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Mechanistic Insights into Chromium Catalyzed Ethylene Trimerization Thilina Gunasekara, Jungsuk Kim, Andrew Preston, David Keith Steelman, Grigori Medvedev, W. Nicholas Delgass, Orson Larry Sydora, James M. Caruthers, and Mahdi M. Abu-Omar ACS Catal., Just Accepted Manuscript • Publication Date (Web): 08 Jun 2018 Downloaded from http://pubs.acs.org on June 8, 2018
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ACS Catalysis
Mechanistic Insights into Chromium Catalyzed Ethylene Trimerization Thilina Gunasekara,a,b Jungsuk Kim,c Andrew Preston,a,b D. Keith Steelman,a Grigori A. Medvedev,c W. Nicholas Delgass, c Orson L. Sydora,d* James M. Caruthers,c* and Mahdi M. Abu-Omarb* a
Department of Chemistry, Purdue University, 560 Oval Drive, West Lafayette, Indiana 47907, United States Department of Chemistry and Biochemistry, and Department of Chemical Engineering, University of California, Santa Barbara, CA 93106-9510, United States
b
c
Charles D. Davidson School of Chemical Engineering, Purdue University, Forney Hall of Chemical Engineering, 480 Stadium Mall Drive, West Lafayette, Indiana 47907, United States d Research and Technology, Chevron Phillips Chemical LP, 1862 Kingwood Drive, Kingwood, Texas 77339, United States Supporting Information Placeholder ABSTRACT: The kinetics of ethylene trimerization by a chromium N-phosphinoamidine (Cr-(P,N)) precatalyst activated by modified methylaluminoxane (MMAO) has been investigated by high-pressure NMR techniques. An in-depth kinetic analysis of this metallacyclic mechanism has been conducted. It was found that an intermediate in the trimerization catalytic cycle, proposed in this study as the chromium-alkenyl-hydride species, degrades into a polymer active site where this degradation step is independent of ethylene concentration and is first-order in catalyst. Additionally, we report that at least one of the first two ethylene coordination steps must be reversible in order to predict the features of the monomer consumption profiles. The reaction order in ethylene is dependent on the reversibility of ethylene coordination steps. The observation of these details of the mechanism explains many of the challenges inherent in the examination of this and similar catalyst systems and emphasizes the usefulness of operando highpressure NMR studies and a quantitative kinetic modeling approach in the study of such systems.
Keywords: ethylene oligomerization, trimerization, chromium, N-phosphinoamidine, hexene, high-pressure NMR, kinetic modeling
INTRODUCTION The global polyolefin production is over a hundred million tons, with a market value of 150 billion US dollars.1 The annual growth rate for various polyolefins is expected to increase significantly, with linear-low-density-polyethylene (LLDPE) claiming the highest annual growth rate of approximately 5%. Essential to the production of LLDPE are the α-olefin comonomers. Traditionally, these are obtained by non-selective processes such as the Shell-Higher-Olefin-Process (SHOP) and the Chevron Phillips full-range alpha olefin process which result in a Schulz-Flory distribution of products and INEOS’s Ethyl Process which results in a Poisson distribution of products. However, due to increasing demand for comonomer range oligomer products, the focus has been largely placed on selective ethylene trimerization catalysts such as the Cr-based homogenous catalyst system of Chevron-Phillips Chemical LP.2,3
A common feature of selective ethylene trimerization systems is their metallacyclic mechanism (Figure 1) where the relative stability of each metallacycle determines the selectivity towards a specific α-olefin. This mechanism was confirmed by Bercaw and co-workers using elegant crossover experiments to distinguish this mechanism from a Cossee-type mechanism.4 However, some inconsistencies in the mechanism remain for which the research community has not come to consensus on yet.2,3,5-7 These include (1) the oxidation states of intermediates,3 (2) the kinetic order of the reaction in ethylene (i.e. the rate law),6 (3) the elementary steps involving the release of α-olefin product(s),5 and (4) the mechanism of formation of a polyethylene by-product, which is an undesirable and quite costly side reaction.2,7 A comprehensive understanding of the reaction mechanism requires a detailed kinetic study. Unfortunately, obtaining kinetic data for reactions involving high pressure gases is not straightforward.8 Thus, most studies have only looked at crude ethylene pressure variations to understand, for example, the effect of ethylene concentra-
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tion on reaction rates.3,6,9,10 Indirect measurements may not allow observation of important details of the reaction mechanism. Multiple simultaneous reactions often occur, which makes the observed reaction rates often meaningless without the required discriminating data.10 Additionally, oligomerization/polymerization reactions can be highly exothermic, especially when highly active catalysts are used. This makes it difficult to maintain isothermal conditions required for proper kinetic studies. Finally, mass-transfer limitations and solubility differences due to temperature variations and constantly changing reaction medium limit the usefulness of monomer consumption data obtained using mass-flow meters.
