Rate of propagation

The kinetic chain length has a slightly different definition in the presence of chain transfer. Instead of being simply the ratio Rp/R, it is redefined to be the rate of propagation relative to the rates of all other steps that compete with propagation specifically, termination and transfer (subscript tr) ... 

For counterions that can form esters with the growing oxonium ions, the kinetics of propagation are dominated by the rate of propagation of the macroions. For any given counterion, the proportion of macroions compared to macroesters varies with the solvent—monomer mixture and must be deterrnined independentiy before a kinetic analysis can be made. The macroesters can be considered to be in a state of temporary termination. When the proportion of macroions is known and initiation is sufftcientiy fast, equation 2 is satisfied. 

Even within the small numbers of studies conducted to date, we are already seeing potentially dramatic effects. Free radical polymerization proceeds at a much faster rate and there is already evidence that both the rate of propagation and the rate of termination are effected. Whole polymerization types - such as ring-opening polymerization to esters and amides, and condensation polymerization of any type (polyamides, polyesters, for example) - have yet to be attempted in ionic liquids. This field is in its infancy and we look forward to the coming years with great anticipation. 

The nature of the gegen ion is probably of the greatest importance in determining the rate of propagation in ionic polymerization. However, it is not clear whether the presence of the gegen ion enhances or inhibits the propagation. One may argue that the... 

The non-penicillin wastewater from a pharmaceutical company was collected and used in the batch aeration wastewater treatment experiment. The pharmaceutical wastewater had a clear orange colour, strong odour, contained toxic chemicals and had a COD value in the range of 3000-30,000 mg per litre. The pH of the wastewater was neutralised and monitored for each experimental ran, as the bacteria would have a higher rate of propagation at neutral pH. 

The addition of radicals and, in particular, propagating radicals, to unsaturated systems is potentially a reversible process (Scheme 4.46). Depropagation is cntropically favored and the extent therefore increases with increasing temperature (Figure 4.4). The temperature at which the rate of propagation and depropagalion become equal is known as the ceiling temperature (rc). Above Tc there will be net depolymerization. 

The rate of initiation of this polymerization is, however, comparable to its rate of propagation, therefore the molecular weight distribution of the resulting polymers is not narrow. 

The latter demonstrates, as expected, that [P ] decreases with increasing [S]. Moreover, the addition of such a coordinating agent affects also the rate of propagation per unit monomer represented by R, of propagation since... 

The rate of propagation is much faster in polar than in nonpolar solvents7). In the case of styrene, for instance, 99 % conversion is obtained in tetrahydrofuran within a few minutes at —70 °C, whereas in nonpolar media at 30 °C, hours are required to get similar yields. 

Equation (l) shows the rate of polymerization is controlled by the radical concentration and as described by Equation (2) the rate of generation of free radicals is controlled by the initiation rate. In addition. Equation (3) shows this rate of generation is controlled by the initiator and initiator concentration. Further, the rate of initiation controls the rate of propagation which controls the rate of generation of heat. This combined with the heat transfer controls the reaction temperature and the value of the various reaction rate constants of the kinetic mechanism. Through these events it becomes obvious that the initiator is a prime control variable in the tubular polymerization reaction system. 

Now assuming that the rate of exchange between associated and unassociated polymer chains is rapid, compared to the rate of propagation, then the distribution of the active polymer, will be equivalent to the total polymer distribution. 

The molar rate of change of polymeric species of degree of polymerization n in a well-mixed, continuous flow tank reactor is related to the kinetic rate of propagation of unassociated polystyryl anions plus their withdrawal rate in the reactor s effluent. Feed streams are void of polymeric substances, but contain monomer initiator and solvent. 

Steady State Population Density Distributions. Representative experimental population density distri-butions are presented by Figure 1 for two different levels of media viscosity. An excellent degree of theoretical (Equation 8) / experimental correlation is observed. Inasmuch as the slope of population density distribution at a specific degree of polymerization is proportional to the rate of propagation for that size macroanion, propagation rates are also observed to be independent of molecular weight. 

The analysis showed that the part cures by reaction wave polymerization. The rate of propagation of the waves from the walls toward the center of the part was proportional to the molding temperatures and was a function of the polymer formulation. 

The rates of propagation and termination in the aqueous phase were also calculated. The radical entry rate, radical generation rate, and aqueous propagation rate were then used to develop an algebraic equation for the rate of formation of primary precursors. This equation is an extension to copolymers of the homogeneous nucleation equation derived by Hansen and Ugelstad (7.) for a homopolymer. 

We shall use Rp to represent the rate of polymerization as well as the rate of propagation, therefore. According to Eq. (12), the rate of polymerization should vary as the square root of the initiator concentration. If/ is independent of the monomer concentration, which will almost certainly be true if / is near unity, the conversion of monomer to polymer will be of the first order in the monomer concentration. On the other hand, if / should be substantially less than unity, it may then depend on the concentration of monomer in the extreme case of a very low efficiency, / might be expected to vary directly as [M whereupon the chain radical concentration becomes proportional to Mand the polymerization should be three-halves order in monomer. 

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