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DFT‑D Investigation of Active and Dormant Methylaluminoxane (MAO) Species Grafted onto a Magnesium Dichloride Cluster: A Model Study of Supported MAO Nina Tymińska and Eva Zurek* Department of Chemistry, State University of New York at Buffalo, Buffalo, New York 14260-3000, United States S Supporting Information *

ABSTRACT: Density functional theory calculations were carried out to study the interaction of various models for methylaluminoxane and the active and dormant species in polymerization with the (110) MgCl2 surface. MAO species may bind to the surface via Al−Cl, Mg−O, and Al−μ-CH3−Mg bonds. Our results suggest that the activity of supported MAO may be higher than of homogeneous MAO because the support stabilizes (AlOMe)n·(AlMe3)m, precursors to the active species in polymerization. Moreover, the support lowers the free energy of formation of species that are active in polymerization relative to those that are dormant. Finally, it may be that the support decreases the energy associated with the cation−anion separation in [Cp2ZrMe]+[Me(AlOMe)n]−, a species that is likely dormant in homogeneous processes, hinting that the support has the possibility of increasing the number of potentially active sites. KEYWORDS: methylaluminoxane, heterogeneous catalysis, density functional theory, olefin polymerization, MgCl2 surface

1. INTRODUCTION The advantages of single-site catalysts over traditional Ziegler− Natta catalysts include their high stereoselectivity and activity and the narrow molecular weight of the polymer produced.1−5 Methylaluminoxane (MAO) is one of the most commonly utilized activators for single-site catalysts in both homogeneous and heterogeneous processes.6,7 Yet, despite MAO’s tremendous industrial importance it harbors many mysteries. For example, whereas in homogeneous processes the typical Al to catalyst ratios required to achieve good activities are ∼10,000:1, in heterogeneous processes this ratio can, in some circumstances, be decreased by a dramatic 2 orders of magnitude.8 Silica is the best and most widely studied support for MAO; however, magnesium chloride and alumina can also be used.8−10 Only a few studies have considered the interaction of MAO with the support (see refs 11−13 for a summary), but most of these used semiempirical orbital approaches and unrealistic models for MAO (e.g., linear or cyclic structures containing three-coordinate aluminum atoms). Recently other related systems, such as methylaluminum dichloride adsorbed to a silica silanol14 and triethylaluminum grafted on silica,15 were studied via MP216 and DFT calculations. Numerous experimental and theoretical investigations11,17−28 have been undertaken to unveil the molecular species comprising homogeneous MAO, which is formed from the controlled hydrolysis of trimethylaluminum (TMA, found as (AlMe3)2 in solution). Recent first-principles calculations concluded that MAO is composed of two different types of species: spherical or cagelike oligomers that have reacted with © 2015 American Chemical Society

very little or no TMA, (AlOMe)n,c, and TMA-terminated nanotubes with the general formula (AlOMe)n,t·(AlMe3)m.29−32 Two examples of these species, (AlOMe)12,c and (AlOMe)12,t· (AlMe3), are illustrated in Figure 1a. Because all of the Al−O bonds in the (AlOMe)12,c body belong to two hexagonal faces or one hexagonal and one square face, they are not strained or reactive and therefore they do not possess latent Lewis acidity (LLA).19,20 The Al−O bonds highlighted in green within (AlOMe)12,t·(AlMe3), on the other hand, belong to two square faces so they may readily react with either 1/2(AlMe3)2 or Cp2ZrMe2. The latter reaction leads to the formation of an Zr− O bond, as illustrated in Figure 1b. On the basis of a comparison of DFT NMR chemical shifts33 with those obtained experimentally,34 as well as computed barriers for the insertion of ethylene,35,36 it has been suggested that a species containing such an Zr−O bond is dormant in olefin polymerization. Reaction of the metallocene with (AlOMe)12,t· (AlMe3) such that the metal center in the metallocene is bound to the MAO species via a five-coordinate bridging methyl group, Al−μ-CH3−Zr, on the other hand, may lead to the formation of species that can be active in polymerization. We refer to species that are likely to be active and dormant in olefin polymerization as A-MAO and D-MAO within this work. Figure 1c illustrates the smallest models for A-MAO, [Cp2ZrMe]+[AlMe3Me(AlOMe)6]−, and D-MAO, Received: April 20, 2015 Revised: October 6, 2015 Published: October 12, 2015 6989

DOI: 10.1021/acscatal.5b01697 ACS Catal. 2015, 5, 6989−6998

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determine how the nature of these species may increase the number of catalytically active sites within heterogeneous MAO in comparison with those in homogeneous systems.

