Ancillary ligand effects on α-olefin polymerization catalyzed by zirconium metallocene: a computational study

Abstract

The polymerization of α-olefins catalyzed by zirconium metallocene catalyst was systematically studied through experiments and density functional theory (DFT) calculations. Having achieved an agreement between theory and experiment, it was found that the effect of the catalyst ligand on the C=C insertion reaction was significantly greater than that on the β-H elimination reaction. Therefore, the molecular weight of polymers can be increased by improving the activity of the C=C insertion. In addition, in comparison with propylene, the chain length of α-olefins can directly affect the stereotacticity of polymerization products, owing to steric hindrance between the polymer chain and monomer.

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Introduction

Poly-α-olefins (PAOs) are oligomers of linear α-olefins, which are used as base stocks for synthetic lubricants in automotive and industrial applications. Synthetic base stocks perform better than conventional mineral base stocks in terms of viscosity index, kinematic viscosity, pour point and volatility, thermal and oxidative stability, etc. Synthetic base stocks can be used to prepare all kinds of high-grade lubricating grease products.^1–3 PAO synthetic base oil plays a key role in cutting-edge technology fields such as the aerospace and military industries. It is also the key raw material in the production of high-grade lubricating oil used in advanced automobile, wind power, high-speed railway, intelligent manufacturing, and other industries.⁴ At present, synthesis of PAO base oils is primarily carried out through the oligomerization of pure α-decenes by foreign companies.⁵

The appropriate selection of catalyst and reaction conditions can aid in the production of PAOs with tailor-made properties. Notably, a catalyst plays a key effect on the polymerization activity, molecular weight, and branching degree.⁶ The commonly used catalysts for α-olefin polymerization mainly include Lewis acid catalysts, Ziegler Natta catalysts, metallocene catalysts, ionic liquid catalysts, etc.^7–16 Among them, Ziegler Natta catalysts are traditional and the most common catalyst for olefin polymerization.^17–19 However, because Ziegler Natta catalysts have multiple active sites, olefins have different growth rates at different sites of catalyst, and the various properties of polymerization cannot be effectively controlled.²⁰ In comparison to Ziegler–Natta, metallocene catalysts can control various important parameters, such as co-monomer distribution, molecular weight, molecular weight distribution, molecular architecture, stereo-specificity, degree of linearity, and branching of the polymer, due to the single active sites available on the metallocene catalysts.^20,21 Thus, metallocene catalysts (with group IV metal) have become a research hotspot in the recent years and have been applied in industrial production owing to their single reaction active center and high catalytic activity.^22,23 There are four types of metallocene catalysts commonly used: (a) monometallocene catalyst,^24–27 (b) constrained geometry catalysts (CGC),^28–30 (c) unbridged metallocene catalysts,^31,32 (d) bridged metallocene catalysts^33–35 (Fig. 1). Compared with other types of metallocene catalysts, rigid bridging groups of bridged metallocene catalysts can produce relatively stable spatial-specific stereoscopic effects on chain propagation and coordination monomers, affording synthesis polymers with high molecular weight and regular structure.^31,36 Moreover, the bridged rigid structure makes the connection between the metallocene ring and the transition metal more stable, and the metallocene ring does not slip at high temperatures.³⁷ Therefore, the bridged metallocene catalyst also shows high catalytic activity at high temperatures.^38,39 As has been reported in the literature,^40–43 different electronic or stereoscopic effects of catalyst ligands can significantly affect the polymerization performance, but the relationship between the ligand of group IV bridged metallocene catalysts and activity or the molecular weight of α-olefins (e.g. 1-decene), polymerization at the molecular level remains poorly understood.^44–50

Fig. 1 Four common metallocene catalyst structures: (a) Monometallocene catalyst (b) Constrained Geometry Catalysts (CGC) (c) unbridged metallocene catalyst (d) bridged metallocene catalyst.