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cant factor, a detailed kinetic study using reliable and reproducible kinetic data is required in order to capture the important features of this reaction. Since ethylene oligomerization reactions are essentially two-phase reaction systems involving gases and liquids, and often done in reactors such as autoclaves, it has been portrayed by some researchers that it is very difficult (or even impossible) to measure the concentrations in solution.10 Therefore, it is important to design an experimental setup that enables the collection of reliable kinetic data. We identified high-pressure NMR (HP-NMR) as a powerful technique to monitor the reaction kinetics.15 Usually, ethylene trimerization reactions involve high pressures (> 10 bar) of ethylene and hydrogen, where the latter is commonly used as a chain-transfer agent to control the molecular weight of the polyethylene byproduct. The commonly available thick-walled glass NMR tubes are not capable of withstanding such high pressures. However, recent improvements in high-pressure NMR tube cells have enabled the collection of reliable operando kinetic data, such as concentrations of ethylene and 1-hexene in solution. Examples can be found in the literature where researchers have used sapphire NMR tubes in standard NMR probes to carry out mechanistic studies.8,15,16 In our studies reported here, we chose a ceramic (zirconia) tube to allow for higher pressures than possible using sapphire tubes.
Figure 1. Selective ethylene trimerization through metallacycle mechanism.
Among catalyst systems that operate under the metallacyclic mechanism, the reaction order in ethylene has been seen to vary between systems. For example, some chromium catalysts show second-order dependence on ethylene.11 This has been interpreted to indicate that the rate-determining step is the formation of the metallacyclopentane intermediate via the coordination of two ethylene molecules. Hessen and coworkers studied (η5-C5H4CMe2C6H5)TiCl3/MAO system where they found that the dependence on ethylene is firstorder, which is typical for titanium catalysts.12 This has been interpreted to indicate that the rate-determining step is the insertion of the third ethylene molecule into the metallacyclopentane. However, contrary to this result, de Bruin and coworkers studied the same catalyst system for ethylene trimerization using computational tools and found that the release of 1-hexene from the metallacycloheptane ring is ratedetermining.13 Furthermore, mixed-order in ethylene and, more interestingly, orders that change with time have also been observed as well, suggesting the co-existence of competing pathways.3,14 Given the relative complexity of the reaction mechanism, particularly when catalyst degradation is a signifi-
Figure 2. Selective ethylene trimerization catalyzed by [4-tertbutyl-N-(diisopropylphosphino)-N'-(2,6dimethylphenyl)benzamidine](THF)CrCl3,Cr-(P,N), activated with modified methylaluminoxane (MMAO).
In this work, we make use of reliable and reproducible kinetic data to verify the metallacyclic mechanism for a recently reported ethylene trimerization system catalyzed by [4-tertbutyl-N-(diisopropylphosphino)-N'-(2,6dimethylphenyl)benzamidine](THF)CrCl3 (Cr-(P,N) in Figure 2).17,18 Precatalyst Cr-(P,N), upon activation with modified methylaluminoxane (MMAO), trimerizes ethylene with a 1hexene selectivity of about 94%. Herein, we describe a study of the mechanism and the reaction kinetics of this system to obtain the best estimates for rate constants for as many elementary reaction steps as experimentally possible. Catalyst degradation and polymer formation, which are common to many catalysts for this reaction, have also been taken into
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ACS Catalysis
consideration. A key finding of this study is that at least one of the first two ethylene coordination steps is reversible even under high ethylene concentrations.