2. COMPUTATIONAL DETAILS The computations (geometry optimizations, frequency calculations) were performed using the rev-PBE48−51 nonhybrid generalized gradient density functional coupled with Grimme’s D3 dispersion correction52 (rev-PBE+D3) as implemented in the Amsterdam Density Functional (ADF) package.53−55 The basis functions consisted of a triple-ζ Slater-type basis set with polarization functions from the ADF basis-set library. The core−shells up to 1s for C, O, 2p for Al, Mg, and Cl, and 4p for Zr were kept frozen. We have previously tested how well this level of theory is able to reproduce the thermochemical parameters for the dimerization of trimethylaluminum (TMA). The experimental results at 298 K and 1 atm are ΔH/ΔG = −20.4/−7.6 kcal/mol.56 Using the aforementioned computational method we obtained −14.8/−4.1 kcal/mol,32 which gives a dramatic improvement over results obtained with standard functionals such as BP86 (ΔG = 0.4 kcal/mol)22 and B3LYP (ΔH/ΔG = −6.6/+12.0 kcal/mol30). Due to the size of the systems studied in this work, meta-GGA functionals (such as M06)57 and MP2 calculations16 would be prohibitively expensive. However, in the case of TMA dimerization they can be used, and previous studies have shown that they afforded dimerization energies in line with experiment.30,31 Note that use of the M06 and rev-PBE+D3 functionals leads to an overestimation of the TΔS term for TMA dimerization. In comparison to the experimental value (TΔS ≈ 8.7 kcal/mol for T = 298 K, based on ΔSd° of liquid TMA dimer, evaluated as 29.3 ± 0.3 cal/(K mol)),56 the error of rev-PBE+D3 is ∼2 kcal/ mol, while for M06 the error is roughly 1 kcal/mol larger. The CCSD//MP2 method is the most accurate and estimates TΔS ≈ 7.7 kcal/mol at room temperature.31 Finite clusters were used to represent the (110) MgCl2 surface, since similar models have been used successfully to study MgCl2-supported Ziegler−Natta catalysis.38,39,58,59 The (110) cut was chosen because preliminary calculations indicated that it was more reactive than the (100) MgCl2 cut (as an example, a comparison is given for the immobilized (AlOMe)6 and (AlOMe)6·(AlMe3) systems in Figure S3 in the Supporting Information), which is to be expected on the basis of previous DFT studies.37,38,40,41,58 The coordinates for MgCl2 were fixed at the experimental parameters60 (a, b = 3.596 Å, c = 17.589 Å, α, β = 90.0°, and γ = 120.0°), and the coordinates of the adsorbate atoms were relaxed. This protocol has previously been adopted.38,39,58,59 The size of the cluster used to model the (110) MgCl2 surface contained 36 MgCl2 formula units: it was 3 sheets thick, wherein each sheet was comprised of 4 surface Mg atoms and was 3 layers deep. Computations were carried out to determine the effect of varying the slab size and relaxation of the surface atoms that interact most strongly with the adsorbate, and the results, discussed in the Supporting Information, illustrated that our conclusions are robust with respect to the surface model employed. The effects of solvation were approximated macroscopically by the COSMO method61−63 as implemented in ADF.64 Single point calculations on gas-phase MAO and MAO/MgCl2 systems were carried out using a dielectric constant of 2.38 and hard−sphere radius of 3.5 Å for the solvent toluene. ADF default atomic radii for H/C/O/Mg/Al/Cl/Zr were used.

Figure 1. (a) Spherical or cagelike (AlOMe)12,c and nanotubular (AlOMe)12,t·(AlMe3) species. A number of methyl groups are omitted for clarity. Two LLA Al−O bonds belonging to two square faces are highlighted in green in (AlOMe)12,t·(AlMe3). (b) [Cp 2 ZrMe] + [AlMe 3 Me(AlOMe) 12,t ] − and [Cp 2 ZrMe] + [Me(AlOMe)12,t]−, which are likely to be active and dormant species in polymerization, respectively. (c) The smallest models for the active and dormant species, [Cp 2ZrMe] + [AlMe 3Me(AlOMe)6 ] − and [Cp2ZrMe]+[Me(AlOMe)6]−. H/C/O/Al/Zr atoms are shown in the colors white/black/red/tan/blue, respectively.

[Cp2ZrMe]+[Me(AlOMe)6]−. Computations suggest that a large Al to catalyst ratio is required for high activities in homogeneous processes because the free energy favors the formation of the dormant species as opposed to the active species,33 and the TMA-capped tubes can interact with at most two catalyst molecules to form the active species.30 Herein, we investigate the interaction of realistic MAO models, such as those shown in Figure 1, with a surface for the first time via DFT calculations. Silica adopts many polymorphs, but because anhydrous or surface-hydroxylated amorphous silica is typically used as a support in heterogeneous catalysis, constructing realistic models for these systems is a daunting task. Because the structure of MgCl2 is well-defined, and because its interaction with the traditional Ziegler−Natta catalyst TiCl4 has been studied extensively via DFT,37−39 we focus on the MgCl2/MAO/Cp2ZrMe2 system. The (110) face of MgCl2 was chosen because the four-coordinate magnesium atoms render this cut the most reactive.40,41 We note that experimentally derived activities for related systems depend on numerous factors,42−47 such as the order in which the components are mixed and the nature of the chemical species used; however, it has been shown that a MAO/MgCl2/ metallocene system can be twice as active in ethylene polymerization in comparison to silica-supported analogues.43 Therefore, we have carried out dispersion-corrected density functional theory (DFT-D) calculations to study the species formed when MAO is grafted to MgCl2. In addition, we aim to 6990

