The penultimate effect

When the reactivity of the centre is determined not only by the last added unit but also by the last but one unit, we speak of the penultimate effect. Merz et al. treated this problem using eight independent reactions [200, 201 ]. 

With the stationary state assumption, they derived and equation for copolymer composition (r, = km/km, r2 = k222Jkm, r = k2n/k2l2, and r2 = 

When one of the copolymerizing monomers is unable to homopolymerize, eqn. (110) is simplified to 

Merz et al. treated this problem using eight independent reactions [200, 201 ]. 

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Termination scheme 11 applies to the geometric mean and phi factor models and scheme 12 Is required for the penultimate effect model. All the above reaction models were used In attempts to simulate kinetic data. 

The original mathematical treatment of the penultimate effect was presented by Merz and coworkers [Barb, 1953 Ham, 1964 Merz et al., 1946], Fukuda and coworkers developed a more extensive treatment, which distinguished between two penultimate models of copolymerization behavior—the explicit penultimate and implicit penultimate models [Coote and Davis, 1999, 2000 Davis, 2001 Fukuda et al., 1985, 1987, 1992, 2002 Ma et al., 2001], The explicit penultimate model for copolymerization involves the use of eight propagation reactions... 

The composition of copolymer and distribution of units in copolymer molecule can be predicted as follows. Let us designate two types of comonomer molecules as A and B and the respective radicals as A and b1 The symbols with an asterisk deal with the process proceeding on the template. In addition, let us assume that we can neglect the penultimate effect. In this case, the process of propagation is expressed by the following set of reactions and respective rates and rate constants ... 

For the above reactions, it is assumed that the reactivity of the propagating radical is dependent only on its terminal radical unit. However, the rate of addition of a monomer to the growing radical depends on the type of monomer in the penultimate position. The importance of the penultimate effects has not been widely investigated. As a result, it is assumed that the simple copolymerization equations given above are valid. 

Living polymerizations continue to attract the attention of theorists studying transfer. Chinese authors have analyzed the penultimate unit effect on transfer to a monomer mathematically [53]. According to their conclusions, the penultimate effect is important when the activities of the growth centres on the polymer chain and on the monomer (after transfer) are widely different, otherwise it can be neglected. 

The mathematical treatment of the penultimate effect [33,34] in a binary copolymerization system involves the use of eight propagating reactions ... 

On the other hand, for a reason why the intermolecular ht addition may be equilibrated, the electrostatic repulsion between the highly polar anhydride units may be considered similar to the well known case in the radical copolymerization of vinyl monomers carrying carbonyl(34) or nitrile group(35) in which the penultimate effect is involved. That is, the polymer(D) obtained via intramolecular hh and intermolecular tt additions in which five-membered anhydride units are separated by two methylene units is sterically and/or electrostatically favorable compared with the polymer(E) formed via intramolecular ht and intermolecular ht additions in which six-membered anhydride units are separated by only one methylene unit. 

The proportions of the triads vary with the monomer feed. As shown in Fig. 15.2, the proportions of the experimentally found triads agree well with the values calculated from Eq. (15-16a) using r obtained from the content of comonomers in the copolymer (method from Ref. 6)). This agreement means that in this system the penultimate effect, reversibility of propagation, interconversion of active species without propagation [Eq. (15-4)] and redistribution of the initially formed copolymer can be neglected and the process can be described by two reactivity ratios. 

A series of telomerizations were performed in which the auxiliaries were varied in an attempt to determine which factors influence the penultimate effect. Bulky auxiliary groups analogous to those shown in Fig. 3 were used, and mixed auxiliary telomerizations were performed in which methyl acrylate was co-telomerized with the acrylimides. In cases where auxiliaries were sterically bulky and especially when... 

Penultimate Model Some copolymerization systems in which the values for reactivity ratios measured at different compositions are inconsistent can be adequately represented by the penultimate model [86]. In this case, the reactivity of the propagating chain depends on the chemical nature of the last two monomeric units the one at the active end and the previous one (penultimate) [87, 88], This is common in systems in which the monomers contain bulky substituents such as the fumaronitrile-styrene copolymerization [89], In other systems, the penultimate effect has been reported to be limited [90], The penultimate model can be formulated as follows. Consider the reaction of a growing chain having a penultimate unit j and terminal unit i with a monomer n, M ... 

The influence of the penultimate member of the growing polymer chain (what is called the penultimate effect) has been often discussed as a cause of deviations from the simple copolymerization equation, especially in the case of strongly polar monomers. Very accurate experiments at very low monomer ratios must be carried out to establish such influences and to correspondingly modify the simple copolymerization equation. However, the penultimate chain end effect can often be better explained by the formation of CT complexes (see Figure 22-11). In this case, the CT complexes function as third monomer. 

The penultimate effect on the kinetics of the activation/deactivation processes may be quite significant. For example, model studies of activation of various dimers in ATRP copolymerization of methyl acrylate (MA) and methyl methacrylate (MMA) showed the following relative values of act for dimeric species H-MA-MA-Br, H-MMA-MA-Br, H-MA-MMA-Br, and H-MMA-MMA-Br to be 1, 4.6, 19, and 96, respectively. The back-strain effect resulting from the presence of a MMA penultimate unit, and formation of a thermodynamically more stable radical from a MMA-Br terminal unit, increased the values of act by 5 and 20 times, respectively, in comparison to MA penultimate/terminal imits. The combined effects resulted in a 100-fold increase of k ct for H-MMA-MMA-Br relative to H-MA-MA-Br (116). 

The number sequence lengths in A monomer, in the presence of the penultimate effect, are given by the following equation ... 

Sato T, Kawasaki S, Seno M, Tanaka H, Kato K. Kinetic and ESR studies on radical polymerization. ESR and kinetic evidences for the penultimate effect in the radical-initiated copolymerization of N-cyclohexyhnaleimide and bis(2-ethylhexyl) itaconate in benzene. Makromol Chem 1993 194 2247-2256. 

Solution copolymerization of the MA-styrene pair has been studied in acetone at high pressure (1-4 kbars). At 40°C, the copolymerization reaction rate between MA and the growing polymer chain, having a MA unit preceding the active styrene moiety, increased with pressure for both bulk and solution copolymerizations condition. Thus, Enomoto and coworkers conclude the penultimate effect diminishes or disappears with pressure escalation. Composition and infrared studies show a 1 1 alternating structure for the material, over a wide range of monomer concentration of one component. 

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