Step polymerization kinetics

The effect of the nitrone stmcture on the kinetics of the styrene polymerization has been reported. Of all the nitrones tested, those of the C-PBN type (Fig. 2.29, family 4) are the most efficient regarding polymerization rate, control of molecular weight, and polydispersity. Electrophilic substitution of the phenyl group of PBN by either an electrodonor or an electroacceptor group has only a minor effect on the polymerization kinetics. The polymerization rate is not governed by the thermal polymerization of styrene but by the alkoxyamine formed in situ during the pre-reaction step. The initiation efficiency is, however, very low, consistent with a limited conversion of the nitrone into nitroxide or alkoxyamine. 

A key point should be to identify the rate-limiting step of the polymerization. Several studies indicate that the formation of the activated open monomer is the rate-limiting step. The kinetics of polymerization obey the usual Michaelis-Menten equation. Nevertheless, all experimental data cannot be accounted for by this theory. Other studies suggest that the nature of the rate-limiting step depends upon the structure of the lactone. Indeed, the reaction of nucleophilic hydroxyl-functionalized compounds with activated opened monomers can become the rate-limiting step, especially if stericaUy hindered nucleophilic species are involved. 

The kinetics of polymerization are of prime interest from two viewpoints. The practical synthesis of high polymers requires a knowledge of the kinetics of the polymerization reaction. From the theoretical viewpoint the significant differences between step and chain polymerizations reside in large part in their respective kinetic features. 

Consider the polyesterification of a diacid and a diol to illustrate the general form of the kinetics of a typical step polymerization. Simple esterification is a well-known acid-catalyzed reaction and polyesterification follows the same course [Otton and Ratton, 1988 Vancso-Szmercsanyi and Makay-Bodi, 1969]. The reaction involves protonation of the carboxylic acid,... 

Another problem is the very high concentrations of reactants present in the low-conversion region. The correct derivation of any rate expression such as Eqs. 2-20 and 2-22 requires the use of activities instead of concentrations. The use of concentrations instead of activities assumes a direct proportionality between concentration and activity. This assumption is usually valid at the dilute and moderate concentrations where kinetic studies on small molecules are typically performed. However, the assumption often fails at high concentrations and those are the reaction conditions for the typical step polymerization that proceeds with neat reactants. A related problem is that neither concentration nor activity may be the appropriate measure of the ability of the reaction system to donate a proton to the carboxyl group. The acidity function ho is often the more appropriate measure of acidity for nonaqueous systems or systems containing high acid concentrations [Ritchie, 1990]. Unfortunately, the appropriate ho values are not available for polymerization systems. 

Yet another possiblity for the nonlinearity in the low conversion region is the decrease in the volume of the reaction mixture with conversion due to loss of one of the products of reaction (water in the case of esterification). This presents no problem if concentration is plotted against time as in Eq. 2-20. However, a plot of 1/(1 — p j2 against time (Eq. 2-22) has an inherent error since the formulation of Eq. 2-21 assumes a constant reaction volume (and mass) [Szabo-Rethy, 1971]. Elias [1985] derived the kinetics of step polymerization with correction for loss of water, but the results have not been tested. It is unclear whether this effect alone can account for the nonlinearity in the low conversion region of esterification and polyesterification. 

The kinetics of step polymerizations other than polyesterification follow easily from those considered for the latter. The number of different general kinetic schemes encountered in actual polymerization situations is rather small. Polymerizations by reactions between the... 

Kinetic analysis of a step polymerization becomes complicated when all functional groups in a reactant do not have the same reactivity. Consider the polymerization of A—A with B—B where the reactivities of the two functional groups in the B—B reactant are initially of different reactivities and, further, the reactivities of B and B each change on reaction of the other group. Even if the reactivities of the two functional groups in the A—A reactant are the same and independent of whether either group has reacted, the polymerization still involves four different rate constants. Any specific-sized polymer species larger than dimer is formed by two simultaneous routes. For example, the trimer A—AB—B A—A is formed by... 

Kricheldorf and coworkers [2001a,b,c] have stressed that step polymerizations can proceed either with kinetic control or thermodynamic control. Polymerizations under thermodynamic control proceed with an equilibrium between cyclic and linear products. Polymerizations under kinetic control proceed without an equilibrium between cyclic and linear products. 

Table 2-8 shows values of some kinetic and thermodynamic characteristics of typical step polymerizatiosn [Bekhli et al., 1967 Chelnokova et al., 1949 Fukumoto, 1956 Hamann et al., 1968 Malhotra and Avinash, 1975, 1976 Ravens and Ward, 1961 Saunders and Dobinson, 1976 Stevenson, 1969 Ueberreiter and Engel, 1977]. These data have implications on the temperature at which polymerization is carried out. Most step polymerizations... 

Consider the situation where one polymer molecule is produced from each kinetic chain. This is the case for termination by disproportionation or chain transfer or a combination of the two, but without combination. The molecular weight distributions are derived in this case in exactly the same manner as for linear step polymerization (Sec. 2-7). Equations 2-86, 2-88, 2-89, 2-27, 2-96, and 2-97 describe the number-fraction, number, and weight-fraction... 

Cationic polymerization has been initiated by a variety of protonic and Lewis acids [Kubisa, 1996 Toskas et al., 2001]. The cationic process is more complicated and less understood than the anionic process. Polymerization under most reaction conditions involves the presence of a step polymerization simultaneously with ROP. This appears to be the only way to reconcile the observed (complicated) kinetics for the overall process [Chojnowski and Wilczek, 1979 Chojnowski et al., 2002 Cypryk et al., 1993 Rubinsztain et al., 1993 Sigwalt, 1987 Wilczek et al., 1986],... 

It is widely acknowledged that polymerization can proceed according two general mechanisms of reaction step polymerization and chain polymerization. These two mechanisms are quite different and consequently their kinetics, molecular weight distribution, influence of reaction parameters on the process, etc., are very different in both cases. For the same reasons, the template reactions differ, depending on their mechanisms of the polymerization processes. 

Experimental investigation of the kinetics of template step polymerization, determination of average molecular weights of the product, and molecular weight distribution are still available for future studies. 

This method is very useful for solving the kinetics of polymerization reactions (e.g., DNA polymerization, Chapter 14) by inspection the time taken to synthesize a polymer is the sum of the transit times for the addition of each monomer. For example, suppose that each step in equation 3.63 is a Michaelis-Menten process of... 

Domine and Gogos (88-90) considered a very long, very wide, and thin mold being fed by a constant temperature mixture of AA, BB molecules. Both types are bifunctional and the feed has a molecular weight Mq. The polymerization, assumed to be reversible, proceeds by the reaction of A-ends with B-ends, and follows idealized step polymerization (condensation) kinetics without the generation of a small molecule (91). Specifically, we have... 

---