Reversible Polymerization Kinetics

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. 

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. 

Thermodynamic and Kinetic Parameters for Reversible Polymerization (Oosawa s Law) 46... 

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. 

MICROSCOPIC DIFFUSION CONTROL MACROSCOPIC DIFFUSION CONTROL MICROSCOPIC REVERSIBILITY CHEMICAL REACTION DETAILED BALANCING, RRINCIRLE OF CHEMICAL KINETICS MICROTUBULE ASSEMBLY KINETICS BIOCHEMICAL SELF-ASSEMBLY ACTIN ASSEMBLY KINETICS HEMOGLOBINS POLYMERIZATION... 

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). 

P. Terech, Physical Gelation of a Steroid-Cyclohexane System Kinetic Phenomenological Approach, in Reversible Polymeric Gels and Related Systems (ed. P. Russo), American Chemical Society Symposium Series (ACS), 350, 115 (1987). 

Krambeck (1994b) has observed that the McCoy reversible polymerization kinetics are rather artificial, and that they do not satisfy detailed balance. 

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]. 

The values for the thermodynamic parameters in the formation of polymers can be used for the characterization of depolymerization reactions. The formation of monomers in a polymer decomposition reaction (depolymerization) is relatively common (see Table 2.1.1). Depolymerization can be considered a reverse polymerization, the two reactions having equal absolute values for the heats of reaction but with opposite signs. Therefore, the heats of polymerization can be used for the thermodynamic characterization of pyrolytic reactions with formation of monomers (kinetic factors are also very important in pyrolytic reactions as further shown in Section 2.3). 

The addition of ions—Mg, K, or Na —to a solution of G-actin will Induce the polymerization of G-actin into F-actin filaments. The process is also reversible F-actln depolymerlzes into G-actln when the ionic strength of the solution is lowered. The F-actln filaments that form in vitro are Indistinguishable from mlcrofllaments Isolated from cells, indicating that other factors such as accessory proteins are not required for polymerization in vivo. The assembly of G-actln into F-actln is accompanied by the hydrolysis of ATP to ADP and Pc however, as discussed later, ATP hydrolysis affects the kinetics of polymerization but is not necessary for polymerization to take place. 

The hysteresis can also result from a reversible polymerization. That results in the measuring of different molecular weights and different kinetics of the different aggregates. 

The kinetics of polymerization with multiple-site catalysts is generally considered to be the same as with single-site catalysts, as described by Eqs. (1)-(14) for homopolymerization and in Table 8.1 for copolymerization, with different polymerization kinetic parameters assigned to each site type. In some cases, the polymerization mechanism may be extended to include site transformation steps, where sites of one type may change into sites of another type, such as the one described with the reversible reaction in Eq. (23), where D could be a catalyst modifier such as an electron donor, for instance. 

It is useful to start the kinetic analysis with an idealized case, which avoids complications that arise due to unequal stoichiometry, chain length-dependent reactivity, monofunctional impurities, cyclization, and reversible polymerization. The model addressed here is a linear AB step polymerization. 

---