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Figure 2. Optimized geometries of (AlOMe)6·(AlMe3) tethered to the (110) MgCl2 surface. Mg−μ-CH3MAO−Al (a−d), Cl−Al (b, d), Mg−O (b− d), and Mg−μ-CH3TMA−Al (c, d) bonds between the surface atoms and the MAO species may form. The binding energies, ΔEB, are provided. Al/ O/C/H/Mg/Cl atoms are shown in the colors tan/red/black/white/pink/green, respectively.

these are illustrated in Figure 2. The binding energies (ΔEB) for these and other species were calculated as

The reaction energies (ΔE) given in the text are energy differences (products minus reactants) for specific systems. They do not include zero-point or vibrational finite temperature corrections. Vibrational frequencies were calculated for select systems so that we were able to obtain Gibbs free energy changes (ΔG) for select reactions at 1 atm and 298 K. It was verified that all of the species corresponded to local minima. However, we note that a few structures exhibited one to three imaginary frequencies with a small magnitude, up to −20 cm−1, which are omitted from the thermochemical calculations as is customary within ADF. These modes were typically associated with rotations of methyl groups, and their effect on the free energy changes is approximated to be less than 1 kcal/mol. Despite the fact that the free energy changes were derived from (partially) frozen structures, they allowed us to estimate entropic penalties associated with reactions that were accompanied by a change in the number of molecules, for example in the following reactions on the surface: m (AlOMe)12,c + (AlMe3)2 → (AlOMe)12,t ·(AlMe3)m 2

ΔE B = EMAO/MgCl − (E MgCl − EMAO) 2

for m = 0−4 as in Figure 3 and 1 (AlMe3)2 2

→ [Cp2 ZrMe]+ [AlMe3Me(AlOMe)6 ]−

(3)

where EMAO/MgCl2 is the energy of the surface−adsorbate complex and EMgCl2 and EMAO are the energies of the MgCl2 cluster and the given MAO species (see the Supporting Information for more details). In general, the strongest binding of the MAO model structures to the (110) MgCl2 surface is observed for species that contained Al−Cl and Mg−O bonds, such as systems II and IV in Figure 2. The strongest bonds of this type were formed when a strained Al−O bond exhibiting LLA within the MAO cage broke, allowing both of these atoms to bind to the surface. The distance between aluminum and oxygen atoms increases from 1.917 to 2.876 Å when an LLA site is broken upon the adsorption of (AlOMe)6·(AlMe3) to the (110) MgCl2 surface as in II. To visualize this process more clearly, Figure S4 in the Supporting Information has been prepared, where also a comparison with the Al−O displacement for the reaction of (AlOMe) 6 with AlMe 3 is made (see the Supporting Information for details). One of the differences between II and IV is that in the former the MAO species is oriented in such a way that the atoms comprising the TMA group that binds to the (AlOMe)6 cage cannot interact with the surface, whereas in IV they can. The TMA−surface interaction is highlighted by the gray oval in IV, within which a carbon atom from the −O−AlMe2 group forms a five-coordinate bond with a surface Mg atom via a bridging methyl group. We therefore denote this as an Mg−μ-CH3TMA−Al bond, and it was found to be somewhat less stabilizing than an Al−Cl bond. Species III also exhibits an Mg−μ-CH3TMA−Al bond, as highlighted by the dark oval, but the bridging methyl group is bound to an aluminum atom that comprises part of the MAO cage (−AlMe2) as opposed to an aluminum that is bound to an oxygen atom within the cage as in IV (−O−AlMe2). Species I and II also tether to the surface via bridging methyl groups, but

(1)

[Cp2 ZrMe]+ [Me(AlOMe)6 ]− +

2

(2)

as in Figures 4 and 5.

3. RESULTS AND DISCUSSION 3.1. How Does MAO Bind to MgCl2? Before embarking on our investigation of how the surface affects the dynamic equilibrium between species that may be present in MAO, it was first necessary to gain an understanding of the possible ways in which MAO can interact with MgCl2. We therefore carried out an in-depth analysis for the simplest TMAcontaining model, (AlOMe)6·(AlMe3), as it can tether to the surface via all of the bonding motifs we found to be important; 6991

