Computational modeling of heterogeneous Ziegler-Natta catalysts for olefins polymerization

Progress in Polymer Science 84 (2018) 89–114

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Progress in Polymer Science journal homepage: www.elsevier.com/locate/ppolysci

Computational modeling of heterogeneous Ziegler-Natta catalysts for olefins polymerization Naeimeh Bahri-Laleh a,∗ , Ahad Hanifpour a , Seyed Amin Mirmohammadi b , Albert Poater c , Mehdi Nekoomanesh-Haghighi a , Giovanni Talarico d,∗ , Luigi Cavallo e,∗ a

Polymerization Engineering Department, Iran Polymer and Petrochemical Institute (IPPI), P.O. Box 14965/115, Tehran, Iran Department of Chemical Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran c Institut de Química Computacional i Catàlisi, Departament de Química, Universitat de Girona, c/ Ma Aurèlia Capmany 69, E-17003 Girona, Catalonia, Spain d Dipartimento di Scienze Chimiche, Università degli Studi di Napoli Federico II, Via Cintia, 80124, Napoli, Italy e King Abdullah University of Science and Technology (KAUST), Physical Science and Engineering Division (PSE), KAUST Catalysis Center (KCC), Thuwal, Saudi Arabia b

a r t i c l e

i n f o

Article history: Received 21 December 2016 Received in revised form 26 May 2018 Accepted 17 June 2018 Available online 23 June 2018 Keywords: Ziegler-Natta catalysts Olefin polymerization DFT Computational modeling Polyolefin

a b s t r a c t Since 1963, when Karl Ziegler and Giulio Natta were jointly awarded the Nobel Prize for their discoveries of the catalytic polymerization of olefins with Ti-chlorides and Al-alkyls, heterogeneous Ziegler-Natta (ZN) catalysts have become the main catalysts for the industrial production of polyolefins. Despite of the relevance of ZN catalysts for the large-scale production of polyolefins, a clear mechanistic understanding of these catalysts is still incomplete due to the elusive nature of the active site structures. Over the last two decades, researchers have used density functional theory (DFT) methods to clarify the polymerization mechanisms and to identify the nature of the active sites, unraveling the influence of supports, cocatalysts, and the effect of internal and external donors on the polymerization processes. Major efforts were dedicated to understanding the origin of stereoselectivity in ␣-olefin polymerization as well as the termination reactions mechanisms, and the role that impurities can play in heterogeneous ZN catalysis. Here, we review the DFT studies on heterogeneous ZN catalysts and suggest promising areas for future research. © 2018 Elsevier B.V. All rights reserved.

Contents 1. 2. 3.

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5. 6.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Benchmarking and models building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Active site model and polymerization behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 3.1. MgCl2 structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 3.2. MgCl2 -donor interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 3.3. MgCl2 -TiCl4 interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 3.4. Role of cocatalyst . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Mechanism of polymerization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 4.1. The chain growth step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 4.2. Stereoselectivity of propylene insertion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 4.3. Regioselectivity of propylene insertion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .105 4.4. Chain transfer reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Stability of ZN catalysts and the effect of undesired parallel reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

∗ Corresponding authors. E-mail addresses: [email protected] (N. Bahri-Laleh), [email protected] (G. Talarico), [email protected] (L. Cavallo). https://doi.org/10.1016/j.progpolymsci.2018.06.005 0079-6700/© 2018 Elsevier B.V. All rights reserved.

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1. Introduction The discovery of Ziegler-Natta (ZN) catalysts in the 1950s for the polymerization of olefins is one of the fundamental events of the last century in chemistry that has also had huge impact on the chemical industry [1–5]. Heterogeneous ZN catalysts, are among the most important industrial catalysts used in polymerization reactions to produce polyethylene (PE) and isotactic polypropylene (iPP) [6–8], because of the extraordinary catalytic activity combined with high stereoselectivity and good molecular mass capability [9,10]. The main advantages of heterogeneous catalysis over homogenous catalysis (metallocenes and non-metallocenes catalysts) [11–14] are the increased efficiency of the catalyst, the decreased product cost and the control of the morphology of the polymer granule, which reduces the reactor fouling [15–17]. Despite the economic relevance of polyolefin commodities [18], with a 2015 production volume on the order of nearly 150 million tons (predominantly PE and iPP), intimate understanding of the active sites of ZN catalysts remains elusive. This limited knowledge is a consequence of the complex multisite nature of ZN catalysts, although they are formed from only four key ingredients, including an inert MgCl2 support, the catalytically active TiCl4 adsorbed on the MgCl2 surfaces, an Al-alkyl (typically AlEt3 ), which activates the adsorbed TiCl4 and, for high yield catalysts, suitable pairs of electron donors (often reported in literature as Lewis bases, LBs). The internal donor (ID) is added to the precatalyst during its synthesis, whereas the external donor (ED) is placed in the reaction medium in combination with the Al-alkyl. The exchange of ID and ED on the catalyst surface, combined with their function of complexing with Al-alkyl, tunes the catalytic behavior and increases the stereoregularity of the produced polymer [19–21]. Despite this simple composition, the characterization of heterogeneous ZN catalysts is a long-established problem that several theoretical [22–29] and experimental studies [30–37] have attempted to solve [38,39].

Fig. 1. Typical cluster models used to mimic the (110) (a) and the (104) facets (b) of MgCl2 . On top of the cluster (a), composed of 13 MgCl2 units mimicking the (110) MgCl2 surface, a TiCl4 molecule is adsorbed; the arrows indicate suitable sites for ligand coordination close to the Ti active center crucial to confer stereoselectivity of propylene insertion. On top of the cluster (b), composed of 14 MgCl2 units mimicking the (104) MgCl2 surface, a dimeric TiCl4 species is adsorbed. The chlorine atoms marked by a * are considered to confer stereoselectivity of propylene insertion. A minimal model of Ti active site is reported in (c) resembling the main features of (a) and (b). The substituents marked by a * (chlorines in (c)) simulate the generic ligands in (a) or the chlorine atoms labeled with a * in (b).

During polymerization of olefins by ZN-catalysts several reactions are competing with chain propagation (fast and consecutive monomer insertions into the Ti-polymeryl bond), the main ones being the chain transfer reactions (also called chain terminations) and the catalyst deactivation. The main chain termination reactions promoted by ZN catalysts are ␤-H elimination from the growing polymer chain to the metal (BHE) or ␤-H transfer from the growing polymer chain to the incoming monomer (BHT) [40–44]; via hydrogenolysis with molecular hydrogen (often referred to as hydrogen sensitivity) [45–47] or by transalkylation with Alalkyl cocatalysts [48,49]. These reactions play important roles in transition-metal-catalyzed olefin polymerizations and they have been extensively studied experimentally [50–55] and theoretically [56–61] on well-defined single site catalysts, obtaining important insights which helped to clarify these steps also on heterogeneous ZN systems. However, the more challenging topic of heterogeneous ZN catalysis still remains the definition of reliable models of the active site adsorbed on the MgCl2 surface. In this review we are focused on these aspects with a special emphasis on the progress achieved by using density functional theory (DFT) methods. In the past, the vast majority of the theoretical studies used small-sized clusters to mimic ZN catalytic systems. As a consequence of the recent increase of computational power, DFT simulations are no longer limited to small-sized model systems. Today large MgCl2 clusters with average dimensions as large as 30 Å can be modeled by DFT, matching the real particle size of ZN catalysts [20,62]. Here, we review work reported so far using DFT on the underlying mechanisms promoted by heterogeneous ZN catalysts and their polymerization behavior.

2. Benchmarking and models building In this section we briefly present the standard approaches used to model supported ZN catalysts, with advantages and limitations. Before starting, we recall that the most recent view of industrially used MgCl2 supported ZN-catalysts is that they consist of small MgCl2 particles that can probably break during the polymerization process, reducing further the average dimension of the MgCl2 particles [15]. Within this scenario, the MgCl2 particles cannot be considered as a perfect 3-dimensional crystal, or as a small cluster of MgCl2 units mimicking the single site of homogeneous catalysts. For these reasons choosing the best computational approach to model MgCl2 -supported ZN catalysts is not straightforward. The most typical approaches used in the field are based on the cluster model or on a solid-state approach based on periodic boundary conditions (PBC). The cluster model reduces the whole MgCl2 support to a cluster composed by few MgCl2 units, normally less than 30 units. The geometry of these clusters can be shaped to model crystallographic surfaces of MgCl2 , as shown in Fig. 1a and b, respectively. On top of these clusters the adsorption of TiCl4 , of the LB or the Al-alkyls, as well as the chain growth event, have been modeled. Moving away from the surface, the cluster is normally composed of 2 to 5 layers of Mg atoms. The possibility of using relatively small clusters is given by the rather inert nature of MgCl2 , which has small impact on the electronics of the Ti-species adsorbed on the surface. The greatest limit of the cluster model is in the limited dimensions of the cluster, which prevents relaxing properly the Mg and Cl atomic positions. The most popular approaches are in freezing completely the MgCl2 positions, which prevents the small cluster to deform in an unphysical way, or in completely relaxing the cluster, which allows to capture some relaxation that naturally occurs at the MgCl2 surface. The most balanced approach probably consists in freezing only the MgCl2 units that do not interact with the adsorbed species, while relaxing the MgCl2 units that interact

N. Bahri-Laleh et al. / Progress in Polymer Science 84 (2018) 89–114

with the adsorbed species. This hybrid approach allows for some relaxation of atoms at the surface, while keeping the overall MgCl2 crystal geometry. From a computational perspective, the cluster model allows to: reduce remarkably the computational cost of the calculations; model a large number of situations in a short amount of time with limited computational resources; use a large variety of computer packages developed to treat molecular systems. Finally, a minimal model reported in Fig. 1c combination of both MgCl2 surfaces allowed to obtain important insights on the mechanisms of polymerization promoted by ZN heterogeneous catalysts, in particular to locate the transition state (TS) geometries for the stereoselectivity, regioselectivity and chain transfer reactions (see Section 4). On the other side, the PBC approach is rooted on solid-state physics, with programs developed to handle metals, semiconductors and metal-oxides, whose properties cannot be modeled by a cluster model. Within the PBC approach the simulation box represents the unit cell that is replicated in the 3-dimensions, as shown in Fig. 2. The main advantage of the PBC model is that all the atomic positions within the simulation box can be relaxed, thus providing a reliable approximation that takes into account the rigidity of the bulk together with the flexibility at surfaces. For this reason, this approach is highly suitable to investigate the relative stability of different facets of MgCl2 . The main drawback of the PBC approach is in the remarkable computational cost, at least one order of magnitude higher than for the cluster model approach. Further, the intrinsic regularity of the PBC approach does not allow for simple modeling of corners and other defective species, which is a limit considering that the industrially most effective ZN-catalysts are known to be small MgCl2 particles that can be further fragmented during polymerization. As for computational protocols to be used for routine work, functionals belonging to the generalized gradient correct approximation, such as BP86 [63,64], PW91 [65], and PBE [66,67], are normally used for geometry optimizations considering that models of ZN catalysts can usually be composed by several MgCl2 units, which are computationally more expensive than first row atoms. As for energies, functionals including a Hartree-Fock contribution, the so-called hybrid functionals, such as B3LYP [68–70], are quite popular. In recent years, with the understanding that dispersion (or Van der Waals) interactions cannot be neglected for accurate interaction energies in general, and are relevant when weakly interacting systems, such as TiCl4 and MgCl2 , have to be calculated, adding an empirical dispersion term [71,72] to a standard functional, thus leading to dispersion corrected functionals, such as PBE-D3, or B3LYP-D3, or to use functionals tuned to incorporate dispersion interactions, such as the M06 functional [73], has become mandatory. Finally, the incompleteness of basis set may determine what is called basis set superposition error (BSSE) [74], whose effects are critically dependent of the basis set used. As mentioned, one of the interactions most affected by dispersion, functional and basis set is the coordination of TiCl4 on MgCl2 support. This explains the large spread reported in literature for the simple energy gain due to the chemical adsorption of TiCl4 on the MgCl2 facets (see next sections) leading to a (large) variety of models of active site. Importantly, we remark that the adsorption energy (Eads ) most often reported in literature is the pure electronic component, lacking the enthalpy and entropy contributions to the fundamental thermodynamic parameter controlling adsorption, which is the Gibbs free energy of adsorption (Gads ). Indeed, an unfavorable entropic term, mostly related to freezing the adsorbed species on the MgCl2 surface should be always added to the adsorption energy. At room temperature it corresponds to a penalty of approximately 10 kcal/mol. For this reason, only adsorption energies larger than 10 kcal/mol have been usually considered in literature to result in the stable adsorption of a given species. Finally, for the sake of con-

