Chain growth constants

An important application of photochemical initiation is in the determination of the rate constants which appear in the overall analysis of the chain-growth mechanism. Although we shall take up the details of this method in Sec. 6.6, it is worthwhile to develop Eq. (6.7) somewhat further at this point. It is not possible to give a detailed treatment of light absorption here. Instead, we summarize some pertinent relationships and refer the reader who desires more information to textbooks of physical or analytical chemistry. The following results will be useful ... 

Studies have shown that, in marked contrast to carbanionic polymerisation, the reactivity of the free oxonium ion is of the same order of magnitude as that of its ion pair with the counterion (6). On the other hand, in the case of those counterions that can undergo an equiUbrium with the corresponding covalent ester species, the reactivity of the ionic species is so much greater than that of the ester that chain growth by external attack of monomer on covalent ester makes a negligible contribution to the polymerisation process. The relative concentration of the two species depends on the dielectric constant of the polymerisation medium, ie, on the choice of solvent. 

The chain polymerization of formaldehyde CH2O was the first example of a chemical conversion for which the low-temperature limit of the rate constant was discovered (see reviews by Goldanskii [1976, 1979]). As found by Mansueto et al. [1989] and Mansueto and Wight [1989], the chain growth is driven by proton transfer at each step of adding a new link... 

The first five telomers (n = 1 - 5) were isolated and identificated. The authors showed that telomers T2 and T3 are preferentially formed in one stereoisomeric form (with minor amounts of other possible isomers), i.e. the radical addition reaction makes it possible to perform asymmetric control at the steps of chain transfer and chain growth. The partial chain transfer constants Cn are given in this work, which are within the range from 0.3 to 0.5 for radicals C2-C5. We consider... 

To determine the rate behavior of chain growth polymerization reactions, we rely on standard chemical techniques. We can choose to follow the change in concentration of the reactive groups, such as the carboxylic acid or amine groups above, with spectroscopic or wet lab techniques. We may also choose to monitor the average molecular weight of the sample as a function of time. From these data it is possible to calculate the reaction rate, the rate constant, and the order of the reacting species. 

The initiation step of chain growth creates a reactive site that can react with other monomers, starting the polymerization process. Before the monomer forms the reactive site, the initiator ( ) (which maybe either a radical generator or an ionic species) first creates the polymerization activator (A) at a rate defined by the rate constant kv This process can be represented as shown in Eq. 4.7. 

Chain-growth polymerizations are diffusion controlled in bulk polymerizations. This is expected to occur rapidly, even prior to network development in step-growth mechanisms. Traditionally, rate constants are expressed in terms of viscosity. In dilute solutions, viscosity is proportional to molecular weight to a power that lies between 0.6 and 0.8 (22). Melt viscosity is more complex (23) Below a critical value for the number of atoms per chain, viscosity correlates to the 1.75 power. Above this critical value, the power is nearly 3 4 for a number of thermoplastics at low shear rates. In thermosets, as the extent of conversion reaches gellation, the viscosity asymptotically increases. However, if network formation is restricted to tightly crosslinked, localized regions, viscosity may not be appreciably affected. In the current study, an exponential function of degree of polymerization was selected as a first estimate of the rate dependency on viscosity. 

After the first dehydration step, the reaction propagates by successive dehydration-methanolation steps, competing with poly-merization-cyclization-aromatization processes. The existence of dehydration-methanolation mechanism is inferred from the constant presence of a small amount of methanol (from in situ C-NMR observation) on the catalyst. Further evidence has been acquired in favor of the carbenium ion chain-growth mechanism from the l C-NMR study of CO incorporation into the products during the conversion of methanol (46). 

All reactions involved in polymer chain growth are equilibrium reactions and consequently, their reverse reactions lead to chain degradation. The equilibrium constants are rather small and thus, the low-molecular-weight by-products have to be removed efficiently to shift the reaction to the product side. In industrial reactors, the overall esterification, as well as the polycondensation rate, is controlled by mass transport. Limitations of the latter arise mainly from the low solubility of TPA in EG, the diffusion of EG and water in the molten polymer and the mass transfer at the phase boundary between molten polymer and the gas phase. The importance of diffusion for the overall reaction rate has been demonstrated in experiments with thin polymer films [10]. 

Chain growth continues at a rate dependent on the concentrations of monomer [M] and of active sites [MJ. Monomer exponents in the range 1.3 to 1.5 or higher had been observed (110, 123, 127) especially at low [M], but first order dependence has now been established over a broad range of [M] (21). A stationary level of [M ] is reached rapidly and is typically of the order of 10-8 molar. Chains grow rapidly by successive monomer additions until the polymer chain is terminated by transfer or by reaction with another radical. The rate constant for propagation (ft2) at 60° in DMF is 1960 m-1 Is-1 (16), which is a comparatively high value [see Table 1 and ref. (76)]. On the other hand it is only about one-tenth of that found for acrylonitrile in aqueous systems (Table 6)... 

When light hydrocarbons terminate predominantly as paraffins (kh>>ko), or when a-olefins are rapidly hydrogenated in secondary reactions (ks>kr), we should obtain a light product distribution with a low and constant value of a. We describe below two such systems. A Fe-based catalyst (a-Fe2C>3) at very high H2/CO ratios (-9) gives only C to C5 paraffins with a constant chain growth... 

Figure 7 Simplified scheme of hydrocarbon chain growth pathways. (S -FT chain growth site k rate constants, see text).

By using the steady state kinetic equations, it is then possible to express k and k3 as a function of the overall turnover frequency for CO-conversion to hydrocarbons (Nco), the overall turnover frequency for methane formation (NCH ), the probability for chain growth (a), the steady state coverage of the precursor A and the value of the equilibrium constant K. In table I the expressions for the kj and k are given. 

Table I. The Reaction Rate Constants for Propagation and Termination Expressed as a Function of Turnover Frequencies, Probability of Chain Growth, Steady-State Surface Coverage of the Precursor A, and the Equilibrium Constant K.

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