Ethylene polymerization rate constant

The existence of a further type of active centers was demonstrated by Pino and Rotzinger93> by polymerizing ethylene with a MgQ2-supported catalyst in the presence of an electron donor. A comparison of the ethylene and propylene kinetic curves shows that, while propylene polymerization is characterized by the well known rapid decrease in rate, the ethylene polymerization rate increases reaching a constant value after about 30 min. This has been attributed to the existence of active... 

Example 10.8 The production of high-pressure low-density polyethylene is carried out in tubular reactors of typical dimensions 2.5 cm diameter and 1 km long at 250°C and 2500 atm. The conversion per pass is 30% and the flow rate is 40,000 kg/h. Assuming that the polymerization reaction is first order in ethylene concentration, estimate the value of the polymerization rate constant. 

Chien and Wang [23] determined the initial active site concentration of this homogeneous catalyst system using a radiolabeling technique based on CHjOT and found that 80% of all the Zr atoms are catalytically active at 70°C and an Al/Zr molar ratio of 1,000, and that 100% of the Zr atoms are active at an Al/Zr ratio of 10,000. Lowering the polymerization temperature to 50°C and the Al/Zr ratio to 550 reduces the Zr active site content to 20%. The ethylene propagation rate constant at 70 C and an Al/Zr ratio of 11,000 was calculated to be 1.6 x 10 M/sec with the maximum ethylene polymerization rate obtained in about one minute at 1.06 x 10 M/sec and the rate decayed to about one-half the maximum rate of polymerization in about 40 minutes. 

Fig. 1. Examples of temperature dependence of the rate constant for the reactions in which the low-temperature rate-constant limit has been observed 1. hydrogen transfer in the excited singlet state of the molecule represented by (6.16) 2. molecular reorientation in methane crystal 3. internal rotation of CHj group in radical (6.25) 4. inversion of radical (6.40) 5. hydrogen transfer in halved molecule (6.16) 6. isomerization of molecule (6.17) in excited triplet state 7. tautomerization in the ground state of 7-azoindole dimer (6.1) 8. polymerization of formaldehyde in reaction (6.44) 9. limiting stage (6.45) of (a) chain hydrobromination, (b) chlorination and (c) bromination of ethylene 10. isomerization of radical (6.18) 11. abstraction of H atom by methyl radical from methanol matrix [reaction (6.19)] 12. radical pair isomerization in dimethylglyoxime crystals [Toriyama et al. 1977].

In several papers (51, 84, 96, 104) the decrease of the polymerization rate with time was assumed to be caused by the decrease of C as a result of diffusional restrictions due to the formation of a polymer film on the catalyst surface. However, as a matter of experience in work with heterogeneous catalysts for ethylene polymerization, it is known that even for polymerization with no solvent, the formation of a solid polymer is possible at high rates (thousands of grams of polymer per gram of catalyst per hour) that are constant until large yields are reached (tens of kilograms of polymer per gram of catalyst). 

It was found 158,159) that the fall of the rate observed when aluminum-organic compound was added to TiCl2 during ethylene polymerization was due to the decrease in the number of propagation centers. The propagation rate constant remained unchanged. In propylene polymerization the number of atactic propagation centers sharply diminished when the aluminum-... 

Ethylene in Xenon Rate Constants for Ionic Polymerization. 

Phenomenological evidence for the participation of ionic precursors in radiolytic product formation and the applicability of mass spectral information on fragmentation patterns and ion-molecule reactions to radiolysis conditions are reviewed. Specific application of the methods in the ethylene system indicates the formation of the primary ions, C2H4+, C2i/3+, and C2H2+, with yields of ca. 1.5, 1.0, and 0.8 ions/100 e.v., respectively. The primary ions form intermediate collision complexes with ethylene. Intermediates [C4iZ8 + ] and [CJH7 + ] are stable (<dissociation rate constants <107 sec.-1) and form C6 intermediates which dissociate rate constants <109 sec. l). The transmission coefficient for the third-order ion-molecule reactions appears to be less than 0.02, and such inefficient steps are held responsible for the absence of ionic polymerization. 

Radiolytic ethylene destruction occurs with a yield of ca. 20 molecules consumed/100 e.v. (36, 48). Products containing up to six carbons account for ca. 60% of that amount, and can be ascribed to free radical reactions, molecular detachments, and low order ion-molecule reactions (32). This leaves only eight molecules/100 e.v. which may have formed ethylene polymer, corresponding to a chain length of only 2.1 molecules/ ion. Even if we assumed that ethylene destruction were entirely the result of ionic polymerization, only about five ethylene molecules would be involved per ion pair. The absence of ionic polymerization can also be demonstrated by the results of the gamma ray initiated polymerization of ethylene, whose kinetics can be completely explained on the basis of conventional free radical reactions and known rate constants for these processes (32). An increase above the expected rates occurs only at pressures in excess of ca. 20 atmospheres (10). The virtual absence of ionic polymerization can be regarded as one of the most surprising aspects of the radiation chemistry of ethylene. 

In the study, the kinetic rate constants applicable to the polymerization of ethylene (, ) were used with an assumed activation volume. These values appear to be a reasonably consistent set of constants for the polymerization of ethylene and, as shown... 