Run
1
0.41
3.24
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EXPERIMENTAL
2
0.98
3.10
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All manipulations of chemicals were performed under a dry inert atmosphere in a glovebox under an N2 atmosphere. Cyclohexane was purchased from Sigma-Aldrich, degassed and dried over activated molecular sieves (4 Å) before use. Cyclohexane-d12 was stored over molecular sieves. The catalyst was prepared according to literature methods.17 Modified methylaluminoxane (MMAO-3A) in heptane (7% Al) was purchased from Akzo Nobel Polymer Chemicals. Ultra high pure (UHP) ethylene and hydrogen were purchased from Airgas and used as received. Diphenylmethane was purchased from Aldrich and stored over molecular sieves before use. A zirconia NMR tube which can withstand high pressures of gases (up to a 1000 bar) and a high-pressure NMR cell manifold were purchased from Daedalus Innovations. Gases were added to the NMR tube using an in-house built gas addition system. NMR scale oligomerization of ethylene was performed. For a typical oligomerization, the Cr-(P,N) catalyst (0.0032 g, 5 µmol), MMAO-3A (1.1783 g, 600 eq) and diphenylmethane, internal standard (1.6823 g, 10 mmol) were mixed and diluted to 10.0 mL in a volumetric flask with cyclohexane. A 0.25 mL portion of this solution was placed in the NMR tube to which a 0.25 mL portion of d12-cyclohexane was added. The sealed NMR tube cell was connected to the gas addition system. Hydrogen gas (2 bar) was added to the NMR cell followed by the addition of ethylene gas (50 bar). As long as the NMR cell is not physically disturbed by shaking/mixing, no gas-liquid mixing occurs before or during the time scale of the reaction, which we have confirmed by probing for the ethylene/hydrogen peak before and after mixing (in the absence of the precatalyst). The reaction was started by shaking the contents of the NMR cell and then the cell was immediately transferred into the spectrometer. Since no additional ethylene or hydrogen was transferred to the liquid from the gas phase, the liquid phase behaves as a batch reactor with uniform concentrations. Reaction was monitored by NMR on a Varian INOVA600 spectrometer. After the data were collected, the NMR tube cell was carefully depressurized and quenched with an acidified methanol solution.
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3.19
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0.50
1.55
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0.83
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3.32
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3.17
2190
8
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3.11
3300
Precatalyst (mM)
Ethylene (M)b
Time of second feed (s)c
a
Reactions were run at 25°C in a mixture of cyclohexane and d12-cyclohexane. 600 eq of MMAO was used as the activator (see Supplementary Information). 2 bar of Hydrogen gas was introduced to each run to promote chain transfer thereby decreasing the molecular weight of the polymer. b As determined by 1H NMR. c Time at which a second amount of ethylene was added to the reaction vessel. The goal of the kinetic analysis is to identify the simplest mechanism that is consistent with the experimental data and to obtain values of rate constants for the elementary reaction steps. Accordingly, we first describe the characteristic kinetic features of ethylene consumption and product formation time profiles for Runs 1 to 8 in Table 1. The kinetic analysis procedure starts with the most basic mechanism which involves only monomer coordination/insertion and α-olefin release steps. Only if a simple mechanism fails to describe the observed data will an additional elementary step be added, e.g., a reversible step or a catalyst degradation step, and the fitting of the experimental data using the revised mechanism is attempted again. As a result, a minimal set of elementary steps (Scheme 1) emerges that can satisfy all the experimental data. Scheme 1. Elementary kinetic steps used in fitting data.
RESULTS Selective ethylene trimerization by the chromium Nphosphinoamidine complex was carried out under several initial precatalyst and ethylene concentrations (Table 1). As previously reported, the reaction produces 1-hexene with about 94% selectivity.17 The amount of 1-octene produced is less than 1%. Since 1-octene is not distinguishable from 1-hexene by 1H NMR, it was assumed in our kinetics studies that the olefin proton signals are solely due to 1-hexene. The reaction also produced polyethylene, which was roughly quantified to be in the range of 3 to 5% by weight.19 Table 1. Experimental conditions for selective ethylene trimerization reactions catalyzed by the chromium Nphosphinoamidine complex activated by MMAO.a
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Crn
k2
Crn
k-2
C1
Crn+2
Crn C2
k1
k3
1-hexene
H Crn+2
Crn+2
n+2
Cr
C3*
C3
kdegrad H Crn+2 Cp
kp
Crn+2
n m
According to the commonly accepted metallacyclic mechanism (Figure 1), two ethylene molecules successively coordinate to the catalytic site that then undergoes an oxidative cyclization to form the metallacyclopentane. This species undergoes a ring expansion by coordination and insertion of a third ethylene molecule to form the metallacycloheptane followed by a β-H elimination and reductive elimination or, as some previous work reports, a concerted 3,7-H-shift to release 1hexene.5,11 Ideally, if there were a way to observe each (or most) of these intermediates, it would have been possible to determine the rate constants associated with each elementary step. Unfortunately, it has proven difficult to identify or quantify these intermediates by NMR spectroscopy due to the chromium species being paramagnetic. However, the data we obtained on ethylene and 1-hexene concentrations allow us to perform a kinetic analysis that provides us a partial but nevertheless important understanding of the mechanism. Specifically, we propose a mechanism requiring at least one reversible monomer coordination step and a degradation of the trimerization active site to a polymerization active site in order to fully describe the data.
