Propagation and Termination

From an extended set of SP-PLP experiments carried out at temperatures between 190 and 230 °C and at pressures between 1950 and 2900 bar, Schweer [24] derived expressions for the temperature, pressure, monomer conversion (X), and viscosity (t)) dependence of termination and propagation rate coefficients for the ethene homopolymerization, eqs (4.6-2) and (4.6-3). 

In these equations jy, = tiltjQ is the relative bulk viscosity, with t o referring to the pure monomer viscosity at identical p and T. The terms and kp refer to the termination and propagation rate coefficients at very low conversion, respectively. Also from SP-PLP experiments, these two quantities are found to be  

A detailed discussion of these results, including the procedure of estimating relative bulk viscosity is given in Reference [24]. Eqs (4.6-2) to (4.6-5) have been extensively used for modeling high-pressure ethene polymerizations during recent years. 

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Elsewhere in this chapter we shall see that other reactions-notably, chain transfer and chain inhibition-also need to be considered to give a more fully developed picture of chain-growth polymerization, but we shall omit these for the time being. Much of the argumentation of this chapter is based on the kinetics of these three mechanistic steps. We shall describe the rates of the three general kinds of reactions by the notation Rj, Rp, and R for initiation, propagation, and termination, respectively. 

In Chap. 5, p was defined as the fraction (or probability) of functional groups that had reacted at a certain point in the polymerization. According to the current definition provided by Eq. (6.66), p is the fraction (or probability) of propagation steps among the combined total of propagation and termination steps. The quantity 1 - p is therefore the fraction (or... 

Autooxidation. Liquid-phase oxidation of hydrocarbons, alcohols, and aldehydes by oxygen produces chemiluminescence in quantum yields of 10 to 10 ° ein/mol (128—130). Although the efficiency is low, the chemiluminescent reaction is important because it provides an easy tool for study of the kinetics and properties of autooxidation reactions including industrially important processes (128,131). The light is derived from combination of peroxyl radicals (132), which are primarily responsible for the propagation and termination of the autooxidation chain reaction. The chemiluminescent termination step for secondary peroxy radicals is as follows ... 

The requirements for a polymerisation to be truly living are that the propagating chain ends must not terminate during polymerisation. If the initiation, propagation, and termination steps are sequential, ie, all of the chains are initiated and then propagate at the same time without any termination, then monodisperse (ie, = 1.0) polymer is produced. In general, anionic polymerisation is the only mechanism that yields truly living styrene... 

Autoca.ta.Iysis. The oxidation rate at the start of aging is usually low and increases with time. Radicals, produced by the homolytic decomposition of hydroperoxides and peroxides (eqs. 2—4) accumulated during the propagation and termination steps, initiate new oxidative chain reactions, thereby increasing the oxidation rate. 

Most ethers are potentially ha2ardous chemicals because, in the presence of atmospheric oxygen, a radical-chain process can occur, resulting in the formation of peroxides that are unstable, explosion-prone compounds (7). The reaction maybe generalized in terms of the following steps involving initiation, propagation, and termination. 

The free-radical mechanism iavolves initiation, propagation, and termination steps. During initiation two radicals are produced for every paraffin molecule. 

Addition polymerisation is effected by the activation of the double bond of a vinyl monomer, thus enabling it to link up to other molecules. It has been shown that this reaction occurs in the form of a chain addition process with initiation, propagation and termination steps. 

A number of important addition polymers are produced by ionic mechanisms. Although the process involves initiation, propagation and termination stages the growing unit is an ion rather them a radical. 

The overall rate of a chain process is determined by the rates of initiation, propagation, and termination reactions. Analysis of the kinetics of chain reactions normally depends on application of the steady-state approximation (see Section 4.2) to the radical intermediates. Such intermediates are highly reactive, and their concentrations are low and nearly constant throughout the course of the reaction ... 