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sistency all the adsorption energies discussed in this review will be considered positive if the adsorption process is exothermic. The conclusion of this section is that critical reading and comparison of computational ZN-literature is required, paying special attention to the specific computational protocol used. Unfortunately, it is not easy to benchmark properly different functionals because of missing experimental interaction energies between the various components of ZN catalysts, or because missing highly accurate theoretical values from state-of-the-art quantum mechanics methods. Within this scenario, the only reliable experimental data available probably are the enthalpies of association between TiCl4 and a series of LB from titration calorimetry [75], and a benchmark study indicated that basically every functional considered was underestimating severely the enthalpy of association [75]. However, the functionals used did not include a dispersion term, and the ability of DFT methods to reproduce these experimental data should be reconsidered. Unfortunately, no accurate experimental data is available for the problematic interaction between TiCl4 and MgCl2 . This lack of reference experimental data spurs some efforts to benchmark DFT methods towards as accurate as possible theoretical data using the so called CCSD(T) approach (coupled cluster with iterative treatment of single and double excitations and perturbative treatment of triple excitations), considered as golden standard in contemporary computational chemistry. For instance, Correa et al. [76] investigated the validity of some common DFT methods in reproducing key interactions (TiCl4 /MgCl2 , TiCl4 /Lewis bases, MgCl2 /Lewis base) present in ZN systems. It was shown that all the DFT functionals considered underestimate the CCSD(T) energies, except for the M06 and M06L functionals [73], which overestimate the CCSD(T) energy. Lower performances were obtained with the B3LYP, BP86 and BLYP functionals, which are nevertheless commonly used in ZN catalyst simulations. In another work, Ehm et al. tested the validity of different DFT functionals to reproduce the CCSD(T) binding energy of a series of bridged dimers [XH2 ]2 (␮-Y)2 and [XMe2 ]2 (␮-Y)2 (X = AlTl, Y = Me, H, OMe, NMe2 , F, Cl) and related compounds [77]. The sharp conclusion was that DFT methods not including dispersion corrections perform poorly, while dispersion corrected functionals proved reasonably accurate energies. Nevertheless, both studies suffer the limited dimension of the systems modeled, and the limited basis sets used, which restricts the accuracy of these studies to qualitative conclusions only. The recent development of much faster approximate CCSD(T) methods [78], already benchmarked to treat with compounds including alkali and alkaline-earth metals and non-covalent interactions [79,80], should allow to expand the scope and accuracy of these benchmarking studies. Nevertheless, the background provided above indicates that it is quite hard to know which computational protocol provides the most accurate energies. Given this mandatory warning, through this review we will try to focus on the chemical insights obtained by applying DFT calculations on the ZN catalysis and try to avoid discrepancy of interpretation due to different DFT protocols.

3. Active site model and polymerization behavior Currently used high-yield ZN catalysts have been improved from simple TiCl3 crystals (which represented the first two catalyst generations) to MgCl2 /TiCl4 /donor systems, in which the electron donor is a LB that is added either during catalyst preparation (internal donor, ID) or during polymerization (external donor, ED), see Table 1. For the sake of simplicity, in the following we will use the acronym LB to indicate a generic Lewis base (sometimes acting both as ID and ED), since this is the term commonly used in theoretical papers, whereas the acronyms ID and ED will be used for the electron donors used specifically as ID or ED in the experiments.

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Fig. 2. Adsorption of an alkoxysilane on the (104) facet of MgCl2 as studied by PBC methods. Part (a), top view from a direction perpendicular to the (104) facet. Part (b), side view of the same structure. In both cases the simulation box, defined by the blue frame, is replicated in the 3 dimensions. The length of the simulation box along the a and b directions is determined by the lattice constants of MgCl2 . The length of the simulation box along the c direction is expanded to prevent interaction between MgCl2 and adsorbed species in contiguous cells.

Fig. 3. (a) ␣-MgCl2 and (b) ␤-MgCl2 structures. Table 1 Development of MgCl2 -supported ZN catalysts in terms of generation following the combination of ID and ED and performances. Generation

Internal Donor (ID)

External Donor (ED)

Productivitya)

XSb)

Mw/Mn

Third Fourth Fifth Sixth

Ethylbenzoate Dialkylphthalate 2,2’-dialkyl-1,3- dimethoxypropane Dialkylsuccinate

Aromatic monoester Alkoxysilane None or Alkoxysilane Alkoxysilane

0.5-0.8 1-2 >2 1-2

3-5 1-5 2-5 1-5

6–9 6–8 4–6 >8

a) 103 kg(PP) g(Ti)−1 . b) Xylene-Soluble Fraction in wt.-%.

The activation of the catalyst requires the addition of alkylating and reducing species (AlEt3 is the most common one) mixed with an ED. As we anticipated in the Introduction, high-yield ZN catalysts can be interpreted as a puzzle (multicomponent system) of four basic pieces: MgCl2 , TiCl4 , LB (both as ID and/or ED) and Al-alkyl. The chemical nature of these pieces as well as their right combination strongly contribute to the catalyst activity and the polymer properties to the point that ZN catalysts are routinely defined following the development of catalyst generations (see Table 1). In this section, we aim to identify one-by-one the role played by these four components, at least as recognized by DFT studies, with the alert that cross-interactions between them are always present during this review (and cited references) and this may complicate the whole picture. 3.1. MgCl2 structure MgCl2 is the fundamental support used in ZN catalysts since the late ‘60 s [81]. According to the literature, there are three crystalline forms of MgCl2 , named ␣, ␤ and ␦ that are highly discussed [82–85].

The ␣-form (belonging to the R3m space group) is the commercial form of MgCl2 . Its chloride anions are arranged in a face-centered cubic (fcc) unit with the magnesium cations occupying half of the octahedral interstices. Although the primary unit cell is rhombohedric, the conventional cell is hexagonal. In the ␤-form (belonging to the P3m1 space group), the chloride anions are arranged in a hexagonal close packing (hcp) unit [86]. In both forms the disposition of the Mg atoms leads to the formation of MgCl2 monolayers kept together by Van der Waals forces, see Fig. 3. The main difference between these two forms is the arrangement of the Cl atoms in the direction of stacking, which is ABCABC. . . for the ␣-form and ABAB. . . for the ␤-form. The inner structures of the hexagonal layers are almost identical in both forms since the Van der Waals interaction keeping together the stacked MgCl2 monolayers is weak. MgCl2 is physically or chemically activated to obtain a support with an extensive surface area, which is indispensable for efficient catalysis [19]. In the physical route, ␣-MgCl2 is ball-milled into nano-sized particles, known as the ␦-phase, for several hours [87–89]. Activated MgCl2 , initially prepared by ball milling a mix-

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Table 2 Structural parameters and lattice constants of ␣- and ␤-MgCl2 obtained experimentally and by DFT calculations [100]. Phase ␣-MgCl2 ␤-MgCl2

a

Fig. 4. Model of the MgCl2 monolayer together with indication of the basal (001) plane, and two lateral cuts: (110) and (104).

ture of MgCl2 and ID, leads to the formation of many small-sized crystallites. X-ray diffracttion studies disclosed that the ␦-form of MgCl2 , possesses a rotational disorder in the Cl-Mg-Cl triple-layer stacking and highly disordered crystalline form can be obtained by chlorination of a Grignard compound [19,85]. Focusing on the possible surface terminations of MgCl2 , those classically considered in the literature are the (001), the (110), the (104) facets (see Fig. 4) [62,90,91], with the recent addition of the (015) facet [22]. We remark that the (104) facet of stacked MgCl2 monolayers is terminated by 5-coordinated Mg atoms, similarly to the (100) facet of a single MgCl2 monolayer. Indeed, in pioneering papers on the MgCl2 side edges [7,92–94] the lateral facet of a monolayer presenting 5-coordinated Mg atoms was labeled (100); in this review, for the sake of clarity, we will use the notation (104) also when discussing works in which the authors used the (100) notation. The (001) facet corresponds to the basal plane composed by Cl atoms only, and it is considered unsuited for adsorption of TiCl4 . The (104) and (110) facets, shown in Fig. 4, have exposed Mg2+ ions that are tetra- and penta-coordinated, respectively, thus having one and two vacancies relative to the hexacoordinated Mg atoms in the bulk [92]. It is now generally accepted that activated MgCl2 particles are built by a number of MgCl2 monolayers that are piled irregularly one above the other, with exposure of the (104) and (110) facets [22,90], although alternative structures consisting of flat chains of MgCl2 have been proposed based in particular on the structures of crystalline ethanol adducts (MgCl2 ·nEtOH) [95–98]. The identification of the catalytically relevant MgCl2 surfaces has been the subject of several combined computational/experimental papers. Bulk and surface relaxation of MgCl2 have been analyzed using various DFT approaches [99] combined with experimental IR spectra of carbon monoxide bound to the MgCl2 surface, leading to the conclusion that relaxed (110) and (104) surfaces (the latter defined as (100) in the original paper) are in good agreement with experiments. Credendino et al. [100] studied the surface and bulk structure of the ordered ␣- and ␤-forms of MgCl2 using periodic DFT methods with an empirical dispersion correction term [72]. The comparison of calculated structural parameters and lattice constants with the experimental results are presented in Table 2. From a computational point of view, among the studied functionals the PW91 functional provided the highest accuracy for the calculation of lattice constants and the ␤-form has been estimated to be slightly higher in energy ( + 0.2 kcal/mol per unit cell) than the ␣-form. The same authors also attempted to simulate the crystal morphologies of MgCl2 to identify the nature of the exposed crystal facets by using Wulff’s construction [101] and the kinetic model of Bravais, Friedel, Donnay and Harker (BFDH)

Exp DFTB1 a Exp DFTB1 a PW91/USP PBE/NCP

a = b (Å)

c (Å)

3.6363 3.7386 3.641 3.741 3.69 3.73

17.6663 18.3002 5.927 6.134 ∼6 ∼6

B3LYP with SVP and TZVP base sets for Mg and Cl, respectively.

