Kinetics of Long-Chain Branch Formation in Polyethylene - ACS

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Kinetics of Long-Chain Branch Formation in Polyethylene Michael D Jensen, Qing Yang, Youlu Yu, and Max Paul McDaniel ACS Catal., Just Accepted Manuscript • DOI: 10.1021/acscatal.7b03267 • Publication Date (Web): 30 Nov 2017 Downloaded from http://pubs.acs.org on November 30, 2017

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KINETICS OF LONG-CHAIN BRANCH FORMATION IN POLYETHYLENE by Michael D. Jensena, Qing Yangb, Youlu Yub and Max P. McDanielb* a) Polyolefins Technology Division, Formosa Plastics Corporation, Point Comfort, Tx 77987 b) Chevron-Phillips Research Dept., Bartlesville, OK 74004

* Correspondence should be addressed to:

[email protected]

ABSTRACT Long-chain branch (LCB) formation was measured in polyethylene homopolymers and 1-hexene-ethylene copolymers made using a variety of metallocene and chromium catalysts while reaction ethylene concentration was varied. Kinetic analysis of this data indicates a marked difference between LCB formation versus short-chain branch (SCB) formation from the incorporation of 1-hexene comonomer. SCB generation exhibits first-order dependence on [Comonomer/Ethylene] concentration whereas LCB creation does not, which indicates a different insertion pathway for the two. SCB formation follows the expected random intermolecular incorporation, whereas LCB generation is consistent with a different, and more selective, intra-molecular mechanism of macromer incorporation. The latter holds that, once terminated by an active site, macromer tends to remain coordinated to the site for a short time before either dissociation or insertion into a successor chain growing on the same site to form a LCB. In this way, structural characteristics of the catalyst can have major consequences for LCB formation while exhibiting comparatively little or no effect on SCB incorporation.

Keywords: ethylene polymerization, long-chain branching, metallocene, Phillips catalyst, SEC-MALS

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INTRODUCTION Long-chain branching (LCB) in polyethylene (PE) has a strong influence on the polymer physical properties and its presence or absence dominates the polymer molding behavior, controlling such characteristics as die swell in blow molding, orientation and bubble stability in blown film, sag resistance in extruded pipe, drums, and geomembrane, the ease of flow (shear thinning) and melt fracture in all molding processes, and other complex melt behavior. Thus, controlling LCB in PE is a matter of great commercial importance. It is widely accepted that long-chain branching in PE results from the incorporation of macromers (i.e. PE chains generated earlier and containing a terminal vinyl group) into a new growing PE chain [1,2,3,4,5,6,7,8,9]. That is, previously created polymer chains having a vinyl end-group re-insert into another growing PE chain, thus producing a long-chain branch, much like the incorporation of α-olefin comonomers generate short-chain branching (SCB). It is generally believed that such macromer incorporation is a random process, like the incorporation of comonomers (i.e., 1-hexene, 1-butene, or 1-octene). Random incorporation of macromers may indeed be possible in a solution process where the macromers are dissolved in hydrocarbons and therefore are mobile, like typical comonomers are dissolved and mobile during the manufacture of copolymers. However, in an earlier paper [10] we questioned how this can happen in a slurry or gas phase process, where the macromers are immediately immobilized into a solid matrix upon formation. In fact, polymers derived from solid-phase polymerization processes via heterogeneous catalysts usually tend to contain more LCB, not less [11,12,13]. Although much has been made of the presence of LCB in polymers derived from solution polymerization [14], often detected by 13C NMR [15], it is important at this point to establish a rigorous definition of LCB. In this and earlier papers we choose to define LCB as a branch long enough to have rheological significance, that is, longer than the critical entanglement length, which for PE is about 140 carbons [16,17]. Obviously, using this definition, NMR cannot be relied upon to measure LCB. Actually, most such reports of LCB using NMR are probably due to incorporated oligomers of less than 140 carbons with no rheological significance. We prefer to rely on rheological measurements and/or SEC-MALS (size-exclusion chromatography with multi-angle light scattering) to detect and quantify LCB, because they are more sensitive than NMR and much more industrially relevant. Therefore, to explain the presence of high amounts of LCB in PE derived through solidphase polymerization, we suggested in a previous paper [10] that another mechanism of LCB formation also operates which is not random, but is instead quite selective. We proposed that macromers generated on an active site tend to remain coordinated to that site, until they eventually either become incorporated into a new PE chain growing from that same active site, or irreversibly dissociate from the site. Thus, like the ancient Greek myth of Cronus, the active sites "eat their own offspring" selectively. However, and unlike soluble comonomers, if displaced from a site, macromers become further immobilized in the solid phase and thus probably have little or no possibility of later insertion. We called this pathway the intra-molecular mechanism of LCB formation to distinguish it from the random and more widely accepted intermolecular mechanism. The two ideas of LCB formation are illustrated in Scheme 1 below.

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Scheme 1 Inter-molecular (1) versus intra-molecular (2) mechanism of long-chain branch formation.

Evidence previously cited [10] in support of the intra-molecular mechanism included the following observations: 1) Metallocene in solution was shown to be visibly precipitated with the PE it formed, but it could be released from polymer precipitate by the addition of small amounts of 1-hexene, which probably competes with the coordinated macromer. 2) Metallocenes of many different structures possessing a suitable pendant vinyl moiety, strongly influence LCB formation, again probably by inhibiting macromer retention. 3) Other structural features of metallocenes also have a strong influence on LCB but no effect on SCB, such as homologous alkyl substituents in unbridged metallocenes and similar-substituents in bridged ones, as long as they are positioned toward the front of the metallocene, or away from the bridge. Thus, LCB and SCB formation were observed to be unrelated when homologous structures are compared, i.e. they do not always parallel one another as would be expected from comonomers or macromers in solution. These substituents were interpreted to interfere with prolonged retention of macromer. 4) When vinyl end-groups are considered to be mobile within the amorphous PE phase, then macromer incorporation is calculated to be much more efficient than the incorporation of comonomers, i.e. LCB formation is (otherwise inexplicably) much easier than SCB formation at equal concentrations. 5) Macromers generated on one active site do not seem to be incorporated by other neighboring active sites. 6) And finally, the retention of olefins was also used to explain >1st order polymerization kinetics, and the "comonomer effect" in which the addition of small amounts of olefins, even some non-incorporating olefins, greatly facilitated the incorporation of ethylene [18,19,20]. The amount of time that a macromer must remain coordinated to the active site is actually quite small. For the three arms of the branch to be rheologically relevant, which is our definition of a long-chain branch, a new growing chain must insert at least 70 ethylene units (140 carbons) before insertion of the coordinated macromer. Under typical commercial reaction conditions, even sluggish zirconocene dichloride yielded turnover values of in excess of 104 Et/Zr/s [21]. At this rate, the minimum coordination time would be less than 1/100th of a second. The intra-molecular mechanism can be considered as an extension of the trigger mechanism first proposed by Ystenes [22,23] to explain the higher order kinetics he observed for propylene polymerization over Ziegler catalysts. He suggested that the chemisorption of propylene on one vacancy on a titanium atom could facilitate or "trigger" the insertion of propylene coordinated to a different vacant orbital on the same titanium atom. The intramolecular mechanism discussed herein is similar, except that it allows for two different types of olefins, ethylene and an α-olefin (comonomer or macromer), to be coordinated simultaneously, each with a different binding strength because of their differing electron donation ability. In this paper, we have studied the kinetic response and the LCB changes resulting from varying reactor ethylene concentrations using several different metallocene and chromium catalysts. We then compare the observed behavior to that modeled from each mechanism to gain further insight into the dominant pathway operating for LCB and SCB formation.