In general, the occurrence of polymerization requires MAO to activate the metallocene catalyst precursor (Fig. 1) to obtain active species with methyl groups, but the overall mechanisms of metallocene catalyst activation are not precisely understood. All computational studies dealing with the MAO activator suffer from its elusive structure, thus the use of DFT model systems is required (Fig. 2a). The starting point of this work was the activation of the dimethylated metallocene complexes, omitting the preceding catalyst alkylation step. This study mainly focuses on the systematic experimental comparison and theoretical calculation of the polymerization of 1-decene catalyzed by bridged metallocene complexes 1 (ref. 51) and 2 (ref. 52) (Fig. 2a) in order to explore the factors affecting both catalyst activity and polymer molecular weight. The research results will provide us with a theoretical basis for the design of high-efficiency catalysts. Four possible modes of olefin coordination insertion are shown in Fig. 2b. Therefore, the four different insertion modes were calculated and the results were compared, and the most favorable reaction path was selected for further analysis.

Fig. 2 (a) The structures of catalysts and monomers used for DFT calculation in this work (b) four possible modes of olefin coordination insertion.

Computational details

All calculations were performed using the Gaussian 16 program.⁵³ The B3PW91 hybrid exchange-correlation functional was utilized for geometry optimization.^54–56 Each optimized structure was subsequently analyzed by harmonic vibration frequencies for the characterization of a minimum (N_imag = 0) or a transition state (N_imag = 1), providing thermodynamic data. The transition state structures were used to connect the reactant and product on either side via intrinsic reaction coordinate (IRC) tracking. The 6-31G* basis set was considered for C, H atoms. The Zr atoms were treated by the Stuttgart/Dresden effective core potential (ECP) and the associated basis sets.⁵⁷ This basis set was denoted as “BSI”. Such a computational strategy has been widely used for the study of transition-metal containing systems.⁵⁸ To obtain more reliable relative energies, the single-point calculations of optimized structures were carried out at the level of M06 (ref. 59)/BSII, taking into account a solvation effect of toluene with the SMD⁶⁰ solvation model. In the BSII, the 6-311G** basis set was used for the nonmetal atoms, whereas the basis sets together with associated pseudopotentials for Zr atoms were the same as that in geometry optimization. Therefore, unless otherwise mentioned, the free energy (ΔG, 298.15 K, 1 atm) in solution, which was used for the description of energy profiles, was obtained from solvation single-point calculation and gas-phase Gibbs free energy correction. The 3D molecular structures displayed herein were created using CYLview.⁶¹

Results and discussion

Catalyst 1 and catalyst 2 have been synthesized according to the procedure reported in the literature^51,52 and are applied for 1-decene (m) polymerization. The experimental results are summarized in Table 1. It can be seen from the experimental results that the activity and molecular weight of catalyst 2 for m are significantly higher than that of catalyst 1. These differences in activity and molecular weight suggest that the ligand of the catalyst significantly influences the polymerization behavior of 1-decene. To systematically explore the factors affecting polymerization performance, density functional theory (DFT) calculations provided additional insight into the polymerization of m with catalysts 1 and 2.

Table 1 Polymerization of 1-decene by catalyst 1 and 2^a

Cat. (μmol)	[Al] : [Zr]	Act.^b	Mn^c
a Conditions: 1-decene, 200 mL; [B] : [Zr] = 1.5 : 1; 90 °C, 1 h.b 10^6 g (mol Cat.)^−1 M^−1 h^−1.c kg mol^−1.
1 (10)	50 : 1	6.3	6875
2 (10)	50 : 1	11.1	14 802

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Effects of catalyst ligands on polymerization activity molecular weight