[102]. Their results suggested that for well-formed MgCl2 crystals, irrespective of the specific phase, both models produce crystals exposing penta-coordinated Mg surfaces (corresponding to the (104), (101), and (012) facets of ␣-MgCl2 ) and that the (110) facet exposing tetra-coordinated Mg atoms should not be formed to a considerable extent. The use of periodic boundary conditions and/or a better selection of a MgCl2 cluster as well as more reliable DFT protocols was a direct consequence of papers revealing that relaxation and/or reconstruction processes affect the surfaces of MgCl2 in varying degrees, according to the different Miller indexes [91,103]. Since then, MgCl2 crystallites of different shapes, sizes, and edges (typically the (104) and (110) edges) were computed and the stability of surfaces was calculated in the presence of several Lewis bases (LB). Interestingly, the stability of the MgCl2 surfaces was reported to be critically dependent also by the extent of MgCl2 coverage operated by the LBs [104,105]. In fact, in the absence of any LB, such as in the simple mechanical milling of MgCl2 , large crystallites presenting (104) edges are predicted, in agreement with previous work (see reference [100]), whereas in the presence of a LB, smaller crystallites presenting (110) edges should be formed [104,105]. The density of vacancies at the Mg atoms (v ) (defined as v/nMg , where v = number of vacancies at the Mg atoms and nMg = number of MgCl2 units), was suggested as the best parameter to describe the relative stability of MgCl2 crystallites; a linear correlation of the formation energy, Ef , of a crystallite composed by n MgCl2 units with v can be used to predict and compare the stability of differently shaped crystallites [104]. The presence of corners [106] and the role of defects of MgCl2 crystallites were also analyzed. Bazhenov et al. [107] used periodic boundary conditions in combination with the PBE0 functional (and with basis set of triple-␨ quality) to stress the role of MgCl2 defects on the stability of the (110) and (104) facets. The defects were simulated by replacing chlorine with bromine atoms and the effects of the percentage of bromine incorporation and surface thickness on the properties of the MgCl2 (104) and (110) surfaces were systematically investigated. They also used a methanol molecule as a model of a LB to calculate the binding energies on the different defected surfaces. The conclusion was that crystallites are stabilized by the substitution of coordinatively unsaturated edges and this also lowers the binding energy of LBs with a stronger effect on the (104) than on the (110) surface. A further extension of this work [108] lead to the formation of two patterns for the step defects on the surfaces: staircase (ST) and battlement (BA) patterns as shown in Fig. 5c. They constructed a set of three to four surfaces with each pattern (BA104, BA110, and ST), by varying the lengths of the terraces between the adjacent steps in a systematic way. Relative stabilities of the studied surfaces as a function of the tetra-coordinated Mg atom fraction (R = (N4 /(N4 +N5 )), where N4 , N5 and N6 is the number of 4-fold, 5-fold and 6-fold Mg atoms) are shown in Fig. 5. The relative stabilities of the defected surfaces had nearly perfect linear relationships with the relative number of tetra- and penta-coordinate sites (see Fig. 5a). This means that surface-site coordination is a dominant factor in determining the

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Fig. 5. Relative stabilities of the studied surfaces as a function of 4-coordinated Mg atoms fraction (R = (N4 /(N4 +N5 )) in the (a) neat and (b) methanol covered surfaces. Part (c), examples of the battlement and staircase defected MgCl2 surface models (6-coordinated Mg atoms in yellow, 5-coordinated Mg atoms in red, 4-coordinated Mg atoms in blue, Cl atoms in green). Adapted from ref. [108].

relative stabilities of the surfaces and favors penta-coordinated Mg sites. On the other hand, upon saturation of the surfaces by methanol (used as a model electron donor), the stability order completely reversed, and the (110) facet is selected as the most stable, while the (104) facet is rejected as the less stable (see Fig. 5b). All the defected structures lie between these two limits and their stabilities are linearly dependent on surface-site coordination. Experimental studies combined with periodic DFT calculations suggests that the MgCl2 (110) (or equivalent) terminations with tetra-coordinated Mg are the most likely catalytic surfaces of highyield heterogeneous ZN systems, because both TiCl4 and LBs can strongly bind to this facet under polymerization conditions (see next sections) [26,109]. The (104) surface is instead the most plausible facet in neat MgCl2 crystals, but their lower Lewis acidity compared with the MgCl2 (110) facet favors the latter when LBs come into play. It should be noted, at the end of this section, that the last conclusion seems contradicting the long-standing models of ZN active sites derived by the analogy with the models proposed for violet TiCl3 systems, which were pointing to MgCl2 (104) (or equivalent) terminations with penta-coordinated Mg as the preferred surfaces for TiCl4 chemisorption [7,92]. This “change of paradigm” is a direct consequence of progress obtained by more refined DFT calculations which allowed the simulation of unrelaxed (small) cluster passing through combined quantum mechanical/molecular mechanical (QM/MM) approach, up to the computation of bulk crystals and slabs of MgCl2 (or calculations on finite cluster model of reliable size). Following these results, we review DFT studies focused on the MgCl2 -donor interaction before the ones on MgCl2 -TiCl4 .

3.2. MgCl2 -donor interactions Since the fourth generation of ZN catalysts was developed, the search for better donors (or for better combination of ID and ED) is a focus at both industrial and academic levels. These efforts are justified by the fact that the catalyst performances as well as the polymer properties strongly depend from the type of electron donor(s) present on the support and in the reaction medium. The LBs are critical to catalyst performance because they can markedly improve the stereoregularity of the polypropylene, the distribution of the molecular mass and the hydrogen response [15,110,111]. Furthermore, the LBs influence the distribution and the amount of TiCl4 in the ultimate catalyst by stabilizing the small primary MgCl2 crystallites and by competing with TiCl4 for coordination to the MgCl2 surfaces. Different reagents have been suggested as LB, including ester, phthalate, succinate, malonic ester, 1,3-diether, 1,3-dione, 1,3-diol ester, 1,4-diol, isocyanate, diamine, and glutaric acid ester. Among these donors, the 1,3-diethers, alkoxysilanes, aromatic esters (phthalates and benzoates) and aliphatic esters (particularly succinates) were found to be the most efficient (see Table 1). A first attempt to rationalize the role of donors was due to Corradini and co-workers [7,112]. In their proposal, the donors mainly play an “indirect” effect because they prefer to be absorbed on the MgCl2 (110) terminations, featuring the more acidic tetracoordinated Mg atoms, thus forcing TiCl4 absorption on the MgCl2 (104) facets in a dimeric Ti2 Cl8 form, supposed to lead to an isotactic polymer (see Fig. 1). In the absence of LBs, the TiCl4 can be absorbed both on the (104) and (110) facets, with the latter hosting non-stereoselective sites (see monomeric TiCl4 on Fig. 1b).

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95

Table 3 Calculated energies of adsorption (Eads ) and activation (Eact ) of several 1,3diether donor molecules on the (110) and (104) lateral cuts of MgCl2 [127]. Values in kcal/mol. 1,3-diether

Eads (110)

Eads (104)

Eact (100)

I.I. (%)

28.6

25.8

0.5

64.9

29.4

24.9

0.9

74.9

29.9

22.0

1.7

87.7

29.3

22.7

1.7

89.8

30.9

21.8

2.2

93.6

29.4

17.8

2.5

95.4

30.7

18.9

4.1

95.8

30.5

17.9

3.9

97.5

Fig. 6. Front view for the 1,3-dimethoxypropane adsorption on the (110) (a) and (104) (b) lateral cuts of MgCl2 . Adapted from ref. [127].

Although this model is in good agreement with many experimental data, it seems an oversimplification when it describes the function of the donors. In fact, experimental studies pointed out a more “direct” effect of the donors on the active site, including improving the stereoselectivity of already selective sites, the possible transformation of non-selective into stereoselective sites, variations of molecular mass and molecular mass distribution (see Table 1), and selectivity in the first monomeric unit insertion [113,114]. Overall, despite the numerous experimental [23,114–118] and theoretical [119–124] studies on electron donors, how they increase catalyst productivity and isotacticity is still matter of debate. Theoretical studies on donor interactions with MgCl2 surfaces confirm that the donor preferentially coordinates to the (110) facet [30,94,125,126], which suggested that this preferential coordination could possibly prevent TiCl4 adsorption onto the (110) surface of MgCl2 , considered to be feebly stereoselective. The straightforward application of such concepts in a simple model was developed by Toto et al. [94] who assumed that the xylene-insoluble and soluble polypropylene fractions are obtained by polymerization on the (104) and (110) facets, respectively, and that donor coordination competes with formation of the Ti catalytic species. This model, although far too simple, was able to rationalize in a quantitative way the industrially relevant dependence of isotactic indexes, I.I. (defined by two substantially equivalent procedures: the extraction with boiling heptane or the crystallization at room temperature from xylene solution) by the chemical structure of the 1,3-diether donors. Later, Lee and Jo [127] investigated in a more detail the relationships among eight 1,3-diethers donors and the isotacticity and productivity of polypropylene (see Table 3). Calculation of conformational energies of these 1,3-diethers indicated that all the considered donors show the same behavior. They have four conformational minima correlated to (G+ G+ ), (G+ G− ), (T T), and (T G+ ) conformations, or similar analogues, around the central C-C dihedral angles. Calculation of adsorption energies, Eads , showed that all 1,3-diethers prefer to bind to the (110) facet rather than to the (100) facet of MgCl2 (see Table 3). The Eads was calculated by subtracting the sum of the energies of the uncovered MgCl2 system (ES,f ) and a free 1,3-diether donor (ED,f ) from the total energy

of the system composed of a 1,3-diether (D) molecule adsorbed on a MgCl2 surface (ED/S ): -Eads = ED/S - ES,f - EDf [127]. The very strong adsorption energies reported in Table 3 clearly indicate that the adsorption of 1,3-diethers is irreversible. The authors also suggested that preferential adsorption of donors on either the (104) or the (110) MgCl2 facets are affected by the activation energy for adsorption. According to their calculations the adsorption of 1,3-diethers on the (104) facet requires that an energy barrier be overcome because the 1,3-diether undergoes a large conformational change (Fig. 6b), whereas adsorption on the (110) facet is a barrier less process since a large rotation of a methoxy group is not required (Fig. 6a). Analogously to the work of Toto et al, [94], a direct relationship between the experimental isotacticity index and the activation energy related to the adsorption of the donor on the (104) facet, Eact (100), was found such that by increasing Eact (100) from 0.5 to 4.1 kcal/mol corresponds to an increase of the isotacticity index from 64.9% to 97.5% (see Table 3) [127]. The chemical nature of donors as well as their chemical mode of absorption on the MgCl2 support was investigated by several other groups. Cavallo and coworkers investigated the interaction between different types of industrially relevant electron donors including 1,3-diethers, alkoxysilanes, phthalates and succinates (see Table 4) and the MgCl2 support by using DFT [128]. The donors were assumed to interact with the (110) and (104) MgCl2 surfaces as depicted in Fig. 7. The 1,3-diether and alkoxysilane have ether sp3 oxygen atoms, whereas phthalate and succinate contain both carboxylic sp2 and ester sp3 oxygen atoms (see the first two and the other three structures, respectively reported in Table 4), which chemically belong to two different groups. Adsorption energies (Eads in this review, ECoord in the original work) for donor adsorption onto the (110) and (104) facets of MgCl2 suggest that donor coordination via carboxylic sp2 oxygen is favored by roughly 10–15 and 1 kcal/mol relative to donor coordination via ester sp3 and ether sp2 oxygen, respectively. The Eads for donor coordination to the (110) and (100) facets of MgCl2 are summarized in Table 4.

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Fig. 7. Possible adsorption modes of the donors reported in Table 4 on (104) and (110) facets of MgCl2 single layer (a) and different layers (b), respectively. Due to the zigzag shape of the (104) surface, (see (b), on the right), the authors did not find a (104)-zip donor coordination. For this reason, the (104)-zip coordination energy is not reported in Table 4. Adapted from ref. [128].