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EXPERIMENTAL Catalysts Most of the metallocenes used in this study were obtained from Boulder Scientific: racEBI, rac-bis(indenyl)(ethane-1,2-diyl)zirconium dichloride; zirconocene dichloride Cp2ZrCl2, (nBuCp)2ZrCl2, so-called constrained geometry catalyst (CGC) [(C5Me4)Si(Me)2(Nt-Bu)]TiCl2, and Ewen’s compound, (H3C)2C(Fl)(Cp)ZrCl2. Derivatives of Ewens-type complexes were synthesized according to [24,25]. The activators used were two different fluorided silica-alumina supports and a sulfated alumina, all made according to references [21,26,27,28,29]. The final catalyst was made by adding the three components (activator, alkylaluminum and metallocene) directly to the reactor. Chromium catalysts were made according to reference [30]. Polymerization Ethylene homopolymers and copolymers made in this study were prepared in a slurry process by contacting the three catalyst components with ethylene and sometimes 1-hexene in an isobutane medium at 80°C to 100°C as indicated, usually the lower temperatures for copolymerization. The medium and temperature were thus selected such that these polymers were produced as solid particles that were cleanly recovered in that form without swelling that could affect mass transport. The ethylene was obtained from Dow Corporation as polymerization grade, and was further purified over activated 13X molecular sieve. Isobutane was degassed by fractional distillation and also dried over molecular sieves. Polymerization reactions were carried out in a 2.2L or 4L stainless steel laboratory reactor. After being purged at 110-120°C with nitrogen for at least 30 minutes, about 0.01-0.2 g of activator support was charged to the reactor under nitrogen, followed by 0.001 to 0.003 g of metallocene in toluene solution, and then 0.5 mL of 1M trialkylaluminum (triisobutylaluminum unless otherwise noted). Next about half of the liquid isobutane charge was added, followed by 1-hexene if used, then followed by the rest of the isobutane liquid. 1.2L of isobutane liquid was added to the 2.2L reactor, and 2L isobutane to the 4L reactor. The reactor was subsequently heated to the desired temperature, with stirring at 500-700 rpm, and then ethylene was added to the reactor and fed on demand to maintain a fixed total pressure, which varied between runs to obtained a variety of ethylene concentrations. The reactor was maintained at the specified temperature within +/- 0.5 degrees C for about 30 minutes and then the isobutane and ethylene were vented from the reactor, which was opened, and the polymer was collected as a dry powder. The reaction was clean, i.e. without wall scale, particle swelling or clumping that could impede mass transport. The ethylene concentration cited herein is in moles of dissolved ethylene per liter of reaction solvent (isobutane). Of course, the isobutane solvent volume changes significantly as it dissolves more ethylene, and as temperature is varied. These effects have been taken into account using the Soave-Redlich-Kwong equation of state [31], which has been found to be quite accurate in the design and operation of commercial loop reactors. Small amounts of 1-hexene comonomer were used in some experiments. Such additions were made to the isobutane solvent at the beginning of the run. This method was deliberately chosen because it was the presence of 1-hexene that was being studied, as a ligand, rather than its incorporation as a comonomer, which was quite small in all of these experimental runs. We believe that this was the correct protocol in this context, however, in many other runs (not presented herein) and in long commercial practice, the 1-hexene was added continuously, with similar results on LCB.

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Rheology Measurements PE powder was stabilized with 0.1 wt% BHT dissolved in acetone and then vacuum dried before molding. Samples were compression molded for viscosity measurements at 182°C for a total of three minutes. They were first allowed to melt at a relatively low pressure for one minute and then subjected to a high molding pressure for an additional two minutes. The molded samples were then quenched in a cold (room temperature) press. 2 mm x 25.4 mm diameter disks were stamped out of the molded slabs for rheological characterization. Small-strain oscillatory shear measurements were performed on a Rheometrics Inc. RMS-800 or ARES rheometer using parallel-plate geometry over an angular frequency range of 0.03–100 rad/s. The test chamber of the rheometer was blanketed in nitrogen in order to minimize polymer degradation. The rheometer was preheated to the initial temperature of the study. Upon sample loading and after oven thermal equilibration, the specimens were squeezed between the plates to a 1.6 mm thickness and the excess was trimmed away. A total of approximately 8 minutes elapsed between the time the sample was inserted between the plates and the time the frequency sweep was started. Strains were generally maintained at a single value throughout a frequency sweep but larger strain values were used for low viscosity samples to maintain a measurable torque. Smaller strain values were used for high viscosity samples to avoid overloading the torque transducer and to keep within the linear viscoelastic limits of the sample. The instrument automatically reduces the strain at high frequencies if necessary to prevent overloading the torque transducer. These data were fit to the Carreau-Yasuda equation [16,32] to determine zero shear viscosity (η0), relaxation time (τ), and a measure of the breadth of the relaxation time distribution (CY-a). Molecular Weight Molecular weights and molecular weight distributions were obtained from a a Polymer Labs PL220 Gel Permeation Chromatograph using 1,2,4-trichlorobenzene (TCB) as the solvent with a flow rate of 1 mL/min at a temperature of 140°C. BHT at a concentration of 0.5 g/L was used as a stabilizer in the solvent. An injection volume of 400 µL was used with a nominal polymer concentration of nominally 1 mg/mL (at room temperature). The column set consisted of three Waters Styragel HMW 6E columns plus a guard column. A broad-standard integral method of universal calibration was used based on a Phillips Marlex BHB 5003 broad linear polyethylene standard. Parameter values used in the Mark-Houwink equation ([η]= KMa) for polyethylene were K = 39.5X10-3 mL/g and a = 0.726. Measurement of LCB Content To be rheologically significant, a branch must be longer than the critical entanglement length, which for polyethylene is known to be about 140 carbons [33,34]. It is very difficult to estimate LCB levels, position, or length, in commercial PE products. NMR cannot be used for this purpose. Two methods were used complimentarily in this study: 1) rheological via the Janzen-Colby relationship, and 2) SEC-MALS (size exclusion chromatography multi-angle light scattering). The former is very sensitive to low LCB levels, especially in the high-MW part of the MW distribution. The latter can detect LCB at high levels, and can even provide an LCB distribution within the higher MW half of the MW distribution. LCB Detection by Rheology: Melt rheology is very sensitive to the effects of LCB, even at trace levels [35,36]. Chains containing LCB entangle in the melt phase, profoundly increasing the low shear melt viscosity. Therefore, the most sensitive method of gauging LCB is to look for increases in low shear melt viscosity that go beyond what would be expected from linear

