Polymer chain length, free-radical

In the 300°C-340°C temperature range, the apparent viscosity of the material under strain decreases with time. After 20min, the final value of viscosity corresponds to 0.6 times the initial value. This result was attributed to strain breaking of the residual polymeric chains and/or to a free radical process leading to a decrease in the polymer chain length. 

The reinforcing action of these small spherical particles of carbon arises from reactions of unsaturations in the main chain with free radicals present on the surface of the particles. Other particles also interact weakly by means of a process in which segments of polymer are absorbed on the porous surface of the carbon black. Figure 3.21 shows how the particles of carbon black act as extra cross-links connecting chains of the elastomer. It can be seen in the scheme that the deformation results from the sliding of the chains located between two spherical particles. Once the deforming force is removed, the chains between particles more or less recover their initial length. 

In each of these mechanisms, the reverse reaction dominates the equihbriimi and keeps the overall concentration of the propagating radical (P ) low, typically [Pn ]/[Pn— X] < 10-5. If tijis reversible radical trapping process occurs frequently, it minimizes the irreversible termination reactions but also means that the polymer chains all have an equal chance to grow, resulting in polymers with a narrow molecular weight distribution. It also follows that, unlike conventional free-radical polymerizations, the polymer chain length will increase steadily with the reaction time, similar to living anionic polymerizations. 

Another convenient and effective scheme for the approximate solution of a mathematical description of the polymerization reaction replaces the discrete variable of infinite range, polymer chain length, by a continuous variable. The difference-differential equations become partial differential equations. Barn-ford and coworkers [16,27,28] used this procedure in their analysis of vinyl (radical chain growth) polymerization. Zeman and Amundson [18,19] used it extensively to study batch and continuous polymerizations. Recently, Coyle et al. [4] have applied it to analysis of high conversion free radical polymerizations while Taylor et al. [3] used it in their modelling efforts oriented to control of high conversion polymerization of methyl methacrylate. A rather extensive review of the numerical techniques and approximations has been presented by Amundson and Luss [29] and later by Tirrell et al. [30]. 

The kinetic chain length v gives the average number of monomer molecules that can be added to a free radical before the free radical is destroyed by a termination reaction. If the termination results solely from polymer and initiator free radicals, then v is defined by... 

The discussion of the rate of bimolecular termination has, up to now, been mainly of a qualitative nature. The scaling of average or macroscopic kt values with viscosity, solvent effects and coil dimensions were discussed without much attention for the chain-length dependence of this process. This dependence originates from the simple fact that free-radical termination is a diffusion-controlled process. Consequently, the overall mobility of polymer chains and/or polymer chain ends determine the overall rate of radical loss in a polymerizing system. As small chains are known to be much more mobile than large ones, the chain length of radicals can be expected to have a profound effect on the termination kinetics. 

It is important to achieve an understanding of how the basic FRP mechanisms control polymerization rate and average polymer chain length. This section starts with the derivation of appropriate kinetic expressions for a single monomer system. Complicating (but industrially important) secondary reactions are then introduced, followed by the extension to multi-monomer systems. Dispersed throughout are up-to-date estimates for important free-radical polymerization rate coefficients, and descriptions of how they are obtained experimentally. 

The calculation of the condition to produce a latex with a given MWD is based on the fact that for linear polymers produced by free-radical polymerization, the polymer chains do not suffer any modification once they are formed. This opens the possibility of decomposing the desired final MWD in a series of instantaneous MWDs to be produced at different stages of the reaction [130]. When chain transfer to a CTA is the main termination event, each of those MWDs can be characterized by the number-average chain length, according to Eq. (76). 

In ATRP, there are reactive and dormant polymer species in equilibrium during the polymerizations, which alternate between halide-capped polymers (dormant) and growing (reactive) polymers with a free radical on the end. The choice of catalyst controls this equilibrium which in turn influences the polymerization rate and the distribution of chain lengths. The mechanism offers flexibihty to conduct reactions in bulk, solution, or emulsions/suspensions, just as fiee-radical polymerizations. Due to the capability to polymerize a large range of monomers with an inexpensive catalyst in a reactor, where purity is nearly as important as in anionic polymerizations, ATRP continues to grow in popularity. For further information, review articles written by the inventors are available [12,16]. 

The three-step mechanism for free-radical polymerization represented by reactions (6.A)-(6.C) does not tell the whole story. Another type of free-radical reaction, called chain transfer, may also occur. This is unfortunate in the sense that it complicates the neat picture presented until now. On the other hand, this additional reaction can be turned into an asset in actual polymer practice. One of the consequences of chain transfer reactions is a lowering of the kinetic chain length and hence the molecular weight of the polymer without necessarily affecting the rate of polymerization. 

The block copolymer produced by Bamford s metal carbonyl/halide-terminated polymers photoinitiating systems are, therefore, more versatile than those based on anionic polymerization, since a wide range of monomers may be incorporated into the block. Although the mean block length is controllable through the parameters that normally determine the mean kinetic chain length in a free radical polymerization, the molecular weight distributions are, of course, much broader than with ionic polymerization and the polymers are, therefore, less well defined,... 

Radiolytic ethylene destruction occurs with a yield of ca. 20 molecules consumed/100 e.v. (36, 48). Products containing up to six carbons account for ca. 60% of that amount, and can be ascribed to free radical reactions, molecular detachments, and low order ion-molecule reactions (32). This leaves only eight molecules/100 e.v. which may have formed ethylene polymer, corresponding to a chain length of only 2.1 molecules/ ion. Even if we assumed that ethylene destruction were entirely the result of ionic polymerization, only about five ethylene molecules would be involved per ion pair. The absence of ionic polymerization can also be demonstrated by the results of the gamma ray initiated polymerization of ethylene, whose kinetics can be completely explained on the basis of conventional free radical reactions and known rate constants for these processes (32). An increase above the expected rates occurs only at pressures in excess of ca. 20 atmospheres (10). The virtual absence of ionic polymerization can be regarded as one of the most surprising aspects of the radiation chemistry of ethylene. 

This is the name given to the series of reactions in which the free radical unit at the end of the growing polymer molecule reacts with monomer to increase still further the length of the polymer chain. They may be represented as shown in Reaction 2.4. 

---