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gle-shot experiments. Green (Run 1): [catalyst] = 0.41 mM, [ethylene] = 3.24 M, purple (Run 2): [catalyst] = 0.98 mM, [ethylene] = 3.10 M, orange (Run 3): [catalyst] = 1.18 mM, [ethylene] = 3.19 M, blue (Run 4): [catalyst] = 0.50 mM, [ethylene] = 1.55 M, red (Run 5): [catalyst] = 0.50 mM, [ethylene] = 0.83 M from Table 1. (a) Ethylene (M) vs. time(s), (b) log([Eth]/[Eth]0) vs. time (s) and (c) 1-hexene (M) vs. time (s). Reactions were run at 25°C in a mixture of cyclohexane and d12-cyclohexane. 2 bar of Hydrogen gas was introduced to each run to promote chain transfer of polymer chains and thereby decreasing the resulting polyethylene byproduct molecular weight. Symbols are data and lines are fits using the proposed model in Scheme 1.
Ethylene consumption (concentration and log([Eth]/[Eth]0) vs. time) and 1-hexene production time profiles are shown in Figure 3. Two issues arise immediately once the ethylene consumption curves are examined. First, the log([Eth]/[Eth]0) vs time behavior (Figure 3b) is curved, exhibiting deceleration toward the end of the reaction. Second, the ethylene consumption is incomplete, where more ethylene remains in the solution with less precatalyst loading (e.g. the orange curve in Figure 3a corresponds to 1.18 mM precatalyst vs the green curve corresponding to 0.41 mM at almost same initial monomer concentration). In principle, non-linear log ([Eth]/[Eth]0) vs time behavior may result from: (1) the reaction being higher than first-order in ethylene, (2) at least one of the ethylene coordination steps being reversible, or (3) catalyst degradation in the course of the reaction (a combination of these Scenarios is indeed possible and will be discussed). Under scenarios (1) and (2), which we will discuss later in this section and in the Supporting Information, the rate of consumption will decrease as the monomer depletes; however, the consumption of monomer will eventually proceed to completion although at a slowing pace. This is not what we observe in the present system, but rather an incomplete conversion of ethylene. Product inhibition was initially suspected, but trimerization runs performed in the presence of 1-hexene at concentrations as high as 1.90 M showed similar monomer consumption behaviors (considering the effect of added 1-hexene on ethylene solubility), thereby, ruling out the possibility of product inhibition (more details in the Supporting Information). Therefore, the non-linear log([Eth]/[Eth]0) vs time data and incomplete conversion of ethylene indicates that, regardless of the presence/absence of scenario (1) and/or (2), the trimerization active site undergoes some degradation (scenario 3). To validate our hypothesis of catalyst degradation, a second feed of ethylene was introduced to three ongoing reactions at varying times, specifically at 600, 2190, and 3300 seconds. Ethylene consumption and 1-hexene production curves are shown in Figure 4.
Figure 3. Ethylene consumption and 1-hexene production in sin-
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ACS Catalysis
Figure 4. Ethylene consumption and 1-hexene production of reactions that were given two feeds of ethylene at varying times. Brown: second feed at 600 seconds (Run 6), green: second feed at 2190 seconds (Run 7), blue: second feed at 3300 seconds (Run 8). (a) Ethylene (M) vs. time (s) and (b) 1-hexene (M) vs. time (s) where symbols are data and lines are fits using the proposed model shown in Scheme 1. Reactions were run at 25°C in a mixture of cyclohexane and d12-cyclohexane with 2 bar of hydrogen gas.