Table 4 Calculated energies of adsorption (Eads ) for selected Lewis bases on the (110) and (104) lateral cuts of MgCl2 [128]. Values in kcal/mol. Donor

(110)chelate

(110)-bridge

(110)-zip

(104)-bridge

25.9

13.4

17.3

14.8

27.6

18.3

21.4

16.5

32.0

34.2

36.8

32.2

32.1

37.1

28.7

31.7

36.5

35.1

33.6

32.6

As indicated by the energy values reported in Table 4, all the studied donors coordinate strongly with both the (110) and (104) MgCl2 surfaces. However, the (110)-chelate coordination mode (see Fig. 7) is imposed for 1,3-diether and alkoxysilane due to the short spacer between the two coordinated oxygen atoms. On the other hand, existence of a larger spacer in succinates and phthalate confers enough flexibility to the donors, so that a variety of coordination modes is possible (see Table 4). This conformational flexibility was suggested to result in a broader diversity of active centers formed [128], and may explain the larger Mw /Mn ratio of the polypropylenes synthesized from phthalate-containing

catalysts with respect to polypropylenes synthesized from diethercontaining catalysts (see Table 1). Zakharov and coworkers [129] explored different modes of ethylbenzoate adsorption on the (110) and (104) surfaces of MgCl2 . Their results showed that ethylbenzoate complexes in both bidentate and monodentate modes can be formed on the (110) and (104) facets. The bidentate adsorption modes were stabilized on the (104) face by the decreased surface Mg-Mg neighboring coordination sites. Cheng and coworkers [130] extended the ethylbenzoate adsorption on different models of MgCl2 surfaces from A0 to A5 and B0 to B5, (by using the original author labels, see Fig. 8), in which A0 and B0 respectively correspond to the ideal model of MgCl2 (110) and (104) surfaces, while A1 to A5 and B1 to B5 respectively correspond to the (110) and (104) surface models bearing some defects. Two modes were considered for EB binding onto the MgCl2 surfaces. The first was coordination via the oxygen atom of the carbonyl C O bond to Mg2+ , i.e., the mono-coordination mode. The second was coordination via both oxygen atoms of the ester O C O group to Mg2+ , i.e., the di-coordination mode. Calculated binding energies for such adsorptions are listed in Table 5. The ethylbenzoate adsorption energies of di- and mono-coordinate modes on the ideal (110) model, A0, were 10.8 and 18.0 kcal/mol, respectively, indicating that the mono-coordinated mode was favored energetically over the di-coordinated mode. On the other hand, the di-coordinated mode was energetically favored in the defective A2 model due to seizing of the vacancy by the carbonyl C O group [130]. The works reported above used DFT calculations aiming to understand the coordination modes of isolated donors (depending on their chemical structure) on MgCl2 surfaces modeled within the cluster approach. However, interesting results were obtained by DFT calculations of LBs adsorption using extended surfaces with a periodic model, in order to define the “coverage limit” of MgCl2 facets. Credendino et al investigated this point by considering the coordination properties of alkoxysilane [131] and dimethyl phtha-

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Fig. 8. Models for (110) (a) and (104) (b) surfaces of MgCl2 . Adapted from ref. [130]. Table 5 Calculated energies of adsorption (Eads ) for the EB on MgCl2 models of Fig. 8 [130]. Values in kcal/mol. Crystal surface of MgCl2

Adsorption site

(110)

A0 A2 A5

34.3 16.7

B0 B1 B2 B3 B4 B5

42.6 28.6 9.9 -a -a

Adsorption energies of EB

Atomic defect

(104)

a

Ionic defect 18.0 58.3 73.1

Ohnishi and coworkers who observed a significant induction period in the TiCl4 /MgCl2 /phthalate catalytic system [132]. Finally, Kumawat et al. have studied donor displacement aided by an AlEt3 cocatalyst, through the formation of an AlEt3 –donor complex. They found that this step competes with the first Ti-Cl cleavage reaction only with ethylbenzoate as the donor, while it is a favorable reaction for phthalate, diether, and the silyl as donors. This confirms experimental observations of donor movement from the MgCl2 surface with ethylbenzoate-type internal donors [122].

4.0 53.8 46.7 80.5 73.3 -a

SCF does not converge.

late, 9,9-bis(methoxymethyl)fluorene [105] donors on the (110) and (104) MgCl2 surfaces. These studies showed that the donor coordination capability decreases with increased surface coverage and that complete coverage of the vacancies on the MgCl2 surface by the donors is prevented by steric repulsion of vicinal coordinated donor molecules. Furthermore, the migration of all three studied donors between the (110) and (104) surfaces of MgCl2 monolayers basically requires donor dissociation. Although 1,3-diethers and phthalates are highly mobile on the (110) surface, alkoxysilanetype donors can barely move on the (110) surface. Kumawat et al. [122] recently proposed that also the activation mechanism in ZN catalysts is influenced by the presence of donors. The modification of TiIV Cl4 precursor species to the TiIII Cl2 Et active site by AlEt3 cocatalyst was studied by including different families of donors (diethers, benzoates, silyl esters, and phthalates) adjacent to the Ti center on the (110) MgCl2 surface (see Fig. 9). Their calculations indicate that during the activation process, transalkylation is the rate-limiting step. This step easily proceeds on bare TiCl4 sites and on coordinated diether and benzoate donors adjacent to the Ti center. However, in models containing coordinated silyl ester and phthalate donors, the transalkylation step barrier is significantly higher suggesting that the systems employing internal donors from silyl ester and phthalate require an additional induction period before the catalytic pathway. These results seem in agreement with the finding of

3.3. MgCl2 -TiCl4 interactions Preferential TiCl4 adsorption can take place on MgCl2 facets, although which MgCl2 crystallographic face is appropriate for its coordination (and in the presence or absence of LBs) has not been established experimentally. The basal (001) MgCl2 plane is energetically the most favorable, but it includes only chlorine atoms and, consequently, cannot adsorb TiCl4 and LBs. Indeed, the surface of primary/non-activated MgCl2 powder is mainly composed of this inactive (001) plane and mechanical and/or chemical activation of MgCl2 is supposed to increase the proportion of (110) and (104) facets [99]. The (110) and (104) crystallographic facets respectively include tetra- and penta-coordinated Mg atoms (see Fig. 1a and b, respectively), which can adsorb TiCl4 . Early models, based on the similarity between the (104)- and the (110)-facets of MgCl2 and TiCl3 monolayers, suggested that the more stable (104)facet could host epitaxially adsorbed dimeric Ti2 Cl8 species, with the benefit that the environment around the Ti atoms would mimic the stereoselective sites proposed for TiCl3 (see Fig. 1b) [133–135]. In this scheme, the (110) facet of MgCl2 is not stereoselective (more details on the stereoselective mechanisms operated by Tispecies on the MgCl2 surfaces will be reported in Section 4) and the LBs would poison the (110) facet preventing TiCl4 adsorption [94]. This scheme, initially accepted in literature, has been questioned as anticipated in the previous section. First, a series of static and dynamic DFT calculations indicated that TiCl4 adsorption on the (104) facet is weak and formation of dimeric Ti2 Cl8 is predicted to be unlikely [91,136,137]. In contrast, TiCl4 was found to adsorb quite strongly on the (110) facet and can act as a stable active site. It is not a surprise, then, that adsorption of TiCl4 on MgCl2 was studied from the computational point of view by numerous groups. The (different) results are summarized in Table 6.

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Fig. 9. Activation of TiIV Cl4 catalyst by AlEt3 in the presence of electron donor. Adapted from ref. [122]. Table 6 Calculated energies of adsorption (Eads ) for the best mode of TiCl4 , Ti2 Cl8 , TiCl3 and (TiCl3 )n complexes on (110) and (104) lateral cuts of MgCl2 . Values in kcal/mol. Species

(110)

(104)

TiCl4 (a) TiCl3 (a) Ti2 Cl8 (a) (TiCl3 )n (a) TiCl4 (b) TiCl4 /TiCl2 (b) TiCl3 (b) TiCl4 (c) Ti2 Cl8 (c) TiCl4 (d) Ti2 Cl8 (d) Ti2 Cl8 (d) zip model TiCl3 (d) TiCl4 (e) Ti2 Cl8 (e) TiCl4 (f) TiCl4 (f) step defect TiCl4 (g)

15.3 29.8

5 24.9 6.4 26 7.3 26.9 20 13 11.1 8.4 32.3 35 28.2 7.4 – 11.9(h) 1.4 – 12.6(h) 2.8 (12.5) (j) 12.5 (26.8) (j)

8.1 24.5 18.2 19.8 22.8 46.8 41.3 15.5 - 28.6(h) 13.9 (25.5) (j) 27

(a)

Values from reference [93]; (b) Values from reference [119]; (c) Values from reference [28]; (d) Values from reference [143]; (e) Values from reference [144]; (f) Values from reference [24]; (g) Values from reference [109]. (h) Variability due to the different functionals combined with dispersion correction. (j) Values obtained with dispersion correction in parentheses.

Monaco et al. simulated adsorption of TiCl4 molecules and TiCl3 fragments on (110) and (104) facets of MgCl2 using clusters with different shapes and sizes [93]. They found that TiCl4 molecules and TiCl3 fragments are preferentially adsorbed on the (110) surface (with binding energies of 15.3 and 29.8 kcal/mol for TiCl4 and TiCl3 , respectively) rather than on the (104) surface (binding energies of 5.0 and 24.9 kcal/mol for TiCl4 and TiCl3 , respectively, see Table 6). Binding of TiCl3 fragments on the (104) facet may take places, leading to the formation of polynuclear (TiCl3 )n species, as initially suggested by Brant and Speca [138,139]. These polynuclear active species might provide an explanation for the silence of a large fraction of TiIII species in electron spin resonance (ESR) studies [140,141]. The absorption energies of TiCl4 on well-formed MgCl2 surfaces were questioned by Ziegler [119]. In fact, he remarked that the TiCl4 binding energy must be large enough to overcome an entropic

barrier due to the loss of translational and rotational degrees of freedom and he estimated the change in entropy (S) for the reaction TiCl4(g) to TiCl4(adsorbed) at 350 K to be −37.2 cal/(mol K), giving a value of −13.0 kcal/mol for TS at 350 K. Because the adsorption energies he calculated were in the range of 10 kcal/mol (depending of the model cluster used), Ziegler figured out that only if one Mg ion on the surface is substituted with a Ti, then TiCl4 should be able to stick to the MgCl2 surface with a large enough binding energy (binding energies ranging from 24.5 to 26.9 kcal/mol, see Table 6) to overcome entropy, without any significant change in the geometry of the MgCl2 clusters [119]. Ziegler suggested also that active sites obtained from these Ti species and MgCl2 should be included in the list of possible ZN site models, at least from a site-stability point of view [119]. Taniike and Terano [142] used periodic density functional calculations for the binding energies of TiCl4 and TiCl3 on the (110) and (104) facets of a MgCl2 crystal (see Table 6) in the presence of a LB located near the active Ti center. They showed that the electronegativity of the Ti species on the (110) surface increases with transfer of electron density from ethylbenzoate (used as LB prototype), to the support. Nevertheless, the electron density that is transferred from ethylbenzoate to MgCl2 does not alter the Ti species coordinated onto the (104) facet. According to the authors, this indicates that using ethylbenzoate in ZN catalyst synthesis preferentially induces coadsorption of TiCl4 and LBs to form active species on the (110) face. Later on, the same authors, extended the work to other LBs with different coordination mode [28] and the main results are reported in Table 7. The adsorption energy, calculated by Taniike et al [28], was 20 kcal/mol for mononuclear TiCl4 species in the (110) facet of MgCl2 and 11 and 13 kcal/mol for TiCl4 adsorption on the (100) lateral cut, as dinuclear and mononuclear species, respectively (Table 7). Electron donors with ester structures in monodentate form showed comparable adsorption energies of roughly 30 kcal/mol on the (110) and (100) surfaces, while adsorption energies for the bifunctional succinate and phthalate donors were even higher, about 30 to 40 kcal/mol, irrespective of the surface type and the adsorption mode. 1,3-Diethers exhibited different behavior on (110) and (100) lateral cuts. On the (110) surface, 1,3-diether coordinates only in a bidentate form, because of the short ether O–O

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99

Table 7 Calculated energies of adsorption (Eads ) for TiCl4 and internal donor on (110) and (104) lateral cuts of MgCl2 [28]. Values in kcal/mol. MgCl2 surface

Adsorbate

Adsorption mode

Eads

(110)

TiCl4 Ethylbenzoate Diethylphthalate

Mononuclear Monodentate Bidentate Intra-layer bridge Inter-layer bridge Bidentate Intra-layer bridge Inter-layer bridge Bidentate Mononuclear Dinuclear Monodentate Intra-layer bridge Intra-layer bridge Intra-layer bridge

19.8 29.8 38.8 32.5 33.7 38.6 36.9 43.3 31.1 13.0 11.1 30.5 42.4 45.0 7.5

(2R,3R)-2,3diisopropyldiethylsuccinate

(104)

2,2-diisopropyl-1,3-dimethoxypropane TiCl4 Ethylbenzoate Diethylphthalate (2R,3R)-2,3-diisopropyldiethylsuccinate 2,2-diisopropyl-1,3-dimethoxypropane

“Intra-layer bridge” corresponds to donor adsorption onto a single MgCl2 layer and “interlayer bridge” corresponds to donor adsorption as a bridge between two adjacent MgCl2 layers.

