Polymerization rate decay

The overall polymerization and decay rates are then the sum of Equations 1 and 2 respectively, over all active species. 

The radical decay according to this equation is depicted by curve ABF in Fig. 17. Observation of the decay in the polymerization rate immediately following cessation of illumination offers an alternative method for determining r, for it follows from Eq. (53) that the slope of the ratio Rp)s/Rp plotted against t should equal 1/r,. 

Compare Eq. 3-229 with 3-224. The decay in monomer concentration depends on the orders of both initiator and activator initial concentrations with no dependence on deactivator concentration and varies with t2/3 under non-steady-state conditions. For steady-state conditions, there are first-order dependencies on initiator and activator and inverse first-order dependence on deactivator and the time dependence is linear. Note that Eq. 3-229 describes the non-steady-state polymerization rate in terms of initial concentrations of initiator and activator. Equation 3-224 describes the steady-state polymerization rate in terms of concentrations at any point in the reaction as long as only short reaction intervals are considered so that concentration changes are small. 

Reports on steady increases of polymerization rates with increasing polymerization temperatures usually refer to an upper limit of polymerization temperature of around 60 °C. At temperatures > 60 °C catalyst deactivation becomes more prominent and overall catalyst activities decrease. There are two reports which point in this direction. A decrease of catalyst activities at elevated temperatures was observed for NdV/DIBAH/fBuCl [455] and for NdN/TIBA/EASC [388]. Pires et al. studied the solution polymerization of BD whereas Ni et al. studied the polymerization of BD in the gas phase. The rate maximum observed by Pires et al. was at 80 °C whereas the reaction maximum in the gas-phase polymerization was at 50 °C. The reduction of polymerization rates at elevated temperatures can be explained by the decay of the number of active species. In gas-phase polymerization deactivation becomes evident at lower temperatures (50 °C) compared to the solution pro-... 

The condition of eqn. (11) must be fulfilled when the overall polymerization rate remains unaffected by the presence of the transfer agent XT In other words, the difference in the decay rate of active centres in the presence or absence of XT must be negligible. 

The yield of the catalyst, 0, was measured at various ethylene concentrations (see Fig. 10). According to the results, initiation is rapid and the catalytic system maintains full capacity for a long time, for at least 1 h. In this interval, the polymeric particles increase their size 5-10 fold. Thus the monomer supply into the pores of the particles by diffusion cannot be hindered. In the subsequent phase, activity already decreases. Either the conditions for monomer transport to the centres by diffusion are deteriorating, and/or the centres are slowly decaying. The polymerization rate, i>pol, can be determined from the slopes of the curves in Fig. 10. The determined values of the initial rates are directly proportional to monomer concentration (except for the lowest values of [M]), as shown in Fig. 11. 

Other, more direct methods have been devised (Burnett, Zoc. ciL) for studying the nonstationary period. Most of them involve complex electronic equipment, because the period is usually very short. However, it can be lengthened by choosing sufficiently low radical concentrations, but this means lower rates of polymerization. If sufficiently sensitive means of observing low polymerization rates are available, single radical decay periods can be studied directly. A method for doing so with simple di-latometric equipment has been described by Benson and North. "... 

The polymerization rate constants were measured by adjustment of the equations above to the experimental polymerization results. The activation energy of chain propagation and decay for active site 1 and 2 were the same because this catalyst system is single site. The results of the fitting of calculation and polymerization are shown in Figure 17.15. 

Rate decay is mainly ascribed to a chemical deactivation of active centers. Nevertheless, in the case of ethylene, it appears that diffusive phenomena play also a certain role in the drop of the polymerization rate88 94. Moreover, diffusivity of monomer in the reaction medium may restrict polymerization rate, as can be concluded from the dependence of catalytic activity on catalyst concentration 95... 

