often to the detriment of the accuracy of the calculations. Nonetheless, aided by rapid and continuing increases to computer power, chemically accurate predictions are now possible, even for solvent-sensitive systems [8]. In this section we examine the best-practice methodology required to generate accurate gas- and solution-phase predictions of rate coefficients in free-radical polymerization. 

Termination rate coefficients, of several acrylate monomers have been determined via SP-PLP experiments. Figure 4.6-13 shows the dependence of on monomer conversion for free-radical polymerizations of methyl (MA), butyl (BA), and dodecyl acrylate (DA) at 40 °C and 1000 bar. 

Peroxides are the most important initiators for free-radical polymerization. Among them, dialkyl or diaryl peroxides, peroxyesters, diacyl peroxides, and per-oxycarbonates are of particular relevance. For a large number of such peroxides, the temperature and pressure dependence of the decomposition rate coefficient. 

An important characteristic of ionic polymerization is that the propagation rate coefficients are several orders of magnitude higher than for free-radical polymerization. In the equation fct[X] is the bimolecular termination rate coefficient multiplied by the impurity concentration. This equation shows that the rate of polymerization is proportional to the first power of initiation rate, i.e., to the first power of dose rate. Water is a common chain breaker of cationic polymerization since it replaces the cation by a hydroxonium ion. As a proton donor it also inhibits the anionic polymerization... 

Chemical methods for structure determination in diene pol3 mers have in large measure been superseded by infrared absorption techniques. By comparing the infrared absorption spectra of polybutadiene and of the olefins chosen as models whose ethylenic structures correspond to the respective structural units, it has been possible to show that the bands occurring at 910.5, 966.5, and 724 cm. are characteristic of the 1,2, the mns-1,4, and the m-1,4 units, respectively. Moreover, the proportion of each unit may be determined within 1 or 2 percent from measurements of the absorption intensity in each band. The extinction coefficients characteristic of each structure must, of course, be known these may be assigned from intensity measurements on model compounds. Since the proportions of the various units depend on the rates of competitive reactions, their percentages may be expected to vary with the polymerization temperature. The 1,2 unit occurs to the extent of 18 to 22 percent of the total, almost independent of the temperature, in free-radical-polymerized (emulsion or mass) poly butadiene. The ratio of trans-1,4 to cfs-1,4, however,... 

The reaction schemes that can be proposed for these alkyls are basically analogous to those discussed for the tetramethyl compound. The initiation step should be Si-C bond rupture followed by various reactions of ethyl and propyl radicals, free radical attack on the parent alkyl and various polymerization processes. Significant chain reactions involving the alkyls are apparently homogeneous processes and lead to first-order kinetics. The rate coefficients for the... 

As mentioned in Section 9.3, Jackson (141) has obtained estimates of the chain-transfer coefficient of the growing radical with polymer in the free-radical polymerization of ethylene, C,p, by choosing the value so as to fit the MWD. As the polymerization conditions for the polymers mentioned in Table 10.1 are not disclosed, it is necessary to choose typical conditions 220° C and 2000 atm will be selected. Under these conditions Ctp, the ratio of the rate constant for attack on polymer (per monomer unit) to that for propagation, in a homogeneous phase, was found to be about 4.0 x 10 3. This is in good agreement with the known transfer coefficients for the lower alkanes (160), when allowance is made for the differences in pressure and temperature (100). The relation between Ctp and k is ... 

Photoinitiated free radical polymerization is a typical chain reaction. Oster and Nang (8) and Ledwith (9) have described the kinetics and the mechanisms for such photopolymerization reactions. The rate of polymerization depends on the intensity of incident light (/ ), the quantum yield for production of radicals ( ), the molar extinction coefficient of the initiator at the wavelength employed ( ), the initiator concentration [5], and the path length (/) of the light through the sample. Assuming the usual radical termination processes at steady state, the rate of photopolymerization is often approximated by... 

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... 

Use of triphenylmethyl and cycloheptatrienyl cations as initiators for cationic polymerization provides a convenient method for estimating the absolute reactivity of free ions and ion pairs as propagating intermediates. Mechanisms for the polymerization of vinyl alkyl ethers, N-vinylcarbazole, and tetrahydrofuran, initiated by these reagents, are discussed in detail. Free ions are shown to be much more reactive than ion pairs in most cases, but for hydride abstraction from THF, triphenylmethyl cation is less reactive than its ion pair with hexachlorantimonate ion. Propagation rate coefficients (kP/) for free ion polymerization of isobutyl vinyl ether and N-vinylcarbazole have been determined in CH2Cl2, and for the latter monomer the value of kp is 10s times greater than that for the corresponding free radical polymerization. 

