Polymerization constants, various

Peaking and Non-isothermal Polymerizations. Biesenberger a (3) have studied the theory of "thermal ignition" applied to chain addition polymerization and worked out computational and experimental cases for batch styrene polymerization with various catalysts. They define thermal ignition as the condition where the reaction temperature increases rapidly with time and the rate of increase in temperature also increases with time (concave upward curve). Their theory, computations, and experiments were for well stirred batch reactors with constant heat transfer coefficients. Their work is of interest for understanding the boundaries of stability for abnormal situations like catalyst mischarge or control malfunctions. In practice, however, the criterion for stability in low conversion... 

The frequency of the transfer reactions (4 a) and (4 b) depends on the competition between substrate (polymer) and monomer for the radicals present in the solution, i.e. on the competition between growth and transfer. This competition is usually characterized by a transfer constant which is equal to the ratio of the transfer rate constant to the propagation rate constant, and which can be determined by measurements of the degree of polymerization at various concentration ratios of transfer agent... 

Table 9.4 Chain Transfer Constants (ktr/kp) for Alkene Polymerization with Various Heterogeneous Ziegler-Natta Catalysts...

SCHEME 35 A series of consecutive reactions produces active sites on supported chromium catalysts. Differing rate constants for these steps can generate many diverse kinetics profiles exhibited during polymerization with various catalysts. 

Another way of determining whether the observed plateau does really correspond to [M]e is to perform polymerization at various ratios of [M to [I]0. The properly determined value of [M]e should be independent of this ratio, provided that [M]o/[I]o is not too small. Thus, for non-living systems it is necessary to carry out polymerizations with increasing initial initiator concentration until a constant ultimate monomer conversion is reached. This method of approaching the equilibrium concentration gave reliable thermodynamic parameters for the cationic polymerization of cyclic esters of phosphoric acid, in spite of termination observed in these systems 11 ... 

Table 18-3. Equilibrium Constants for the Dissociation of Ion Pairs into Free Ions in the Anionic Polymerization of Various Monomers with a Series of Gegenions (According to a Collection by S. Bywater)...

In general, carbocationic homopolymerization is characterized by low activation enthalpy, low concentration of active species (10 -10 mol/dm ), high propagation rate constants (10 -10 dm /mol/sec), and short lifetime of the car-benium ion (94). Table 4 lists propagation rate constants determined in bulk carbocationic polymerization of various monomers initiated by y-radiation, electron pulse, or field ionization techniques. 

The majority of commercial methacrylic ester polymers are produced by free-radical initiators. Peroxides and azo compounds ftinction as t5ipical initiators for this type of polymerization. Other possible routes for producing methacrylic polymers with radicals include photoinitiation and radiation-induced polymerization. Both Y ray and electron-beam radiation have been employed in the production of methacrylic ester polymers (36-38). At constant temperature, there is a first-order dependence of the polymerization rate on monomer concentration and a one-half-order dependence on initiator concentration. Rate data for the polymerization of various methacrylic monomers using the azo compoimd 2,2 -azobisisobut5ironitrile [78-67-1] (AIBN) are shown in Table 8. 

Forring-opening polymerizations of various cyclic ethers, kp is in the range 10- -10"3 L/mol-s (CZhien et al., 1988 Mijangos and Leon, 1983 Penczek and Kubisa, 1989). These values are seen to be much closer to the rate constants for step-growth polyester cation than to those for various chain polymerizations. 

Furthermore, m-cresol and m-halogenated phenols have been polymerized in aqueous buffer solution only in the presence of 2,6-di-0-methyl-[)-cyclodextrin [90]. In the absence of cyclodextrin, only insoluble materials in very low yields were obtained under aqueous conditions from these phenols [81]. The structure of the host-guest complexes between cyclodextrin and the phenols was characterized by 2D NMR [48,90] and the association constants of the cyclodextrin complexes were determined by the Benesi-Hildebrand method. Firrthermore, 3-fluorophenol, 3-chlorophenol, and 3-bromophenol were successfully polymerized in various aqueous organic solvents such as methanol, acetone, or isopropanol [115]. 

Table 4 Ratio of rate constants for propagation and termination for the polymerization of various thietanes ...

As simple as this seems, some serious difficulties can be encountered, particularly in free-radical bulk polymerizations. One of them is illustrated in Figure 12.1 [1], which indicates the course of polymerization for methyl methacrylate by either bulk polymerization or solution polymerization using various concentrations of benzene, an inert solvent. The reactions were carefully maintained at constant temperature. At low polymer concentrations, the conversion versus, time curves are described by Equation 9.19. As polymer concentrations increase, however, a distinct acceleration of the rate of polymerization is observed which does not conform to the classical kinetic scheme. This phenomenon is known variously as autoacceleration, the gel effect, or the Tromsdorff effect. 