Fig. 11. Fragmentation of MgCl2 creating: (a) perfect (104)-facets; (b) (104)-facets presenting a step-defect. (c) geometry of the step defect on the (104)-facet; (d) TiCl4 adsorbed on the (104) step defect. Adapted from ref. [24].

Fig. 10. Zip-model complexes of TiCl4 and Ti2 Cl8 adsorbed on different layers of (110) (a) and (104) (b) MgCl2 surfaces. Ti, Mg, and Cl atoms are colored in black, dark blue, and sage-green, respectively. Adapted from ref. [143].

distance, with an adsorption energy as high as 31 kcal/mol, while the energy of adsorption on the (100) lateral cut was less than half of this. Keeping in mind that TiCl4 prefers to adsorb more firmly on a (110) facet in mononuclear form, coadsorption of donors with isolated TiCl4 on the (110) lateral cut of MgCl2 was deemed to be the most acceptable scenario from an energy point of view. The coordination of TiCl4 on different layers of MgCl2 facets was explored by Stukalov et al. [143]. They modeled mononuclear zip Ti species on the (110) surface and dinuclear zip Ti complexes on the (104) surface (see Fig. 10a and b, respectively) [143]. Interestingly, the absorption of zip Ti2 Cl8 species on the (104) facet proved to be the most stable among all Ti(IV) species residing on the (104) MgCl2 surface (see Fig. 10b and Table 6). Furthermore, these species can produce both non-selective and stereoselective centers, in contrast to Ti2 Cl8 species located within one Cl-Mg-Cl layer on the (104) surface (see Fig. 1b) that must generate only stereospecific centers. The long-standing question about the capability of TiCl4 to adsorb on the surfaces of MgCl2 crystals was revisited by using

periodic hybrid DFT methods with dispersion forces and several DFT functionals by D’Amore and co-authors [144], which concluded that the adsorption of TiCl4 on well-formed MgCl2 crystals can only occur on MgCl2 (110) or equivalent lateral facets, whereas the interaction with MgCl2 (104) is too weak for the formation of stable adducts, at least under catalytic conditions (see Table 6). Competition between TiCl4 and ethylbenzoate for absorption on regular and defective (110) and (104) MgCl2 surfaces was reported in 2013 by Cheng and coworkers using the models reported in Fig. 8 [130]. Neutral and cationic defects by respective omission of Cl atoms and Cl− ions from ordinary surfaces were considered, with the former easier to be formed than the latter, due to charge separation occurring in the heterolytic dissociation of Cl− . Adsorption of ethylbenzoate on all surface models was generally more stable than that of TiCl4 , except for the model A5 reported in Fig. 8, which was then indicated as the most plausible active site for propylene polymerization. More recently, Cavallo and coworkers proposed a low-energy defect on the (104)-facet that could strongly coordinate TiCl4 [24]. In this regard, starting from bulk MgCl2 , they imagined different fragmentation modes generating perfect or step-defected (104)facets (see Fig. 11). The perfect (104)-facet corresponds to a perfectly flat surface, whereas the step-defected facet corresponds to a fragmentation event generating a symmetric step defect on the two surfaces. Comparison between the fragmentation energy of the bulk into the perfect or into step-defected (104)-facets of different sizes converged to a single-step defect costing only 7.1 kcal/mol. To relate the surface energy, ESurf , of the step-defected (104)-facet to that of

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the perfect (104) and (110) facets, Cavallo et al. calculated defected (104) facets with a variable number of isolated defects. They found that the perfect (104) facet, with an ESurf of 0.410 J/m2 , is remarkably more stable than the perfect (110) facet, with an ESurf of 0.722 J/m2 . Interestingly, the ESurf of the (104) facet presenting 10%, 20%, and 30% of isolated step-defects was only 0.429, 0.448, and 0.466 J/m2 , respectively, indicating that even a highly defected (104) facet is clearly more stable than the well accepted (110) facet. Considering that preparation of MgCl2 supports is usually performed under rather drastic conditions, these results indicate that defected surfaces can have a relevant role in ZN catalysis. They also investigated TiCl4 adsorption on the (104) step-defect. According to calculations, TiCl4 can be easily accommodated on the (104) stepdefect with an overall binding energy of 12.5 kcal/mol (see Fig. 11d). This value is much higher than that calculated for TiCl4 adsorption on the perfect (104) facet, favorable by only 2.8 kcal/mol, and it is comparable to the value obtained for TiCl4 adsorption on the perfect (110) facet, 13.9 kcal/mol (see Table 6). In conclusion, all DFT studies reported in this section lead to an amazing variety of models for the active sites on heterogeneous ZN systems. From the seminal models based on crystallographic consideration (reported in Fig. 1), a large set of new models sorted out by DFT methods. For some aspects, it is not too ambitious to say that DFT results boost new experimental techniques aiming to understand heterogeneous ZN systems at molecular level. However, some common features can be envisaged from the large set of experimental and computational data. At first, strong adsorption of monomeric TiCl4 on the MgCl2 (110) facet yields a structure containing octahedral Ti centers that appear proper precursors of an active site model. It is still a matter of debate if TiCl4 in a monomeric or dimeric form species can be adsorbed on the (104) facet of MgCl2 , whose presence has been reported in several experimental papers [22,31,90,145]. In this respect, the zip-model reported by Stukalov [143]) and the recent model on defected surfaces reported by Cavallo [24] (see Figs. 10b and 11b, respectively) are energetically feasible and seems bypass the very low adsorption energy estimated by DFT calculations for TiCl4 species adsorption on the (104) facet. 3.4. Role of cocatalyst The use of a cocatalyst, such as alkylaluminium compounds, as an activating agent is required in the ZN polymerization process [3,19,146]. It has long been known that the activity and stereospecificity of catalysts change with the use of different AlR3 compounds [143,147,148], where R represents different alkyl groups or Cl ligands [77,129,149]. A key issue is the variation in the oxidation state of the titanium chloride, since TiIV is considered to reduce to TiIII or TiII under catalytic conditions. The second important function of the alkylaluminum is alkylation of TiCln leading to the creation of active sites by formation of a Ti-C bond. In the alkylation mechanism of Ti compounds, the alkyl group of trialkylaluminum can exchange with the Cl atom of TiCl4 . However, TiIV species, with Ti atoms in octahedral Cl surroundings without any vacancies, are supposed to be the most probable active-site precursors in TiCl4 /MgCl2 systems, which makes difficult to hypothesize a simple mechanism. Generally, the reduction stage may take place prior to the alkylation stage with such surface TiIV species. Stukalov et al. [29] tried to clarify active-site formation by studying complexation, alkylation and reduction reactions resulting from the interaction between alkylaluminum compounds and TiCl3 or TiCl4 species with DFT calculations (Fig. 12a). The reaction paths and related energies they studied are listed in Table 8. Analysis of TiCl4 reduction by various organoaluminum compounds determined that (a) all TiCl4 species, with or without Cl vacancies, undergo reduction processes with direct participation

Fig. 12. Capability of TiIV species towards alkylation by triethylaluminum: (a) 5coordinated TiIV complex on the MgCl2 (104) facet; (b) 6-coordinated TiIV complex on the MgCl2 (110) facet. Adapted from ref. [29]. Table 8 Calculated energies of different paths for the reduction of TiIV species by organoaluminum compounds [29]. All relative energies with respect to the reactants are in kcal/mol. path

Reaction

TS

products

1

TiCl4 + Al(C2 H5 )3 → TiCl2 .Al(C2 H5 )2 Cl + C2 H5 Cl TiCl4 + 2Al(C2 H5 )3 → TiCl2 .2Al(C2 H5 )2 Cl + C4 H10 TiCl4 + 2Al(C2 H5 )3 → TiCl2 .2Al(C2 H5 )2 Cl + C2 H4 + C2 H6 2TiCl4 + 2Al(C2 H5 )3 → 2[TiCl3 .Al(C2 H5 )2 Cl] + C2 H4 + C2 H6 2TiCl3 (C2 H5 ) → Ti2 Cl6 + C2 H4 + C2 H6 TiCl3 (C2 H5 ) + Al(C2 H5 )3 → TiCl2 .Al(C2 H5 )2 Cl + C2 H4 + C2 H6 TiCl4 + 2Al(C2 H5 )2 (i-Bu) → TiCl2 .2Al(C2 H5 )2 Cl + i-C4 H8 + i-C4 H10 TiCl4 + 2Al(C2 H5 )3 → TiCl2 .2Al(C2 H5 )Cl2 + C2 H4 + C2 H6

42.0

25.0

39.2

−57.2

36.6

−31.5

34.6

−42.0

67.3

2.8

51.0

8.3

32.9

−37.8

44.7

−19.5

2 3 4 5 6 7

8

of organoaluminum compounds; (b) under reduction processes, the release of three organic gaseous products, i.e., ethyl chloride, butane, ethylene with ethane, is possible although formation of ethyl chloride is thermodynamically unfavorable; (c) although the energy barriers for the formation of TiIII and TiII species from TiCl4 are similar, the formation of TiIII seems to be preferred, which is the reason why TiIII dominates over TiII in the reaction pool; (d) reduction of TiIV species is significantly affected by the chemical structure of alkylaluminum compounds. In this regard, Stukalov et al. proposed that Al(i-Bu)3 and AlEt2 Cl are the strongest and the least effective reduction agents, respectively. A four-membered ring type transition state for the transalkylation reaction (TS in Fig. 13) was proposed, which leads to the formation of an active center. Focusing on Ti alkylation by AlEt3 , they found that an energy barrier of 9.7 kcal/mol must be overcome to alkylate TiIV species by exchanging Et from AlEt3 with Cl from TiCl4 . During TiCl3 alkylation, a TiCl3 ·AlEt3 complex is first formed and then it undergoes a dissociation process. The dissociation is assisted by another AlEt3 molecule because AlEt3 facilitates the release of AlEt2 Cl, bound to

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101

Fig. 14. Single step (above) and two steps (below) pathways for the Ti-C bond formation. Fig. 13. A 4-center (a) and 6-centered (b) TSs for the interaction of Al-compounds with Ti center. Table 9 Thermodynamics of the TiCl4 reduction process, Ediss , via the homolytic cleavage of a Ti Cl bond [203]. Values in kcal/mol.