From the above results, it is clear that the rate decay must be attributed to a chemical deactivation of the polymerization centers with time. Different mathematical expressions have been proposed, for those catalyst systems most widely studied in the literature, in order to express the law of the decay. For propylene polymerization with TiCyMgCl2—AlEt3/EB or with TiCyEB/MgCl2 - Al Et3/EB, Spitz 45-97) proposed an expression of the following type ... 

Actually, studies on the propylene polymerization at atmospheric pressure carried out in our laboratories 101 > have demonstrated that R0 and the deactivation rate depend, in a complex manner, on both the organoaluminum and external donor concentrations (see Sect. 6.1.2 and 6.1.3). The kinetic curves obtained cannot be reduced to a single model for the deactivation of active centers according to a simple 1 st and 2nd order law, but rather they seem to follow a more complicated behavior. This is not surprising if one considers that the decay of polymerization rate is probably the effect of an evolution, in time, of a plurality of different catalytic species having different stability, reactivity and stereospecificity (see Sect. 6.3). 

Pino 109), in turn, with the catalyst system TiCl4/MgCl2 TIB A, noticed a progressive decrease in the induction period with a simultaneous increase in the maximum polymerization rate and in the activity decay. 

If diffusion phenomena are not involved, the formation and deactivation of polymerization centers should reflect in rate-time dependences, other conditions being constant. Rate acceleration period of very widely differing lengths is often observed, followed either by a more or less steady rate or by a deceleration (rate decay) period. As for the polymerization center deactivation, it is quite important to know whether a macromolecule or a metal-polymer bond is formed due to this reaction (see Sect. 4). 

Iguchi [266] considered a mechanism in which growing chains are occluded, and thus become non-propagating, by a process kinetically analogous to the interaction of crystallites growing from the polymer melt and following Avrami kinetics. (It was assumed that chemical transfer and termination reactions do not occur.) The polymerization rate is given by the concentrations of monomer and active centres at any time, i.e. Rp = kp [C ], [M],. If the decay of catalytic activity follows the relationship... 

Waters and Mortimer [235] with catalysts (Tr-CjHs )2TiRCl/AlR Cl2 found polymerization rates to be unaffected by the structure of the alkyl groups, for ethyl and higher homologues. The rate in toluene was lower (by a factor of 4 at Al/Ti = 1.0) than in dichloromethane, which was attributed to involvement of the aromatic solvent in the polymerization, presumably in the monomer coordination step. Rates increased with ethylene pressure and with Al/Ti ratio, and, as the latter was increased, the time before which a decay in rate occurred decreased maximum rates with 0.01 mole 1 of titanium complex, 760 torr ethylene pressure and 0°C, increased from 8 to 120 x 10 mole 1 sec with increase in Al/Ti ratio from 1.0 to 4.0. Assuming ethylene solubility of approximately 0.15 mole r these would correspond to apparent rate coefficients of 0.5 to 7 1 mole sec , not greatly different from other quoted values (Table 10). 

B is a constant which depends on the ZnEt2 concentration, f and k are constants defining the decay of polymerization rate, and PC3H6 ... 

Another aspect49 is the initial presence of persistent species in nonzero concentrations [Y]o, and it will be discussed more closely in section IV. In the absence of any additional initiation, the excess [Y]o at first levels the transient radical concentration to an equilibrium value [R]s = A[I]o/[Y]o. This is smaller than that found without the initial excess and lowers both the initial conversion rate and the initially large PDI. Further, it provides a linear time dependence of ln-([M]o/[M]), which is directly proportional to the equilibrium constant. Later in the reaction course, [Y] may exceed [Y]0 because of the self-termination, then [R] is given by eq 18. If there is additional radical generation, the first stages will eventually be replaced by a second stationary state that was described above. Further effects are expected from a decay or an artificial removal of the persistent species that increases the concentration of the transient radicals and the polymerization rate (see section IV). Radical transfer reactions to polymer, monomer, or initiator have not yet been incorporated in the analytical treatments. 