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polymers of the same molecular weight. Like many other polymers, PE having no LCB follows a log dependence of melt viscosity on molecular weight. If the log of the extrapolated zero-shear viscosity (designated η0) is plotted against the log of the weight-average molecular weight (MW), a straight line is obtained having a slope of 3.4. The presence of LCB is indicated by deviations from this “power law” or Arnett line [16,33,34,37]. Many “Arnett plots” were obtained in this study and some are presented in the supporting information. The Arnett line running diagonally near the bottom and labeled “0 LCB/C”, indicates the position of polyethylene having no longchain branches. Deviations above the line indicate that traces of LCB are present. The effect of LCB on viscosity is more pronounced at high MW than at low MW, because entanglements are less easily overcome during flow. This relationship was defined by Janzen and Colby [33], giving rise to the curved contour lines for given LCB levels on these plots. This relationship provides a helpful reference to compare LCB levels in polymers at different molecular weights. At very low MW, for example 10 kg/mol, the effects of LCB become barely noticeable. The Janzen-Colby method provides only an average or “effective average” LCB content. For example, a large amount of LCB in the low-MW can be rheologically equivalent to a tiny amount in the high-MW part of the MW distribution. Thus, the effect of MW breadth and LCB distribution can be important. Consequently, a small correction according to Yau [37] was applied in some cases where the polydispersity was higher than the usual 2.0. LCB Analysis by SEC-MALS: LCB content was also obtained through a combined method of size exclusion chromatography (SEC) with multi-angle light scattering (MALS). In the SECMALS system used in this study [38], a DAWN EOS photometer (Wyatt Technology, Santa Barbara, CA) was attached to a Waters 150-CV plus GPC system (Waters, Milford, MA) or a PL-210 GPC system was used (Polymer Labs, now part of Varian) through a hot-transfer line controlled at 145°C. Degassed mobile phase, 1,2,4-trichlorobenzene (TCB) that contained 0.5 wt % of BHT was pumped through an inline filter before being passed through the SEC column bank. Polymer solutions injected into the system were brought downstream to the columns by the mobile phase for fractionation. The fractionated polymers first eluted through the MALS photometer where light scattering signals were recorded before being passed through the differential refractive index detector (DRI) where their concentrations were quantified. The DAWN EOS system was calibrated with neat toluene at room temperature to convert the measured voltage to intensity of scattered light. During the calibration, toluene was passed through a 0.02 µm Whatman filter and directly into the flowcell of the MALS. At room temperature, the Rayleigh ratio at the given conditions was 14,060/cm [39]. A narrow polystyrene (PS) standard (American Polymer Standards) of MW 30 kg/mol and a concentration of 5-10 mg/mL in TCB was employed to normalize the system at 145°C. At the given chromatographic conditions, the radius of gyration (Rg) of the polystyrene (PS) was estimated to be 5.6 nm using the Fox-Flory equation coupled with its Mark-Houwink exponent in the chromatographic conditions [40,41]. At a flow rate set at 0.7 mL/min (actual flow rate: 0.60 – 0.65 mL/min), the mobile phase was eluted through three 7.5 mm x 300 mm 20-µm mixed A columns (Polymer Labs, now an Agilent company). PE solutions with nominal concentrations of 1.0-1.2 mg/mL were prepared at 150°C for 3-4 h before being transferred to GPC injection vials sitting in the carousel heated at 145°C. In addition to a concentration chromatogram, seventeen light scattering chromatograms at different angles were also acquired for each injection. At each chromatographic slice, both the absolute molecular weight (MW) and the root mean square radius, also known as radius of gyration, Rg, were obtained from Debye plots [42]. The linear PE reference employed in this study was HiD9640, a high-density PE with broad MWD (Chevron Phillips Chemical). The refractive index increment dn/dc used in this study was 0.097 mL/g for PE dissolved in TCB at 135°C [43]. At the run temperature, 145 °C, it was found that dn/dc equals to 0.095 mL/g by 6


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assuming refractive index changes linearly as a function of temperature and the polymer standard is 100% soluble.

RESULTS AND DISCUSSION 1. Theoretically Predicted Response To interpret the experimentally observed insertion behavior, it is necessary to first consider what response to varied ethylene concentration would be predicted from the two mechanisms of LCB formation. Therefore, in Schemes 2-4 various mechanisms were considered and the resulting kinetic rate expressions were presented for incorporation of ethylene versus macromer. In both the experimental polymerization runs and the theoretical treatment, ethylene concentration was held constant during each run but it was varied between runs within an experimental data set, which mimics commercial practice. Macromer vinyl endgroups were assumed to be semi-mobile inside the amorphous phase of the polymer, where the catalyst active sites were also assumed to reside. If each chain contains one vinyl end-group, and if the reaction volume is considered to be the amorphous regions of the polymer, then the concentration of vinyl end-groups per unit volume is unchanging with time. Therefore, the macromer concentration was considered to be constant during each polymerization run, and (ignoring minor changes in PE molecular weight) it was also assumed to be constant between runs of an experimental data set. In each scheme, the starting point is Cp2ZrCl2. After + activation, i.e. after alkylation and then ionization to yield the cationic species [Cp2Zr-R] , it is assumed to possess one (for the inter-molecular pathway) or two (for the intra-molecular pathway) coordination vacancies. Rate equations were then derived for the next insertion step, i.e. all pathways that involve monomer, comonomer or macromer incorporation. Inter-Molecular Pathway: Scheme 2 shows the inter-molecular (random) model and the resultant rate expression. This model assumes first order dependence on ethylene and macromer, which is consistent with the accepted Langmuir-Hinshelwood pre-adsorption before insertion. Thus, the inter-molecular model treats both macromer and ethylene identically, as though adsorption of both is random. Only the concentrations, and the values of k1 and k2, distinguish one olefin from the other in the theoretical treatment.

Scheme 2 Mechanism and rate expression for the inter-molecular route to long-chain branch formation.