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In order to verify the previously noted trends regarding the bond strengths, we proceeded to use the ETS-NOCV (ETSnatural orbitals for chemical valence)66−71 scheme to decompose ΔEoi, which is associated with covalent bonding, into contributions from complementary orbital pairs, NOCVs, wherein each NOCV pair defines a particular charge transfer event between the fragments. Herein, we describe the NOCV pairs that contribute most toward the total orbital interaction energy and neglect the (sometimes many) charge transfer events that contribute 2 kcal/mol or less to the total ΔEoi value. Analyzing the NOCV pairs therefore provides us with information about the most important covalent bonding interactions between (AlOMe)6·(AlMe3) and the MgCl2 substrate. Species I binds to the MgCl2 surface via three Mg−μCH3MAO−Al bonds, and the three main NOCV pairs that lie along each of these bonds constitute 61% of the total ΔEoi. The orbital interaction results in CH3→Mg donation from occupied orbitals with C sp character to unoccupied Mg s-like orbitals. This type of interaction is present in all of the species studied. The NOCV analysis confirmed that Mg−μ-CH3MAO−Al bonds are somewhat stronger than Mg−μ-CH3TMA−Al bonds. For example, in IV, the latter contributes only ∼5 kcal/mol toward the total ΔEoi, whereas the former are almost twice as large. The ΔEoi associated with donation from O p-like orbitals to unoccupied orbitals that show a majority of Mg s character (as found in II−IV) was found to be around 10 kcal/mol, illustrating that this bond is about as strong as the CH3TMA→ Mg interaction. It should be noted, however, that this Mg−O bond measured 2.364 Å, which is slightly longer than the typical Mg−O bond length of 2.335 Å found for all of the MAO/MgCl2 systems we studied; thus, it is likely that in other MAO species the magnitude of the orbital interaction energies associated with this bond type is somewhat larger. Finally, Cl p→Al sp charge transfer contributes around 22−25 kcal/ mol to the total interaction energy in II and IV, and it was always the most significant component of ΔEoi. Thus, the ETSNOCV analysis confirmed that the charge transfer events that occur between MAO and the surface are, in decreasing order of their importance toward |ΔEoi|, Cl→Al > O→Mg ≈ CH3TMA→ Mg > CH3MAO→Mg. However, other factors, such as the energy associated with the geometric distortion of the MAO species, as well as the attractive dispersion and repulsive steric interactions, are also non-negligible when rationalizing the total binding energies. For example, let us take a closer look at species IV, since it has the largest binding energy. The orientation of IV on the surface allows it to maximize dispersion forces between the MAO species and the surface. It has been shown before that dispersion is very important for adsorption of TiCl4, the TMA dimer, and other small alkylaluminum compounds on the MgCl2 surface.72,73 Indeed, without this contribution the binding energies of all of the four species would range from −3 to −10 kcal/mol, and IV would be the most weakly bound whereas I would be the most strongly bound. However, because of the close proximity to the surface, the attractive interactions are counteracted by large steric repulsion. Hence, the bonding decomposition analysis not only confirms that dispersion is essential for computing appropriate binding energies within MAO/MgCl2 systems but also shows that it is one the major stabilizing forces along with ΔEoi. The orbital interactions were found to be important also in other systems such as within the [(C5H4)2CMe2MoH(H2)]+ complex74 and in the description of

because these methyls originate from the MAO cage, we refer to this as an Mg−μ-CH3MAO−Al bond. This was found to be the weakest interaction between the substrate and the adsorbate. When Mg−O bonds were not accompanied by Al−Cl bonds, they were typically found with Mg−μ-CH3MAO− Al bonds in which the magnesium atoms were six-coordinate, as in II. The magnesium atoms in Mg−μ-CH3TMA−Al bonds are often five-coordinate (III and IV). Finally, adsorption to the surface can also affect the bonding within the MAO species itself. This type of interaction is seen in IV, where a bridging methyl group is formed between two aluminum atoms within (AlOMe)6·(AlMe3). This so-called Al−μ-CH3TMA−Al bond motif is denoted by the solid blue lines, and we previously found it to be integral in stabilizing MAO nanotubes that had reacted with at least two AlMe3 groups, e.g. (AlOMe)n,t· (AlMe3)m with m ≥ 2.32 Note that the Mg−μ-CH3−Al, Al−Cl, and Mg−O bond lengths averaged over all of the species studied measured 2.610, 2.534, and 2.335 Å, respectively. An ETS (extended transition state)54,65 analysis was used to decompose the binding energy into chemically intuitive terms such as the energy associated with distorting (AlOMe)6· (AlMe3) into the geometry it assumes on MgCl2 (ΔEgeo), the repulsive steric energy (ΔEsteric), and the attractive terms due to the orbital interaction (ΔEoi) and dispersion (ΔEdisp) (see Table 1). A larger geometric change in the adsorbate typically Table 1. Binding Energies, ΔEB, for the Interaction of (AlOMe)6·(AlMe3) with a (110) MgCl2 Surface in the Geometries Illustrated in Figure 2a ΔEB ΔEgeo ΔEsteric ΔEoi % ΔEoi(CH3MAO→Mg) % ΔEoi(CH3TMA→Mg) % ΔEoi(Cl→Al) % ΔEoi(O→Mg) ΔEdisp