The ethylene polymerization was carried out using a 12 OZ glass reactor equipped with a two blade impeller under a constant ethylene pressure of 20 psi. A predetermined amount of solvent (n-heptane), monomer, MAO and embedded catalyst were charged in series into the reactor. Polymerization was carried out at 70"C with agitation speed of 800 rpm. The polymer obtained was washed with excess amount of methanol containing hydrochloric acid solution and dried in vacuo for 24 hrs. The polymerization rate was determined from the amount of consumed ethylene, measured using a mass flow meter. DSC analyses (Dupont V4.0B) was carried out at a rate of 10 C /min, and the results were obtained in the second scan. 

At 24 °C and 15-60 bar ethylene, [Rh(Me)(0H)(H20)Cn] catalyzed the slow polymerization of ethylene [4], Propylene, methyl acrylate and methyl methacrylate did not react. After 90 days under 60 bar CH2=CH2 (the pressure was held constant throughout) the product was low molecular weight polyethylene with Mw =5100 and a polydispersity index of 1.6. This is certainly not a practical catalyst for ethylene polymerization (TOP 1 in a day), nevertheless the formation and further reactions of the various intermediates can be followed conveniently which may provide ideas for further catalyst design. For example, during such investigations it was established, that only the monohydroxo-monoaqua complex was a catalyst for this reaction, both [Rh(Me)3Cn] and [Rh(Me)(H20)2Cn] were found completely ineffective. The lack of catalytic activity of [Rh(Me)3Cn] is understandable since there is no free coordination site for ethylene. Such a coordination site can be provided by water dissociation from [Rh(Me)(OH)(H20)Cn] and [Rh(Me)(H20)2Cn] and the rate of this exchange is probably the lowest step of the overall reaction.The hydroxy ligand facilitates the dissociation of H2O and this leads to a slow catalysis of ethene polymerization. 

Consider the condensation polyesterification reaction between ethylene glycol, H0-(CH2)2-0H, and terephthalic acid, HOOC-Ph-COOH, each of which has an initial concentration of 1.0 mol/liter. Calculate the number average and weight average degrees of polymerization at 1, 5, and 20 hours. The forward reaction rate constant for the polymerization reaction is 10.0 liter/mol hr, and second-order, catalyzed kinetics can be assumed. 

As mentioned in Section 9.3, Jackson (141) has obtained estimates of the chain-transfer coefficient of the growing radical with polymer in the free-radical polymerization of ethylene, C,p, by choosing the value so as to fit the MWD. As the polymerization conditions for the polymers mentioned in Table 10.1 are not disclosed, it is necessary to choose typical conditions 220° C and 2000 atm will be selected. Under these conditions Ctp, the ratio of the rate constant for attack on polymer (per monomer unit) to that for propagation, in a homogeneous phase, was found to be about 4.0 x 10 3. This is in good agreement with the known transfer coefficients for the lower alkanes (160), when allowance is made for the differences in pressure and temperature (100). The relation between Ctp and k is ... 

Optical cells can also be used to investigate the kinetics of radical polymerization reactions under high pressure by means of the rotating sector method. Again, the apparatus is presented in Chapter 4.3.4. An example of the method for the evaluation of individual rate constants in radical polymerization of ethylene is given below. 

The rotating-sector method was applied to determine the individual rate constants of chain propagation and chain termination of the radical polymerization of ethylene [23,24]. The photo-initiator was diphenyldisulfide. First, the overall rate of polymerization was measured under steady illumination at pressures of 50 - 175 MPa and 132 - 199°C (Fig. 3.3-9). It increases first steeply and then less steeply with increasing pressure. At 175 MPa the rate of polymerization is ten times higher than at the low pressure of 50 MPa. 

Figure 3.3-10. Rate constants of chain propagation (left) and termination (right) of radical polymerization of ethylene. X, 189°C O, 153°C X, 132°C.

After an induction period, the polymerization rate reaches a maximum and then becomes almost constant for over 20 hours. The constant rate of polymerization of the homogeneous system indicates that living polymers are present in this case. Indeed, block copolymers of propylene and ethylene could be obtained with this homogeneous system when ethylene was dissolved in liquid propylene [see also, related experiments with the heterogeneous system (3/)]. 

It is interesting to note the effect of chromium content on reaction rate at high pressures (,—500 p.s.i.g.). Experiments (5) were carried out with normal air-activated catalysts (Figure 4). Catalysts were used with chromium contents ranging from 0.7 to 0.0005 wt. % of the total catalyst. Results of one-hour ethylene polymerization tests at 132°C. and 450 p.s.i.g. with these catalysts, activated at 500°C., are given. As the concentration of chromium was decreased, catalyst charge was increased to compensate for poisoning of catalyst sites by trace impurities and to keep total rate of production about constant. 

From the rate of polymerization rp0j measured at different pressures (Figure 3) an activation volume for the polymerization of ethylene catalyzed by metallocenes can be determined. For this purpose first an overall rate constant kpo] was evaluated from the relation... 

Table 7, Number of polymerization centers and values of propagation and transfer rate constants for ethylene polymerization... 

Table 10. Maximum concentration of active species and elementary rate constants for the polymerization of ethylene and a-olefins with supported catalysts... 

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