It is evident from this data that the longer the initial reaction (with the first feed of ethylene) is allowed to continue, the less activity is observed for the reaction of the second feed of ethylene, i.e. significant ethylene consumption and corresponding 1-hexene production for the brown curve (second feed at 600 s) and almost no consumption and production for the blue curve (second feed at 3300 s). This is strongly indicative of catalyst degradation during the course of the reaction. The slow consumption of ethylene after 3000 seconds and almost no formation of 1-hexene in the same time range (Figure 3b ad 3c) suggest that ethylene is consumed to make a different product, presumably polyethylene. Although some amount of polyethylene could be isolated in a larger scale reaction, it was not sufficient for analysis by NMR. However, following literature precedent,7 we postulate that the catalyst degradation is in fact a conversion of the trimerization active site into a polymerization active site. This does not preclude the simultaneous occurrence of a conventional deactivation where trimerization active site becomes completely inactive towards ethylene. However, the improvements to the quality of the fit by this additional reaction turned out to be only marginal; therefore, this additional deactivation channel cannot be justified based on the available data. The details of this analysis are given in the Supporting Information. In our experiments, we used hydrogen gas as a chain transfer agent. We noticed a reduction in the amount of hydrogen in solution as the reaction progresses (Figure S21). To confirm that this reduction is due to its reaction and not due to any physical phenomenon, such as solubility changes, we performed a labelling experiment with deuterium gas. A 2H NMR of the polymer shows that deuterium is incorporated in the resulting polymer in roughly the same amount as the reduction in the amount of hydrogen in an experiment performed with hydrogen (Figure S17) confirming its role as a chain transfer agent. No discernible effect on the ethylene consumption profiles was seen with varying hydrogen pressures (the effect of hydrogen pressures of 2, 5, and 10 bar on initial ethylene solu-
bility was taken into consideration, Figure S20). In principle, hydrogen can interact with metallacyclic species or Cosseetype metal-alkyl species. Both these species can lead to the formation of a polymer chain. However, the lack of any significant effect of increasing hydrogen pressure on ethylene consumption profile indicates that, in this system, dihydrogen does not react with metallacyclic intermediates but rather it reacts with an off-cycle (i.e. one not included in the closed catalytic cycle that produces the trimer) Cossee-type intermediate. Can this off-cycle intermediate be formed from any of the intermediates in the trimerization cycle? Careful kinetic analysis shows that non-specific site degradation results in an overestimated production of 1-hexene in the second ethylene addition and, therefore, an unsatisfactory fit to the second feed data as shown in Figure S12 (more details in the Supporting Information). The question then arises which specific catalytic intermediate undergoes degradation. After ruling out the free active sites (see Supplementary Information), we considered chromium-alkenyl-hydride species as the intermediate that degrades into a polymer active site. Unlike the free active site, this intermediate has the required structural characteristics to act as a Cossee-type polymer active site, namely a vacant site for ethylene/olefin binding and a growing alkyl chain (or a metal-hydride bond to initiate a polymerization cycle). One would expect the polymers produced by this intermediate to have cylopentyl end-groups and, since the reaction is performed in the presence of dihydrogen, some of the light products to have cyclopentyl groups. As mentioned before, the amount of polymers made by this precatalyst even in a larger scale reaction was not sufficient for an end-group analysis by NMR. However, gas chromatographic analysis of the volatile products showed the presence of methylcyclopentane and methylenecyclopentane.20 Our ongoing studies with a slightly modified precatalyst, [N(diisopropylphosphino)-N'-(3,5dimethylphenyl)benzamidine](THF)CrCl3, which reportedly produced 4% polymers,17 shows that the polymer chains indeed have cyclopentyl end-groups. All these observations indicate that the chromium-alkenyl-hydride is the likely precursor for the polymer active site.21 This implies that once the chromium-alkenyl-hydride is formed, there are two possible channels of reaction: the release of 1-hexene or the degradation to polymer site. We then investigated the order of each elementary step with respect to ethylene. In principle there are four possibilities: (a) both are independent of ethylene, (b) both are first-order in ethylene, (c) release of 1-hexene is independent and degradation is firstorder in ethylene, and (d) release of 1- hexene is first-order and degradation is independent of ethylene. The most discriminating experiments in this regard are Runs 7 and 8 as they involve adding a second feed of ethylene after significant degradation has already occurred during the first feed of ethylene. Our attempts to obtain a fit to these monomer consumption data showed that only case (d) can result in a satisfactory fit. The reasons for the unsatisfactory behavior of other fits are explained in detail in the Supplementary Information. We conclude from this analysis, as shown in Scheme 1, that chromium-alkenyl-hydride is the active site that degrades to the
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polymer forming site and that this elementary step does not involve ethylene. After our kinetic analysis showed that neither degradation alone (scenario (3)), nor degradation plus the assumption that the trimerization reaction is second order in ethylene (scenarios (1) and (3)) can adequately account for the monomer consumption data with time (see Supplementary Information for details), we then considered the next simplest case where at least one of the ethylene coordination steps is reversible (Scenario (2)) and the chromium-alkenyl-hydride degrades into the polymer active site (Scenario (3)). Fitting of the data for the second feed of ethylene requires that the reductive elimination of 1-hexene should be ethylene dependent. Consequently, the first coordination of ethylene cannot be reversible when it is formed from the chromium-alkenyl-hydride intermediate, because 1-hexene cannot undergo an oxidative addition to make the chromium-alkenyl-hydride. However, once formed, the intermediate with a single coordinated ethylene can detach ethylene to produce the free catalyst. Addition of this reversible step to the sequence produces a model that can fit the data well. On the other hand, reversibility of the second ethylene coordination and third ethylene coordination can be distinguished by considering their kinetic behaviors (Figure 5). The dashed line is the fit if the second ethylene coordination is assumed to be reversible, whereas the solid line is the fit if the third ethylene coordination is reversible and a finite rate of the following ring formation is assumed. The sigmoidal shape of the latter is due to a combination of reaching the steady state concentrations of intermediates (up to 1000 seconds) and faster degradation towards the higher monomer conversions. Clearly, the reversible third ethylene coordination scenario cannot predict the experimental data. Based on these kinetic observations, we conclude that a reversible first coordination or second coordination is more likely. The model, however, could not differentiate these two possibilities, since both gave identical fits (Figure S13). It is worthwhile to note that making two coordination steps reversible does not create a new scenario as the rate constants for any coordination step and its reverse are parameters that are not independently determined.