Throughout this section we have used mostly p and u to describe the distribution of molecular weights. It should be remembered that these quantities are defined in terms of various concentrations and therefore change as the reactions proceed. Accordingly, the results presented here are most simply applied at the start of the polymerization reaction when the initial concentrations of monomer and initiator can be used to evaluate p or u. The termination constants are known to decrease with the extent of conversion of monomer to polymer, and this effect also complicates the picture at high conversions. Note, also, that chain transfer has been excluded from consideration in this section, as elsewhere in the chapter. We shall consider chain transfer reactions in the next section. 

Table 1. Polymerization and Chain-Transfer Constants for Various Monomers ...

The solubilities of the various gases in [BMIM][PFg] suggests that this IL should be an excellent candidate for a wide variety of industrially important gas separations. There is also the possibility of performing higher-temperature gas separations, thanks to the high thermal stability of the ILs. For supported liquid membranes this would require the use of ceramic or metallic membranes rather than polymeric ones. Both water vapor and CO2 should be removed easily from natural gas since the ratios of Henry s law constants at 25 °C are -9950 and 32, respectively. It should be possible to scrub CO2 from stack gases composed of N2 and O2. Since we know of no measurements of H2S, SO, or NO solubility in [BMIM][PFg], we do not loiow if it would be possible to remove these contaminants as well. Nonetheless, there appears to be ample opportunity for use of ILs for gas separations on the basis of the widely varying gas solubilities measured thus far. 

Lack of termination in a polymerization process has another important consequence. Propagation is represented by the reaction Pn+M -> Pn+1 and the principle of microscopic reversibility demands that the reverse reaction should also proceed, i.e., Pn+1 -> Pn+M. Since there is no termination, the system must eventually attain an equilibrium state in which the equilibrium concentration of the monomer is given by the equation Pn- -M Pn+1 Hence the equilibrium constant, and all other thermodynamic functions characterizing the system monomer-polymer, are determined by simple measurements of the equilibrium concentration of monomer at various temperatures. 

The rate of fl-scission of benzoyloxy radicals is such that in most polymerizations initiated by these radicals both phenyl and benzoyloxy end groups will be formed (Scheme 3.4). A reliable value for the rate constant for p-xcission would enable the absolute rates of initiation by benzoyloxy radical to be estimated. Various values for the rale constant for p-scission have appeared. Many of the early estimates are low. The activation parameters (in CCI4 solvent) determined by Chateauneuf et a(.m are log]0 A = 12.6 and Ea = -35.97 kJ mol 1 which corresponds to a rate constant of 9xl06 s 1 at 60 °C. 

Mahabadi and O Driscolm considered that segmental motion and center of mass diffusion should be the dominant mechanisms at low conversion. They analyzed data for various polymerizations and proposed that k, J should be dependent on chain length such that the overall rale constant obeys the expression ... 

The absolute rate constants for attack of carbon-centered radicals on p-benzoquinone (38) and other quinones have been determined to be in the range I0M08 M 1 s 1.1 -04 This rate shows a strong dependence on the electrophilicity of the attacking radical and there is some correlation between the efficiency of various quinones as inhibitors of polymerization and the redox potential of the quinone. The complexity of the mechanism means that the stoichiometry of inhibition by these compounds is often not straightforward. Measurements of moles of inhibitor consumed for each chain terminated for common inhibitors of this class give values in the range 0.05-2.0.176... 

Various methods for estimating transfer constants in radical polymerization have been devised. The methods are applicable irrespective of whether the mechanism involves homolytic substitution or addition-fragmentation. 

More recent work has shown that the observed variation in propagation rate constants with composition is not sufficient to define the polymerization rates.5" 161,1152 There remains some dependence of the termination rate constant on the composition of the propagating chain. Thus, the chemical control (Section 7.4.1) and the various diffusion control models (Section 7.4.2) have seen new life and have been adapted by substituting the terminal model propagation rate constants (ApXv) with implicit penultimate model propagation rate constants (kpKY -Section 7.3.1.2.2). 

Tung et al21> have reported on the use of a polymeric thiol transfer agent for use in block copolymer production. Various methods have been used for the anion thiol conversion. Near quantitative yields of thiol arc reported to have been obtained by terminating anionic polymerization with ethylene sulfide and derivatives (Scheme 7.27). Transfer constants for the polymeric thiols are reported to be similar to those of analogous low molecular weight compounds.273... 

---