Firstly, four possible modes of m coordination insertion in Cat.1 and Cat.2 systems were calculated (Tables S1 and S2†). The computed results indicate that 1,2-insertion is both kinetically and thermodynamically more favorable than 2,1-insertion in the chain initiation stage. Based on this results, only 1,2-insertion mode was considered here for the chain propagation stage. Next, all kinetically favorable paths of chain initiation and chain growth stages are summarized in Fig. 3 and Fig. 4. As shown in Fig. 3, the average insertion barrier of Cat.1 in the chain propagation (second to fourth monomer insertion) was 11.6 kcal mol⁻¹, which is 0.9 kcal mol⁻¹ higher than that of Cat.2 (10.7 kcal mol⁻¹, Fig. 4). These results are consistent with the experimental results shown above. In addition, For the rate-limiting step (first insertion), the energy barrier of Cat.1 (12.1 kcal mol⁻¹) is slightly lower than that of Cat.2 (12.9 kcal mol⁻¹), but the coordination complex of Cat.1 (−0.7 kcal mol⁻¹) is significantly higher in energy than that of Cat.2 (−3.2 kcal mol⁻¹). If taking Cat.1 and Cat. 2 as one system, one can roughly estimate the probability ratio of the occurring of the two rate-limiting steps via Boltzmann statistics⁶² on the basis of the energies of the complexes and transition states. The result indicates that the insertion probability ratio of the first monomer by Cat.1 and Cat.2, respectively, was calculated to be 5.4/94.6, suggesting the higher activity of Cat.2 compared to Cat.1. Besides, the calculation results show that the isotactic polymers (si-re-re-re) can be obtained by Cat.1 and Cat.2 (Tables S1 and S2†). Moreover, the calculation results show that dispersion correction does not affect the energetic significantly in this work (Fig. 3 vs. S1†).

Fig. 3 Computed energy profiles for Cat.1 mediated chain initiation and chain propagation of m. The C=C insertion and β-H elimination pathways are indicated in black and blue, respectively.

Fig. 4 Computed energy profiles for Cat.2 mediated chain initiation and chain propagation of m. The C=C insertion and β-H elimination pathways are in black and blue, respectively.

Moreover, it can been seen that isomerization of the third molecule insertion product is always easier to occur than next C=C coordination (Fig. 3 and 4). It is worth noting that the formation of the P3’₁ intermediate (−29.7 kcal mol⁻¹) is more favorable than the m coordination (C4₁, -16.5 kcal mol⁻¹) by more than 13 kcal mol⁻¹ (Fig. 3), thus potential wells (P3’₁) may be formed to reduce the polymerization activity. However, for Cat. 2, it can be seen from Fig. 4 that the thermodynamic energy difference between P3’₂ (−30.5 kcal mol⁻¹) and C4₂ (−23.2 kcal mol⁻¹) is only 7.3 kcal mol⁻¹. At the same time, the β-H elimination is an obvious endothermic process, which makes the β-H elimination is less favorable than C=C insertion. Therefore, it can be further proved that the polymerization activity of Cat. 2 is higher than that of Cat. 1, which can partially explain the experimental results.

To obtain a deeper insight into the activity difference in chain propagation, activation strain analysis⁶³ was performed for the corresponding two transition states (TS4₁ and TS4₂, Fig. 5). For this purpose, the transition state (TS) structures were divided into two fragments, viz., the catalyst part (cat.) and monomer moiety (mono). The energies of the fragments in the TS geometries were evaluated via single-point energy calculations. Such single-point energies of the fragments and the energy (corrected by BSSE) of the TS were used to estimate the interaction energy ΔE_int between the two fragments. The single-point energies, together with the energies of the respective fragments in their optimal geometries, allowed for the estimation of the distortion energies of the two fragments, ΔE_strain(cat.) and ΔE_strain(mono.). As the energy of TS, ΔE_TS, is evaluated with respect to the energy of the two separated fragments, the relation ΔE_TS = ΔE_int + ΔE_strain(cat.) + ΔE_strain(mono.) holds. As shown in Fig. 5, in the case of TS4₁, the interaction energy ΔE_int was significantly stronger than that in TS4₂ (−71.7 kcal mol⁻¹ vs. −34.1 kcal mol⁻¹), but the total distortion energy of TS4₁ was larger (67.2 kcal mol⁻¹). Therefore, TS4₁ needed to overcome the higher energy barrier 11.9 kcal mol⁻¹. Therefore, the larger steric repulsion between the metal center and monomer moiety in TS4₁ accounted for its lower stability in comparison with TS4₂.