1 2 3 4 5 6 7 a

Reaction

Ediss

TiCl4 → TiCl3 • + Cl• [Mg]/TiCl4 → [Mg]/TiCl3 • + Cl• [Mg]/TiCl4 + AlCl3 → [Mg]/TiCl3 • + AlCl4 • [Mg]/TiCl4 + Al2 Cl6 → [Mg]/TiCl3 • + Al2 Cl7 • [Mg]/TiCl4 + AlEt3 → [Mg]/TiCl3 • + AlEt3 Cl• [Mg]/TiCl4 + Al2 Et6 → [Mg]/TiCl3 • + AlEt3 + AlEt3 Cl• [Mg]/TiCl4 + CH2 CH2 → [Mg]/TiCl3 • + CH2 CH2 Cl•

83.1 62.3 42.5 54.0 8.8 25.8a 44.8

A value of 17 kcal/mol is also considered as Al2 Et6 dissociation enthalpy.

TiIII species, by the formation of an AlEt2 Cl·AlEt3 complex. By this, AlEt3 decreases deactivation of the catalyst associated with AlEt2 Cl or AlEtCl2 adsorption on the active center [29]. Depending on the concentration of the cocatalyst for active center (C*) formation, Paulik et al. proposed a six-membered ring-type TS (see Fig. 13b) [150]. The DFT calculation of the transalkylation reaction showed energy barriers of 9.7 and 10.3 kcal/mol for the four-member and six-member TSs, respectively, promoted by monomeric TiCl4 adsorbed on the (110) facet. Since the energy barriers for both TSs are comparable, Paulik et al. proposed that both may occur for transalkylation reactions [150]. They also proposed that increased amount of TiII on the ZN catalyst would be due to the faster transalkylation reaction via the six-center TS. Skalli and coworkers investigated the role of AlR3 as a cocatalyst [151]. It has been observed that AlR3 allows the exchange between R and Cl ligands. This exchange is necessary to make the reduction exothermic. In fact, in the reduction process, the cocatalyst is not directly involved although providing alkyl groups is essential to stabilize the end products. Bahri et al. [152] considered possible ways to activate TiCl4 to yield TiIII species containing a coordination vacancy. In this regard, three different paths were proposed for adsorbed TiCl4 reduction based on the usual chemical components in the polymerization medium. These paths essentially consist of the homolytic bond breaking of a dangling Ti-Cl bond with spontaneous breaking; dissociation induced by Al-compounds, such as AlCl3 , Al2 Cl6 , and AlEt3 , which are used as reducing agents; or dissociation promoted by C2 H4 . The Ediss energies of the reduction process for different studied paths are summarized in Table 9. According to these calculations, among all considered dissociation processes, the pathway assisted by AlEt3 (either as a monomer or dimer) is the only one that seems viable, with Ediss of 8.8 and 25.8 kcal/mol, respectively. In fact, by moderate heating of the polymerization medium, these values can be easily achieved. Then, Bahri et al. explored possible pathways for Ti-C bond formation. They considered two mechanisms: (1) Cl-ethyl exchange promoted by AlEt3 , which in a single step would form the TiIII active site containing a vacancy on the Ti atom and a newly formed Ti-C bond that is ready for monomer insertion; (2) reoxidation of the TiIII

Table 10 Calculated energies for TiCl4 alkylation as a function of the cocatalyst nature, i.e. Et2 Al–R, at the B3LYP/6-31G* level [153]. Values in kcal/mol. R

Ealk

CH2 CH3 Cl OCH3 Oi Pr SCH3 Si Pr NHCH3

−9.5 −3.6 −7.2 −7.2 −6.4 −6.7 −7.2

center via reaction with AlEt3 Cl• (this compound is formed during activation of TiCl4 by AlEt3 ) and then homolytic cleavage of another Ti-Cl dangling bond. These paths are shown in Fig. 14. Based on the calculated energies, direct transalkylation was introduced as the most likely mechanism for the formation of the [Mg]/TiCl2 Et• center. The energy profile for transalkylation is illustrated in Fig. 15. Champagne et al. [153] evaluated the ability of R–AlEt2 -type cocatalysts [with R = Cl, Et, O-iPr, O–Me, NH–Me, S–iPr, or S–Me] to alkylate titanium chloride. For catalyst alkylation, they used the reference reaction: R–AlEt2 +TiCl4 → R–AlEtCl + TiEtCl3 Table 10 presents alkylation energies (Ealk ) as a function of the R substituent in the cocatalyst. Based on their calculations, Champagne et al. selected AlEt3 as the strongest alkylating agent. Furthermore, they showed that the exothermicity of the alkylation reaction increased by both complexation (with LB) and dimerization reactions but, in some cases, there was a relatively large activation barrier. In addition, the alkylation strength of R–AlEt2 cocatalysts depends mainly on the nature of the R substituent so that with R = NH–Me, O–Me, and O–iPr very stable aggregates were formed, leading to weak alkylation (EA = 7.2 kcal/mol). When they added LBs, the alkylating strength of iPr-S–AlEt2 and Me-S–AlEt2 compounds increased while LBs made AlEt3 less strong for alkylation. Finally, they found that Cl–AlEt2 (DEAC) is less affected by the presence of LB. Besides the most important role of alkylating agent, Al-alkyl species converted to AlR3-x Clx species can compete with both TiCl4 and LBs for adsorption on MgCl2 . Cavallo et al. described the impact of a such species on stereo- and regioselectivity of propylene insertion by coordination in the near vicinity of the Ti center to a step defect on a (104) facet, as shown in Fig. 16 [24]. First, they observed that both these Al-alkyls strongly coordinate on a perfect (104)face, with calculated adsorption energies of 12.5 and 19.9 kcal/mol for AlEt3 and AlEt2 Cl, respectively. Second, they found that the stereoselectivity of Ti active site is enhanced by coordination of Al-alkyls in close proximity [24], particularly when the growing chain is in the less-hindered outward environment (for major details on the inward and outward growing chain positions and the stereo and regioselectivity of propylene insertion see next sections), with  EStereo close to 1 kcal/mol (compared with 0.1 kcal/mol for the active site without coordination of

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Fig. 15. Energy profile for direct single step transalkylation reaction. Energies are in kcal/mol. Adapted from ref. [152].

Fig. 16. Models of primary (1,2) propylene insertion TSs in the presence of AlEt2 Cl molecules for the re-propylene (a) and si-propylene (b) insertions. Adapted from ref. [24].

any Al-alkyls or LBs). Even though the differences were in the limit of accuracy of DFT methods, these results were expected because steric hindrance did not restrict the conformational space available to the outward growing chain, whereas the chlorine atom (indicated by a star in Fig. 16) somewhat restricted the conformational space available to the inward growing chain [24]. They also calculated the impact of the Al-alkyls in the growing chain positioned in the somewhat stereoselective inward environment. Further, primary propylene insertion remained favored by both Al-alkyls, with  ERegio always above 1 kcal/mol. In short, TiCl4 adsorption on a low-energy (104) step defect, with unsaturated Mg atoms decorated with Al-alkyls close by, creates a moderately stereoselective and regioselective site, in agreement with experiments. Very recent DFT calculations seem to confirm this role for the Alalkyl, suggesting that conformational interlocking of ID and AlEt2 Cl enhanced stereorigidity of the active site obtaining higher stereoselectivity in propylene polymerization [154]. 4. Mechanism of polymerization 4.1. The chain growth step The reaction pathway for the insertion of the monomer into the Ti C(polymeryl) bond and the mechanism for propagation most commonly accepted was first proposed by Arlman and Cossee [155], and it is schematically shown in Fig. 17. First, a ␲-complex is formed by coordination of the monomer to the metal. Because

the electropositive metal interacts with the ␲-bond electrons of the alkene substrate, formation of a ␲-complex is barrierless and accompanied by an energy gain. Then, the propagation step takes place by olefin slipping towards the Ti polymeryl bond to form a four-centers TS that ends with the next intermediate, where the alkyl chain bears the inserted olefin [44,156]. The insertion barrier ranges approximately in the 6–12 kcal/mol range [157–160]. The overall insertion step is favored by approximately 20 kcal/mol, which indicates that the insertion reaction is a very favored process [156,161,162]. The important implication of the Cossee’s mechanism is that the monomer and the growing chain exchange their coordination positions at each insertion step (“chain migratory mechanism”), which is crucial to explain the relationship between active site symmetry and stereoselectivity mechanism, particularly for well-defined homogeneous systems [51]. The role of the oxidation state of Ti (from TiIV to TiIII and TiII ) on the monomer insertion step was explored by Ziegler et al. [119] by modeling TiCl4 , TiCl3 and TiCl2 attached to the surface of MgCl2 . This study was stimulated by experimental data suggesting that, after reaction with the cocatalyst, Ti may be present in the +4, +3, and +2 oxidation states [138,148,163–165]. Overall, the calculated internal insertion energy barriers for TiClx -based sites fall in the range 8–16 kcal/mol, similar to the values of 8.6 and 6.6 kcal/mol obtained by Cavallo [44] for ethylene insertion in the polymer chain modeled as a methyl and ethyl group, respectively. In a different work Ziegler and coworkers [166] studied propylene and ethylene copolymerization using a TiCl3 /MgCl2 -based site model with the growing polymer chain modeled as methyl, isobutyl, 2-butyl, and n-propyl moieties. Their DFT calculations revealed that complexation of propylene to the active site is energetically more favored in comparison with ethylene but, quite surprisingly, the insertion energy barrier for propylene was found to be lower than for ethylene, at odss with experimental results. In the same paper, the authors argued on the suitable selection of the active site model (in particular, for the sterical environment) and suggested that sites based on TiCl4 , which would be more sterically hindered, may well be better candidates as models of copolymerization active sites [166]. Later on a better agreement was obtained by Bahri et al. [111] who studied ethylene and propylene insertion on TiCl4 molecule octahedrally coordinated on the (110) MgCl2 surface by using [MgCl2 ]/TiCl2 Et and [MgCl2 ]/TiCl2 H centers (obtained via hydrogenolysis of growing polymer chains) using the B3LYP/TZVP level of theory (see Table 12). As can be seen, propylene primary and secondary insertion (also known as 1,2 and 2,1 insertion, respectively) at the (MgCl2 )3 /TiCl2 Et site

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103

Fig. 17. Main stages of propylene insertion into Ti-C bond active center according to the mechanism suggested by Cossee and Arlman for TiCl3 catalysts.

requires energy barriers of 12.6 and 13.9 kcal/mol, respectively, to be overcome and these barriers are higher than the corresponding insertion barrier for ethylene (6.2 kcal/mol). Furthermore, lower insertion barrier values for both ethylene and propylene insertion at the [MgCl2 ]/TiCl2 H center confirmed the higher reactivity of the Ti-H bond versus the Ti C bond. 4.2. Stereoselectivity of propylene insertion The main feature of ZN catalysts is the stereoselectivity of the olefin insertion process as emphasized by the words used to award Ziegler and Natta for the Nobel prize in the 1963: “Nature synthesizes many stereoregular polymers, for example, cellulose and rubber. This ability has so far been thought to be a monopoly of Nature operating with biocatalysts known as enzymes. But now Professor Natta has broken this monopoly.” In fact, Natta was the first to hypothesize that steric control is due to the chiral structure of catalytic sites on the border of crystal layers of TiCl3 , (see Fig. 18) where the metal atoms have opposite configurations, which may be labeled as  and  [167]. However, the origin of stereoselectivity of ZN catalysts was rationalized by Corradini et al. [92] combining the following symmetry elements: a) the chiral site; b) the prochiral monomer enantiofaces (re and si enantiofaces); c) the chiral orientation of the growing polymer chain (with G+ or G− orientation). Following such a model, the “chiral orientation of the growing chain” is dictated by the chirality of the active site which forces the chain to assume a conformation pointing the first C C bond to minimize repulsive interaction with the catalytic site (see Fig. 19a). The preferred enantioface is that orienting the methyl substituent anti to the cited first C C bond of the growing chain and the stereoerrors are due to the chain misorientation (see Fig. 19b) or to the monomer misorientation relative to the chain (see Fig. 19c). Interestingly, the model originally developed on still elusive active site of heterogeneous ZN systems has been successfully extended to stereoselective well-defined metallocene and non-metallocene homogeneous systems used for propylene polymerization [168], and is still, with few exceptions [169] the general model adopted to explain the stereoselectivity in olefin polymerization catalyzed by transition metal complexes. Following this model, theoretical stereoselectivity can be computed calculating the energy of the TS for the “right” propylene insertion (see Fig. 19a) and comparing it with the energy of the lower TS path leading to stereomistakes (see Fig. 19b and c). A larger difference in energy between the TSs of propylene inserting into the active site with si- and re-enantiofaces (EStereo ) corresponds to either a more isotactic polypropylene evaluated or in a term of statistical models, on the basis of the enantiomorphic site control developed for the interpretation of statistical distributions [170,171], or, more easily, by the content % of isotactic pentad mmmm from 13 C NMR spectra [172]. Often, a correlation of the EStereo with the isotactic index is also reported in literature. However, due to the multisite nature of ZN systems, this correlation should be considered with caution.