I

II

III

IV

−39.5 8.1 20.4 −38.4 61 N/A N/A N/A −29.7

−54.8 36.4 31.6 −74.0 17 N/A 33 14 −48.8

−54.6 28.6 36.6 −70.4 15 14 N/Ab 15 −49.7

−64.5 39.3 55.4 −98.1 5 21 23 10 −61.1

ΔEB is further decomposed into the energy required to distort the geometry from that of the free species (ΔEgeo), steric repulsion (ΔEsteric), orbital interaction (ΔEoi), and dispersion (ΔEdisp). ΔEB = ΔEgeo + ΔEsteric + ΔEoi + ΔEdisp. The atoms involved in the charge transfer and the direction of charge flow are denoted in parentheses. All energies are given in kcal/mol. The percentage of contributions to ΔEoi, which are calculated as a sum of all interactions from charge transfer channels of the same type, are provided. bBecause the distance between Al and Cl atoms was ∼3 Å, we did not consider this to be a formal Al−Cl bond. Nonetheless, the ETS-NOCV analysis finds Cl→ Al donation between these atoms, and this charge transfer channel contributes ∼14% to ΔEoi. a

signifies a stronger bond to the substrate; thus, systems with a smaller magnitude of the binding energies (|ΔEB|) also typically had a smaller ΔEgeo value. Species IV experiences the largest geometric distortion, likely because this system forms all of the types of bonds we found. Because a stronger interaction energy is typically correlated with a shorter surface−adsorbate distance, a similar trend was observed for ΔEsteric and |ΔEdisp|. In addition, unsurprisingly, larger values of the orbital interaction energy (|ΔEoi|) were typically found for systems where MAO was more strongly bound. 6992

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Figure 3. Optimized geometries of (AlOMe)12,c and (AlOMe)12,t·(AlMe3)m (m = 0−4) MAO species tethered to the (110) MgCl2 surface. Changes in the electronic energy (ΔE) and the Gibbs free energy (ΔG at 298 K and 1 atm) for the reaction (AlOMe)12,c + m/2(AlMe3)2 → (AlOMe)12,t· (AlMe3)m and m = 0−4 on the surface are provided. Values in parentheses are gas-phase values from ref 32. The binding energies to the surface, ΔEB, were calculated as being (a) −42.7, (b) −48.5, (c) −49.7, (d) −54.9, (e) −53.9, and (f) −63.9 kcal/mol.

these sites, the abundance of (AlOMe)n,t within homogeneous MAO is likely to be minimal, but a number of (AlOMe)n,t· (AlMe3)4 species are expected to be important components of MAO.30,32 These saturated nanotubes can tether to the surface only via Mg−μ-CH3−Al bonds. Furthermore, if this weakest interaction between MAO and the surface can affect the aforementioned equilibrium, we can expect an even larger effect for stronger surface−adsorbate interactions, when such bonds can be formed. Our calculations clearly illustrate that interaction with the surface shifts the equilibrium from (AlOMe)12,c and free TMA toward the TMA-capped tubes. Whereas in homogeneous systems the free energy change (ΔG) is exergonic only for the reaction with m = 3, 4, on the surface the formation of (AlOMe)12,t·(AlMe3)2 is favored as well. The increased stability of the immobilized TMA-capped species is a result of their stronger binding to the surface. Nanotubes capped with two or fewer AlMe3 groups can also interact with MgCl2 via Al−Cl and Mg−O bonds when they lie perpendicular to the surface (see the Supporting Information), and the 298 K free energies of the resulting structures are similar to those shown in Figure 3. In our previous study we have shown that in the case of a homogeneous MAO mixture an increase of the temperature from 298 K to a temperature that is typical for industrial polymerization processes, 358 K, leads to a significant reduction (by about 22%) in the overall percentage of the (AlOMe)n· (AlMe3)m species.32 We expect similar results for the heterogeneous case, albeit with a smaller drop in the amount of TMA that is bound. This is because nanotubular MAO, especially those with a longer body (n > 12), should be stabilized further due to the formation of a larger number of Mg−μ-CH3−Al bonds and because a larger contact area will be available between these oligomers and the surface, which in turn will increase the dispersion forces. The shape of the

surface−adsorbate interactions of the formaldehyde molecule with copper and silver sites in zeolites (in particular ZSM-5).75 However, in the latter case the authors note that due to the use of the QM/MM method there is no simple relation between ligand binding energies and orbital interaction, nor should any be expected. 3.2. The (AlOMe)12,c + m/2(AlMe3)2→ (AlOMe)12,t·(AlMe3)m Equilibrium on the MgCl2 Surface. Our previous DFT calculations have shown that MAO cages are significantly more stable than their nanotubular counterparts.32 However, because TMA readily reacts with strained LLA bonds in the tubes, the formation of some (AlOMe)n,t· (AlMe3)m species is exergonic with respect to cages and free TMA. Since species with the formula (AlOMe)n·(AlMe3)m (see, for example, the right panel of Figure 1a) are precursors to the active species in polymerization,30,33,35 it is important to determine if the surface can affect the (AlOMe)12,c + m /2(AlMe3)2→(AlOMe)12,t·(AlMe3)m equilibrium. To study this further, we investigated the interaction of (AlOMe)12,c and (AlOMe)12,t·(AlMe3)m, some of the most prominent systems discussed in the literature,23,30,32 with the (110) MgCl2 surface. Figure 3 illustrates the optimized geometries of these MAO species tethered to the surface via one of the weakest binding motifs, Mg−μ-CH3−Al bonds, which have been discussed in the previous section. The reason we decided to focus on this particular binding motif is because it may be the most common for both cagelike and nanotubular MAOs. This is because the (AlOMe)n,c species that have a non-negligible abundance within homogeneous mixtures have n > 10 and few, if any, LLA sites; thus, it is much more likely that they will tether to the surface via Mg−μ-CH3−Al bonds than via Al−Cl and/or Mg−O bonds.23,32 Moreover, each nanotube has four LLA sites, two on each end, and because it is favorable for TMA to react with 6993

