Rate of initiation

In general the rate of initiation is determined by two reactions the generation of the initiating particle R° from the initiator I, and of the active centre from R° and monomer 

In simpler cases, one of these reactions is significantly slower than the other, thus representing the controlling step. 

Measurement of the initiation rate has been best developed for radical polymerizations. 

The generation of primary radicals can generally be represented by eqn. (1) which for an ideal case assumes the rate form  

A part of the radicals just generated decays by mutual collisions. The creation rate of primary initiating particles will therefore be lower than indicated by eqn. (3). The lowering of the rate is quantitatively described by the coefficient of initiation efficiency, / 

---

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 ... 

Any one of these expressions gives the rate of initiation Rj for the particular catalytic system employed. We shall focus attention on the homolytic decomposition of a single initiator as the mode of initiation throughout most of this chapter, since this reaction typifies the most widely used free-radical initiators. Appropriate expressions for initiation which follows Eq. (6.6) are readily derived. 

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... 

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... 

If the rate of initiation is investigated independently, the rate of polymeri-... 

The rate of initiation was measured directly and radical lifetimes were determined using the rotating sector method. The following results were obtained.f... 

Demonstrate that the variations in the rate of initiation and r are consistent with free-radical kinetics and evaluate k. ... 

Even though the rates of initiation span almost a 10-fold range, the values of k, show a standard deviation of only 4%, which is excellent in view of experimental errors. Note that the rotating sector method can be used in high-pressure experiments and other unusual situations, a characteristic it shares with many optical methods in chemistry. 

This suggests that polymerizations should be conducted at different ratios of [SX]/[M] and the molecular weight measured for each. Equation (6.89) shows that a plot of l/E j. versus [SX]/[M] should be a straight line of slope sx Figure 6.8 shows this type of plot for the polymerization of styrene at 100°C in the presence of four different solvents. The fact that all show a common intercept as required by Eq. (6.89) shows that the rate of initiation is unaffected by the nature of the solvent. The following example examines chain transfer constants evaluated in this situation. 

In both cases take the rate of initiation to be 1.0 X 10 mol liter sec What would be the effect on Rp and v in each of these cases if Rj were decreased by a factor of 4 ... 

AlkyUithium compounds are primarily used as initiators for polymerizations of styrenes and dienes (52). These initiators are too reactive for alkyl methacrylates and vinylpyridines. / -ButyUithium [109-72-8] is used commercially to initiate anionic homopolymerization and copolymerization of butadiene, isoprene, and styrene with linear and branched stmctures. Because of the high degree of association (hexameric), -butyIUthium-initiated polymerizations are often effected at elevated temperatures (>50° C) to increase the rate of initiation relative to propagation and thus to obtain polymers with narrower molecular weight distributions (53). Hydrocarbon solutions of this initiator are quite stable at room temperature for extended periods of time the rate of decomposition per month is 0.06% at 20°C (39). 

Initiators. The degree of polymerization is controlled by the addition rate of initiator(s). Initiators (qv) are chosen primarily on the basis of half-life, the time required for one-half of the initiator to decay at a specified temperature. In general, initiators of longer half-Hves are chosen as the desired reaction temperature increases they must be well dispersed in the reactor prior to the time any substantial reaction takes place. When choosing an initiator, several factors must be considered. For the autoclave reactor, these factors include the time permitted for completion of reaction in each zone, how well the reactor is stirred, the desired reaction temperature, initiator solubiUty in the carrier, and the cost of initiator in terms of active oxygen content. For the tubular reactors, an additional factor to take into account is the position of the peak temperature along the length of the tube (9). 

Propagation. Propagation reactions (eqs. 5 and 6) can be repeated many times before termination by conversion of an alkyl or peroxy radical to a nonradical species (7). Homolytic decomposition of hydroperoxides produced by propagation reactions increases the rate of initiation by the production of radicals. 

