Szwarc equations

This is not the first time that the kinetics of bulk polymerizations has been analysed critically. Szwarc (1978) has made the same objection to the identification of the rate constant for the chemically initiated bulk polymerization of tetrahydrofuran as a second-order rate constant, k, and he related the correct, unimolecular, rate constant to the reported by an equation identical to (3.2). Strangely, this fundamental revaluation of kinetic data was dismissed in three lines in a major review (Penczek et al. 1980). Evidently, it is likely to be relevant to all rate constants for cationic bulk polymerizations, e.g., those of trioxan, lactams, epoxides, etc. Because of its general importance I will refer to this insight as Szwarc s correction and to (3.2) as Szwarc s equation . 

The theory of unimolecular propagation for the cationic polymerisation of a bulk monomer was first developed by Szwarc (1978), and Equation (44) introduced by him has been named Szwarc s equation (Plesch, 1993). 

Szwarc and coworkers have reported equilibrium constants for the disproportionation reaction given in equation 40 ... 

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],... 

Table III and the plot of Figure 3 compare values of kd (obs.) and kd (calc.) in several solvents. The values of kd (obs.) were taken from the data of Szwarc (7) and Eirich (2) as well as from our laboratory and involve an extrapolation from 60° to 80°C. for the data of Eirich. This was done by making the crude approximation that AG varies with solvent in the same way at the two temperatures. A close parallel exists between the observed and calculated rates. This suggests that the assumption equating ki and kg is not bad and provides a firmly established case in which the dependence of the rate of decomposition of a radical initiator on solvent viscosity in a homologous series of solvents results from the varying importance of cage recombination in the various solvents. Pryor and Smith (19) using data from p-nitrophenylazotriphenylmethane decompositions have suggested that a general criterion for radical cage...

Fig, 9. Graphic solution of the balance equation for the reaction aa + -methyl-styrene aa its living dimer and aax its living trimer. 1// is the reciprocal of the resident time in the stirred-fiow reactor. Reproduced, with permission, from Lee, Smid, and Szwarc J. Am. Chem. Soc. 85,912... 

A different and independent approach to determine the parameters of KC8 is made by conductivity measurements. The dissociation constant of carbanionic compounds displays no simple temperature dependence according to the van t Hoff equation as Worsfold and Bywater (32) and Szwarc (33) have already shown. When we assume two types of ion pairs, the experimentally measured dissociation constant is given by... 

The existing equilibrium monomer concentrations have been measured by several authors (9,17, 30, 31) for anionic polymerizations (from the type described by Szwarc (24) at different temperatures. The thermodynamic terms AH and AS° can be calculated from these data according to Equation 3. Table I shows the results of these calculations and a value for AH which was measured calorimetrically (20). (The values... 

Szwarc and Zimm described the consequences of transfer in the sense of eqn. (41) by means of differential equations [29], and O Driscoll simulated the system corresponding to the above scheme by the Monte Carlo method [30], Both kinds of approach produced polydispersity coefficient (PJPn) vs. time plots which were practically identical at longer times. 

The frequency factor is considerably higher than would be expected from an ordinary first order decomposition, but it was shown by standard methods that the reaction was homogeneous and that there was no chain. Because of this anomalously high frequency factor, the reaction was studied again by Murawski, Roberts, and Szwarc 62 They measured the rate of decomposition in the presence of excess toluene both in a static and in a flow system, so as to cover the widest possible temperature range. The reactions found to occur were as given in equations 4.2.6.1, 2, and 3 above, together with... 

Another experimental approach involves application of Szwarc s plot derived from Ea. (80) and in which kpPP is plotted against [living ends]" / (kpPP = k + k [LEJ" ) In the derivation of this equation it has been assumed that the rate constant involving macroions is much higher than that of the macroion pairs and that the concentration of mactoions is much lower than that of the macroion pairs. 

The kinetics are much more complex and depend on the reorganization of the molecular framework [125], the solvation shell, and the electrostatic interaction. A semi-quantitative estimation of rate constants may be obtained with the well-known Marcus equation [126]. The calculated data compare quite well with experimental values. Most of the experimental hydrocarbon data have been provided by Szwarc and his school [5]. The state of the art has been discussed in an excellent review [121]. 

Another general treatment of the copoljnnetization equilibrium was provided by Szymanski, ° who used, while deriving his relationships, similarly as O Driscoll and co-workers, the reverse conditional probabilities (of a copolymer unit to be preceded by the same or a different unit). This treatment looks simpler than the one proposed earlier by Szwarc and Perrin, and similarly their equations can be applied to the systems of any number of comonomers and any average degree of polymerization. The proposed solution also applies to the systems of ideal copolymerization Besides, the... 

It was Szwarc and Perrin, who first made this observation and calculated the correct equilibrium constants of homoaddition of TXN on the basis of the experimental data of Schulz et and determined the thermodynamic parameters of its polymerization. The corresponding equation, the version modified by Szymanski, that enables us to compute the equilibrium constant of homoaddition of TXN is shown in Chapter 4.30. 

Measurements of the conductivity of. .. -St and Cat (symbols are self-explanatory) in DIOX and THF solutions have shown that only in the latter are solvent ions (sometimes called free ions ) present. No conductivity was noticed in DIOX (ion pairs themselves are electrically neutral). The dissociation is due to the exothermidty of solvation otherwise, the coulombic forces would keep the ions in a pair together, with no reason to go apart. Thus, it became a problem to determine rate constant on ions (fep). Since there are (at least) two kinds of species of different reactivities, the pertinent final kinetic equation (called also Szwarc plot ) reads as follows ... 

The concept of shelf life (shelf time) of a chain polymerization has been discussed by Szwarc. Shelf life in this context is defined as the time available to the operator to complete a given synthetic task, for example, block copolymer synthesis by sequential monomer addition, or end-capping (functionalization) of the polymer chains by reaction with a quenching agent. The equations dealing with chain breaking in the previous section may be used to demonstrate the concept of shelf life and how it is favorably affected by the operation of a reversible-deactivation equilibrium. 

For an ideaUzed, Uving polymerization k, = 0 and kp = 0. A discovery of the anionic living polymerization of vinyl and diene monomers by Szwarc and coworkers opened a new chapter in macromolecular science [18-20]. ROP, being the subject of the present chapter, may also proceed as a living process. However, molar mass and end group control of the resultant polymer is only possible when kj > kp (Equations 1.3a and 1.3b). 

Equation 1.38b allows kp and R, to be determined for several other systems (including the anionic polymerization of EO and D3), that previously had been analyzed using numerical calculations [158]. Szwarc el al. indicated that such an analytical solution should exist, and discussed in more detail the problems of aggregation in anionic polymerizations and the related kinetic consequences [159]. 

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