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Figure 4. (a) Thermodynamic relationships (ΔE and ΔG at 298 K and 1 atm) between (b) (AlOMe)6, (AlOMe)6·(AlMe3) (as illustrated in Figure 2d), (c) D-(AlOMe)6, and (d) A-(AlOMe)6 in the gas phase and on the (110) MgCl2 surface. (b−d) The most stable geometries of these species found on (110) MgCl2. The binding energies to the surface, ΔEB, were calculated as being (b) −54.1, (c) −63.7, and (d) −71.3 kcal/mol.

Figure 5. (A) Same as Figure 4a except for a geometry where the atoms originating from TMA and Cp2ZrMe2 that are bound to the (AlOMe)6 cage do not interact with the (110) MgCl2 surface. Such an (AlOMe)6·(AlMe3) configuration is the same as in Figure 2b. (B) Same as Figure 4a except for (AlOMe)12,t.

MAO is immobilized the temperature effect on the shift in the equilibrium among (AlOMe) n,c , free (AlMe 3 ) 2 , and (AlOMe)n,t·(AlMe3)m is smaller than in the homogeneous

cagelike structures prevents them from interacting with the surface via either one of these mechanisms, at least not as efficiently. Hence, it is not unreasonable to assume that when 6994

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Figure 6. Dissociation curves for stretching (a) the Zr−O bond in D-(AlOMe)6 and (b) the Zr−C bond in A-(AlOMe)6 in homogeneous and heterogeneous polymerization in the gas phase and toluene. ΔE is the difference between the energy of the structure with a given internuclear distance and the energy of the fully optimized species. Legend: (*) relaxation of all of the atoms within D-(AlOMe)6 and A-(AlOMe)6, except the Zr−C and Zr−O bonds yield the points denoted by the crosses; (**) the same as (*), but for a geometry that promotes interaction of the metallocene with the surface; the values are given by red and blue stars. The geometries of the partially dissociated structures are given in Figure 7. rTS corresponds to the Zr−O and Zr−C distances in the transition states found for the trans insertion of ethylene in ref 35. The trans approach had a lower barrier than the cis approach for the first insertion in solution.35

is endergonic by ∼3 kcal/mol, the concentration of A(AlOMe)6 is likely to be small. Remarkably, adsorption to the surface in the geometries illustrated in Figure 4 reverses this trend so that the formation of A-(AlOMe)6 via eq 6 or eq 7 is exergonic by 1−2 kcal/mol. The large magnitude of the binding energy of A-(AlOMe)6 to the surface is able to overcome the entropic penalty for its formation. We also explored this equilibrium for a configuration where only the atoms in the MAO body were tethered to the surface, whereas those bound to TMA and the zirconocene were positioned so that they could not interact with the surface. All of the species in Figure 5a were 6−13 kcal/mol less stable than those in Figure 4 because they had neither Mg−μ-CH3TMA−Al nor Mg−μ-CH3Cp2ZrMe2−Al bonds. The free energy changes associated with the formation of A-(AlOMe)6 adsorbed to the surface as shown in Figure 5a via eq 6 or eq 7 resembled those in the gas phase, highlighting the importance of the metallocene−MgCl2 interaction in the stabilization of the surface-supported active species. Further calculations were carried out to determine how the size of the parent MAO structure affects the (free) energy changes associated with this equilibrium. We focused on (AlOMe)12,t oriented so that its body lay perpendicular to the surface as shown in Figure 5b, tethered to MgCl2 via Al−Cl and Mg−O bonds. The free energy of this geometry at 298 K is roughly the same as that of the configuration illustrated in Figure 3b (see the Supporting Information for further details). Despite the fact that the metallocene in A-(AlOMe)12,t does not interact with the support in this orientation, the presence of the surface stabilizes the active species so that the difference between its Gibbs free energy of formation via eq 6 or eq 7, but with n = 12 (i.e., with either (AlOMe)12,t·(AlMe3) or D(AlOMe)12,t as the reactant), is ∼0 kcal/mol. A geometry that promotes interaction of the metallocene with the surface is likely to shift the equilibrium to further favor the active species, but because frequency calculations on such a system would be prohibitively expensive since they would necessitate the use of a longer MgCl2 cluster, we did not explicitly consider this