In Figure 1A the expected ethylene to macromer insertion ratio (Et/LCB) is plotted against ethylene concentration in the reactor. The model in Scheme 2 produces straight lines passing through the origin in typical first-order behavior. Three lines are shown, illustrating

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three different sets of k1 & k2 values, chosen to represent hypothetical catalysts of different responses. That is, the upper line represents poor efficiency of macromer incorporation, whereas the lower line represents high efficiency. Of course, in an actual experiment where the ethylene concentration is raised, a small increase in molecular weight is often observed, which could decrease the vinyl end-group concentration slightly. In the derivation in Scheme 2 this effect has been considered small and therefore ignored. If considered, however, it would decrease the slope of the lines in Figure 1A slightly, but it would not change the main characteristic to be noted in Figure 1A, which is that these lines always pass through the origin.

Figure 1 Expected ethylene to macromer incorporation ratio as a function of the LCB mechanism.

Intra-Molecular Pathway (First-Order): Scheme 3 illustrates the simple intra-molecular pathway and shows the expected rate expression for the ethylene to macromer insertion ratio. In this version of the intra-molecular mechanism, first-order dependence on both ethylene and macromer is assumed. This pathway starts with a macromer already coordinated to the active site. Ethylene is then adsorbed on the remaining vacant orbital which then "triggers" one of three events: 1) ethylene insertion (k1, chain growth); 2) macromer insertion (k2, LCB formation), or 3) macromer displacement (Keq), which is then followed by further ethylene adsorption and insertion (k3, chain growth). The macromer displacement route in Scheme 3 is probably not reversible. Once the macromer dissociates from the site, it probably cannot easily re-adsorb, because it becomes tied into the solid polymer matrix and therefore immobile. Nevertheless, note that the first

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species in Scheme 3, containing coordinated macromer, is continuously replenished by termination of growing chains. Therefore, the displacement pathway is treated mathematically as an equilibrium with a constant of Keq. In Figure 1B the expected ethylene to macromer insertion ratio (Et/LCB) is plotted against ethylene concentration in the reactor for the simple intra-molecular pathway. Again, straight lines are obtained, but this time they do not pass through the origin. Instead they have a Y-intercept, which distinguishes this pathway from the inter-molecular mechanism in Figure 1A. Three lines are shown in Figure 1B, illustrating three different sets of k1,, k2,, k3, and especially Keq values. This again represents three hypothetical catalysts having different responses to ethylene concentration. The value of Keq determines how easily the macromer is displaced by ethylene, with the upper line (high Keq) representing weak coordination and easy displacement, and the lower line (low Keq) representing strong macromer coordination. Notice that low Keq can lead to an almost horizontal (pseudo-zero order) line.

Scheme 3 Mechanism and rate expression for the intra-molecular route to long-chain branch formation.

Intra-Molecular Pathway (Second Order): As we shall see below, a simple modification of Scheme 3 produces a better fit to much of the experimental data. This modification introduces second-order ethylene dependence into the third (k3) pathway in Scheme 3. Second order dependence has sometimes been reported, and greater than first order dependence is often observed, for ethylene homo-polymerization over various catalysts [22,44,45,46,47,48,49,50]. This could be interpreted as further evidence that the active site is capable of coordinating two ethylene molecules simultaneously. As noted in our earlier report [10], coordination of the site to α-olefin (either comonomer or macromer) provides increased electron density which was shown to stabilize the site, and facilitate ethylene insertion. Thus, coordination to α-olefin was shown to be more stabilizing for the active site than to ethylene, and therefore, as also reported by other authors [19,51], the addition of α-olefin can convert second-order ethylene dependence into pseudo first-order. This is the result of α-olefins being better electron donors to an electron-deficient metal. Because the lower left species in Scheme 3 has lost its coordinated macromer, it could then exhibit

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second-order dependence on ethylene again, and hence a modification to Scheme 3 could be warranted. This would also explain why intermediate order dependence (between 1st and 2nd order) is often observed. The resulting second-order treatment of Scheme 3 produces a similar final outcome, except that the ethylene term is now squared. This modified expression (Equation 1) yields a different ethylene to macromer (Et/LCB) insertion response, which is illustrated in Figure 1C. These lines are now curved, and again they do not pass through the origin, allowing for clear distinction from the inter-molecular mechanism in Scheme 2. Ethylene/LCB = (k1 + k3[Et]2Keq) / k2

Eq 1

Intra-Molecular Pathway, Copolymerization: α-Olefin comonomers, such as 1-hexene which has been used occasionally in this report, are often added to the reactor to produce PE containing short-chain branching (SCB), which disrupts the crystallinity and enhances flexibility and toughness. From commercial experience, the incorporation of such comonomers is known to be proportional to the comonomer to ethylene concentration ratio in the reactor for nearly all catalysts. This is equivalent to the behavior illustrated in Figure 1A since the Et/SCB insertion ratio passes through the origin. Thus, it is clear that SCB incorporation occurs through the intermolecular pathway. It has sometimes been reported that adding α-olefins to the reaction can also affect the degree of LCB formation [4,8]. This is not predicted by the inter-molecular mechanism, according to which the macromer incorporation should be independent of SCB incorporation. Consequently, under the inter-molecular mechanism, the Et/LCB insertion ratio found in the polymer should be governed only by the ethylene and macromer concentrations. However, in the intra-molecular mechanism it is conceivable that LCB formation could be influenced by comonomers like 1-hexene. Scheme 4 shows the intra-molecular pathway in the presence of comonomer. Unfortunately, the pathway becomes more complex with the addition of comonomer. The direct growth reactions, e.g. k1 and k2, are analogous to k1 in Scheme 3, except that growth can now occur through the addition of either ethylene (k1) or comonomer (k2). In each case a first-order dependence on monomer has been assumed. Similarly, macromer incorporation can be triggered by coordination of ethylene (k3) or comonomer (k4). Macromer can also be displaced by either ethylene (Keq1) or comonomer (Keq2). Both are again treated as an equilibrium, even though the macromer dissociation is probably irreversible, because the species is regenerated through chain termination. From there, growth can occur through subsequent ethylene (k5 and k7) or comonomer (k6) insertion. What is different in Scheme 4 is that both comonomer and macomer are more electron donating than ethylene, so that coordination to the Zr is expected to be stronger than Zr coordination to ethylene. Hence, displacement of macromer by comonomer is expected to be high compared to displacement by ethylene as shown in Scheme 3. This would tend to lower LCB formation. On the other hand, comonomer may also be a strong trigger for macromer incorporation, since it too is a relatively strong electron donor, which would enhance the k4 reaction. This would tend to enhance LCB formation. Consequently, LCB formation could be either decreased or increased, as has been reported for different metallocenes. Thus Scheme 4 becomes complex enough to obtain many differently shaped curves, depending on the choice of rate constants. However, a few judgments about the relative magnitude of some rate constants can be made, based on known facts. For example, given the steric differences between ethylene and α-olefin, and the known lower comonomer incorporation efficiency compared to ethylene, one might conclude that k2 should be significantly smaller than k1, and likewise for k6 relative to k5. Similarly, k7 should be approximately equal to

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ACS Catalysis

k1, and both of these somewhat larger than k5,due to the increased electron donation by a coordinated α-olefin compared to ethylene. When sterically permitted, k4 is presumably greater than k3, again due to the increased electron donation of coordinated comonomer. And the measured LCB concentration, in addition to the enhancement in activity by comonomer, helps in determining the magnitude of k3 and k4 relative to k1, k5 and k7. When these relationships are taken into account, some representative curves are shown in Figure 1D.

