Constant rate copolymerization reaction

In evaluating the kinetics of copolymerization according to the chemical control model, it is assumed that the termination rate constants k,AA and A,Br are known from studies on homopolymerization. The only unknown in the above expression is the rate constant for cross termination (AtAB)- The rate constant for this reaction in relation to klAA and kmB is given by the parameter . 

In fact the copolymerization of two olefins is characterized by their reactivityratiosi.e. the ratios of the rate constant for the reaction of a radical with a monomer of the same kind, to that of the rate constant for cross... 

The emulsion copolymerization of BA with PEO-MA (Mw=2000) macromonomer was reported to be faster than the copolymerization of BA and MMA, proceeding under the same reaction conditions at 40 °C [100]. Polymerizations were initiated by a redox pair consisting of 1-ascorbic acid and hydrogen peroxide in the presence of a nonionic surfactant (p-nonyl phenol ethoxylate with 20 moles ethylene oxide). In the macromonomer system, the constant-rate interval 2 [9,10] was long (20-70% conversion). On the other hand, the interval 2 did not appear in the BA/MMA copolymerization and the maximum rate was lower by ca. 8% conversion min 1 and it was located at low conversions. 

The rate of dispersion (co)polymerization of PEO macromonomers passes through a maximum at a certain conversion. No constant rate interval was observed and it was attributed to the decreasing monomer concentration. At the beginning of polymerization, the abrupt increase in the rate was attributed to a certain compartmentalization of reaction loci, the diffusion controlled termination, gel effect, and pseudo-bulk kinetics. A dispersion copolymerization of PEO macromonomers in polar media is used to prepare monodisperse polymer particles in micron and submicron range as a result of the very short nucleation period, the high nucleation activity of macromonomer or its graft copolymer formed, and the location of surface active group of stabilizer at the particle surface (chemically bound at the particle surface). Under such conditions a small amount of stabilizer promotes the formation of stable and monodisperse polymer particles. 

The low effect of the structure of oligomer alkyl radicals on the rate constant of their reaction with oxygen also follows from the review article on the copolymerization of vinyl monomers with oxygen in the liquid phase. 

The effect of temperature on reactivity ratios in free radical copolymerization is small. We can reasonably assume that the propagation rate constants in the reactions (7-2)-(7-5) can be represented by Arrhenius expressions over the range of temperatures of interest, such as... 

Comprehensive Models. This class of detailed deterministic models for copolymerization are able to describe the MWD and the CCD as functions of the polymerization rate and the relative rate of addition of the monomers to the propagating chain. Simha and Branson (3) published a very extensive and rather complete treatment of the copolymerization reactions under the usual assumptions of free radical polymerization kinetics, namely, ultimate effects SSH, LCA and the absence of gel effect. They did consider, however, the possible variation of the rate constants with respect to composition. Unfortunately, some of their results are stated in such complex formulations that they are difficult to apply directly (10). Stockmeyer (24) simplified the model proposed by Simha and analyzed some limiting cases. More recently, Ray et al (10) completed the work of Simha and Branson by including chain transfer reactions, a correction factor for the gel effect and proposing an algorithm for the numerical calculation of the equations. Such comprehensive models have not been experimentally verified. 

TEMPO, />substituted TEMPO based alkoxyamines 3, and compounds such as 4, 5, and 7 have been applied successfully for polymerizations of styrene, substituted styrenes, and 4-vinylpyridine, and some copolymerizations and block copolymerizations were reported. However, living and controlled radical polymerization of other monomers, especially acrylates, require the use of the more recently developed structures 6, 8, or 9. These also yield well-controlled and living block copolymers, but methacrylates have so far resisted all efforts to obtain large conversions. Undoubtedly, many failures are due to unfavorable rate constants or side reactions. 

