Propagation in free-radical polymerization

Table 20-7. Activation Volume for Initiator Decomposition and Polymer Propagation in Free Radical Polymerizations...

The collection of data and critical evaluation of possible influences of parameters on the CLD (as was carried out by Heuts et al. ) might help to elucidate the current question of the true nature of chain length dependence of the rate constant of propagation in free radical polymerization. Therefore, the investigation of the polymerization behaviour of monomers other than styrene and methyl methacrylate is necessaryf and the use of the correction procedures should eliminate the error introduced by the effect of BB. Thus, comparison of data obtained from either different research groups and/or with the aid of different techniques (MALDI, SEC) should be better feasible. 

Olaj OF, Schnoll-Bitai I. Solvent effects on the rate constant of chain propagation in free radical polymerization. Monatsh Chem 1999 130 731-740. 

J. P. A. Heuts, R. G. Gilbert, and L. Radom,/. Phys. Chem., 100,18997 (1996). Determination of Arrhenius Parameters for Propagation in Free-Radical Polymerizations An Assessment of Ab Initio Procedures. 

Heuts JPA, Radom L, Gilbert RG A priori prediction of rate coefficients for propagation in free-radical polymerizations , manuscript in preparation... 

The theory of radiation-induced grafting has received extensive treatment [21,131,132]. The typical steps involved in free-radical polymerization are also applicable to graft polymerization including initiation, propagation, and chain transfer [133]. However, the complicating role of diffusion prevents any simple correlation of individual rate constants to the overall reaction rates. Changes in temperamre, for example, increase the rate of monomer diffusion and monomer... 

Styrene and its derivatives can be polymerized by all possible propagation mechanisms. Free-radical polymerization, however, is the primary process for industrial production of polystyrene. Free-radical polymerization of styrene can be carried out without chemical initiators simply by heating the monomer.223,224 On heating, isomeric 1-phenyltetralins are formed in the Diels-Alder... 

Propagation in free-radical styrene polymerization proceeds through stable benzylic radicals by head-to-tail addition of the monomer ... 

It is not possible at our present stage of knowledge to place all of the catalysts in exact position relative to their ionic nature. The "mid point may be displaced some to either direction. Most catalysts contain several different components with different degrees of ionicity. Which component acts as the active catalyst for a particular double bond is unknown in most cases. Only crude presentations are possible until techniques have been developed to determine the actual ionic nature of the propagating species in isotactic ionic polymerization s such as ESR is capable of in free radical polymerizations. 

These findings imply that the use of probabilities for i-ad formation at a given temperature in a given solvent is insufficient to describe the monomer constitutions influence on the stereocontrol in free radical polymerizations. The lack of correlation is either the result of the combined action of more than one parameter (size of substituent, resonance stabilization and/or structure of propagating radicals, etc.) or the result of noncomparable experimental conditions. 

As in free radical polymerization, there are initiation and propagation steps. Various initiators, such as organometallic compounds, alkali metals, Grignard reagents, or metal amides, like sodium amide, shown in Figure 3-31, can be used. Propagation proceeds in the usual manner, but there is no termination... 

The number-average degree of polymerization can be obtained from the rates of propagation (eqn 10.65) and chain breaking (sum of eqns 10.66 and 10.67) as in free-radical polymerization with termination by chain transfer to a transfer agent (see eqn 10.42) ... 

Reaction (6-14a) is the initiation step, while reactions (6-14b) and (6-l4c) are atom abstraction propagation reactions. Atom abstraction reactions in free-radical polymerizations are called chain transfer reactions. They are discussed in some detail in Section 6.8. 

The choice of initiator has no effect on the propagation reactions in free-radical polymerizations but it can influence ionic propagations because the reactivity of the active center is partly determined by the nature of the counterion that is derived from the initiator. 

Anionic polymerizations are generally much faster than free-radical reactions although the A p values are of the same order of magnitude for addition reactions of radicals and solvated anionic ion pairs (free macroanions react much faster). The concentration of radicals in free-radical polymerizations is usually about 10 -10 M while that of propagating ion pairs is 10 -10 M. As a result, anionic polymerizations are lO -lO times as fast as free-radical reactions at the same temperature. 

The above kinetic expressions illustrate some basic differences between cationic and free radical processes. In the cationic polymerization, the propagation rate is of first order with respect to the initiator concentration, whereas in free radical polymerization it is proportional to the square root of initmtor concentration (Eq. [34]). Furthermore, the molecular weight (or DP) of the polymer synthesized by the cationic process is independent of the concentration of the initiator, regardless of how termination takes place, unlike free radical polymerization where DP is inversely proportional to [I] in the absence of chain transfer (Eq. [35]). 

The basic steps in free-radical polymerization are initiation, propagation, chain transfer, and termination. 

A limited number of attempts have been made to set up a general mechanistic scheme describing cationic systems in terms of fundamental reactions, in a similar manner to that used in free radical polymerizations, and to derive generally applicable kinetic equations [3—4]. Because of the individuality of each cationic system, however, this approach has met with little success, and there has been a greater tendency towards treating each polymerization in isolation for detailed kinetic analysis. It is possible, however, to postulate at least token schemes which can be used as a guide. After the pre-initiation equilibria, polymerization can be considered in terms of classical initiation, propagation, transfer and termination reactions, i.e. for vinyl monomers... 