Scheme 4 Mechanism and rate expression for the intra-molecular route to long-chain branch formation in the presence of 1-hexene comonomer assuming first-order dependence on ethylene.

2. Experimentally Observed Behavior In the following studies, various metallocenes, in combination with several solid acid activators, were tested in ethylene polymerization experiments in which the ethylene concentration in the reactor was varied. The polymers so obtained where then analyzed for LCB content by SEC-MALS [52], or in some cases also by rheology using the Janzen-Colby method [33,34]. Thus, the ethylene to macromer insertion rate could be obtained and plotted as a function of ethylene concentration for comparison to the various theoretical mechanisms described in the preceding section. Complete details of the experimental results have been made available to the reader for each study. However, to reduce journal space, information that was not considered central to the main point being made is shown in the supporting information. These graphs and tables are always designated by the prefix "S".

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Page 12 of 27

Homopolymer from rac-EBI: Homopolymerization was first conducted at 80°C using Brintzinger’s complex, i.e. racemic ethylene-bridged bis-indenyl zirconocene dichloride, commonly referred to as EBI. Fluorided silica-alumina was used as the ionizing agent, and triisobutylaluminum as the cocatalyst. During polymerization tests, the ethylene concentration was varied over a wide range. These polymers were then analyzed for LCB concentration using two methods, e.g. the Janzen-Colby rheological method [33] and the SEC-MALS method [52]. Table 1 is a summary of all the results obtained in these experiments. The reaction rate was found to be a little higher than first order in ethylene concentration, producing a curved line through the origin which is shown in Figure 2. Table 1 Change in activity and polymer characteristics as a function of ethylene concentration during the production of homopolymer at 80°C. Ethylene Concentration, mol/L

0.38

0.38

0.82

1.27

1.72

Activity, kgPE/g-h

0.27

0.33

0.75

1.29

2.10

Melt Index 2.16 kg weight, g/10min

2.62

2.45

0.67

0.35

0.19

21.6 kg weight, g/10min

65.9

61.3

18.7

9.42

5.34

MW Averages M N , kg/mol

29.3

32.4

44.1

56.8

62.1

M W , kg/mol

110

112

147

173

197

M Z , kg/mol

316

314

349

374

430

Transfer to Zr, %

66%

66%

47%

36%

30%

MW Distribution M W /M N

3.7

3.5

3.3

3.0

3.2

2.9

2.8

2.4

2.2

2.2

M Z /M W Rheology, Janzen-Colby JC-α, LCB/106 C Ethylene to LCB molar ratio

12.4

12.3

9.4

5.9

5.1

40,242

40,802

53,143

84,106

97,844

SEC-MALS Peak, LCB/106 C Ethylene to LCB molar ratio

70

68

44

26

20

14,285

14,705

22,726

38,461

49,999

Figure 2 Activity and PE molecular weight (number average) from EBI as a function of ethylene concentration during the production of homopolymer at 80°C.

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ACS Catalysis

Scheme 5 Chain transfer by β-H transfer to Zr (above) or to monomer (below).

Also shown in Figure 2 is the number-average molecular weight as a function of ethylene concentration. The line, which is a remarkably good fit to the MW data, was produced under the assumption that all chain transfer was either to zirconium or to ethylene, as depicted in Scheme 5. The upper pathway is independent of monomer concentration whereas the lower one is dependent. Since chain growth is also dependent on ethylene, termination to Zr produces a dependence of MW on ethylene concentration, whereas termination to ethylene does not. Thus, at the lowest ethylene concentration in these experiments, chain transfer was about 64% to zirconium and 36% to ethylene, and it was about 25% to Zr and 75% to ethylene at the highest ethylene concentration. The equation can be written: MN = Kinsertion / Ktermination

where

Ktermination = KZr + [Et]*KEt

Eq 2

Supplemental Figure S1 shows the single-site molecular weight distributions obtained, and how they shifted with ethylene concentration. The broadened MW distribution is a result of the high LCB formed. This occurs even for single site catalysts, because the act of inserting a long-chain branch significantly increases the MW of the now-branched chain. Consequently, LCB tends to concentrate into the high-MW, broadening the distribution on the high-MW side. This is always observed for metallocenes that produce LCB. The effect is not true of SCB however. Figure S2 shows the Janzen-Colby plot from which LCB values were obtained and Figure S3 shows how the radius of gyration for each polymer varied with reactor ethylene concentration. Finally, Figure S4 shows the SEC-MALS distribution of LCB as function of molecular weight. Figure 3 presents the Et/LCB insertion ratio obtained from both methods of LCB analysis used in this study, SEC-MALS and rheological. Both the LCB concentration itself and the derivative Et/LCB insertion ratio are plotted as a function of reactor ethylene concentration. From Figure 3, it is immediately clear that the Et/LCB ratio does not go through the origin as required by the inter-molecular mechanism (Figure 1A). Instead Figure 3 resembles the behavior predicted from the intra-molecular pathway in Figure 1C, which includes second order dependence. This is another strong argument in favor of the intra-molecular mechanism as the dominant source of LCB in these polymers which were obtain through a solid-phase process. Although the trends derived from the two methods of LCB analysis are identical, the absolute values of LCB obtained are quite different. This is an inevitable consequence of what the two tests are measuring. The rheological Janzen-Colby method provides an average LCB content over the entire polymer, hence the LCB values are lower. In contrast, SEC-MALS is only sensitive to the highest MW fractions of the polymer, in which the LCB tends to be concentrated. This is because the act of adding a branch to a chain increases its mass. This biases the measurement in favor of the high MW region where SEC-MALS is most valid. In

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Figure 3 it is the highest LCB concentration measured that is plotted, but, as seen in the figure, these results provide a valid measure of the trend of Et/LCB incorporation. A second run was made with EBI at 80°C but using a different, more active, fluorided silica-alumina and the results of this test are shown in supporting Figures S5-S7. Very similar curves were generated and again (as in Figure 3) the SEC-MALS plot of Et/LCB against reactor ethylene concentration did not pass through the origin, which is inconsistent with the intermolecular pathway. Figure S7 shows the ethylene to macromer incorporation ratio obtained from SEC-MALS analysis. Again, the shape is a curved line, intersecting the y-axis at about 5000 Et/LCB, very similar to Figure 3. This result is again inconsistent with LCB formation through a random inter-molecular mechanism. But it is very similar to curves in Figure 1B or 1C, which is indicative of LCB formation through the intra-molecular pathway.

