Kinetics of Reversible Polymerization

Some readers will be interested in the fact that Huang and Wang [75] in 1972 presented a newer theoretical treatment of the reaction kinetics of reversible polymerization in which this classic derivation of Dainton and Ivin is a special case. The thermodynamics of equilibrium polymerizations have recently been reviewed by Sawada [76]. 

Although reversible or equilibrium polymerizations would almost always be carried out in an irreversible manner, it is interesting to consider the kinetics of polymerization for the case in which the reaction was allowed to proceed in a reversible manner. (The kinetics of reversible ring-opening polymerizations are discussed in Sec. 7-2b-5). 

In conclusion, in the kinetics of dioxolane polymerizations with many catalysts, the initiation mechanism is complex and inefficient. The degree of efficiency seems to be related both to the cation and to the anion. Again as in the case of cyclic ethers and cyclic sulphides, an independent measurement of the number of active sites seems essential for precise kinetics. The most probable fep for the polymerization seems to be of the order of 10—501 mole sec . With careful choice of polymerization conditions a kinetically reversible polymerization occurs, but the molecular weight of the polymer produced is not related to the initiator concentration, probably as a result of a transfer reaction. 

Styrene is capable of forming moderately stable Co-C bonds.370 The formation and decomposition of adducts between the CCT catalysts and the propagating radicals results in reversible inhibition .123-271 In this case, an induction period is observed at the beginning of polymerization. This induction period is characterized by the steady growth of the rate of polymerization similar to the classic kinetics of a polymerization inhibited by a weak inhibitor. Depending upon conditions, the time required to reach steady-state polymerization kinetics (eq 42) may require tens of minutes. 

The kinetics of the ADMET reaction is not amenable to study by many traditional means, as these polymerizations are mostly conducted in bulk. The most effective way to measure the kinetics of the polymerization is to monitor the volume of evolved ethylene. This technique has been used to probe the difference in activity between [Mo] 2 and [Ru]l for ADMET polymerization of 1,9-decadiene [37]. At 26 °C in bulk monomer, [Mo] 2 promotes ADMET polymerization of 1,9-decadiene at a rate approximately 24 times that of [Ru]l. Additionally, [Mo] 2 polymerizes 1,5-hexadiene 1.7 times faster than 1,9-decadiene, while [Ru]l only cyclodimerizes 1,5-hexadiene to 1,5-cyclooctadiene. Monomers with coordinating functionality, specifically ethers and sulfides, were also investigated. Predictably, these monomers did not undergo polymerization as rapidly as hydrocarbon monomers however, this difference was dramatically more pronounced with [Ru]l than with [Mo]2. In fact, the dialkenyl sulfide monomers that were studied completely shut down the polymerization with [Ru]l, whereas the catalytic activity of [Mo]2 was only slightly lowered. This reduction in polymerization rate is most likely due to coordination of the heteroatom to the vacant coordination site of [Ru] 1, following phosphine dissociation. This reversible coordination of heteroatoms to the ruthenium complex likely occurs both intramolecularly and intermolecularly. Conversely, the steric bulk of the ligands in [Mo] 2 makes it less likely to intramolecularly form a coordinate complex, despite molybdenum being far more electrophilic than ruthenium. 

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

In this chapter, we have presented the kinetics of reversible step-growth polymerization based on the equal reactivity hypothesis. We have found that the polymerization consists of infinite elementary reactions that collapse into a single one involving reaction between flmctional groups. This kinetic model has been tested extensively against experimental data. It is found that in most of the systems involving step-growth polymerization, there are either side reactions or the equal reactivity hypothesis does not hold well. This chapter presents the details of chemistry for some industrially important systems motivated readers are referred to advanced texts for mathematical simulations. 

General features of the polymerization kinetics for polymerizations with deactivation by reversible coupling have already been mentioned. Detailed treatments appear in reviews by Fischer," Fukuda et ai and Goto and I vikuda" and will not be repeated here. 

In summary, then, polymerization of ATP-actin under conditions of sonication displays two characteristic deviations from the simple law described by equation (4), which is only valid for reversible polymerization. These are (a) overshoot polymerization kinetics, and (b) the steady-state amount of polymer formed decreases, or the steady-state monomer concentration increases, with the number of filaments. These two features are the direct consequence of ATP hydrolysis accompanying the polymerization of ATP-actin, as will be explained now. 

In vitro culture isolated brain cells exposed for 20 h to graded concentrations of nickel chloride up to 116 mg Ni/L DOMESTIC DOG, Canis familiaris Diet Time- and dose-dependent effects on kinetics of brain microtubule polymerization effects reversed on removal of Ni2+ from culture media 4... 

Kinetic Data. Let us now consider the kinetics of a reversible cyclic ether polymerization. For such a polymerization in... 

The above theory can be extended to deal with other more complex cases. For example, the two ends of a biopolymer need not behave identically, and, as noted earher, MTs are helical polymers of asymmetric protomer units. Thus, two sets of on- and off-constants might be necessary. In other cases, such as in the polymerization of tubulin in the presence of tubulin-colchicine complex (Sternlicht et one may need to consider copolymerization. The kinetics of microtubule depolymerization are the reverse of elongation, and are gener-... 

A quantitative kinetic model of the polymerization of a-pyrrolidine and cyclo(ethyl urea) showed,43 that two effects occur the existence of two stages in the initiation reaction and the absence of an induction period and self-acceleration in a-pyrrolidine polymerization. It was also apparent that to construct a satisfactory kinetic model of polymerization, it was necessary to introduce a proton exchange reaction and to take into consideration the ratio of direct and reverse reactions. As a result of these complications, a complete mathematical model appears to be rather difficult and the final relationships can be obtained only by computer methods. Therefore, in contrast to the kinetic equations for polymerization of e-caprolactam and o-dodecalactam discussed above, an expression... 

The rapid development of biotechnology during the 1980s provided new opportunities for the application of reaction engineering principles. In biochemical systems, reactions are catalyzed by enzymes. These biocatalysts may be dispersed in an aqueous phase or in a reverse micelle, supported on a polymeric carrier, or contained within whole cells. The reactors used are most often stirred tanks, bubble columns, or hollow fibers. If the kinetics for the enzymatic process is known, then the effects of reaction conditions and mass transfer phenomena can be analyzed quite successfully using classical reactor models. Where living cells are present, the growth of the cell mass as well as the kinetics of the desired reaction must be modeled [16, 17]. 

Dormant centres should not be confused with the inactive form of chain ends to which active centres are sometimes transformed by termination and which can be reversed to living forms only by slow re-initiation. Centres whose reactivity has been lost by termination are dead. The existence of living, dormant and dead centres is manifested in the mechanism and kinetics of the whole polymerization. The consequences of their occurrence will be discussed in the appropriate parts of the subsequent text (see Chap. 5, Sect. 8.1). 

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