The propagation step in ionic polymerizations is considerably more comphcated than in free radical polymerization (5). In addition to monomer structure and temperature, solvent and counter ion type are of importance. The separation between the counter ion and the active polymer chain end is the primary rate determining factor it can be represented schematically as an equilibrium between four species of different level of separation ... 

Determination of Quotient kp/kf. Theory of Pre- and Aftereffect (3). kp is the absolute propagation constant of the chain propagation reaction in free radical polymerization corresponding to... 

The propagation reaction in free-radical polymerizations is rapid.1 One important feature of the polymerization is that high molecular weight polymer is formed even at very low levels of monomer conversion. Thus, each propagating radical or its progeny lives for well under a minute. To control molecular weights in these polymerizations, the use of chain... 

Table 2 Energies of activation for propagation ( p) and termination ( t) in free-radical polymerization...

Though ionic polymerization resembles free-radical polymerization in terms of initiation, propagation, transfer, and termination reactions, the kinetics of ionic polymerizations are significantly diflFerent from free-radical polymerizations. In sharp contrast to free-radical polymerizations, the initiation reactions in ionic polymerizations have very low activation energies, chain termination by mutual destruction of growing species is nonexistent, and solvent effects are much more pronounced, as the nature of solvent determines whether the chain centers are ion pairs, free ions, or both. No such solvent role is encountered in free-radical polymerization. The overall result of these features is to make the kinetics of ionic polymerization much more complex than the kinetics of free-radical polymerization. 

The reactivity ratios rj and T2 can be determined from the composition of the copolymer product. However, a serious complication exists because the propagation rate constants, k j, are composite rate constant, being composed of free-ion contributions and ion-pair contributions, and hence the reactivity ratios also will be composite quantities, having contributions from both ion pairs and free ions. Because the relative abundances of free ions and ion pairs are strongly dependent on the reaction conditions, the reactivity ratios will also depend on these conditions and they can be applied only to systems identical to those for which they were determined. Therefore the utility of such ratios is much more limited in anionic than in free-radical polymerization. 

Effect of Solvents and Reaction Conditions. The term "solvent" is customarily used rather loosely in polymerization reactions because such "solvents" may refer either to the actual medium in which the reaction is carried out, or to trace materials present in the medium. Hence, the term really encompasses any component other than monomer and initiator. Thus, in free-radical polymerization, the role of the solvent is limited to "interfering" with the normal propagation reaction, either through chain transfer or even by termination (inhibition or retardation). Either of these events can affect only the chain length or the overall rate, or both. 

In a recent publication Okamura et ah (12) describe similar results in a different system. It is believed that the unusual rate increase observed in these various systems which are chemically so different is caused by the physical state of the reaction medium at temperatures a few degrees above Tg. The high viscosity of this gel-like medium presumably favors chain propagation in its competition with termination. This effect, which is kinetically similar to the "gel-effect in free radical polymerizations, can only arise if the termination step (charge recombination) becomes diffusion controlled. The latter process would arise if both ionic species involved in the reaction were of macromolecular size. This is undoubtedly true for the growing chain, but the mobility of the counter ion should only be significantly reduced in such a medium if it is of a polymolecular structure, involving perhaps a voluminous solvation cluster. 

The concentration of radicals in free-radical polymerizations is usually about M while that of propagating ion pairs is M depending upon initiator concen-... 

The chain lengthening of the polymeric radical is the propagation step. The polymer can be formed as any combination of 1,2-, 1,4-cis or 1,4-trans additions the polymer can be a result of one or all of the three addition processes. The termination step of a polymerization reaction puts a stop to the growing polymer. In free radical polymerization, the termination step rids the growing polymer of its free electron. This generally proceeds by any one of three different methods dimerization, disproportionation and abstraction. Dimerization involves the joining of two growing polymer radicals. It can be shown as ... 

In this chapter, we review the theoretical work on thermal FP. We begin with a derivation of a base mathematical model which governs propagation of free-radical polymerization waves. We demonstrate that this model reduces in a limiting case to the famous gasless combustion (GC) model, which has been extensively studied in the context of SHS. We discuss some theoretical approaches to the simpler GC model and then apply them to the base model of free-radical FP. Some extensions of the base model are also discussed. 

Ttp 4 Chain microstructure and propagation reactions. Propagation reactions are mainly responsible for the development of polymer chain microstructure (and control chain composition and sequence length distribution in copolymerizations). In free radical polymerization, the stereoregularity of a high molecular weight homopolymer chain depends on polymerization temperature almost exclusively. It is usually independent of initiator type and monomer concentration. Calculations on stereoregularity... 

Three basic steps are involved in free-radical polymerization Initiation, which begins the chain growth propagation, which increases the size of the polymer molecule and termination, which ends the growth of the molecule. 

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