Activation temperature polymerization kinetics

In special case when constants of chain propagation and active sites deactivation rates do not depend on temperature, polymerization kinetic scheme corresponds to fast initiation and to the first orders of chain propagation reaction on monomer and active sites deactivation on their concentration the expression for polymer yield was received [1,62] ... 

The bulk polymerization of acrylonitrile in this range of temperatures exhibits kinetic features very similar to those observed with acrylic acid (cf. Table I). The very low over-all activation energies (11.3 and 12.5 Kj.mole-l) found in both systems suggest a high temperature coefficient for the termination step such as would be expected for a diffusion controlled bimolecular reaction involving two polymeric radicals. It follows that for these systems, in which radicals disappear rapidly and where the post-polymerization is strongly reduced, the concepts of nonsteady-state and of occluded polymer chains can hardly explain the observed auto-acceleration. Hence the auto-acceleration of acrylonitrile which persists above 60°C and exhibits the same "autoacceleration index" as at lower temperatures has to be accounted for by another cause. 

Evidence in support of a carbonium ion type of mechanism for low temperature polymerization was also obtained in an investigation of the kinetics of the homogeneous liquid phase polymerization of propene in the presence of aluminum bromide and hydrogen bromide at about —78° (Fontana and Kidder, 89). The rate of reaction is approximately proportional to the concentration of the promoter, no polymerization occurring in its absence. During the main portion of the reaction, the rate is independent of the monomer concentration toward the end, it decreases, due apparently to the low-concentration of the monomer, addition of more olefin resulting in an increase in the rate. It was concluded that the reaction involves an active complex, which may be regarded as a carbonium ion coupled with an anion ... 

The ceiling temperature of a polymerizable system may be obtained from studies of its polymerization kinetics at a series of rising temperatures. For many polymerizations, the sum of the activation energies... 

For this particular case, both a, and a2 are unique functions of conversion, meaning that dx/dt depends only on conversion and temperature i.e., the polymerization kinetics may be described by the phenomenological Eq. (5.1). Moreover, if one of the mechanisms (e.g., the catalytic) predominates over the other one (e.g., the noncatalytic), Eq (5.2) may be used to correlate experimental results and the activation energy may be obtained using isoconversional methods. 

If ionization is strongly exothermic, polymerization may be faster at lower temperatures due to the increased concentration of carbenium ions. Temperature affects kinetics by the activation enthalpy of propagation (AHP ) and by the enthalpy of the ionization equilibrium (AH). The apparent activation enthalpy is therefore a sum of both components and may become negative, if AH > AH/ ... 

Figure 22 includes the temperature dependent polymerization rates (1), (2) and (3). The thermal polymerization kinetics (1), they — (2), and the UV photopolymerization kinetics (3) have been investigated by the method of diffuse reflection spectroscopy and other methods The activation energy of the thermal reactions (2) and (3) following the photoinduced dimerization processes, (150 + 30) meV, is appreciable lower than those of the dimer DR intermediates. However, the processes which dominate the polymerization reaction are determined not by the short diradicals with n 6 but by the long chains with n 7, which all have a carbenoid DC or AC structure. The discrepancy of the activation energies therefore may be due to the different reactivities of the diradical and carbenoid chain ends. The activation energies of the thermal addition reactions of the AC and DC intermediates at low temperatures have not been determined and therefore a direct comparison with those of the diradicals is not possible. 

Figure 1. Dependence of polymerization kinetics on activation temperature.

FIGURE 21 Polymerization kinetics at 110 °C of Cr/silica-titania catalysts (1 wt% Cr) activated at various temperatures. 

This interpretation explains why Ziegler, Ballard, and metallocene catalysts, which have a different initiation chemistry, can be supported on the same silicas, but display totally different kinetics (and much faster reactions) without a gradual rise in activity. It also explains how the kinetics of polymerization with a single Cr/silica catalyst can be so easily manipulated by the choice of the reaction temperature, the activation temperature, CO reduction (Figure 16), and incorporation of metal alkyls and poisons in the reaction mixture. 

FIGURE 175 Polymerization kinetics on Cr/AlP04 catalyst (P/Al atomic ratio of 0.8) activated at three temperatures, and tested at 95 °C without cocatalyst. 

Cr/aluminophosphate catalysts respond to activation temperature in many of the same ways that Cr/silica does, and there are some differences too. The activity of the catalyst is generally increased at higher activation temperatures. Figure 175 shows how the kinetics of polymerization with a 0.8 P/Al catalyst responded to the activation temperature of the catalyst. There was little change in the overall shape of the kinetics profile only the height varied. The average activity of the catalyst improved when the activation temperature was raised from 300 up to 700 °C. 

As mentioned previously, most continuous anionic polymeri tion studies have been conducted at relatively low temperatures ( < 50 °C). Even then, mixing kinetics have been of considerable concern due to the fast polymerization kinetics. In the recent anionic polymerization studies of Priddy and Pirc [1,73], the polymerization temperature range of 80-140 °C was studied (typical free radical temperature range). At these temperatures, the polymerization kinetics are extremely fast Also, the high polymerization temperature results in significant thermal termination of active polystyryl chains. Kem et aL [74] found that the termination reaction involved liberation of lithium hydride (1) and was first order. They found the apparent rate constant K at 65, 93, and 120°C are 0.15, 0.78, and 1.3 h respectively. 

ATRP a transition metal complex is needed for the activation of the alkyl-halide-ended macromolecules, and a wider range of temperatures can be applied. In both cases, the polymerization kinetics are governed by the activation-deactivation equilibrium and by the persistent radical effect [6]. The number-average degree of polymerization DP ) is calculated by the ratio of the initial monomer concentration to the initiator (i.e., alkoxyamine or alkyl halide) concentration, multiplied by monomer conversion. 

Fig. 27 Ethylene polymerization kinetic curves of catalysts activated by TEA cocatalyst during slurry polymerizatimi (a) Phillips catalyst al) and Cat-A/1.5 catalyst a2) (Al/Cr molar ratio = 20.0) (b) Cat-A/1.5 catalyst (W) and S-2 catalyst b2) (Al/Cr molar ratio = 15.0). Polymerization conditions catalyst amount, 160 mg polymerization temperature, 90°C ethylene pressure, 0.15 MPa solvent, heptane, 70 mL...

Olefin polymerization reactors will now be modeled using a bottom-up approach, from microscale to macroscale. In this section polymerization kinetic models will be introduced to describe polymerization rates and polymer microstructures, ignoring any phenomena that may take place in the mesoscale and macroscale. These models depend on the concentration of reagents and temperatures at the active site. As explained in the previous... 

One of the nice features of free-radical polymerization is that values of the preexponential coefficients and activation energies (or alternately half-life values at various temperatures) can be obtained in the literature (such as in Odian (1991)) or from their manufacturers (such as Wako Chemical Corp.) for a variety of initiators, and these numbers do not normally change no matter what the fluid environment the initiator molecules are in. Thus, if we want to decompose more than 99% of the starting initiator material in the reactor, we just have to wait for the reaction to proceed up to five times the initiator half-life. The other attractive feature of free-radical polymerization is that free-radical reactions are well known and radical concentrations can be directly measured. Thus, we know, for example, that if we want to preserve radicals in solution, we should not allow oxygen gas (O2) in our system, because reactive radicals will combine with oxygen gas to form a stable peroxy radical. That is why reaction fluids were bubbled with N2, CO2, Ar, or any inert gas, in order to displace O2 gas that comes from the air. Finally, Iree-radical polymerization is not sensitive to atmospheric or process water, compared to other polymerization kinetic mechanisms. 

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