A deeper analysis of the model reported in Fig. 19 shows that the presence and bulkiness of the Cl atoms marked with a * play a crucial role to obtain a stereoselective process. This induced Busico and coworkers to develop a three-site model (see Fig. 20) explaining isotactic, isotactoid and syndiotactic stereosequences [33,173], which are the main building blocks of polypropylenes obtained by heterogeneous ZN systems. The interconversion between these three sites (faster than termination) is responsible of the non-uniform distribution of stereodefects along the single polypropylene chains resembling a stereoblock microstructure, which affects the physical properties of polymers obtained by ZN heterogeneous catalysts. This fact has been claimed as the main difference of iPPs synthesized by using heterogeneous with respect to homogeneous single-site catalysts [174]. The assumption that L1 and L2 of Fig. 20 might be donor molecules adsorbed on the MgCl2 surface stimulated the modeling the stereoselectivity of propylene insertion at active sites with the donors in close contact. The (110) facet of MgCl2 was considered the optimal choice because it allowed to modulate the stereoselectivity of adsorbed mononuclear TiCl4 by modifying the donor chemical structures in close contact (see e.g. Figs. 7 and 16). Chemical bonding of TiCl4 with the LB was excluded because experimental studies of Terano et al. indicated that e.g. ethylbenzoate used as LB individually coordinates onto MgCl2 surfaces without the formation of a TiCl4 ·ethylbenzoate complex [175]. According to Wondimagegn and Ziegler [176], the structure of external alkoxysilane donors influence the stereoselectivity and molecular weight distributions in MgCl2 -supported Ziegler-Natta catalysis and the EStereo calculated are in accordance with the experimental isotacticity data (see Table 13). In the same study, the structures of alkoxysilane donors were correlated also with the average molecular weight of the resulting isotactic polymer product by computing the energetic difference between insertion and ␤-hydrogen transfer to the monomer (BHT) TSs, respectively (EBHT , see next section) [176]. Taniike and Terano [28] studied the feasibility of donor coadsorption, steric and electronic interactions during the coadsorption process, and the influence of these parameters on the stereospecificity of the catalyst as well as on the regiospecificity and the molecular weight (see next sections) of the polymer product. They considered the energetic states of TiCl4 and donors on catalyst surfaces (reported in Table 7). Ethylbenzoate coadsorption adjacent to the Ti center has three distinct effects: (1) it turns the specific mononuclear Ti species into an isoselective center by sterically controlling the growing chain orientation at the rate-determining step for which the cost is defined by the energy barrier of the corresponding TS. Consequently, the lowest energetic value for the 1,2-re insertion (named as Eap in the paper) became 2.3 kcal/mol higher than that for the 1,2-si insertion, indicating that the nearest coadsorption of ethylbenzoate transforms the aspecific Ti mononuclear species into isospecific one; (2) it increases electronic repulsion in the secondary propylene (2,1) insertion mode, thereby improving the regioselectivity; and (3) it enables the chain growth on

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Fig. 18. Possible lateral cut of a TiCl3 layer (a) Nonequivalent coordination positions, available to monomer and growing polymer chain, are indicated by a star. In (b) the dashed line indicates the local 2-fold axis. Adapted from ref. [168].

Fig. 19. Optimized geometries TSs (right) for 1,2 propylene insertion into a C2 -symmetric octahedral Ti model site with  configuration (a) and for stereoerrors coming from chain misorientation (b) or monomer misorientation relative to the chain (c). The primary growing chain is simulated with an iBu group. The quadrants representation of the same systems is reported on the left. Gray quadrants correspond to crowded zones occupied by the Cl atoms marked by a star on the right. The steric interaction between monomer and chain (c) is reported with arrow. Adapted from ref. [168].

Fig. 20. A three-site model proposed by Busico and coworkers for the interconversion of active sites on heterogeneous ZN surface leading to highly isotactic (a), isotactoid (b) and syndiotactic propagation (c) (see text). L1 and L2 may be Cl atoms or donor molecules. The quadrants representation of the same systems is reported on the bottom. Adapted from ref. [33].

the mononuclear Ti center by preventing chain transfer to the monomer reaction [28]. Terano and coworkers [177] also investigated the structure–performance relationship of external donors to the R2 (MeO)2 Si structure in propylene polymerization. They experimentally found that high polymer yield can be achieved with an alkoxysilane-containing system that has high adsorption energy on the MgCl2 surface as shown by DFT calculations. The

experimentally observed polymer stereoregularity was successfully explained by DFT calculations based on the coadsorption model. To understand the interaction of a catalyst precursor with alkoxysilane donors, they used different pre-treatment conditions. They found that by employing electron donors, new isospecific catalyst sites are formed, which explains the higher isotacticity of the resulting polypropylenes, whereas catalyst deactivation via poisoning happens in a rather non-selective manner [177].

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Fig. 21. Optimized geometries TSs for the favored 1,2-propylene insertion (re enantioface, (a)), and for the two possible 2,1-insertions (si enantioface, (b) and re enantioface, (c)) at a C2 -symmetric octahedral Ti model site with  configuration. The primary growing chain is simulated with an iBu group. Adapted from ref. [185].

Recently Bahri and coworkers [178] investigated the influence of di-n-butylphthalate and ethylbenzoate on the isospecifity of TiCl4 centers on Fe-doped MgCl2 (110) surfaces. To this end, two donor molecules were placed on both sides of the mononuclear Ti species, and the approximate barriers corresponding to insertion of si- and re-enantiofaces of propylene at the Ti-CH(CH3 )2 active center were calculated. Their results clearly indicated that, although isospecificity is improved in the presence of both donors, this improvement is more pronounced for di-n-butylphthalate.

4.3. Regioselectivity of propylene insertion Heterogeneous ZN catalysts are commonly referred to as highly regioselective in favor of 1,2-insertion of propylene [179,180]. As a matter of fact, low amount (less than 1%) of regioirregular enchainments by isolated 2,1 unit were detected in less isotactic fractions of polypropylene (e.g., xylene- or boiling-heptane-soluble) whereas such enchainments were not detected in the “isotactic” polymer fraction by 13 C NMR analysis at isotopic abundance. This experimental fact limited studies on the regiochemistry of propene insertion at a marginal role until studies by Chadwick et al. [181]. These authors, analyzed the chain end groups of polypropylenes produced by heterogeneous ZN catalysts of fourth generation, and found the presence of up to around 20% -butyl chain ends, indicative of regioirregular (2,1-) monomer insertion followed by chain transfer with hydrogen [181]. The same authors postulated that occasional 2,1 insertion changes the active site into a “dormant state” due to the high steric hindrance of the secondary polymeryl chain at the active metal, with severe implications on the catalysts activity, molecular mass and hydrogen response. This renewed interest in the regiochemistry of propylene polymerization promoted by heterogeneous ZN catalysts [87,182–186] spurred experimental studies to measure the amount of 2,1 units in polypropylenes obtained by last generation ZN catalysts. Busico and coworkers developed the methods of copolymerization with ethylene-1-13 C used in the place of ethylene at natural 13 C abundance [187] to measure the propylene regiochemistry at catalysts claimed to be extremely regioselective. This method consists in experiments at variable ethene-1-13 C/propylene feeding ratios, to locate the value of ethylene incorporation above which “all” 2,1 propylene units are followed by an ethylene. These signals can be taken as markers of the regioirregular propylene units and analyzed alternatively to those of the regioirregular units themselves. With this method, the amount of regiomistakes found for MgCl2 /TiCl4 activated by Al(iBu)3 was ca. 0.7 mol % [185]. Subsequently, lower amount of regiomistakes (0.26 and 0.18%) were determined for MgCl2 -supported Ziegler-Natta catalyst systems for the industrial production of isotactic polypropylene based on 1,3 diether and alkoxysilane modified catalysts [186,188].

Fig. 22. Top (left) and side (right) views of the TSs leading to primary, (a) and the two secondary, propylene insertion ((b) and (c)) into the Ti-iBu bond. For the sake of clarity, in the top views only a part of the MgCl2 cluster is reported. The whole cluster used is reported in Fig. 1 a. Adapted from ref. [128].

DFT calculations on models of epitactic octahedral catalytic Ti models found an energy difference in the TSs of the preferred 1,2 versus 2,1 insertions (Eregio ) of about 1.5 kcal/mol (see Fig. 21a and b). Two aspects of the model of Fig. 21 deserve to be mentioned here: a) the Eregio is not really high, (clearly lower than the experimental value); b) the 2,1 insertion is highly enantioselective in favor of the enantioface orienting the methyl group anti to the nearest Cl atom (compare in Fig. 21 the structures b and c). The results obtained by using the minimal model of Fig. 1c, were confirmed by Ziegler et al. [166] and by Cavallo and coworkers [128] by using a cluster approach. The last authors calculated the regioselectivity of propylene insertion promoted by mononuclear Ti species on the (110) lateral facet of MgCl2 (see Fig. 22) in absence or in presence of an external donor coordinated to MgCl2 . The computed Eregio value in the absence of the donors is of the same magnitude of the one reported in Fig. 21, whereas the Eregio computed in the presence of the donors is (slightly) higher and the enantioselectivity of 2,1 insertion is more pronounced. The whole

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Fig. 23. Quadrants representation of the regiochemistry of propylene insertion promoted by a monomeric TiCl4 adsorbed on the (110) face of MgCl2 with no LB, one LB and two LBs coordinated close to the active Ti atom (see Fig. 1 a). Gray quadrants represent regions sterically occupied by the donors. Adapted from ref. [128].

Table 11 Calculated stereoselectivity (EStereo ) and regioselectivity (ERegio ) of the catalytic sites with nothing, AlEt3 or AlEt2 Cl coordinated next to the Ti-center by using the cluster model of ref. [24]. Outward and inward positions are defined in Fig. 16. Values in kcal/mol.

outward Inward Outward Inward Outward Inward

Table 12 Calculated energies of different steps corresponding to propylene and ethylene insertion in the [MgCl2 ]/TiCl2 Et and [MgCl2 ]/TiCl2 H species [111]. Eact is the overall insertion barrier from the olefin coordinated species (Ecomplex ) to the transition state for insertion (ETS ). Values in kcal/mol.