Figure 5. Validation by kinetic analysis that a reversible third ethylene coordination step cannot predict the observed monomer consumption profile. Ethylene consumption profiles
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for Run 3 shown as second-order plots*, 1/[ethylene] vs. time. [catalyst] = 1.18 mM, [ethylene] = 3.19 M. Symbols are data, Dashed line is assuming the second ethylene coordination step is reversible. The solid line is assuming the third ethylene coordination is reversible with finite rate of the metallacycloheptane formation. Both models have considered a degradation of the chromium-alkenyl-hydride intermediate. *The secondorder plot shows the difference in prediction for second vs. third reversible ethylene coordination steps more clearly than a first-order plot. However, this does not imply that the reaction is second-order in our proposed mechanism; see text. As stated earlier, since it was not possible to quantify intermediate catalytic species, we were unable to individually determine rate constants for the three ethylene coordination steps. Therefore, we assumed that all three forward reaction steps have the same rate constant. Consequently, of the three reverse steps associated with ethylene coordination, only the first or the second reverse rate constant (k-1 or k-2) was determined by fitting the data. To summarize, the kinetic model, shown in Scheme 1, comprises the elementary steps leading to 1-hexene (with rate constants k1, k2, and k3 for forward reactions of ethylene coordination steps and k-1 or k-2 for reverse reactions, depending on which of the two possible reversible steps is chosen for the accepted model), the degradation of the chromium-alkenylhydride site to the polymerization site (kdegrad), and the polymer production (kp) by the polymerization site (Scheme 1). Furthermore, we assign k1 = k2 = k3, and consider only one reversible step, though both could be reversible as discussed above. In Addition, since no induction period was observed even at as early a stage as 72 seconds, we considered a fast initiation compared to the trimerization reaction. The results of fitting the proposed kinetic mechanism (i.e. Scheme 1) are shown in Figures 3 and 4 as solid lines. The overall quality of the fit is quite good suggesting that the proposed mechanism captures the essential features of the system. The optimized values of the rate constants are given in Table 2. Note that the value of the polymerization rate constant kp is only a rough estimate based on the final weight of polymer product, which was found to be between 3 and 5 wt% of the starting ethylene. The lower bounds of the rate constants given in parenthesis, except for kp, arise by assuming 100% catalyst participation and these are reported since an independent measurement of catalyst participation could not be performed due to experimental limitations. The lower and upper bounds for kp arise from the range of polymer masses obtained. The catalyst participation for optimum rate constants are provided in the Supporting Information, Table S1. The rate constants determined here are for the case where it is assumed that the catalyst participation was 100% for the fastest consumption (i.e. Run 3). If the actual participation was in fact lower, then the values of all rate constants will have to be adjusted accordingly, as in the illustrative example is given in the Supplementary Information. Table 2. Optimized rate constants for each elementary step (values in parenthesis indicate the boundaries of rate constants defined by maximum catalyst participation and, for kp, polymer mass).
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ACS Catalysis k1(=k2=k3)/ M-1 s-1
k-2/ s-1
kdegrad/ s-1
kp/ M-1s-1
11 (>9)
40 (>33)
0.0065 (>0.0050)
0.10 (0.09
