Polymerization rate coefficients

Catalysts Reaction order Transition metal Monomer Polymerization rate coefficient (fep/ ) E (kcal mole" ) Ref. 

The bimolecular termination model in its simplified, partly integrated form (equation (4.11)) has been extensively used for the estimation of the polymerization rate coefficients in cross-linking systems [2,6,7,18,20-25]. 

Da - Damkohler number, dimensionless [7] - concentration of initiator, mol/1 hi - initiator decomposition rate coefficient, s h - termination rate coefficient, mol/1 s - propagation rate coefficient, 1/mol s k - effective polymerization rate coefficient (defined in Eq. 1.5.4), s km - polymer interdomain distance, cm Mm - molecular weight of monomer, g/mol Mp - molecular weight of polymer, g/mol Ms - molecular weight of solvent, g/mol [M] - concentration of monomer, mol/1 7 p - propagation rate, mol/1 s r - generalized spatial variable, cm - defined in Eq. (1.5.12),... 

It is important to achieve an understanding of how the basic FRP mechanisms control polymerization rate and average polymer chain length. This section starts with the derivation of appropriate kinetic expressions for a single monomer system. Complicating (but industrially important) secondary reactions are then introduced, followed by the extension to multi-monomer systems. Dispersed throughout are up-to-date estimates for important free-radical polymerization rate coefficients, and descriptions of how they are obtained experimentally. 

In this case, the polymerization rate coefficient, a (s ) is independent of [m] . 

The concentration of monomers in the aqueous phase is usually very low. This means that there is a greater chance that the initiator-derived radicals (I ) will undergo side reactions. Processes such as radical-radical reaction involving the initiator-derived and oligomeric species, primary radical termination, and transfer to initiator can be much more significant than in bulk, solution, or suspension polymerization and initiator efficiencies in emulsion polymerization are often very low. Initiation kinetics in emulsion polymerization are defined in terms of the entry coefficient (p) - a pseudo-first order rate coefficient for particle entry. 

In dealing with radical-radical termination in bulk, polymerization it is common practice to divide the polymerization timeline into three or more conversion regimes.2 "0 The reason for this is evident from Figure 5.3. Within each regime, expressions for the termination rate coefficient are defined according to the dominant mechanism for chain end diffusion. The usual division is as follows ... 

Table 5.1 Parameters Characterizing Chain Length Dependence of Termination Rate Coefficients in Radical Polymerization of Common Monomers 1...

T = temperature p = density AH = heat of reaction h = heat-transfer coefficient D = reactor diameter Cp = heat capacity Rp = polymerization rate Tj = reactor jacket temperature P = pressure... 

This quadratic in Rp is of the form required by the data for styrene-benzoyl peroxide shown in Fig. 14. The first term, corresponding to the intercept, represents the creation of chain ends through transfer with monomer. It occurs to an extent which is independent of the polymerization rate. The second term corresponds to 1/2 according to Eq. (27) it represents the pairs of ends created at the initiation step. Its coefficient is given by the initial slope of the line in Fig. 14. The third term, which accounts for the curvature at higher rates, represents the contribution of chain transfer with benzoyl peroxide. This becomes more prominent at higher rates because of the larger amounts of the initiator which are present. The marked rise in the curves for... 

The reaction schemes that can be proposed for these alkyls are basically analogous to those discussed for the tetramethyl compound. The initiation step should be Si-C bond rupture followed by various reactions of ethyl and propyl radicals, free radical attack on the parent alkyl and various polymerization processes. Significant chain reactions involving the alkyls are apparently homogeneous processes and lead to first-order kinetics. The rate coefficients for the... 

Consider the condensation polymerization of a bifimctional monomer A in a CSTR with all rate coefficients k equal. 

The rate coefficients appearing in Eqns. 17 through 19 should not be strongly temperature dependent since radical-atom and radical-radical recombination are most often either unactivated or weakly activated processes. In the case of the recombination of two surface free radicals, the rate is likely to be limited by the mobility of the polymer chains attached to the radicals. For very short chains, as are commonly produced in plasma polymerization , only those radicals which are nearest or next nearest neighbors are likely to react. If one of the radicals... 

Figure 8 illustrates a comparison between measured and computed rates of butadiene polymerization in an rf plasma sustained at 13.56 MHz. A perfect fit is achieved by adjusting the rate coefficients appearing in the model to the following values ... 

For the conditions shown in Fig. 8, it was estimated that the electron density was 8x 10 cm" . This means that kj = 2.5 x 10" cm /s, a value in good agreement with measured rate coefficients for dissociation of small molecules by electron impact . The gas phase propagation rate coefficient kp was also found to be in very good agreement with values determined for conventional butadiene polymerization. The agreement of the adjusted parameter values with those measured independently lends further support to the validity of the proposed model of plasma polymerization. 

Table 7. Fitted Rate Coefficients for the Plasma Polymerization of Unsaturated Hydrocarbon Monomers...

Differing rates of monomer addition to cis and trans centers are also indicated by a sharp change of the temperature coefficient of polymerization rate at -30 where "freezing-in" of structure first becomes important - the trans centers add monomer faster in this solvent. In view of these observations care should be taken in interpretation of literature data on microstructure, often determined at one particular temperature and monomer/ initiator ratio. The results may not be typical of the reaction under all conditions. 

More recently Teyssie determined the rate constants in the polymerization of e-caprolactone (eCL) initiated with aluminium alkoxides, believing that the covalent species are the only ones responsible for propagation [4]. For the same monomer Yamashita estimated tentatively rate coefficients of propagation using an anionic initiator [ ]. Lenz in his studies of substituted g-propiolactones (gPL) observed peculiar influence of structure on reactivity that can have its origin in the multiplicity of ionic structures involved [fi]. 

Square brackets denote molar concentrations. Units are moles, liters, seconds, degrees centigrade and kilocalories per mole. En refers to the energy of activation for the step in which kn is the velocity coefficient, the latter term being used to avoid reference to variable rate constants . Since the polymerization rate, Rp, is commonly... 

In traditional liquid solvents, the polymerization reaction rates are often limited by the local increase in viscosity during the process, as this lowers the mass transfer rate of the monomer to the reaction site. A lower viscosity and a higher diffusion coefficient in SCFs each contribute to overcome this limitation, however, allowing the polymerization rate to be significant up to high value of monomer conversion. 

I - concentration of initiator molecules dm j - ratio of molar volumes of polymer and monomer (approx, degree of polymerization of polymer) — k - Dankwerts reaction rate coefficient dm s 1 k - Boltzmann constant JK-1 ... 

The same authors used photoDSC to obtain time- or conversion-dependent ratios of the termination and propagation rate coefficients 2kt/kp for the polymerization of VA. The starting point of this approach is the classical equation derived from formal kinetics ... 

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