Figure 3 Two methods of LCB detection in homopolymers produced with EBI at varying ethylene concentration.

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ACS Catalysis

Copolymer from rac-EBI: In still another series of tests, the same experiment was conducted using the same metallocene (EBI), solid acid activator, and cocatalyst as was used above in the homopolymer tests represented in Figures 2 and 3. The only difference was that a small amount of 1-hexene was added to the reactor in a constant concentration of 0.11 mol/L. The details of the results are presented in the supporting information. Table 2 summarizes all the results from this test. Table 2 Change in activity and polymer characteristics as a function of ethylene concentration during the production of copolymer (80°C, 1-hexene: 0.11 mol/L). Ethylene Concentration, mol/L

0.40

0.85

1.30

1.74

Activity, kgPE/g-h

0.39

1.54

2.10

2.81


3.92

0.01

0.01

0.05


143

3.47

1.91

4.41

Average Molecular Weight M N , kg/mol

19.8

33.8

38.1

41.0

M W , kg/mol

152

225

250

244

M Z , kg/mol

915

879

798

693

7.7

6.7

6.6

6.0

6.0

3.9

3.2

2.8

Melt Index

Molecular Weight Distribution M W /M N M Z /M W 6

SEC-MALS Peak, LCB/10 C Ethylene to LCB molar ratio

150

155

149

125

6666

6451

6710

7999

1-Hexene Incorporated, mol%

3.58

1.66

1.29

0.90

26.9

59.4

76.6

110

Ethylene to 1-hexene molar ratio

Note that the activity is higher this time due to the presence of comonomer. This is the comonomer effect in which ethylene insertion is enhanced by the presence (probably the coordination) of a α-olefin, which is a better electron donor than ethylene. Plots of these variables are shown in the supporting information. Figure S8 plots the activity against reactor ethylene concentration, as in Figure 2 above, but this time a straight line is obtained rather than a curve, but again passing through the origin. This indicates that the presence of comonomer has changed the dependence on ethylene to first order, consistent with two extra vacancies, not one. The number-average MW of the polymer is also plotted in Figure S8, which is similar response to that in Figure 2. A curve based on Equation 2 is again fit to the experimental MW values. By this treatment, about 70% of chain transfer was calculated to be to zirconium at the lowest ethylene concentration in this study, and about 33% at the highest ethylene concentration. The melt viscosities (MI and HLMI in Table 2) are a result of two competing forces in this series. With increasing ethylene concentration, MW rises, which tends to increase the viscosity, but LCB declines, which tends to lower the viscosity. The MW distributions are also shown in Figure S9, and the SEC-MALS-derived LCB content in Figure S10, both as a function of molecular weight. There is very little change in the amount of LCB found in the polymers made at the lowest ethylene concentrations (the fourth point is not shown because it overlapped).

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The ethylene to LCB insertion ratio found in the polymer is plotted in Figure 4 as a function of ethylene concentration. It is almost flat, as predicted for copolymers in Figure 1D which was derived from Scheme 4. Once again, this is strong evidence for the intra-molecular mechanism of LCB formation. Comparison of Figure 4 with Figure 3 indicates that in this experiment the addition of 1-hexene increased the amount of LCB present.

Figure 4 Ethylene to macromer and ethylene to 1-hexene incorporation ratios as a function of reactor ethylene concentration. Copolymers made using EBI at 80°C with 0.11 mol/L 1-hexene.

However, it is revealing to consider the short-chain branch (SCB) level from incorporation of 1-hexene as measured by 13C NMR in these experiments. The ethylene to SCB insertion ratio (Et/Hex) is also plotted in Figure 4, and is quite different from the ethylene to macromer insertion ratio (Et/LCB). Because this series of tests was made with a constant concentration of 1-hexene in the reactor, the amount of 1-hexene incorporated into the polymer was purely a function of the varying ethylene concentration in the reactor. Figure 4 shows this Et/Hex insertion ratio is first order as expected, and as predicted by the inter-molecular mechanism. There is a straight line passing through the origin. To repeat for emphasis, the 1hexene incorporation is first order whereas the macromer incorporation is almost flat. This indicates that the two comonomers incorporate in different ways, e.g. one via the intra-molecular process and the other via the well-known inter-molecular process. Thus, one must conclude that the two comonomers are not equivalent in their reactivity. Mechanistically, macromer is not just a longer comonomer. The flat (almost zero-order) response of Et/LCB to ethylene in Figure 4 suggests the diminishing relative importance of the Keq1 reaction in the presence of 1-hexene. This could be due to accelerated incorporation of macromer through k4, or enhanced desorption through Keq2. It is interesting to compare Figure 4 (copolymer) to Figure 3 (homopolymer). The copolymer LCB content is generally similar at low ethylene concentration, but significantly higher than homopolymer at high ethylene concentration. This again would be consistent with a loss of the ethylene dependence that comes from Keq1. Generally, depending on the stereoelectronic

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ACS Catalysis

requirements of the metallocene, the competing reactions of k4 and Keq2 could account for higher or lower LCB content in the copolymer compared to the homopolymer. Zirconocene Dichloride: In another series of experiments, simple zirconocene dichloride was used to make both homopolymers at 90°C and copolymers at 85°C, both at varying ethylene concentrations. The activator was fluorided-silica-alumina and the cocatalyst was triethylaluminum. The activity of the catalyst is plotted in the upper half of Figure S11. During homopolymerization, the dependence of activity on ethylene concentration was found to be higher than first order. However, when copolymer was introduced at a constant 0.07 mol/L, the kinetic response changed to simple first order. In Figure 5 the ethylene to 1-hexene insertion ratio (Et/SCB) for copolymers is plotted against reaction ethylene concentration. As expected, first order dependence was obtained. That is, the ethylene to 1-hexene ratio (Et/SCB) in the polymer (as determined by C13 NMR) shows first-order dependence on the ethylene concentration in the reactor. This is normal for almost all catalysts, supporting a random inter-molecular pathway. Also plotted in Figure 5, however, is ethylene to macromer insertion ratio (Et/LCB), as determined by SEC-MALS, for both homopolymers and copolymers. Both lines have a Yintercept, which is inconsistent with the inter-molecular pathway. Instead, they do resemble the plots predicted by the intra-molecular mechanism in Figure 1B (homopolymer, first order) and Figure 1D (copolymer, first order). Notice also that in these experiments, unlike those with EBI above, the addition of 1-hexene lowered LCB content (higher Et/LCB ratio).

Figure 5 Comparison of the ethylene to 1-hexene insertion ratio (Et/SCB) to the ethylene to macromer insertion ratio (Et/LCB) for both homopolymers and copolymers made with zirconocene dichloride, all as a function of ethylene concentration in the reactor.

