Chain kinetic treatment

Eqs. (3), (4), (5), and (7) describe the mechanism of an initiated free radical polymerization in a form amenable to general kinetic treatment. The rate of initiation of chain radicals according to Eqs. (3) and (4) may be written... 

The kinetic treatment corresponds to that given above for the case of chain transfer with polymer. We have merely to write for the rate of generation of cross-linked units... 

Since the depolymerization process is the opposite of the polymerization process, the kinetic treatment of the degradation process is, in general, the opposite of that for polymerization. Additional considerations result from the way in which radicals interact with a polymer chain. In addition to the previously described initiation, propagation, branching and termination steps, and their associated rate constants, the kinetic treatment requires that chain transfer processes be included. To do this, a term is added to the mathematical rate function. This term describes the probability of a transfer event as a function of how likely initiation is. Also, since a polymer s chain length will affect the kinetics of its degradation, a kinetic chain length is also included in the model. 

In many binary copolymerizations, there is a pronounced tendency for the two types of monomer unit to alternate along the copolymer chain. In extreme cases, there is almost perfect alteration, notably for pairs of monomers, e.g, maleic anhydride and stilbene, which do not polymerize on their own. Ternary copolymenzations are of practical importance die kinetic treatments developed for binary copolymerizations can be extended to diese systems. 

The kinetic treatment of a simple polymerization is readily extended to nonpolymerization chain reactions such as that of Scheme 9. Here we again... 

Recently, Sawamoto et al. have restudied this system in 1,2-dichloroethane, nitrobenzene and mixtures of 1,2-dichloroethane and benzene, at 50 °C. They noticed again that esterification of styrene accompanied the polymerisation, but limiting yields were not detected. In fact, even in the media of lower polarity the polymerisation proceeded slowly but steadily over periods of days. The authors argued in favour of ionic chain carriers because the monomeric trifluoroacetate failed to promote the polymerisation of styrene. They also used alternative kinetic treatments to prove that only... 

More detailed information on the activation pathway, which distinguishes the polymeric photoinitiators from the corresponding low-molecular-weight structural models, has been obtained by photophysical measurements [22,27,28] in terms of quantum yield and average lifetime of the triplet excited state of benzophenone moieties in the above systems. However, in order to get a better comprehension of this point, it is necessary to introduce some basic concepts about the kinetic treatment of a photoinitiated chain polymerization. 

Main chain scission followed by depolymerization is a very frequently observed mechanism of thermal degradation. Kinetic treatments allowing... 

The kinetic treatment of these polymerization reactions depends upon the establishment of stationary state equations for the rates of formation and disappearance of all the transitory intermediates. The form of the expressions derived for the rate of the main reaction depends largely upon the mode of chain ending, and the constants entering into the formulae are those characterizing initiation, propagation, and termination respectively. Special means may be employed for the study of some of these constants in isolation, whereby rather complicated relations can be unravelled. For example, the reaction may be excited photoohemically, in which case the rate of initiation is calculable from the number of quanta of light which are absorbed. This method can be applied with ease to those polymerization reactions which are started by radicals formed, for example, in the photolysis of aldehyde ... 

It is important to emphasize that this kinetic treatment is valid for any chain polymerization mechanisms, i.e., free radical, cationic, anionic, and coordination. However, in the case of the ionic mechanisms, the type of initiator used and the nature of the solvent medium may influence the ri and r2 values. This is due to the fact that the growing chain end in ionic systems is generally associated with a counterion, so that the structure and reactivity of such chain ends can be expected to be affected by initiator and the solvent. This will be discussed in Section 2.8.3. 

It is very useful to know whether this situation prevails, because such knowledge will gready facilitate the kinetic treatment of chain reactions. In deed, for chain reactions with long chains, the steady-state concentration of active centers is determined by the relation f< = where n represents the rate of initiation and r< the rate of termination. Termination includes the destruction of all types of active centers present in the system. Clearly, the kinetic treatment will be simplified if only one termination step needs to be taken into account because it is the one that expresses the rate of destruction of the most abundant active centers. 