case. Further studies will be required to verify this hypothesis. Since cagelike MAO structures do not contain any LLA sites, they can only bind to a flat surface via bridging methyls. Thus, we have found at least one configuration of each (AlOMe)12,t· (AlMe3)m (m = 2−4) species that is more stable than (AlOMe)12,c when it is tethered to MgCl2. In addition, for (AlOMe)12,t·(AlMe3) the free energy change for this reaction is reduced by ∼4 kcal/mol on MgCl2. This suggests that the surface facilitates the formation of MAOs that are precursors to the active species in polymerization, and this is one of the reasons heterogeneous systems may have higher activities, mainly by increasing the amount of active centers, than homogeneous systems. 3.3. Dormant and Active Species in MgCl2-Supported MAO. How does the presence of the surface affect the equilibrium between the active (A-MAO) and dormant (DMAO) species and TMA-capped MAOs? To study this further, we optimized the smallest models for A-MAO, [Cp2ZrMe]+[AlMe3Me(AlOMe)6]−, and D-MAO, [Cp2ZrMe]+[Me(AlOMe)6]−,35 illustrated in Figure 1c, tethered to the (110) MgCl2 surface. The most stable geometries we found are shown in Figure 4c,d. In the gas phase the Gibbs free energy changes for the reactions (AlOMe)6 + Cp2 ZrMe2 → D‐(AlOMe) 6

(4)

and (AlOMe)6 +

1 (AlMe3)2 → (AlOMe)6 ·(AlMe3) 2

(5)

are about the same (see Figure 4a). However, because the formation of the active species via either one of the reactions D‐(AlOMe) 6 +

1 (AlMe3)2 → A ‐(AlOMe) 6 2

(6)

or (AlOMe)6 · (AlMe3) + Cp2 ZrMe2 → A ‐(AlOMe) 6

(7) 6995

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ACS Catalysis situation. These findings reiterate the role of the surface in stabilizing species that are likely to be active in polymerization relative to those that are dormant. 3.4. Approximating Barriers to Insertion. It has been shown that the barrier for the first insertion into the Zr−Me bond is ∼10 kcal/mol higher in energy for [Cp2ZrMe]+[Me(AlOMe)6]− in comparison with [Cp2ZrMe]+[AlMe3Me(AlOMe)6]−.35 During the insertion mechanism the bonds between the cationic and anionic components of the active (μCH3−Zr) and dormant (Zr−O) species, i.e. cation−anion separation, increases, and they assume their largest values at the transition state. We wondered if the surface could influence the kinetics of the polymerization process. Because calculation of the ethylene insertion barriers with A-(AlOMe)6 and D(AlOMe)6 tethered to the surface would be very expensive, we investigated how adsorption to the (110) MgCl2 surface affects the energy profiles associated with the cation−anion separation: that is, stretching the Zr−C bond of the active species and Zr− O bond of the dormant species. The elongation of this bond corresponds to increasing the displacement between the counterion and the metal center successively. To facilitate modeling the dissociation procedure, the active and dormant species were initially constructed so that the metallocene did not interact with the surface, using the configurations shown in Figure 5a. Single-point energy calculations were performed by varying the Zr−C and Zr−O distances but keeping all other atoms fixed. Since the transition states for the trans/cis approach of ethylene insertion into A-(AlOMe)6 and D(AlOMe)6 were found to have Zr−C and Zr−O distances of ∼4.1/2.5 and 4.2/3.3 Å, respectively,35 the dissociation curves were calculated for distances up to 5.1 Å. Because solvation can significantly stabilize charged species in the insertion mechanism,35 calculations were carried out in the gas phase and using a continuum solvation model with parameters for toluene. The results are presented in Figure 6. Consistent with the description of the oxygen-bound and bridging-methyl bound species as being dormant and active in homogeneous systems, the dissociation curves for A-(AlOMe)6 at a given distance were invariably lower than those of D(AlOMe)6: e.g., by 11 and 18 kcal/mol near r = 4.8 Å in gas phase and in solution, respectively. In the heterogeneous case these values were calculated to be 5 and 15 kcal/mol instead. Adsorption to the (110) MgCl2 surface did not significantly affect the dissociation curve for D-(AlOMe)6. At a Zr−O distance of 4.2 Å, the anion−cation separation energies (aka ΔE) for the surface-supported species differed by no more than 0.85 kcal/mol in comparison to those for the homogeneous system, and the two sets of solution-phase dissociation curves fell nearly on top of each other. The dissociation curves in Figure 6b, on the other hand, suggest that adsorption has a non-negligible effect on the dissociation curve of A-(AlOMe)6. In order to study this further, calculations were carried out on the aforementioned systems, fixing the Zr−C and Zr−O bonds to ∼4.2 Å but letting all other atoms within the active and dormant species relax, whereas MgCl2 atoms were kept fixed as before (i.e., Figure 7b). The results, given by the crosses in Figure 6, illustrate that the cation−anion separation energies are smaller than those obtained in the single-point calculations, as expected. For both the active and dormant species the surface does not have much of an effect on the computed cation−anion separation energies, suggesting that the aforementioned difference between the homogeneous and hetero-

