Terminal monomer unit

Copolymer composition can be predicted for copolymerizations with two or more components, such as those employing acrylonitrile plus a neutral monomer and an ionic dye receptor. These equations are derived by assuming that the component reactions involve only the terminal monomer unit of the chain radical. The theory of multicomponent polymerization kinetics has been treated (35,36). 

Even when only the terminal monomer unit is considered, radical-radical termination in binary copolymerization involves at least seven separate reactions (Scheme 7.12). There are two homoterminalion processes and one cross termination process to consider. In the case of cross termination, there arc two pathways for disproportionation. There are then at least three pieces of information to be gained ... 

Each monomer is characterized by two monomer reactivity ratios. One monomer reactivity ratio represents the propagating species in which the penultimate and terminal monomer units are the same. The other represents the propagating species in which the penultimate and terminal units differ. The latter monomer reactivity ratios are signified by the prime notations. Each radical reactivity ratio is the ratio of the propagation rate constant for reaction of a radical in which the penultimate unit differs from the terminal unit compared to the rate constant where the penultimate and terminal units are the same. 

The polymerization of a 1,3-diene involves delocalization of the radical over carbons 2 and 4 of the terminal monomer unit (XLVIII). The predominance of 1,4-propagation... 

While termination leads to the irreversible disappearance of an active center, chain transfer results in the growth of a second chain while the first one is terminated. Here, the active center is transferred to another molecule (solvent, initiator, monomer,...) where it is able to initiate further chain growth. The resulting dead polymer, on the other hand, can continue its growth only when activated in a subsequent transfer step. Because this re-activation in general does not occur at the terminal monomer unit but somewhere in the chain, branched or cross-linked products will result ... 

IT number of terminal monomer units ID number of dendritic monomer units IL number of linear monomer units... 

A single step of the polymerization is analogous to a diastereoselective synthesis. Thus, to achieve a certain level of chemical stereocontrol, chirality of the catalytically active species is necessary. In metallocene catalysis, chirality may be associated with the transition metal, the ligand, or the growing polymer chain (e.g., the terminal monomer unit). Therefore, two basic mechanisms of stereocontrol are possible (145,146) (i) catalytic site control (also referred to as enantiomorphic site control), which is associated with the chirality at the transition metal or the ligand and (ii) chain-end control, which is caused by the chirality of the last inserted monomer unit. These two mechanisms cause the formation of microstructures that may be described by different statistics in catalytic site control, errors are corrected by the (nature (chirality) of the catalytic site (Bernoullian statistics), but chain-end controlled propagation is not capable of correcting the subsequently inserted monomers after a monomer has been incorrectly inserted (Markovian statistics). 

Atactic polypropylenes are produced in catalysis by C2v-symmetric metallocenes that are achiral, such as Cp2MCl2 or (Me2Si(FLu)2)ZrCl2. The only stereocontrol observed is both of the chain-end type and low because the chiral center of the terminal monomer unit of the growing chain is in the P position as a consequence of the 1,2 insertion of the monomers. A significant influence on the tacticity is observed only at low temperatures, being much more pronounced for titanocenes and hafnocenes than zirconocenes as a consequence of their shorter M-Ca bonds, bringing the chiral p-carbon closer to the active center (147,148). 

Two steps occur in the microbial polymer degradation process, first, a depolymerisation or chain cleavage step, and second, mineralisation. The first step normally occurs outside the organism due to the size of the polymer chain and the insoluble nature of many of the polymers. Extracellular enzymes are responsible for this step, acting either endo (random cleavage of the internal linkages of the polymer chains) or exo (sequential cleavage of the terminal monomer units in the main chain). 

The X-ray crystal structure shows methyl 4,6-0-benzylidene-2,3-0-dibutylstannylene-D-mannopyranoside to be a pentamer.51 In the pen-tamer, the two terminal monomer units have 0-2 dicoordinate. The... 

Although some block copolymers can be made by other techniques, anionic polymerizations are particularly useful in this application. This is mainly because of the absence of an inherent termination step in some anionic systems and because anions with terminal monomer units of one type can be used to initiate the polymerization of other selected monomers. The different anionic reaction sequences that are employed include sequential monomer addition, coupling reactions, and termination with reactive groups. 

The above mechanisms for cis-1,4 polymerization of isoprene or isotactic polymerization of acrylates assume that the configuration of each unit is fixed at the moment of reaction and that no racemization occurs between additions of monomer molecules. Little evidence for the validity of the mechanisms was available when suggested. Recently it has been possible to obtain information, from NMR studies, on the reaction path. This evidence is of two types and depends on the polymerization of stereospecifically deuterated monomers to determine the mode of approach of monomer molecules and on direct observations of NMR spectra of the terminal monomer unit in the polymer. 