Depth of localized corrosion should be reported for the actual test period and not interpolated or extrapolated to an annual rate. The rate of initiation or propagation of pits is seldom uniform. The size, shape, and distribution or pits should oe noted. A distinction should be made between those occurring underneath the supporting devices (concentration cells) and those on the surfaces that were freely exposed to the test solution. An excellent discussion of pitting corrosion has been pubhshed [Corro.sion, 25t (January 1950)]. 

The rate of initiation, V-, i.e. the rate of formation of growing polymer radicals, can be shown to be given by... 

The overall rate of a chain process is determined by the rates of initiation, propagation, and termination reactions. Analysis of the kinetics of chain reactions normally depends on application of the steady-state approximation (see Section 4.2) to the radical intermediates. Such intermediates are highly reactive, and their concentrations are low and nearly constant throughout the course of the reaction ... 

The result of the steady-state condition is that the overall rate of initiation must equal the total rate of termination. The application of the steady-state approximation and the resulting equality of the initiation and termination rates permits formulation of a rate law for the reaction mechanism above. The overall stoichiometry of a free-radical chain reaction is independent of the initiating and termination steps because the reactants are consumed and products formed almost entirely in the propagation steps. 

Setting the rate of initiation equal to the rate of termination and assuming that is the dominant termination process gives ... 

Generally the oxidant is compounded in one part of the adhesive, and the reductant in the other. Redox initiation and cure occur when the two sides of the adhesive are mixed. There also exist the one-part aerobic adhesives, which use atmospheric oxygen as the oxidant. The chemistry of the specific redox systems commonly used in adhesives will be discussed later. The rates of initiation and propagation are given by the following equations ([9] p. 221). 

This shows that the rate of initiation equals the rate of termination. Thus,... 

It will be known that for the radical polymerization the increase on the rate of initiation would increase the polymerization rate Eq. (I) and decrease the degree of polymerization Eq. (2). In the present systems, the monomer concentration was relatively high so that initiating radicals are formed to some extent from the monomer and solvent, i.e., / , in Eq. (1) may be represented as follows [51] ... 

Studies in the photoinitiation of polymerization by transition metal chelates probably stem from the original observations of Bamford and Ferrar [33]. These workers have shown that Mn(III) tris-(acety]acetonate) (Mn(a-cac)3) and Mn (III) tris-(l,l,l-trifluoroacetyl acetonate) (Mn(facac)3) can photosensitize the free radical polymerization of MMA and styrene (in bulk and in solution) when irradiated with light of A = 365 at 25°C and also abstract hydrogen atom from hydrocarbon solvents in the absence of monomer. The initiation of polymerization is not dependant on the nature of the monomer and the rate of photodecomposition of Mn(acac)3 exceeds the rate of initiation and the initiation species is the acac radical. The mechanism shown in Scheme (14) is proposed according to the kinetics and spectral observations ... 

This alone is inadequate, since it predicates a linear relation between the rate of initiation and the monomer concentration, and, therefore, it is believed that monomer and ethyl acetate (E) are, to some extent, interchangeable in the reaction and that E may also form as exciplex (CE). ... 

In contrast to /3-PCPY, ICPY did not initiate copolymerization of MMA with styrene [39] and AN with styrene [40]. However, it accelerated radical polymerization by increasing the rate of initiation in the former case and decreasing the rate of termination in the latter case. The studies on photocopolymerization of MMA with styrene in the presence of ICPY has also been reported [41], /8-PCPY also initiated radical copolymerization of 4-vinylpyridine with methyl methacrylate [42]. However, the ylide retarded the polymerization of N-vinylpyrrolidone, initiated by AIBN at 60°C in benzene [44]. (See also Table 2.)... 

The effective rate of initiation (7 s) in the case of thermal decomposition of an initiator (T) decomposing by Scheme 3.11 is given by eq. 2... 

If, as is usual, the k are not rate detennining the rate of initiation is given by... 

---