Figure 7. Structures of [Cp2ZrMe]+[AlMe3Me(AlOMe)6]−, and [Cp2ZrMe]+[Me(AlOMe)6]− (a) in the gas phase and (b, c) on the MgCl2 surface. In (b) the metallocene does not interact with the surface, whereas in (c) it does. The purple dashed line denotes the C− Zr and O−Zr distance that was stretched to generate the data for Figure 6. In the geometries shown it measures ∼4.2 Å.

geneous dissociation curves for A-(AlOMe)6 may be an artifact of fixing the atoms in the calculation. To determine if the interaction of the metallocene with the surface could potentially affect the cation−anion separation energies, we optimized the geometries of active and dormant species whose geometries resembled those in Figure 4c,d, but where the Zr−C and Zr−O bonds were fixed at ∼4.2 Å and the rest of the atoms of these model MAO species were allowed to relax. The geometry of the surface was kept fixed as usual. Figure 7 illustrates the structures of these ion pairs in the gas phase (Figure 7a), ones tethered to the MgCl2 surface in such a way so that the metallocene does not bind to the surface (Figure 7b), and ones where the metallocene forms a Zr−μMe−Al bond with the surface (Figure 7c). For clarity the displacements between the metal center and the counterion are shown in purple. The results for the situation where the metallocene interacts with the surface (i.e., in the geometries shown in Figure 7c) are given by the red and blue stars in Figure 6. For the active species, the cation−anion separation energies resembled those computed for the configuration where the metallocene did not interact with the surface. For the dormant species, however, the cation−anion separation energies were dramatically reduced, suggesting that the interaction of the metallocene with the surface may have a significant impact on the reaction barrier associated with 6996

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ACS Catalysis Notes

insertion into the Zr−C bond, so that this species may potentially become active when immobilized on the surface. Interestingly, experiments have shown that an MgCl2/ Cp2TiCl2-trialkylaluminum catalyst system for ethylene polymerization exhibits unusual activity wherein a particularly stable active site may be formed via adsorption of Cp2TiR+ on the surface.76 It is important to note that herein we have only considered a model that is applicable for the first insertion, and further studies are required to make assertions regarding how immobilization affects the chain growth and termination. Previous DFT investigations on homogeneous systems illustrated that the barrier for the first insertion was ∼5 kcal/ mol higher than for the most favorable mechanisms for subsequent insertions.35 Further studies will illuminate if this is also the case for the immobilized species and reveal how the metallocene−surface interaction affects which species become active in olefin polymerization upon immobilization.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Acknowledgment is made to the Donors of the American Chemical Society Petroleum Research Fund for support of this research (grant 51672-DNI6). We acknowledge support from the Center of Computational Research at SUNY Buffalo. E.Z. thanks the Alfred P. Sloan Foundation for a Research Fellowship (2013−2015).

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4. CONCLUSION We have carried out a first-principles investigation of the interaction of realistic models for methylaluminoxane (MAO) and of the (110) MgCl2 surface for the first time. MAO can tether to the surface via strong Al−Cl and Mg−O bonds and weaker Mg−μ-CH3−Al bonds. Because cagelike MAO species have few sites exhibiting latent Lewis acidity (LLA), they can interact with a flat surface only via Mg−μ-CH3−Al bonds. Nanotubular species can tether to MgCl2 in a variety of different ways and bind more strongly than cages. Consequently, the nanotubes and their trimethylaluminum (TMA) capped variants, which are precursors to the active species in polymerization, are stabilized with respect to cages and free TMA by the surface. The calculated free energy pathways for the formation of various models for the dormant and active species show that the interaction of the zirconocene with the surface is key in stabilizing the latter. Our computations suggest that the surface shifts the equilibrium toward the active species and their precursors. Moreover, they hint that the surface may lower the barrier for ethylene insertion into the Zr−C bond of species that are dormant in homogeneous systems. Future studies will be undertaken to study the latter point, since such a mechanism could potentially lead to the formation of a greater number of active sites in immobilized MAO.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acscatal.5b01697. Further computational details, thermodynamic relationships between (AlOMe)12,t and (AlOMe)12,t·(AlMe3) that lie parallel and perpendicular to the MgCl2 surface, the effect of partial relaxation of the MgCl2 cluster on the energy profiles for the reactions shown in Figure 4, optimized structures of (AlOMe)6 and (AlOMe)6· (AlMe 3) grafted onto the (100) MgCl2 surface, illustration of the change in the Al−O distance upon breaking an LLA site, and Cartesian coordinates of relevant species (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail for E.Z.: ezurek@buffalo.edu. 6997

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ACS Catalysis

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