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(n-BuCp)2ZrCl2: By substitution of a butyl moiety for a hydrogen on each ring, a much more active catalyst is obtained, presumably as a consequence of better charge separation in the activated ion pair. This compound, first introduced by Exxon Corp. [53], is used commercially by some companies to produce PE film grades. Its popularity derives mainly from the high activity it displays. However, although not appreciated by many of its users, this metallocene could not be used for such applications if it produced significant LCB content, which causes resin processing and property issues in these applications vs. their linear PE counterparts. Therefore, it was of interest to study the response of this metallocene too. Homopolymers and copolymers were produced with (n-BuCp)2ZrCl2 using fluorided silica-alumina and a number of other activators. Ethylene concentration was varied in the usual way. However, testing of the polymer by both rheological and SEC-MALS methods indicated no detectable long-chain branching from any of these polymers, even those made at lowest ethylene concentration. Apparently, the combination of being unbridged and possessing an alkyl substituent, both of which would reduce the electron deficiency on the Zr (i.e. its Lewis acidity), make it difficult to incorporate macromer. Steric repulsion resulting from a rotating nBuCp ring undoubtedly inhibits macromer retention and incorporation, but without significantly affecting comonomer incorporation. These observations are consistent with the intra-molecular mechanism of LCB formation, which depends on retention of the coordinated macromer for a significant time interval as another chain grows on the same site. In contrast, short-chain branching, being intermolecular, requires a configuration of butyl substituents that permits association and insertion at any time during chain growth. Ewen's Compound: Similar studies were conducted using Ewen's compound, (H3C)2CFluCpZrCl2. This bridged-metallocene presents an even more open, more Lewis acidic, cationic site than rac-EBI. First homopolymer was made at 90°C using the same fluorided silica-alumina activator and triisobutylaluminum cocatalyst used earlier. The supporting information provides various plots for this data. Figure S12 shows the activity plotted against ethylene concentration, a slight curve indicating a little higher dependence on ethylene concentration than first order. Figure S13 shows the MW plotted against ethylene, which was almost flat in this case, indicating very little contribution from beta-hydride termination to metal. Figure S14 shows the GPC analyses, which are typical single site MW distributions, approximately constant with ethylene concentration. LCB concentration is illustrated by the rheological plot in Figure S15. It shows how the zero-shear viscosity decreased with rising ethylene concentration, despite a relatively constant MW. The zero-shear viscosity is obtained by an extrapolation using the Yasuda-Carreau equation [32]. Unfortunately, in this case that extrapolation is too distant to obtain accurate values. Nevertheless, it is qualitatively obvious from Figure S15 that LCB increases as ethylene concentration decreases. For comparison, instead of the rheological Janzen-Colby method [33], using SEC-MALS [52] for analysis of LCB produces the plot obtained in Figure S16, which shows the LCB concentration plotted against MW for polymers made at different ethylene concentrations. Using this data, the upper half of Figure 6 plots the resulting LCB concentration obtained as a function of reactor ethylene concentration. Also plotted in upper Figure 6 is the ethylene to macromer insertion ratio (Et/LCB) derived from SEC-MALS. Note that again the Et/LCB ratio does not pass through the origin, but instead it has an intercept at about 4000 Et/LCB. This is yet another indication that macromer incorporation does not take place through the intermolecular mechanism, but rather through another means, such as the intra-molecular pathway. And, as might be expected when compared to EBI in figure 3, Ewen’s catalyst more effectively retains macromer during subsequent chain growth.

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ACS Catalysis

The test was then repeated at 85°C, again using Ewen’s compound and the same solid acid activator and cocatalyst, but with the addition of a small amount (0.07 mol/L) of 1-hexene to the reactor. Adding 1-hexene slightly lowered the LCB content. The results, via SEC-MALS and 13C NMR, from this series are plotted in the lower half of Figure 6. Notice that the ethylene to 1-hexene insertion ratio in the polymer (Et/SCB) was linear with ethylene concentration, passing through the origin, which indicates the expected inter-molecular mechanism of SCB formation. However, the ethylene to macromer insertion ratio (Et/LCB) once again does not pass through the origin. Instead, it has an intercept at about 6000, which indicates a different pathway, such as the intra-molecular mechanism predicts.

Figure 6 Above: LCB concentration and Et/LCB insertion ratio in homopolymers made using Ewen’s compound at varying ethylene concentrations. Below: Et/LCB and Et/SCB insertion ratios for copolymers.

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Tethered Butenyl: For most PE applications, Ewen's compound tends to produce an undesirably high level of long chain-branching, and one way of lowering that LCB is to attach an alkenyl pendant to the bridge or to one of the rings. This approach has been confirmed in commercial practice for over two decades [24] and through the synthesis of a wide variety of such metallocenes at the laboratory scale [54]. The tethered olefin probably interferes with long-term coordination of macromer, and it was primarily this observation that led to the proposal of an intra-molecular pathway of LCB formation [10].

Figure 7 Two structurally similar metallocenes are compared, one with a butenyl substituent and the other with a simple butyl group. (7A) In the upper plot the ethylene to macromer insertion ratio is plotted as a function of ethylene concentration in the reactor. (7B) In the lower graph, the activity of each catalyst is plotted.

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ACS Catalysis

Therefore, another series of experiments was carried out with a derivative of Ewen's compound which contains a pendant butenyl group attached to the bridge. The structure can be seen in Figure 7A (upper line), which plots the Et/LCB ratio obtained from this compound in a series of homopolymers made at varying ethylene concentrations. The original LCB levels found by SEC-MALS can be seen in Figure S17. Except for the butenyl group, these experiments were conducted identically to those in Figure 6 with Ewen's compound itself. Comparing Figures 6 and 7A shows that the butenyl group caused a pronounced drop in longchain branching (higher Et/LCB). Once again, the line does not pass through the origin, indicating that LCB formation still does not occur through a random inter-molecular pathway. The lower line in Figure 7A displays results derived from the analogous complex containing, in this instance, a saturated, butyl pendant in the place of the butenyl moiety. It produced the lower line in Figure 7A. This saturated version yields much more LCB than the butenyl compound, and about the same as that from Ewen's parent complex in Figure 6. This strongly indicates that it is the vinyl group, and not the C4 chain itself, that is responsible for the lowered LCB. It also strongly suggests that the tethered vinyl group interacts with zirconium to prevent LCB formation. Despite this interaction, however, it does not inhibit comonomer incorporation at all. The addition of a pendant butenyl group also caused a remarkable jump in activity, comparable to, or larger than, the "comonomer effect" in which the activity surges with the addition of small amounts of α-olefin. A comparison of the activities from the two compounds is plotted in Figure 7B. The butenyl-containing compound exhibited much higher activity than the butyl group (note the different scales on each side of the plot). The butenyl group also produced a linear first-order kinetic profile, unlike the butyl group whose curved line suggests higher order. This is similar to the change often seen by adding comonomer, which was noted above with EBI (compare to Figures 2 and S8). Both of these responses, e.g the huge boost in activity and the change in kinetics, are yet more indications that the tethered vinyl group is interacting with the zirconium. That is, when sterically permitted, the cationic, catalyst site often depicted in the literature, actually possesses two vacant orbitals that may be simultaneously filled in the transition state leading to growth by ethylene, comonomer or macromer; formally an 18 e- species. Constrained Geometry Catalyst: Another well-known commercially-relevant complex, called the constrained geometry catalyst (CGC) [55,56], [(C5(CH3)4)Si(CH3)2(Nt-Bu)]TiCl2, was introduced by Dow Corp. [57] for use in its high-temperature solution process. This compound has often been praised [58] for its ability to make long-chain branching, which (rather surprisingly) was thought to be beneficial in film applications. Therefore, it was of interest to investigate this metallocene in the present study. CGC was used to make homopolymers and copolymers under the same conditions described above, i.e. in a slurry process. The activator was fluorided silica-alumina and triisobutylaluminum was the cocatalyst. When tested by SEC-MALS, no evidence of LCB was observed. In our experience [59], this has been typical of such half-sandwich titanium compounds which, like their Ziegler counterparts, have typically not produced detectable LCB in the slurry process. How can one explain this seeming contradiction with so many literature reports of CGC producing LCB? We suspect that the LCB obtained in the solution process, which is usually measured by NMR [15], is actually due to the incorporation of oligomers in solution. These are probably too short to impart any rheological response, in contrast to the LCB detected in the above metallocene studies (such as from Ewen’s compound in Figure 6). Since these oligomers are in solution in a solution process, and in greater concentration than a true

