Kinetics of Living Polymerization

Living polymerization constitutes a particularly useful model system for conducting rigorous and systematic kinetic studies to determine the absolute rate constants of involved elementary reactions. As the kinetics of ROP has been reviewed on several occasions in the past [3a, 4, 7,12, 23, 24,105-107], we will at this point present only a brief summary of the most important phenomena, complemented with some recent findings. 

During the 1970s, when the field of Hving cationic ROP underwent extensive developmenf the absolute rate constants were determined only for THE [106]. Nonetheless, a number of kinetic investigations were conducted with the cationic polymerization of substituted aziridines [121] and 1,3-oxazoHnes [122-124], and this in turn led to the revelation of a variety of attributes of livingness associated with these processes. 

It should also be noted that the anionic and cationic polymerization of cycHc trisiloxanes were both found to be devoid of termination and irreversible transfer, such that-in principle-the criteria of the Hving process were fulfilled. In contrast. 

The rate of polymerization in nonterminating systems can be expressed as the rate of propagation 

Equation 5-84 applies for the case where initiation is rapid relative to propagation. This condition is met for polymerizations in polar solvents. However, polymerizations in nonpolar solvent frequently proceed with an initiation rate that is of the same order of magnitude as or lower than propagation. More complex kinetic expressions analogous to those developed for radical and nonliving cationic polymerizations apply for such systems [Pepper, 1980 Szwarc et al., 1987], 

It is useful to understand the reasons for the faster reaction rates encountered in many anionic polymerizations compared to their radical counterparts. This can be done by comparing the kinetic parameters in appropriate rate equations Eq. 3-22 for radical polymerization and Eq. 5-84 for anionic polymerization. The kp values in radical polymerization are similar to the fc pp values in anionic polymerization. Anionic fc pp values may be 10-100-fold lower than in radical polymerization for polymerization in hydrocarbon solvents, while they may be 

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Nyrkova, I.A., and Semenov, A.N. "Non-linear scission-recombination kinetics of living polymerization". Eur. Phys. ]. 24,167-183 (2007). 

Application of FT-NIR Spectroscopy for Monitoring the Kinetics of Living Polymerizations... 

The kinetics of living polymerizations with reversible termination may be treated as follows. The rate of propagation is given by the following ... 

The effect of slow initiation on kinetics of living polymerizations is treated in the following way. Rearranging eqn (2.27) to yield [M] as a function of p]. 

Harrison et c /.146,147 have used PLP (Section 4.5.2) to examine the kinetics of MMA polymerization in the ionic liquid 18 (bmimPFfi). They report a large (ca 2-fold) enhancement in Ay and a reduction in At. This property makes them interesting solvents for use in living radical polymerization (Chapter 9). Ionic liquids have been shown to be compatible with ATRP14 "1 and RAFT.I57,15S However, there are mixed reports on compatibility with NMP.1 Widespread use of ionic liquids in the context of polymerization is limited by the poor solubility of some polymers (including polystyrene) in ionic liquids. 

The literature on Nitroxide-Mediated Polymerization (NMP) through 2001 was reviewed by Hawker el al. vu 7 More recently the subject has been reviewed by Sluder and Schulte10 and Solomon.109 NMP is also discussed by Fischer110 and Goto and Fukuda" in their reviews of the kinetics of living radical polymerization and is mentioned in most reviews on living radical polymerization. A simplified mechanism of NMP is shown in Scheme 9.17. 

Complexation with TMEDA. The kinetic of the polymerization has been studied by varying the concentration of living ends and the molar ratio r = [tMEDa] / [living ends ... 

Fig. 8. The apparatus for kinetic studies of living polymerizations under an electric field. Reproduced, with permission, from Ise, Hirohara, Makino, and Sakurada J. Phys. Chem. 72, 4543 (1968)...

The alkylaluminum component combined with V(acac)3 has an influence on the kinetic behavior of the propylene polymerization at —78 °C47 82 83). In the polymerization with V(acac)3 and dialkylaluminum monohalide like Al(i-C4H9)2C1, Al(n-C3H7)2C1, A1(C2HS)2C1 or Al(C2H5)2Br, M of polypropylene increased proportionally to the polymerization time, and the polydispersity (M Mj was as narrow as 1.15 0.05 (see Fig. 9). This is the case of living polymerization. As can be seen from Fig. 9, the rate of increase of Mn, i.e. the rate of propagation of living chains as expressed by lvln/(42 t), is influenced by the kind of aluminum component and decreases in the series... 

Active centres of ionic polymerizations do not usually decay by mutual collisions as the radical centres. The stationary state, when it exists at all, results from quite different causes, mostly specific to the given system. Therefore the kinetics of ionic polymerizations is more complicated and its analysis more difficult. The concentration of centres cannot usually be calculated. On the other hand, ionic systems with rapid initiation give rise to the kinetically very simple living polymerizations (see Chap. 5, Sect. 8.1). 

When living centres are slowly generated, the polymerization accelerates with time. Older centres have time to grow to larger dimensions than the fresh centres. Several authors [22-24] have paid attention to kinetic analysis of living polymerizations with slow initiation, the most recent of these studies being that of Pepper [25]. 

The lack of termination greatly simplifies studies of the kinetics of anionic polymerization. The living polymer may be prepared at the desired concentration, then mixed with monomer. A reaction then ensues and its progress can be followed by any suitable technique. Since termination is eliminated, the polymerization is first order with respect to monomer, and hence its concentration is given by the usual equation ... 

In a series of papers43 4S), the kinetics of anionic polymerization of ethylene oxide in conjunction with different catalysts were studied. These studies expand our understanding of the mechanism of living polymerization systems and provide new information on the processes of active center association. Herein, primarily, lies the specific nature of the heteroatomic systems, as compared with the vinyl monomers studied earlier 9 ... 

Kinetics Most epoxide polymerizations have the characteristics of living polymerization, that is, initiation is fast relative to propagation and there is an absence of termination processes. The expressions for the rate and degree of polymerization used in living chain polymerizations (see Chapter 8) can thus be applied for epoxide polymerizations. The polymerization rate is given by... 

The kinetics of these polymerizations is complex. Both complexed ion pairs and free ions are involved in the propagation reactions and the free ion rate constants depend on monomer concentration. The relative reactivity of complexed ion pairs and free ions is temperature dependent. Above the inversion temperature of —35°C, free ions are more reactive than ion pairs, but below this temperature the ion pairs are more reactive. At 30 °C in DMF, the observed (average) propagation rate constant is 0.13 l/(mol s) [146], The anionic polymerization of a,a-dialkyl-P-propiolactones such as pivalolactone (a,a,-dimethyl-P-propiolactone) initiated with carboxylate anions exhibits the main characteristics of living polymerizations. 

Axel H. E. Muller obtained his PhD in 1977 from Johannes Gutenberg University in Mainz, Germany, for the work on the kinetics of anionic polymerization with G. V. Schulz. Since 1999, he has been professor and chair of macromolecular chemistry at the University of Bayreuth. In 2004, he received the lUPAC MACRO Distinguished Polymer Scientist Award and since 2011, he has been a Fellow of the Polymer Chemistry Division of the American Chemical Society. He is senior editor of the journal Polymer. His research interests focus on the design of well-defined polymer stmctures by controlled/living polymerization techniques and on self-organized nanostructures and hybrids obtained from them. He has coedited five books and published over 400 research papers. 

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