Effective rate of initiation

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... 

The simple two-reactor series shown in Figure 1 will be analyzed to demonstrate the effect of inhibitor on the performance of continuous systems. Since inhibitor will be present in the continuously added feed stream, it will serve to reduce the effective initiation rate in the first reactor. Since inhibitor is very reactive with free radicals, all inhibitor fed must be destroyed before significant reaction can take place. Thus the effective rate of initiation in the first reactor is given by Equation 1. 

A semibatch system will be influenced differently by the presence of inhibitor. If inhibitor is present in the recipe ingredients of a batch reactor it will delay the start of polymerization, after which the reaction will proceed in a normal manner. Inhibitor in the delayed feed stream(s) to a semibatch system will reduce the effective rate of initiation. This reduction may require the use of more initiator, and because the inhibitor reacts rapidly, the polymerization rate may increase dramatically when the delayed-feed part of the cycle is finished. 

Inhibitors are used in most monomers to prevent premature polymerization during processing, shipping and storage. In addition, trace chemicals in other recipe ingredients, e.g., oxygen in water, can also inhibit or retard polymerization. When inhibitors are present in a batch reactor, they delay the start of pol)rmerization but the reactions proceed normally after the inhibitor has been spent. Inhibitors in the feed stream(s) to a CSTR, however, reduce the effective rate of initiation as expressed by Equation 1. 

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). 

Lastly, the effect of temperature on PIB yield for the r-BuX/Et2 AlX/MeX systems can be explained. In general, the yield is unaffected or decreases somewhat with decrease in temperature. At a certain temperature, yield drops to zero. Such an effect of temperature indicates, in agreement with our assumption, that the yield is dependent on the rate of initiation. 

The effect of temperature on Mv has been studied by a number of workers (Table 8) and in all cases, a decrease in temperature increased PIB molecular weight. Since solvent dielectric constant increases with decreasing temperatures, molecular weights also areexpected to decrease. Apparently such effect is small as shown by the increase in Mv s with decreasing temperature. At very low temperatures, Mv suddenly drops as shown above. This was explained4 by assuming a reduced rate of initiation leading to an increase in transfer to initiator. 

It is important to note that and C2 are quantitative descriptors of the gel effect which depend only on the monomer, temperature and reaction medium. The full description of given by equation (11), requires g and g2 which are functions of the rate of initiation and extent of conversion. The kinetic parameters used in these calculations and their sources are given in Table 1. All data are in units of litres, moles and second. Figure 5 shows the temperature dependencies of and C2 and Table 2 lists these and other parameters determined by fitting the model to the data in Figures 1-4. 

The rate of initiation via this reaction is v (InH + 02) = i2 i2[InH][02], where the coefficient e12 describes the effectiveness of initiation by the reaction. Normally, such reaction occurs... 

For initiated oxidation, the inhibitory criterion could be defined as the ratio v0/v or (v0/ v — v/v0), where v0 and v are the rates of initiated oxidation in the absence and presence of the fixed concentration of an inhibitor, respectively. Another criterion could be defined as the ratio of the inhibition coefficient of the combined action of a few antioxidants / to the sum of the inhibition coefficients of individual antioxidants when the conditions of oxidation are fixed (fx = IfiXi where f, and x, are the inhibition coefficient and molar fraction of z th antioxidant terminating the chain). It should, however, be noted that synergism during initiated oxidation seldom takes place and is typical of autoxidation, where the main source of radicals is formed hydroperoxide. It is virtually impossible to measure the initial rate in the presence of inhibitors in such experiments. Hence, inhibitory effects of individual inhibitors and their mixtures are usually evaluated from the duration of retardation (induction period), which equals the span of time elapsed from the onset of experiment to the moment of consumption of a certain amount of oxygen or attainment of a certain, well-measurable rate of oxidation. Then three aforementioned cases of autoxidation response to inhibitors can be described by the following inequalities (r is the induction period of a mixture of antioxidants). 

Case 1 appears to accurately predict the observed dependence on persulfate concentration. Furthermore, as [Q]+otal approaches [KX], the polymerization rate tends to become independent of quat salt concentration, thus qualitatively explaining the relative insensitivity to [Aliquat 336]. The major problem lies in explaining the observed dependency on [MMA]. There are a number of circumstances in free radical polymerizations under which the order in monomer concentration becomes >1 (18). This may occur, for example, if the rate of initiation is dependent upon monomer concentration. A particular case of this type occurs when the initiator efficiency varies directly with [M], leading to Rp a [M]. Such a situation may exist under our polymerization conditions. In earlier studies on the decomposition of aqueous solutions of potassium persulfate in the presence of 18-crown-6 we showed (19) that the crown entered into redox reactions with persulfate (Scheme 3). Crematy (16) has postulated similar reactions with quat salts. Competition between MMA and the quat salt thus could influence the initiation rate. In addition, increases in solution polarity with increasing [MMA] are expected to exert some, although perhaps minor, effect on Rp. Further studies are obviously necessary to fully understand these polymerization systems. 

For any specific type of initiation (i.e., radical, cationic, or anionic) the monomer reactivity ratios and therefore the copolymer composition equation are independent of many reaction parameters. Since termination and initiation rate constants are not involved, the copolymer composition is independent of differences in the rates of initiation and termination or of the absence or presence of inhibitors or chain-transfer agents. Under a wide range of conditions the copolymer composition is independent of the degree of polymerization. The only limitation on this generalization is that the copolymer be a high polymer. Further, the particular initiation system used in a radical copolymerization has no effect on copolymer composition. The same copolymer composition is obtained irrespective of whether initiation occurs by the thermal homolysis of initiators such as AIBN or peroxides, redox, photolysis, or radiolysis. Solvent effects on copolymer composition are found in some radical copolymerizations (Sec. 6-3a). Ionic copolymerizations usually show significant effects of solvent as well as counterion on copolymer composition (Sec. 6-4). 

An interesting approach [62,63] to this problem, the use of 02 instead of 02, further substantiated the electron attachment to vdW molecules. For the BB mechanism, the isotope effect may be expected to appear as a change in the rates of initial attachment and autoionization channels, which are caused by a decrease of the resonance energy for 2 in comparison with 02. 

Under such conditions, the effects of the rate of initiation, Vh the reagent concentration, and the oxygen pressure can be determined. A zero order was always obtained with respect to the oxygen at pressures varying from 0.2-1.5 atm. At low concentration, all of the reagents... 

For experimental reasons (discussed below) the relative rate of decrease should be smaller than 0.01 sec."1. Since kA is of the order of 104 liter per mole per sec., [AH] must be of the order of 10 6 mole per liter. This low concentration of inhibitor will only have an appreciable effect on the rate of autoxidation if the rate of initiation—and consequently the rate of oxidation—is low. To measure the decrease in rate during the short-lived non-steady state, one must be able to determine these low velocities within short periods of time. From the usual inhibition formulas one can compute, for instance, that in order to obtain a ratio of original to inhibited rate of about 5 with [AH] = 10 6 mole per... 

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