Free radical addition polymerization termination

According to free radical addition polymerization theory, the rate of polymerization of monomer M is proportional to the square root of the initiator I concentration (Equation 3) when termination is bi mol ecular (18). 

Figure 5.9. Reactions involved in free-radical addition polymerization. Shown are (a) (i)-(iii) generation of free radicals from a variety of initiators, (b) initiation of polymer chain growth through the combination of a free radical and unsaturated monomer, (c) propagation of the polymer chain through the combination of growing radical chains, (d) chain-transfer of free radicals between the primary and neighboring chains, and (e) termination of the polymer growth through either combination (i) or disproportionation (ii) routes.

The specificity of the reaction mechanism to the chemistry of the initiator, co-initiator and monomer as well as to the termination mechanism means that a totally general kinetic scheme as has been possible for free-radical addition polymerization is inappropriate. However, the general principles of the steady-state approximation to the reactive intermediate may still be applied (with some limitations) to obtain the rate of polymerization and the kinetic chain length for this living polymerization. Using a simplified set of reactions (Allcock and Lampe, 1981) for a system consisting of the initiator, I, and co-initiator, RX, added to the monomer, M, the following elementary reactions and their rates may be... 

Since emulsion polymerization is a free-radical addition polymerization, all the kinetic events, namely, initiation, propagation, termination and transfer reactions which have already been described in Chapter 1, are applicable to describe the overall rate of the polymerization and molar mass development of the latex polymer. However, the heterogeneous nature of the polymerization adds some complications due to partitioning of the various ingredients between the phases ... 

The chain length distribution of free radical addition polymerization can also be derived from simple statistics. Thus, for polymer formed at any given instant, the distribution will be the most probable and will be governed by the ratio of the rates of chain growth to chain termination. 

As in step-growth polymerization, a distribution of chain lengths is always obtained in a free-radical addition polymerization because of the inherently random nature of the termination reaction with regard to chain length. Expressions for the number-average... 

FIGURE 9.4 Instantaneous number- and weight-fraction distributions of chain lengths in free-radical addition polymerization. Equations 9.47 and 9.48 are for termination by disproportionation and/or chain transfer Equations 9.58 and 9.59 are for termination by combination. 

The classical kinetic scheme for free-radical addition polymerization neglects one other possible form of termination, primary-radical termination (PRT), in which a growing chain is killed by reaction with a free-radical R- from initiator decomposition ... 

From a practical standpoint, most copolymers are made by free-radical addition polymerization, although step-growth polymerization can also be used. For the sake of simplicity in our discussion, we will focus only on the free-radical meehanism A quantitative treatment of random copolymerization is based on the assumption that the reactivity of a growing chain depends only on its active terminal unit. Therefore, when two monomers, Mj and M2, are copolymerized, there are four possible propagation reactions ... 

We now know that the termination reaction in free-radical addition polymerization is diffusion controlled right down to 0% conversion. This is not really surprising given the extremely high chemical reactivity of free-radical pairs and the size of the reacting species. 

In order to simplify the kinetic scheme a steady-state approximation has to be made. It is assumed that under steady-state conditions the net rate of production of radicals is zero. This means that in unit time the number of radicals produced by the initiation process must equal the number destroyed during the termination process. If this were not so and the total number of radicals increased during the reaction, the temperature would rise rapidly and there could even be an explosion since the propagation reactions are normally exothermic. In practice it is found that the steady-state assumption is usually valid for all but the first few seconds of most free radical addition polymerization reactions. 

In order to be able to predict the degree and rate of polymerization for a particular free radical addition polymerization system it is necessary to know the individual rate constants A , kp and kt. Also in order to determine Xn, the mechanism of termination must be known. This can be done using radioactively labelled initiator molecules. The rate constant for the breakdown of initiator ki can be determined from measurements upon the initiator alone. However, ki, so determined, may be different from that in the presence of monomer molecules. So far we have developed two equations that can be used to determine the three rate constants. The equations are... 

In free radical addition polymerization the distribution of molar mass depends upon the mechanism of termination. The simplest case to consider is when the mechanism is through disproportionation and is equal to the kinetic chain length v. In this case the chain grows and terminates at the length to which it had grown. At this point it is necessary to define a new... 

The tacticity of the polymer produced is controlled by the way in which addition takes place which in turn depends upon interaction between the terminal chain carbon atom and the approaching monomer molecule. For free radical addition polymerization reactions it is presumed that the terminal carbon atom has sp hybridization and so has planar bonds. If this is the case then there are two ways in which it can be approached by the monomer molecule ... 

This reaction proceeds through a chain mechanism. Free-radical additions to 1-butene, as in the case of HBr, RSH, and H2S to other olefins (19—21), can be expected to yield terminally substituted derivatives. Some polymerization reactions are also free-radical reactions. 

Acrylamide polymerization by radiation proceeds via free radical addition mechanism [37,38,40,45,50]. This involves three major processes, namely, initiation, propagation, and termination. Apart from the many subprocesses involved in each step at the stationary state the rates of formation and destruction of radicals are equal. The overall rate of polymerization (/ p) is so expressed by Chapiro [51] as ... 

As for any chain reaction, radical-addition polymerization consists of three main types of steps initiation, propagation, and termination. Initiation may be achieved by various methods from the monomer thermally or photochemically, or by use of a free-radical initiator, a relatively unstable compound, such as a peroxide, that decomposes thermally to give free radicals (Example 7-4 below). The rate of initiation (rinit) can be determined experimentally by labeling the initiator radioactively or by use of a scavenger to react with the radicals produced by the initiator the rate is then the rate of consumption of the initiator. Propagation differs from previous consideration of linear chains in that there is no recycling of a chain carrier polymers may grow by addition of monomer units in successive steps. Like initiation, termination may occur in various ways combination of polymer radicals, disproportionation of polymer radicals, or radical transfer from polymer to monomer. 

The simplest way to catalyze the polymerization reaction that leads to an addition polymer is to add a source of a free radical to the monomer. The term free radical is used to describe a family of very reactive, short-lived components of a reaction that contain one or more unpaired electrons. In the presence of a free radical, addition polymers form by a chain-reaction mechanism that contains chain-initiation, chain-propagation, and chain- termination steps. 

Reactivity ratios rj are defined by r, = ka/kij, the ratio of homopropagation, ka, to cross-propagation, rate coefficients, where fcy refers to the addition of monomer j to a free-radical chain-end terminating in species i. Under ideal polymerization conditions the mole fraction of monomer units i contained in the copolymer Fj is given by eq (4.6-14), which holds for both the terminal and the implicit penultimate unit models (see Section 4.6.4.3) [45]. 

The growing polymer in chain-reaction polymerization is a free radical, and polymerization proceeds via chain mechanism. Chain-reaction polymerization is induced by the addition of free-radical-forming reagents or by ionic initiators. Like all chain reactions, it involves three fundamental steps initiation, propagation, and termination. In addition, a fourth step called chain transfer may be involved. 

The types of compounds that can be polymerized readily by the radical-chain mechanism are the same types that easily undergo free-radical addition reactions. Alkenes with aryl, ester, nitrile, or halide substituent groups that can stabilize the intermediate radical are most susceptible to radical polymerization. Terminal alkenes are generally more reactive toward radical-chain polymerization than more highly substituted isomers. The dominant mode of addition in radical-chain polymerization is head-to-tail. The reason for this orientation is that each successive addition of monomer takes place in such a way that the most stable possible radical intermediate is formed. For example, the addition to styrene occurs to give the phenyl-substituted radical to acrylonitrile, to give the cyano-substituted radical ... 

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