Polyethylene is the simplest of so-called high polymers. The reaction for low density polyethylene (LDPE) follows the classical free radical polymerization steps of initiator decomposition, initiation, propagation, and termination. The reaction is... 

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 ... 

An emulsion polymerization reaction follows three conventional steps, namely, initiation, propagation, and termination. These steps can be described by the conventional reactions that are valid for any free radical polymerization. Smith and Ewart [10] proposed that a forming latex particle in an ideal emulsion polymeriza-... 

In this equation, Mp is the monomer concentration within forming particles, pa is the adsorption rate of oligomeric radicals by the forming particles, Vp is the volume fraction of forming particles within the system, and kp and k, are the rate constants of propagation and termination, respectively. 

The polymerization of vinyl chloride monomer, in common with other vinyl monomers, proceeds by a free-radical mechanism involving the usual steps of initiation, propagation, and termination. Poly(vinyl chloride) is formed in a regular head-to-tail manner Eq. (1) [3-6]. 

Like many radical reactions in the laboratory, methane chlorination requires three kinds of steps initiation, propagation, and termination. 

Recall from Section 5.3 that radical substitution reactions require three kinds of steps initiation, propagation, and termination. Once an initiation step has started the process by producing radicals, the reaction continues in a self-sustaining cycle. The cycle requires two repeating propagation steps in which a radical, the halogen, and the alkane yield alkyl halide product plus more radical to carry on the chain. The chain is occasionally terminated by the combination of two radicals. 

Figure 10.1 Mechanism of the radical chlorination of methane. Initiation step Three kinds of steps are required initiation, propagation, and termination. The propagation steps are a repeating cycle, with Cl- a reactant in step 1 and a product in...

Any understanding of the kinetics of copolymerization and the structure of copolymers requires a knowledge of the dependence of the initiation, propagation and termination reactions on the chain composition, the nature of the monomers and radicals, and the polymerization medium. This section is principally concerned with propagation and the effects of monomer reactivity on composition and monomer sequence distribution. The influence of solvent and complcxing agents on copolymerization is dealt with in more detail in Section 8.3.1. 

The book commences with a general introduction outlining the basic concepts. This is followed by a chapter on radical reactions that is intended to lay the theoretical ground-work for the succeeding chapters on initiation, propagation, and termination. Because of its importance, radical copolymerization is treated in a separate chapter. We then consider some of the implications of these chapters by... 

Figure 4. Bulk polymerization of MM A at 22.5° C with AIBN Ri = 8.36 X 10 mol/L sec. Effect of conversion on propagation and termination rate constants (6).

The polymerization rate equations are based on a classical free radical polymerization mechanism (i.e., initiation, propagation, and termination of the polymer chains). 

Chain polymerisation typically consists of these three phases, namely initiation, propagation, and termination. Because the free-radical route to chain polymerisation is the most important, both in terms of versatility and in terms of tonnage of commercial polymer produced annually, this is the mechanism that will be considered first and in the most detail. 

Chain polymerisation necessarily involves the three steps of initiation, propagation, and termination, but the reactivity of the free radicals is such that other processes can also occur during polymerisation. The major one is known as chain transfer and occurs when the reactivity of the free radical is transferred to another species which in principle is capable of continuing the chain reaction. This chain transfer reaction thus stops the polymer molecule from growing further without at the same time quenching the radical centre. 

The peroxide-initiated, free radical, dispersion polymerization of the single monomer is assumed to progress according to the simultaneous reactions of initiator decomposition, initiation, propagation and termination with appropriate reaction orders described elsewhere.(2-6)... 

Aj.ApAi = Arrhenius factor for dissociation, propagation and termination respectively c= xp(-AS/R)... 

The rates of propagation and termination in the aqueous phase were also calculated. The radical entry rate, radical generation rate, and aqueous propagation rate were then used to develop an algebraic equation for the rate of formation of primary precursors. This equation is an extension to copolymers of the homogeneous nucleation equation derived by Hansen and Ugelstad (7.) for a homopolymer. 

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