Radical concentrations Initiators

Vivo, 1955 Fukuzumi et al., 1975). Radical formation at pH 6 apparently depends on both the concentration of hydroquinone and the amount of oxide. This is in accord with the studies of Fukuzumi et al. (1975) and Ono et al. (1977) at pH 9, in which the formation of radicals obeys first-order kinetics with respect to both phenol concentration and the amount of Mn oxides. The presence of semiquinone radicals indicates that the reduction of hausmannite involves a one-electron transfer process. The radical concentration initially increases, but then decreases simultaneously with the consumption of dissolved O2 (Fig. 8-12). Once O2 is depleted, the concentration of free radical gradually increases again. The rapidly generated semiquinone anion radical is apparently slowly oxidized by dissolved O2 in solution. The radical becomes more abundant at relatively high concentrations of hydroquinone. Oxide suspensions containing high concentrations of hydroquinone have insufficient capacity to oxidize hydroquinone to quinone completely, resulting in the accumulation of the semiquinone radicals. 

It is seen from Fig. 34 that the fluorescence wavelength of the dye was situated at the red end of the SPA absorbance curve, which may lead to fluorescence-induced polymerization. This problem can be solved by optimizing the fabrication-laser-pulse energy and the concentration of Rhodamine B so that local radical concentrations initiated by the TPA fluorescence are lower than the polymerization threshold, and then the radicals are quenched by dissolved oxygen. 

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] ... 

We recall some of the ideas of kinetics from the summary given in Sec. 5.2 and recognize that the rates of initiator decomposition can be developed in terms of the reactions listed in the Table 6.1. Using the change in initiator radical concentration d[I-]/dt to monitor the rates, we write the following ... 

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... 

For an initiator concentration which is constant at [l]o, the non-stationary-state radical concentration varies with time according to the following expression ... 

Instead of using 2fk j [I] for the rate of initiation, we can simply write tliis latter quantity as Rj, in which case the stationary-state radical concentration is... 

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... 

Styryl free radicals simultaneously initiate micelle nuclei at points of high fumarate concentration. The micelles continue to expand, interacting with free... 

Photolysis or thermolysis of persulfate ion (41) (also called peroxydisulfate) results in hoinolysis of the 0-0 bond and formation of two sulfate radical anions. The thermal reaction in aqueous media has been widely studied."51 232 The rate of decomposition is a complex function of pH, ionic strength, and concentration. Initiator efficiencies for persulfate in emulsion polymerization are low (0.1-0.3) and depend upon reaction conditions (Le. temperature, initiator concentration)."33... 

The triazolinyl radical 116 is thermally unstable with a half-life of -20 min at 95 °C. The compound 117 is stable under similar conditions. The decomposition mechanism involves loss of a phenyl radical and formation of a stable aromatic triazene (Scheme 9.26).24 This provides a mechanism for self regulation of the stable radical concentration during polymerization and a supplemental source of initiating radicals. 

The newly formed radical (R[) can initiate another sequence of reactions, thus multiplying the number of broken chains while keeping the total radical concentration constant. 

M] = monomer concentration [l] = initiator concentration [R ] = radical concentration f = initiator efficiency k-j g = chain transfer rate "constant" ktr = termination (combination or disproportionation) rate constant... 

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. 

On the other hand, the limiting conversion in a reactor of fixed size is dependent on the temperature and the radical concentration in the reactor and results from a predominating radical-radical interaction precipitated by an increased initiator concentration and the accompanying temperature excursion. At this point the solvent concentrations have little effect on the molecular... 

First, in composites with high fiber concentrations, there is little matrix in the system that is not near a fiber surface. Inasmuch as polymerization processes are influenced by the diffusion of free radicals from initiators and from reactive sites, and because free radicals can be deactivated when they are intercepted at solid boundaries, the high interfacial area of a prepolymerized composite represents a radically different environment from a conventional bulk polymerization reactor, where solid boundaries are few and very distant from the regions in which most of the polymerization takes place. The polymer molecular weight distribution and cross-link density produced under such diffusion-controlled conditions will differ appreciably from those in bulk polymerizations. 

The free-radical concentrations will be small—and the quasi-steady state hypothesis will be justified— whenever the initiation reaction is slow compared with the termination reaction, kj /f[CH3CHO]. 

A series of simulations were performed to study the effect of variables such as initiator concentration, initiator half-life and activation energy on the optimum temperature and optimum time. It was assumed that initially the polymerization mixture contained S volume percent monomer, the rest of the mixture being solvent and polymer formed earlier. It was required to reduce the monomer concentration from S volume percent to 0.S volume percent in the minimum possible time. The kinetic and tbeimodyamnic parameters used are similar to those of free radical polymerization of MMA. The parameter values are given in Appendix B. 

From the prevailing NO and HONO levels occurring during this period of the irradiation, the HONO photolysis rate (11,14), and the rate constant for the OH + NO reaction (15), we estimate that steady state OH levels of "2 x 1Q7 molecule cm" were present. From this OH radical concentration and assuming an UDMH + OH rate constant similar to those observed for N2Hi and MMH (, j ) we calculate a UDMH decay rate which is in reasonable agreement with what is observed. Thus, the HONO level measured during the initial period is entirely consistent with our assumed mechanism. 

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. 

Eqs. (26) and (27) apply irrespective of the nature of the initiation process it is required merely that the propagation and termination processes be of the second order. They emphasize the very general inverse dependence of the kinetic chain length on the radical concentration and therefore on the rate of polymerization. The kinetic chain length may be calculated from the ratios k /kt as given in Table XI and the rate of polymerization. Thus, for pure styrene at 60°C... 

Although we shall prefer the general equation (27) in later discussion, the expressions obtained specifically for initiated and for thermal polymerizations are of interest also. In the former case, the radical concentration is given by Eq. (10) hence from Eq. (26)... 

The curve OAE in Fig. 17, calculated according to Eq. (50), shows the course of the rise in the radical concentration following the commencement of illumination when the initial radical concentration is zero, i.e. o = 0. Observation of the rate of polymerization as a function of the time during the interval preceding the steady state (i.e., for t < 2ts) would provide information suitable for the evaluation of r. ... 

Two steady state conditions apply one to the total radical concentration and the other to the concentrations of the separate radicals Ml- and M2-. The latter has already appeared in Eq. (2), which states that the rates of the two interconversion processes must be equal (very nearly). It follows from Eq. (2) that the ratio of the radical population, Mi - ]/ [Mpropagation reaction rate constants. The steady-state condition as applied to the total radical concentration requires that the combined rate of termination shall be equal to the combined rate of initiation, i.e., that... 

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... 

In two limiting cases differing in the values of stationary concentration of chemisorbed radicals and initial electric conductivity of adsorbent the expression (2.94) acquires the following shape ... 

The cummulative values of the initiator loading calculated with equations 20a and 28 should agree, betwen themselves and with the measured values. As it is shown in Figure 5 this is not the case, a correction for the Initiator balances seems to be required. Larger efficiency values can be obtained if it Is assumed that all the initiator radicals have the same efficiency. Under this condition, the radical concentration is given by... 

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