Polymer radical, concentration

The polymer radical concentration in Eq. (6.14) represents the total concentration of all such species, regardless of their degree of polymerization that is. 

Chain termination occurs by combination or disproportionation of different polymer radicals. The termination rate, v is proportional to the polymer radical concentration, [ PJ, squared, with kt being the termination rate constant. Other possible chain termination processes are chain transfer and reaction of polymer radicals wifh inhibitors and radical trapping. ... 

Chain termination occurs by combination or disproportionation of different polymer radicals. The termination rate vt is proportional to the polymer radical concentration... 

Neither of these explanations is entirely satisfactory. In particular the former would not allow for significant radiation protection by small concentrations of additive in fact, the gelation dose can be doubled by only 1% of additive in solid polymer and considerably less in liquid polymer. The second explanation would lead to almost complete protection since the additive concentration vastly exceeds the polymer radical concentration, and radicals would react with the additive before meeting another radical. In practice partial protection is observed. 

The concentration of polymer radicals increases during exposure until a steady-state polymer radical concentration is reached. The steady-state concentration of the polymer radical [P ]s is given by Eq. (68) ... 

The propagation reaction is described in terms of an average rate coefficient, k, and the polymer radical concentration, [R ]. The value of k is very large, 10 -10" dm moP s and is independent of chain length. This is the reaction that consumes monomer and grows the polymer chain. 

The polymer radical concentration cp , which is part of the propagation rate, can be obtained by applying the Bodenstein quasi-steady state principle. 

Since both P and are constant, (pi is also constant. Given that the total polymer radical concentration ([P ]) varies during the reaction, one can readily solve for the time-varying monomer feed rates, Pj and p2,m> using Equations 6.70-6.76. 

In Fig. 2.4.5, simulations results for polydispersity indices are seen to be greater than those from experimental values, but they are reasonably accurate. In Fig. 2.4.6, polymer radical concentrations from the simulations exhibited a jump behavior, which occurred at the critical conversion values. 

The transition to the polymer-rich phase resulted in radical trapping. However, compared to experimental data in Fig. 2.3.16, polymer radical concentrations from the simulations slowly drifted down rather than staying at asymptotic values. What this means is that in the FRRPP process, there seems to be this enhanced radical... 

Fig. 2.4.6 Result of simulation of polymer radical concentration vs time for the polystyrene/styrene/ether reactive system at 80°C (Replotted from Dar, 1999 Dar and Caneba, 2002 with permission)...

The number of available sites for polymer grafting is dictated by the initial vinylsilane surface density. However, the initial surface vinylsilane concentration should have the same degree of rate enhancement for both polymer grafting and graft polymerization since both rates are proportional to the grafted polymer radical concentration (S ), whose magnitude is in turn proportional to the initial concen-... 

Once the radicals diffuse out of the solvent cage, reaction with monomer is the most probable reaction in bulk polymerizations, since monomers are the species most likely to be encountered. Reaction with polymer radicals or initiator molecules cannot be ruled out, but these are less important because of the lower concentration of the latter species. In the presence of solvent, reactions between the initiator radical and the solvent may effectively compete with polymer initiation. This depends very much on the specific chemicals involved. For example, carbon tetrachloride is quite reactive toward radicals because of the resonance stabilization of the solvent radical produced [1] ... 

Tlie formation of initiator radicals is not the only process that determines the concentration of free radicals in a polymerization system. Polymer propagation itself does not change the radical concentration it merely changes one radical to another. Termination steps also occur, however, and these remove radicals from the system. We shall discuss combination and disproportionation reactions as modes of termination. 

Polymer propagation steps do not change the total radical concentration, so we recognize that the two opposing processes, initiation and termination, will eventually reach a point of balance. This condition is called the stationary state and is characterized by a constant concentration of free radicals. Under stationary-state conditions (subscript s) the rate of initiation equals the rate of termination. Using Eq. (6.2) for the rate of initiation (that is, two radicals produced per initiator molecule) and Eq. (6.14) for termination, we write... 

This important equation shows that the stationary-state free-radical concentration increases with and varies directly with and inversely with. The concentration of free radicals determines the rate at which polymer forms and the eventual molecular weight of the polymer, since each radical is a growth site. We shall examine these aspects of Eq. (6.23) in the next section. We conclude this section with a numerical example which concerns the stationary-state radical concentration for a typical system. 

The propagation of polymer chains is easy to consider under stationary-state conditions. As the preceding example illustrates, the stationary state is reached very rapidly, so we lose only a brief period at the start of the reaction by restricting ourselves to the stationary state. Of course, the stationary-state approximation breaks down at the end of the reaction also, when the radical concentration drops toward zero. We shall restrict our attention to relatively low conversion to polymer, however, to avoid the complications of the Tromms-dorff effect. Therefore deviations from the stationary state at long times need not concern us. 

Dividing both sides of Eq. (6.58) by [M-], the total radical concentration, gives the number fraction of n-mer radicals in the total radical population. This ratio is the same as the number of n-mers in the sample containing a total of N (no subscript) polymer molecules ... 

Polymerization begins in the aqueous phase with the decomposition of the initiator. The free radicals produced initiate polymerization by reacting with the monomers dissolved in the water. The resulting polymer radicals grow very slowly because of the low concentration of monomer, but as they grow they acquire surface active properties and eventually enter micelles. There is a possibility that they become adsorbed at the oil-water interface of the monomer... 

In the case of emulsion polymerisation, half the micelles will be reacting at any one time. The conversion rate is thus virtually independent of radical concentration (within limits) but dependent on the number of micelles (or swollen polymer particles). 

The above-mentioned mode of reactions changes when the irradiation is carried out in the presence of gases such as oxygen. In this case, energy transfer, the reaction of oxygen with polymer radicals [32] (leading to the formation of peroxy radicals) and other reactions may affect the type and concentration of products formed [33]. The same can be said for certain additives mixed into the elastomer for one or the other purpose. 

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. 

The termination constants kt found previously (see Table XVII, p. 158) are of the order of 3 X10 1. mole sec. Conversion to the specific reaction rate constant expressed in units of cc. molecule" sec. yields A f=5X10". At the radical concentration calculated above, 10 per cc., the rate of termination should therefore be only 10 radicals cc. sec., which is many orders of magnitude less than the rate of generation of radicals. Hence termination in the aqueous phase is utterly negligible, and it may be assumed with confidence that virtually every primary radical enters a polymer particle (or micelle). Moreover the average lifetime of a chain radical in the aqueous phase (i.e., 10 sec.) is too short for an appreciable expectation of addition of a dissolved monomer molecule by the primary radical prior to its entrance into a polymer particle. 

Initiator s concentration Monomer s concentration Chain radical concentration Dead polymer chain of x units Growing polymer chain of y units Initiator free radical Absolute temperature Reactor volume... 

Material Balances. The material (mass) balances for the ingredients of an emulsion recipe are of the general form (Accumulation) = (Input) - (Output) + (Production) -(Loss), and their development is quite straightforward. Appendix I contains these equations together with the oligomeric radical concentration balance, which is required in deriving an expression for the net polymer particle generation (nucleation) rate, f(t). 

---