Chain copolymerization statistical

There are several examples of random copolymers of methacrylates (R-l to R-3). MMA/nBMA copolymerization was carried out with a copper catalyst, but the products were of low molecular weight because this study was directed to mechanistic studies.263 Random copolymers of MMA and nBMA (R-l) were also obtained in emulsion (MJMn = 1.2—1.3).254 Two monomers were consumed almost simultaneously to give a random or statistical distribution of repeat units along the chains. Copolymerization of MMA... 

Functional and end-functional polymers are precursors to block and graft copolymers and, in some cases, polymer networks. Copolymers with in-chain functionality may be simply prepared in copolymerizations by using a functional monomer. However, obtaining a desired distribution requires consideration of the chain statistics and, for low molecular weight polymers, the specificity of the initiation and termination processes, l hese issues are discussed in Section 7.5.6... 

Crosslihkinq Density Distribution. Let us consider the statistical copolymerization of vinyl/divinyl monomers without chain transfer to polymer for simplicity. In this case the crosslinking density p is defined as follows. 

Monomer concentrations Ma a=, ...,m) in a reaction system have no time to alter during the period of formation of every macromolecule so that the propagation of any copolymer chain occurs under fixed external conditions. This permits one to calculate the statistical characteristics of the products of copolymerization under specified values Ma and then to average all these instantaneous characteristics with allowance for the drift of monomer concentrations during the synthesis. Such a two-stage procedure of calculation, where first statistical problems are solved before dealing with dynamic ones, is exclusively predetermined by the very specificity of free-radical copolymerization and does not depend on the kinetic model chosen. The latter gives the explicit dependencies of the instantaneous statistical characteristics on monomers concentrations and the rate constants of the elementary reactions. 

This is the simplest of the models where violation of the Flory principle is permitted. The assumption behind this model stipulates that the reactivity of a polymer radical is predetermined by the type of bothjts ultimate and penultimate units [23]. Here, the pairs of terminal units MaM act, along with monomers M, as kinetically independent elements, so that there are m3 constants of the rate of elementary reactions of chain propagation ka ]r The stochastic process of conventional movement along macromolecules formed at fixed x will be Markovian, provided that monomeric units are differentiated by the type of preceding unit. In this case the number of transient states Sa of the extended Markov chain is m2 in accordance with the number of pairs of monomeric units. No special problems presents writing down the elements of the matrix of the transitions Q of such a chain [ 1,10,34,39] and deriving by means of the mathematical apparatus of the Markov chains the expressions for the instantaneous statistical characteristics of copolymers. By way of illustration this matrix will be presented for the case of binary copolymerization ... 

In agreement with Flory s predictions, hyperbranched polymers based on A,jB monomers reported in the literature exhibit a broad molecular weight distribution (typically 2-5 or more). The polydispersity of a hyperbranched polymer is due to the statistical growth process. A strategy to overcome this disadvantage is to add a By-functional core molecule, or a chain terminator, which Hmits the polydispersity and also provides a tool to control the molecular weight of the final polymer. The concept of copolymerizing an A2B monomer with a B3 functional core molecule was first introduced by Hult et al. [62] and more recently also utilized by Feast and Stainton [63] and Moore and Bharathi [64]. 

Styrene-SQ., Copolymers. I would now like to discuss two systems which illustrate the power of C-13 nmr in structural studies. The first is the styrene-SO system. As already indicated, this is of the type in which the chain composition varies with monomer feed ratio and also with temperature at a constant feed ratio (and probably with pressure as well.) The deviation of the system from simple, first-order Markov statistics, —i.e. the Lewis-Mayo copolymerization equation—, was first noted by Barb in 1952 ( ) who proposed that the mechanism involved conplex formation between the monomers. This proposal was reiterated about a decade later by Matsuda and his coworkers. Such charge transfer com-... 

Under the condition that the reaction capability is only affected by the nature of the last monomer unit of the growing polymer chain end (terminal model, Bernoulli statistics), the copolymerization equation can be transformed according to Kelen and Tudos ... 

The side chains are of a predetermined size and composition via anionic chemistry and based on the reactivity placed at the terminus of the MACROMER and the comonomer with which it will be reacted. The number of side chains per backbone and a distance apart can be reasonably estimated. This distance between side chains must be sufficient that the backbone can manifest its Tg. Considering the earlier comments of molar concentration of the MACROMER in a typical copolymerization recipe, there will not be many MACROMERS per backbone on a statistical basis. 

According to this model the structure of the crosslinked polymer is not considered as a homogeneous infinite network of polyester molecules, connected by styrene bridges. Since the styrene is a poor solvent for polyester chains the copolymerization takes place at statistically placed radicals (R )85). 

Secondary metathesis reactions are sometimes encountered during metathesis copolymerization, leading to a reshuffling of the units in the chain and eventually to a random distribution for example in the copolymerization of 248 and 258 using RUCI3 as catalyst, statistical copolymers are produced no matter whether the monomers are mixed initially or added sequentially576. See also the copolymers of 128 Section Vm.B.6. 

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