One of the most important parameters in the S-E theory is the rate coefficient for radical entry. When a water-soluble initiator such as potassium persulfate (KPS) is used in emulsion polymerization, the initiating free radicals are generated entirely in the aqueous phase. Since the polymerization proceeds exclusively inside the polymer particles, the free radical activity must be transferred from the aqueous phase into the interiors of the polymer particles, which are the major loci of polymerization. Radical entry is defined as the transfer of free radical activity from the aqueous phase into the interiors of the polymer particles, whatever the mechanism is. It is beheved that the radical entry event consists of several chemical and physical steps. In order for an initiator-derived radical to enter a particle, it must first become hydrophobic by the addition of several monomer units in the aqueous phase. The hydrophobic ohgomer radical produced in this way arrives at the surface of a polymer particle by molecular diffusion. It can then diffuse (enter) into the polymer particle, or its radical activity can be transferred into the polymer particle via a propagation reaction at its penetrated active site with monomer in the particle surface layer, while it stays adsorbed on the particle surface. A number of entry models have been proposed (1) the surfactant displacement model (2) the colhsional model (3) the diffusion-controlled model (4) the colloidal entry model, and (5) the propagation-controlled model. The dependence of each entry model on particle diameter is shown in Table 1 [12]. 

On the other hand, Casey and Morrison et al. [52,96] derived the desorption rate coefficient for several limiting cases in combination with their radical entry model, which assumes that the aqueous phase propagation is the ratecontrolling step for entry of initiator-derived free radicals. Kim et al. [53] also discussed the desorption and re-entry processes after Asua et al. [49] and Maxwell et al. [ 11 ] and proposed some modifications. Fang et al. [54] discussed the behavior of free-radical transfer between the aqueous and particle phases (entry and desorption) in the seeded emulsion polymerization of St using KPS as initiator. 

There seems little doubt that in radiation induced polymerizations the reactive entity is a free cation (vinyl ethers are not susceptible to free radical or anionic polymerization). The dielectric constant of bulk isobutyl vinyl ether is low (<4) and very little solvation of cations is likely. Under these circumstances, therefore, the charge density of the active centre is likely to be a maximum and hence, also, the bimolecular rate coefficient for reaction with monomer. These data can, therefore, be regarded as a measure of the reactivity of a non-solvated or naked free ion and bear out the high reactivity predicted some years ago [110, 111]. The experimental results from initiation by stable carbonium ion salts are approximately one order of magnitude lower than those from 7-ray studies, but nevertheless still represent extremely high reactivity. In the latter work the dielectric constant of the solvent is much higher (CHjClj, e 10, 0°C) and considerable solvation of the active centre must be anticipated. As a result the charge density of the free cation will be reduced, and hence the lower value of fep represents the reactivity of a solvated free ion rather than a naked one. Confirmation of the apparent free ion nature of these polymerizations is afforded by the data on the ion pair dissociation constant,, of the salts used for initiation, and, more importantly, the invariance, within experimental error, of ftp with the counter-ion used (SbCl or BF4). Overall effects of solvent polarity will be considered shortly in more detail. 

The termination reaction of free radical polymerization is a typical example of an intermacromolecular diffusion controlled reaction.3 Photophysical studies carried out in the 1980 s demonstrated for the first time that the reaction is solvent- and molecular weight-dependent. The experiments involved triplet quenching of probes attached to polymer chain ends. A benzil group was linked to the end of one PS sample (PS-B) and an anthryl group was linked to the end of a second PS sample (PS-A). The quenching rate coefficient kq of the benzil phosphorescence by anthryl groups is given by Eq. (3.26), where r0 is the lifetime of benzil phosphorescence in the absence of anthryl and ris the benzil phosphorescence lifetime in the presence of anthryl in concentration [A],... 

The rapidity of the reaction can be seen by the large effect low pressures ( 1 torr) of oxygen can have on the free radical polymerization of a reactive olefin such as styrene [22]. The reaction rate coefficients are expected to be typical for exothermic radical—radical reactions with essentially no activation energy. Thus, if R is alkyl, log(feQ/l mole-1 s-1) would be 9.0 0.5, and be independent of temperature. For simple resonance-stabilized radicals, log(feD/l mole-1 s-1) would be 8.5 0.5. 

Section 4.6.2 illustrates the experimental procedures that have recently been applied toward the study of high-pressure free-radical polymerization processes. Section 4.6.3 presents results of propagation, termination, chain-transfer (to monomer and to polymer), and P-scission rate coefficients for ethene homopolymerization. Recent results from experiments and modeling investigations into high-pressure copolymerizations (with ethene being one of the monomers) are reported in Section 4.6.4, together with information on homopolymerization rate coefficients of the comonomer species. 

Scheme 1.1 General kinetics scheme for free-radical polymoization x is the numbo of primary free radicals R formed from one molecule of the initiator I (usually jr = 1 or 2) M represents either a molecule of monomer or a monomer unit in a polymer chain RM and RMp are propagating chain radicals with degrees of polymerization equal to n and p respectively RM , RMp and RM -MpR are terminated ( dead ) polymer chains with degrees of polymerization equal to n, p and n + p respectively T—A represents species which undergo chain transfer, the symbols for the individual rate coefficients are given above the reaction arrows for each process...

Zammit, M. D., Davis, T. R, and Haddleton, D. M., Determination of the Propagation Rate Coefficient (kp) and Termination Mode in the Free-Radical Polymerization of Methyl Methacrylate, Employing Matrix-Assisted Laser Desorption Ionization Time-of-Flight Mass Spectrometry for Molecular Weight Distribution Anal5 is, Macromolecules, 29, 492, 1996. 

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