Fig. 5 Geometric structures (a) and activation strain analysis (b) of TS4₁ and TS4₂.

When considering the polymerization behavior, it is necessary to clarify the nature of the monomer and active species. First, the frontier molecular orbital energy gap between m and two active species (Cat.1 and Cat.2) was calculated. Generally, the reactivity is strongly influenced by the frontier molecular orbital energy gap of the two reactants: the smaller the energy gap between the two reactants, the higher the reaction activity. As shown in Fig. 6, the energy gap between m and Cat.1 is significantly smaller than that between m and Cat.2; therefore, there is a relatively strong interaction between m and Cat.1 in TS4₁ (−71.7 kcal mol⁻¹). The difference in the reactivity between the two catalysts originates mainly from the steric hindrance effect. However, the difference in activity is not manifested in the topographical steric map analyses,⁶⁴ because buried volume %V_Bur of Cat. 1 and 2 are close to each other (81.7 vs. 82.3, Fig. S2†). Therefore, in the subsequent sections, we will discuss the structures of the two transition states TS4₁ and TS4₂ in detail (Fig. 7). In TS4₁, the polymer chain has to be twisted to a certain extent for coordination and insertion of the next monomer, but the steric hindrance of the fused-ring on the ligand of Cat.1 is large, resulting in a large repulsion between the polymer chain and the fused-ring. As such, TS4₁ needs to overcome the higher energy barrier. However, one of the metallocene rings of Cat.2 is cyclopentadienyl with small steric hindrance. The above-mentioned repulsion does not exist in this system, and thus, the energy barrier is relatively low. Consequently, the polymerization activity can be improved by reducing the repulsion between the ligands and polymer chains.

Fig. 6 Comparison of the frontier molecular orbital energy gap between m and Cat.1(a)/Cat.2(b).

Fig. 7 Geometric deformation of the transition states TS4₁ and TS4₂.

Next, the effects of different catalyst ligands on the molecular weight of polymers will be discussed. In general, the larger the energy barrier difference of the C=C insertion and β-H elimination, the higher the molecular weight of the polymerization products. In this study, the insertion of the fourth molecular monomer and β-H elimination based on the third insertion product mediated by Cat.1 and Cat.2 were investigated (Fig. 3 and 4). The results showed that when the catalyst was changed from Cat.1 to Cat.2, the C=C insertion barrier decreased by 1.8 kcal mol⁻¹ and the β-H elimination energy barrier decreased by 1.5 kcal mol⁻¹. As a result, the energy barrier difference between the C=C insertion and β-H elimination mediated by Cat.2 was 0.3 kcal mol⁻¹ higher than that by Cat.1, indicating that C=C insertion is relatively easier when using Cat.2. These results are consistent with the above-mentioned experimental results (Table 1). In addition, the effect of changing the ligand on C=C insertion is greater than that on β-H elimination. In other words, the molecular weight of the polymerization product can be increased by reducing the C=C insertion energy barrier.