Chain scission. The midchain radical structure formed by intra- or intermolecular transfer to polymer is less reactive than a chain-end radical. Under higher temperature conditions, the radical may undergo -ffagmentation (chain scission) as shown in Scheme 3.10 for BA. As well as lowering polymer MW, sdssion produces an unsaturated chain end that can react further (Scheme 3.7b). Scission is important for acrylate polymerizations at temperatures > 140°C [18,21], is a dominant mechanism in styrene polymerizations at 260-340°C [15], and also occurs during LDPE production [14]. Kinetic treatment is difficult, as scission is coupled with LCB and/or SCB formation. 

Photopolymerization systems, like thermally initiated systems, contain initiator, monomer, and other additives that impart desired properties (color, strength, flexibility, etc) (6). The reaction is initiated by active centers that are produced when light is absorbed by the photoinitiator. One important class of active centers includes free-radical species, which possess an impaired electron (5,7). The highly reactive free-radical active centers attack carbon-carbon double bonds in imsaturated monomers to form pol5nner chains. Although the kinetic treatment of photopoljnner systems is similar to that in thermal systems, significant differences arise in the description of the initiation step, which in turn affect the... 

Autoacceleration, where the rate of polymerization increases with conversion in isothermal conditions, is observed in both thermal- and photoinitiated free-radical polymerizations because the termination mechanisms are the same for both. As the chains grow longer, it becomes more difficult for the active centers to diffuse and imdergo bimolecular termination thus, termination frequency decreases and active centers at the chain ends can become trapped. In cases where termination is controlled by diffusion, the pseudo-steady-state assumption is no longer valid and chain length dependent termination (CLDT) may occur (67). As is discussed for chain cross-linking photopolymerizations below, more complicated kinetic treatments must then be considered, including unsteady-state kinetics. 

The above discussion highlights the fact that the simple initiation process of most polymer texts is the exception rather than the rule, with the fraction of primary radicals that initiate a new polymer chain a complex function of the reaction system. Nonetheless, the kinetic treatment is usually simplified by the introduction of a fractional initiator efficiency (/), formally defined by Eq. (1), where n is the number of moles of primary radicals generated per mole of initiator n = 2 for most common initiators. 

Kinetic treatment of these more complex mechanisms is often difficult. Equations (32)-(34) are a network of reactions developed to treat intramolecular transfer, short-chain branch formation, and jS-scission for butyl acrylate polymerization [47]. 

The peculiar name normal mode needs a comment. As will be explained in detail in the next chapter, chain dynamics in melts may be described with the aid of two theoretical models known as the Rouse-model and the reptation model . In the frameworks of these treatments chain kinetics is represented as a superposition of statistically independent relaxatory normal modes . As... 

A valid molecular-kinetic treatment of the formation of adhesive bonds has been given by Voronin and Lavrentyev. When discussing the mechanism of formation and failure of adhesion joints, it is assumed that for segments of the pol5mieric chain in the boundary layer there are two possible states ... 

Very many kinetic models have been proposed for both heterogeneous and homogeneous Ziegler-Natta polymerization (c.f. 2,8,18) but for the purposes of this paper only the recent models proposed by Tait et al (26,29f30), Yermakov et al (31) and Bohm (39) will be considered. These three kinetic treatments have the common features that chain propagation is treated as a two-stage reaction, monomer... 

Synthetic polymers can be derived either from the chemical modification of existing ones or through polymerization of simple molecules (called monomers). Such conversions of monomers into polymers can be obtained either through the basic condensation/addition reactions of organic chemistry or via chain reactions whose requirements and kinetic treatment are quite different. It leads to two categories of polymerization step-growth polymerization and chain polymerization, which will be presented in this chapter and Chapter 8, respectively. 

Hydrolysis and Polycondensation. As shown in Figure 1, at gel time (step C), events related to the growth of polymeric chains and interaction between coUoids slow down considerably and the stmcture of the material is frozen. Post-gelation treatments, ie, steps D—G (aging, drying, stabilization, and densification), alter the stmcture of the original gel but the resultant stmctures aU depend on the initial stmcture. Relative rates, of hydrolysis, (eq. 2), and condensation, (eq. 3), determine the stmcture of the gel. Many factors influence the kinetics of hydrolysis and... 

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