In the derivation of copolymer composition equation, Eq. (7.11), we considered only the rates of the four possible propagation steps in a binary system. However, the overall rate of copolymerization depends also on the rates of Initiation and termination. In deriving an expression for the rate of copolymerization in binary systems the following assumptions will be made [25] (a) rate constants for the reaction of a growing chain depend only... 

The kinetics of copolymerization provides a partial explanation for the copolymerization behavior of styrenes with dienes. One useful aspect of living anionic copolymerizations is that stable carbanionic chain ends can be generated and the rates of their crossover reactions with other monomers measured independently of the copolymerization reaction. Two of the four rate constants involved in copolymerization correspond at least superficially to the two homopolymerization reactions of butadiene and styrene, for example, and k, respectively. The other... 

The quantity ijij represents the ratio of the product of the rate constants for the reaction of a radical with its own kind of monomer to the product of the rate constants for the cross-reactions. Copolymerization may therefore be classified into three categories depending on whether the quantity rir2 is unity, less than unity, or greater than unity. 

Monomer-radical reaction rates are also influenced by steric hindrance. The effect of steric hindrance in reducing monomer reactivity can be illustrated by considering the copolymerization reaction rate constants (ku) for di- and tri-substituted ethylene. Table 8.4 lists some of these values. 

The derivation of eqn [13] is based on the observation that the average propagation rate constant in a copolymerization reaction is the weighted average over the four individual propagation reaaions (eqns [l]-[4]). This leads to a mathematical expression as shown in eqn [14] ... 

The quantities k , k,p, kpp, and kp, are the rate constants of the four basic propagation reactions of copolymerization. The Stockmayer distribution function takes into account only a chemical polydispersity resulting fi om the statistical nature of copolymerization reactions. This means that all units of all chains are formed under identical conditions. If a monomer is removed from the reacting mixture at a rate which changes the monomer concentration ratio, the monomer concentration will drift, forming a copolymer which varies in the average composition and is broader in the chemical distribution. No such chemical polydispersity can be described by the Stockmayer distribution. Therefore, Eq. (84) has to be restricted in its application to random copolymers synthesized at very low conversions or under azeotropic conditions. For azeotropic copolymers, the feed monomer concentrations [a ] and are chosen in such a way that the second factor on the right-hand side of the basic relation of copolymerization kinetics... 

In copolymerization reactions, the monomer reactivity ratio is often referred to in order to discuss how the reaction proceeds. The monomer reactivity ratios and F2i are defined as the ratios of the rate constant of the reaction of a given radical with its own monomer (Afj) to the rate constant of its addition to the other monomer (M2). Thus, rj2 > 1 means that the radicalMj prefers the addition ofMj, whereas r 2 < 1 means that it prefers the addition ofMj. In these copolymerization methods, comonomers satisfying the following requirements are used as the base material r 2 > 1, T2i < 1, and the refractive index oftheMj homopolymer is lower than that of the M2 homopolymer. More details about monomer reactivity ratios are described later in this chapter. 

FIGURE 12.14 Continuous UV data at 305 nm from ACOMP foUow the evolution of the TTC during 2-(dimethylamino)ethyl acrylate (DMAEA)/styrene (sty) copolymerization reactions by RAFT with different initial composition and indicate that the degradation process is slower for higher amount of styrene. Shown in the inset to figure are the plotted TTC decomposition rate constants versus styrene %. The rates were from exponential fits used as first-order approximations. Reprinted from Li Z, Serelis AK, Reed WF, Alb AM. Online monitoring of the copolymerization of 2-(dimethylamino(ethyl acrylate with styrene by RAFT deviations from reaction control. Polymer 2010 51 4726-4734. 2010 with permission from Elsevier. 

Q-E Scheme The Q-E scheme is used for quantitatively correlating relative monomer reactivities in copolymerization reactions, introduced by Alfrey and Price in 1947 for the purpose of defining an equation for each cross-propagation rate constant ki2 or fei), in a copolymerization reaction in terms of three constants characteristic of P is considered to be a function of the structures of the monomer P, Q and e. 

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