For stereospecific polymerization of a-olefms such as propene, a chiral active center is needed, giving rise to diastereotopic transition states when combined with the prochiral monomer and thereby different activation energies for the insertion (see Figure 2). Stereospecificity may arise form the chiral /0-carbon atom at the terminal monomer unit of the growing chain - chain end control - or from a chiral catalyst site - enantiomorphic site control . The microstructure of the polymer produced depends on the mechanism of stereocontrol as well as on the metallocene used [42-44]. 

Scheme 6 Reactions occurring in a copolymerization in the simplest model, the reactivity of the propagating chain is considered to be dependent only on the terminal monomer unit.

These problems might be overcome by using randomly branched polymer structures as supports [ 13,82,112]. In contrast to dendrimers, hyperbranched polymers are easily available in one reaction step. This allows the production of large quantities of material [82]. They contain dendritic, linear and terminal monomer units in their skeleton and hence can be considered as inter me-... 

The number of radicals to be considered equals the number of monomers. The terminal monomer unit in a growing chain determines almost exclusively the reaction characteristics the nature of the preceding monomers has no significant influence on the reaction path. 

The simplest kinetics model for free-radical copolymerization, known as the terminal model, will be analysed here. The principal assumption is that the reactivity of an active centre depends only upon the terminal monomer unit in which it is located, hence the name of the model. As in the analysis of homopolymerization kinetics, it is further assumed that the amount of moncHn consumed in reactions other than propagation is negligible and that copolymer molecules of high molar mass are formed. Thus for free-radical copolymerization of monomer A with moncHno- B, only two types of active centre need be considered ... 

Copolymer composition can be predicted for copolymerizations with two or more components, such as those employing acrylonitrile plus a neutral monomer and an ionic dye receptor. These equations are derived by assuming that the component reactions involve only the terminal monomer unit of the chain radical. This leads to a collection of N x N component reactions and x 1) binary reactivity ratios, where N is the number of components used. The equation for copolymer composition for a specific monomer composition was derived by Mayo and Lewis [74], using the set of binary reactions, rate constants, and reactivity ratios described in Equation 12.13 through Equation 12.18. The drift in monomer composition, for bicomponent systems was described by Skeist [75] and Meyer and coworkers [76,77]. The theory of multicomponent polymerization kinetics has been treated by Ham [78] and Valvassori and Sartori [79]. Comprehensive reviews of copolymerization kinetics have been published by Alfrey et al. [80] and Ham [81,82], while the more specific subject of acrylonitrile copolymerization has been reviewed by Peebles [83]. The general subject of the reactivity of polymer radicals has been treated in depth by Jenkins and Ledwith [84]. 

Fig. 5 Fraction P of the terminal monomer units located at a distance r from the center of a star-shaped PE at different contents of a linear PE. z is the degree of charge compensation, which reflects the linear PE content. Reprinted from [89] with permission from the American Chemical Society...

Fig. 10 Radial distribution (P) of the terminal monomer units of side chains as a function of the distance (r) from the backbone at different degrees of charge compensation (z). Reprinted from [84] with permission from the Royal Society of Chemistry...

If more than one monomer species is present in the reaction medium, a copolymer or an interpolymer can result from the polymerization reaction. Whether, however, the reaction products will consist of copolymers or just mixtures of homopolymers or of both depends largely upon the reactivity of the monomers. A useful and a simplifying assumption in kinetic analyses of free-radical copolymerizations is that the reactivity of polymer radicals is governed entirely by the terminal monomer units. " For instance, a growing polymer radical, containing a methyl methacrylate terminal unit, is considered, in terms of reactivity, as a poly(methyl methacrylate) radical. This assumption, not always adequate, can be used to predict satisfactorily the behavior of many mixtures of monomers. Based on this assumption, the copolymerization of a pair of monomers involves four distinct growth reactions and two types of polymer radicals. 

A further parameter, introduced by Erey et al., allows a comparison to be made of the density of branching of different AB polymers. This average number of branches (ANBs) deviating from the linear direction per non-terminal monomer unit, and was 0.333 for AB2 systems, 0.421 for AB3 systems, and converges to 0.582 for growing x, again for random polymerization and full conversion [57]. 

As early as the 1940s, radical copolymerization models were already developed to describe specific features of the process. Initially, these models were relatively simple models where the reactivity of chain-ends was assumed to depend only on the nature of the terminal monomer unit in the growing chain (Mayo-Lewis model or terminal model (TM)). This model by definition leads to first-order Markov chains. 

Figure 1 shows the NMR spectra of poly( -co- ) whose monomer ratios ( and ) were 1 9, 1 1, and 9 1. Since monomer 3 is very bulky, the propagation process of this copolymerization is considered to be influenced by not only a terminal monomer unit but also the penultimate one of the growing chain, and is interpreted as a penultimate model. 

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