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macromer, they could be incorporated by the inter-molecular pathway, in contrast to the other studies described above. Many other Ti half sandwich complexes, including those without bidentate moieties, produce in the solid phase strictly linear PE chains. Electronically, these should be more deficient sites than the Zr metallocenes presented here, possessing, like CGC, only one Cp donor. Currently we can only speculate that these cationic Ti species do not possess two accessible vacant orbitals, one of which can retain macromer during chain growth. This, along with titanocenes and hafnocenes may be the subject of future reports. Chromium Catalysts: The Phillips Cr/silica catalyst is also known to produce long-chain branched PE. This has been the subject of earlier reports [11,12,13,18,60], including LCB measurement by SEC-MALS [30] as a function of ethylene concentration. The latter study was performed using a special type of silica designed to produce high long-chain branching for more precise SEC-MALS measurements. Thus, a study was carried out in which the catalyst, calcined at 800°C, was used to make homopolymers at 80°C with varying ethylene concentrations in the reactor. Figure 8 plots the Et/LCB insertion ratio from this series against ethylene concentration in the reactor. A straight line was obtained, not passing through the origin, but having a Y-intercept at about 25,000 Et/LCB. As with the metallocenes above, this behavior is inconsistent with the inter-molecular mechanism of LCB formation. However, it agrees with behavior expected from the intramolecular pathway as predicted in Figure 1B. It is also consistent with most of the LCB responses to catalyst and reactor variables which were cataloged in earlier reports [11,12,13,60,30,61,62]. Such behavior can be interpreted in terms of macromer retention on the active Cr site, including: Cr loading (which determines dichromate formation), poison levels (competing with the macromer for coordination), cocatalysts (decreasing electron density on the Cr which favors macromer retention), porosity (enhancing macromer retention in crowded pores), and calcination temperature (again driving Lewis acidity of the Cr).

Figure 8: Et/LCB insertion ratios from polymers made with Cr/silica catalyst at varying ethylene reaction concentrations.

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ACS Catalysis

CONCLUSIONS For a variety of catalyst types, it has been shown that the incorporation of macromer to yield LCB varies with reactor ethylene concentration in a way that is quite different from the incorporation of comonomer to yield SCB. Et/SCB in the polymer varies linearly with ethylene concentration, passing through the origin, affording a first order dependence when the comonomer reactor concentration is held constant. In other words, Et/SCB in the polymer is proportional to [Et]/[Comonomer] in the reactor. Mechanistically, this is expected from the intermolecular pathway. However, we were unable to find, using either rheological or SEC-MALS methods, a single catalyst where the analogous Et/LCB ratio in the polymer passed through the origin. This indicates that macromer is incorporated through a different pathway. The presence of a Y-intercept is consistent with expectations from the previously-described [10] intramolecular mechanism of LCB formation. Furthermore, LCB and SCB formation have been shown to be independent of each other. That is, seemingly small changes in the steric or electronic characteristics of the catalyst can have major consequences for LCB content, without a parallel effect on SCB formation. The existence of an intra-molecular pathway explains how this can happen, because anything that inhibits macromer retention would also inhibit LCB, but not necessarily SCB, formation. Once dissociated from the active site, the macromer is probably immobilized in the solid polymer matrix and it cannot easily return to the site, unlike comonomer coordination. This reasoning would apply to gas-phase and slurry-phase polymerization, but not necessarily to solutionphase reaction, in which both mechanisms could in principle operate. Many questions remain concerning the precise identity of the active site species. The presence of two vacancies, as well as a growing chain, are supported by not only the intramolecular pathway, but also the comonomer effect [10,18], and the function of pendant olefins [10]. Where sterically allowed, one could be used for retention of macromer, and the other for coordination to ethylene monomer. Coordination of two olefins would formally result in an 18electron species. However, other variations are also conceivable, such as ring-slippage between η5 and η3 in some complexes.

SUPPORTING INFORMATION AVAILABLE Additional plots obtained while conducting the experiments described in this paper are provided in the accompanying supporting information. This material is available free of charge via the Internet at http://pubs.acs.org. It includes molecular weight distributions, activity plots, Janzen-Colby plots, radius of gyration and SEC-MALS plots, and additional insertion ratio plots against ethylene concentration (Et/LCB and Et/SCB).

REFERENCES 1 Wang, W.J., Yan, D., Zhu, S., Hamielec, A.E., Macromolecules 1998, 31, 8677–8683. 2 Kolodka, E., Wang, W.J., Charpentier, P.A., Zhu, S., Hamielec, A.E., Polymer 2000, 41, 3985–3991. 3 Gabriel, C., Kokko, E., Löfgren, B., Seppälä, J., Münstedt, H., Polymer 2002, 43, 6383–6390. 4 Kokko, E., Malmberg, A., Lehmus, P., Lofgren, B.L., Seppälä, J.V., J. Polym. Sci: A: Polym. Chem., 2000, 38, 376–388.

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Graphical Abstract Blow-molding is just one example of the importance of controlling longchain branching (LCB) in commercial HDPE. Here it governs the degree of parison swell and sag, which can cause defects in the final bottle. Polymerization data presented herein suggests a new mechanism of LCB formation.

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Kinetics of Long-Chain Branch Formation in Polyethylene - ACS

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