Effect of monomer chain length on stereoselectivity

It has been reported in the literature⁵² that a syndiotactic polymerization product can obtained through the polymerization of propylene catalyzed by Cat.2, which in contrast to what is mentioned above, that isotactic products can be obtained through the polymerization of m catalyzed using the same catalyst. To further understand the effect of the monomer chain length on stereoselectivity, propylene polymerization with Cat.2 was conducted and the results are depicted in Fig. 8. The computational results are consistent with those reported in the literature,⁵² and syndiotactic polymerization products (si-re-si-re) were obtained. Further, m and propylene showed different stereoselectivities at the third molecule insertion (si-re-re-re vs. si-re-si-re). Therefore, the activation strain analysis for the TSs of the third insertion (both m and propylene) was performed. As shown in Fig. 9a, in the case of re-TS3₂, the total distortion energy ΔE_strain is 60.5 kcal mol⁻¹, which could be partly balanced out by its ΔE_int (−69.3 kcal mol⁻¹) leading to a ΔE_TS of −8.8 kcal mol⁻¹. By contrast, a larger total distortion energy (ΔE_strain = 73.8 kcal mol⁻¹) in the si-TS3₂ is difficult to be compensated by the interaction energy of −82.6 kcal mol⁻¹, thus producing a slightly higher ΔE_TS (si-TS3₂, −8.1 kcal mol⁻¹). Therefore, the larger steric repulsion between the metal center and monomer moiety in si-TS3₂ could account for its lower stability in comparison with re-TS3₂. In addition, as displayed in Fig. 9b, the interaction energy between the monomer and catalyst in si-TS3₂^P and re-TS3₂^P are almost the same, and the large total deformation energy of the monomer and catalyst in re-TS3₂^P is the primary reason for the higher energy barrier (13.0 kcal mol⁻¹).

Fig. 8 Computed energy profiles for 2 mediated chain initiation and chain propagation of propylene.

Fig. 9 Activation strain analysis of si-TS3₂, re-TS3₂, si-TS3₂^P and re-TS3₂^P.

Based on the above-mentioned results, it was observed that the different types of stereoselectivity in the polymerization of m and propylene can be explained based on the steric hindrance between the catalyst and monomer. Therefore, by analyzing the geometric structure of the key transition states, the main causes of different deformations can be explored. As can be seen in Fig. 10, in si-TS3₃, due to the long monomer (m) and polymer chain, it is easy to produce a large repulsion between the monomer and polymer chain, resulting in a relatively high energy barrier (11.4 kcal mol⁻¹). However, in re-TS3₃, the relative orientation of monomer insertion is changed from si surface to re surface, effectively avoiding a large repulsion and lowering the energy barrier (9.9 kcal mol⁻¹). However, such a steric repulsion does not exist in propylene polymerization because the molecular chain of propylene is relatively short. Therefore, syndiotactic products can be obtained by the polymerization of propylene.

Fig. 10 Geometric structures of si-TS3₃ and re-TS3₃.

Conclusion

In summary, the origin of activity and molecular weight metallocene difference in the polymerization of 1-decene, catalyzed by various zirconium catalysts, have been computationally elucidated. The obtained results indicate that the effect of different catalyst ligands on β−H elimination is less than that on C=C insertion. Therefore, these systems can be used to indirectly regulate the molecular weight of polymerization products, by changing the energy barrier of the C=C insertion. The easier the C=C insertion, the higher the molecular weight of the polymerization product. Moreover, improving the activity of catalytic polymerization can be achieved by reducing the repulsion between the catalyst ligand and the polymer growth chain, such as reducing the steric hindrance of one aromatic ring of the catalyst. In addition, through the analysis of the transition state structure, the chain length of α-olefins will directly affect the stereoselectivity of polymerization products. When the length of the monomer is short, syndiotactic products are obtained, otherwise isotactic products are obtained. It is worth noting that, in practice, a polymerization reaction system is more complex. When the steric hindrance is regulated, the electronic factors may also change accordingly. Therefore, specific analysis must be carried out for specific systems.

Conflicts of interest

The authors declare no competing financial interest.

Acknowledgements

This work was partly supported by the NSFC (22101041, 22071015, U1862115) and China Postdoctoral Science Foundation (2021M700664). The authors also thank the RICC (RIKEN Integrated Cluster of Clusters) and the Network and Information Center of the Dalian University of Technology for part of the computational resources.

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Footnote

† Electronic supplementary information (ESI) available: Optimized cartesian coordinates of all stationary points together with their single-point energies (a.u.) in solution and the imaginary frequencies (cm⁻¹) of transition states (XYZ file). See https://doi.org/10.1039/d2ra03180a

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