Termination rate coefficients can be measured using the y-radiolysis relaxation method. This involves initiation using y-radiation, followed by removal of the reaction vessel from the y-source. Conversion during the relaxation period is monitored by dilatometry, and the decay in polymerization rate over time is related to the rate of radical loss. When large particles are used, radical loss is dominated by intraparticle termination, rather than exit into the aqueous phase, and the rate coefficient for termination can be determined from the decay curve. By using multiple insertions and removals, the termination rate coefficient is determined over a wide range of polymer mass fraction (wp). 

Some other catalysts, such as Cr /aluminophosphate, exhibit polymerization rates that do decay with time. In these systems, at least, polymer accumulation over time might cause the declining activity, because of increasing resistance to mass transport. However, this interpretation would mean that the polymerization rate would be a function, not of time itself, but of the amount of polymer accumulation. Investigation of the kinetics variables makes it clear that the rate is dependent not on polymer build up but on the reaction time. Similar rate-decay kinetics can be obtained with a high or a low polymer yield, by variation of ethylene concentration and other variables. In one experiment, the ethylene in the reactor was removed just as the peak reaction rate was reached, and not... 

Cr/alumina exhibits a "fast" kinetics profile that is quite different from that of Cr/silica. The polymerization rate develops rapidly, especially when the alumina has been acidified by treatment with silica, fluoride, phosphate, or sulfate. Cr/alumina exhibits polymerization kinetics similar to that of Cr/AlP04, a topic that is discussed in Section 15. The polymerization rate rises quickly when ethylene is added, but later it tends to decay slowly. The rapid initial rise indicates that reduction of Cr(VI), or desorption of redox by-products, and/or alkylation of the chromium, may be more facile on alumina than on silica. Alumina is known as a strong adsorbent in its own right, so that adsorption of by-products from chromium onto the neighboring surface is one possible contributing cause of the rapid development of polymerization rate. 

The gradual decay with time in the polymerization rate characteristic of Cr/aluminophosphate is different from that of Cr/silica. It has sometimes been attributed to mass transport limitations caused by polymer buildup around the active sites. To test this hypothesis, a stopped-flow experiment was conducted, as represented in Figure 170. In this run, the polymerization rate with Cr/AIPO4 was allowed to build up to its highest value, which occurred in 10 min. Then the ethylene flow was stopped, and the reactor was depressurized to remove residual ethylene. After about 75 min, the ethylene was readmitted and polymerization continued. However, it continued not at the rate at which it had left off,... 

For example, both the rapid development in rate and the subsequent decay were found to be dependent on the ethylene concentration with Cr/AIPO4 catalysts. This dependence is shown in Figure 171, in which the kinetics of three polymerization runs are shown as the ethylene concentration was varied. It is perhaps not surprising that the reduction and/or initiation slowed substantially with decreased ethylene concentration. When these curves were analyzed according to the model in Scheme 35, the polymerization rate itself was found to be first-order in ethylene concentration. However, the development in activity was found to be more sensitive to ethylene concentration. In contrast, the decay in activity was found to be unaffected by ethylene concentration. 

The development of polymerization rate was not found to be highly sensitive to temperature. The rate peaked in about 10-20 min even at the lowest temperature tested, as shown in Figure 173. However, the decay in polymerization rate was highly sensitive to temperature. Arrhenius plots of fc j, the decay constant, indicate an activation energy (for the decay only) of about 26 k cal mol 1. The higher temperature caused faster decay of the... 

This finding indicates that reduction is not usually the rate-limiting step for rate development on these catalysts. Both the reduction of Cr(VI) in CO and the addition of cocatalysts to the reactor, however, did increase the polymerization rate substantially, by two- and fivefold, respectively. The higher rate suggests that CO reduction or metal alkyl cocatalyst produced active sites that would not otherwise have become active. BEt3 cocatalyst resulted in a more rapid decay in the activity, suggesting that these new sites created by BEt3 were less stable. 

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