Nearby species

EStereo

ERegio

Active centre

Monomer

Ecomplex

ETS

Eact

Eproduct

None None AlEt3 AlEt3 AlEt2 Cl AlEt2 Cl

0.1 1.2 0.9 1.2 0.9 1.4

1.2 1.1 1.4 1.1 1.2 1.3

[MgCl2 ]/TiCl2 H

ethylene (1,2) propylene (2,1) propylene

−16.7 −17.8 −16.9

−15.8 −16.0 −13.3

0.9 1.8 3.7

−41.1 −33.2 −38.4

[MgCl2 ]/TiCl2 Et

ethylene (1,2) propylene (2,1) propylene

−1.3 −5.2 −4.7

4.9 7.4 9.2

6.2 12.6 13.9

−21.6 −17.6 −17.0

regiochemistry was rationalized by using the quadrant scheme (see Fig. 23). Similar Eregio values are obtained also changing the MgCl2 facet so analyzing the regioselectivity with the TiCl4 adsorbed on the (104) step defect (see Fig. 11 and Table 11). This trend was reported also by Taniike, who estimated the probability of regiomistakes to be ca. 15% in the absence of donors, (incidentally this value is greater than the experimentally reported value) and that the probability of 2,1 insertion moderately

decreases from 15% to 6% by coadsorption of ethylbenzoate (used as ED) [28]. Overall, the various DFT calculations on the regiochemistry of propylene polymerization by heterogeneous ZN catalysts with different model sites converge on a preference for 1,2 over 2,1 insertions below 2 kcal/mol and on a clear enantioselectivity of the 2,1 insertion due to the symmetry of the active site. The only exception was claimed by Boero that found a much higher regioselectivity [91].

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107

Fig. 24. Ligand design principle derived by homogeneous single-site catalysts, which allows to move from low (on top) to high (bottom) molecular mass polymers by suitable modification of ancillary ligands. Adapted from ref. [195].

Nevertheless, high yield ZN catalysts of the last generations are known to be experimentally highly regioselective with a dominant 1,2-insertion. The incidence of 2,1-insertion, although is less than 1 in every 300 insertions for the overall polymer and less than 1 in every 1000 insertions for isospecific active species, is sufficient to give high hydrogen response and therefore easy molecular weight control as a result of a high probability of chain transfer with hydrogen at “dormant” 2,1-inserted sites [40]. 4.4. Chain transfer reactions Chain transfer in olefin polymerization is an important class of reactions because their frequency with respect to the propagation step determines the molecular weight of the polymers. Since the discovery of single-site metallocene and non-metallocene systems these reactions have been studied experimentally [50,52,58,189–192] and theoretically [57,60,61,193–195] in great detail. However, all this background was only partially moved to a better knowledge of chain transfer reactions in MgCl2 -supported catalyst systems at atomic level. It has been reported that the chain transfer to the monomer (BHT) is the dominant chain transfer reaction for heterogeneous ZN systems [41,196] analogously to ansa-metallocene [57,61] and non-metallocene systems [191,197]. Nevertheless, in condition of low monomer concentration and/or higher concentration of Al-alkyls, chain transfer to the metal (BHE) and chain transfer to cocatalysts may be predominant [48]. For industrial ZN catalysts, the use of hydrogen to control the molecular mass makes hydrogenolysis the predominant chain transfer reaction [41,45]. Before coming into details of the limited computational works focused on chain transfer reactions with heterogeneous ZN catalysts, let us briefly summarize the main achievements obtained by DFT calculations on well-defined homogeneous systems. It has been claimed that an increase of polymer molecular weight may well be obtained by suitable ancillary ligand substitution by destabilizing the BHT as reported in Fig. 24 [195]. If we translate this concept to the minimal model reported in Fig. 1c used for both stereoselectivity (see Fig. 19) and regioselectivity (see Fig. 21) paths to compare the propagation and BHT TSs, we found that the BHT is a 6-centre TS spanning an angle of ca. 130◦

Fig. 25. Optimized geometries TSs for propylene insertion a) and for ␤-hydrogen transfer to the monomer (BHT), b), calculated for the minimal model reported in Fig. 1c. The role of chlorine atoms which destabilize the BHT by steric contact with the growing polymer chain is reported with a red circle in b) [198].

(see Fig. 25b) with respect to the 4-centre TS with an angle of 90◦ for propagation (see Fig. 25a). The larger angle makes the BHT more easily destabilized by sterical bulk of substituents marked with * [198]. Interestingly, the substituents marked with * occupy the positions crucial for increasing the stereoselectivity of monomer insertion (compare Fig. 21 and Fig. 25); it is not unexpected that the more isoselective active sites are producing also higher molecular weights polypropylenes [19]. These considerations fit well the data of Ziegler et al. [176] on cluster models reported in Table 13 where the external donors with higher EStereo show also higher EBHT . 5. Stability of ZN catalysts and the effect of undesired parallel reactions In previous sections we highlighted the main effects of electron donors in ZN olefin polymerization, which consist into increasing the polymer stereoregularity as well as the molecular weight and, in some case, catalytic activity. However, a number of undesired side reactions between donors and some catalytic ingredients having a Lewis acid character are prone to take place [199]. The more effective donors are therefore those showing low or no tendency to participate in undesired parallel reactions while positively influ-

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Table 13 Calculated stereoselectivity (EStereo ) and energetic difference (EBHT ) between the activation of propagation and ␤-hydrogen transfer to the monomer energies, respectively, as a function of donor structures for the TiCl4 /MgCl2 active site model reported in reference [176]. Values in kcal/mol. Donor

Hstereo a)

HBHT

2.0

15.8

3.4

18.4

3.2

17.2

1.7

15.2

2.2

16.9

1.8

4.1

3.7

17.5

1.6

13.7

1.5

13.7

1.6

19.3

2.2

17.3

2.6

19.9

-c

17.9

6.4

17.1

b)

a) Energetic difference between the activation energies of 1,2 si and 1,2 re propene enantiofaces, respectively. b) Energetic difference between the propagation (insertion barrier relative to the alkyl complex and propylene) and BHT (␤-hydrogen transfer to monomer barrier relative to the alkyl complex and propylene). c) Transition state was not located.

encing ZN catalyst functioning. Some pathways were proposed for decomposition of esters by Al-alkyls cocatalyst in the literature (see Fig. 26) [200]. Chien and coworkers suggested two ketone and aldehyde pathways for ester decomposition by triethylaluminium cocatalyst and demonstrated these pathways by characterization of single products reported in Fig. 26 using GC–MS analysis [200]. Because it had already been shown that the LB easily binds to a TiIII precursor or an Al-alkyl moiety [201] apart from MgCl2 , Kumawat et al. studied aldehyde and ketone decomposition pathways, imposed by AlEt3 (as dimeric Al2 Et6 ) and TiCl2 Et on MgCl2 supports, for ethyl p-ethoxybenzoate, ethyl p-isopropoxybenzoate and ethylbenzoate [202]. The pathways for decomposition by TiCl2 Et are shown in Fig. 27. As can be seen, the slowest step in the reaction pathways is the first step (1a-1a’ or 1a-1a”). Since the barrier of the first step in the Al2 Et6 case is higher than it is in the TiCl2 Et case (E = 31.1–31.4 kcal/mol with Al2 Et6 versus 24.7–30.0 kcal/mol for TiCl2 Et), they concluded that donor decomposition imposed by titanium species is significantly greater than with the AlEt3 . On the other hand, Kumawat et al.’s calculations showed that silyl esters

Fig. 26. Mechanism for ester decomposition imposed by AlEt3 proposed by Chien and coworkers. Adapted from ref. [200].

with bulky alkyl groups are decomposed by both Al2 Et6 and TiCl2 Et species on the MgCl2 surface [202]. Other studies focused on the capability of halogenated organic compounds to improve activity of ZN-catalysts. Indeed, it has been shown that halogenated organic compounds can probably reactivate less active TiII species produced by over reduction of TiIV species by the AlR3 cocatalyst [203,204], as it is known that Ti can be in different oxidation states, from +2 to +4 (see Section 4.1). The most widely accepted theory is that TiIII , formed from TiIV reduction, has the highest activity among different oxidation states, whereas TiII , formed from over reduction of TiIV , has less polymerization activity, or actually does not lead to higher olefin polymerization. Despite improvements from an experimental point of view, only a few theoretical works have been conducted to shed light on the mechanism of this effect. Bahri et al. [203] studied TiII oxidation/reactivation mechanisms by chloromethanes. In this regard, two oxidation pathways were evaluated. Both were based on the homolytic cleavage of the C-Cl bond in chloromethanes. The first pathway was the addition of both the organic part and the Cl atom of the chloromethane into the TiII site to oxidize the TiII center to TiIV (Fig. 28a). The second was the addition of a Cl atom of chloromethane to the TiII center to oxidize the TiII site to TiIII (Fig. 28b). The calculated energies corresponding to different steps of one of these mechanisms (TiII to TiIV ) (Fig. 28a) are summarized in Table 14.

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109

Fig. 27. Free energy diagram for ethylbenzoate decomposition by TiCl2 Et adsorbed on MgCl2 (110) surface via the aldehyde and ketone pathways (AP and KP, respectively). Adapted from ref. [202].

Fig. 28. Oxidation of TiII to (a) TiIV and (b) TiIII by n-chloromethanes. Adapted from ref. [203].

As can be seen, the coordination capability of the chloromethanes,  ECoord , decreases when the number of Cl atoms is increased, so that coordination of CCl4 is less favored. This was connected to the reduced donor ability of halide-rich species [205]. The oxidative addition step is more favored with Cl-rich organohalides (see  EOA and the  ETot in Table 14), so that

oxidation/reactivation of a TiII center becomes more facile when a Cl-rich organohalide is employed [203]. The energies of the second pathway (Fig. 28b), which is related to the oxidation of TiII to TiIII , are presented in Table 15. The ETot energies indicate that CH2 Cl2 and CH3 Cl, with ETot of −4.3 and +2.2 kcal/mol, respectively, are rarely able to oxidize the TiII site via a radical mechanism.

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Table 14 Calculated energies of different steps for path a, reported in Fig. 28, for the oxidation of a [Mg]/TiCl2 species by CHn Cl4-n (n = 0–3) compounds [203]. Values in kcal/mol. Reaction

ECoord

EOxAdd

ETotal

[Mg]/TiCl2 + CH3 Cl → [Mg]/TiCl3 CH3 [Mg]/TiCl2 + CH2 Cl2 → [Mg]/TiCl3 CH2 Cl [Mg]/TiCl2 + CHCl3 → [Mg]/TiCl3 CHCl2 [Mg]/TiCl2 + CCl4 → [Mg]/TiCl3 CCl3

−15.9

−16.2

−32.1

−15.6

−18.6

−34.2

−13.7

−20.9

−34.6

−11.8

−25.2

−37.0

Table 15 Calculated energies of the reaction associated with the oxidation of TiII species adsorbed on MgCl2 (110) surface to the related TiIII site by CHn Cl4-n (n = 0–3) [203]. Values in kcal/mol. HTotal

Reaction [Mg]/TiCl2 [Mg]/TiCl2 [Mg]/TiCl2 [Mg]/TiCl2

+ CH3 Cl → [Mg]/TiCl3 + CH3 + CH2 Cl2 → [Mg]/TiCl3 + CH2 Cl + CHCl3 → [Mg]/TiCl3 + CHCl2 + CCl4 → [Mg]/TiCl3 + CCl3

2.2 −4.3 −11.4 −19.8

This is particularly true for CH3 Cl because it has a positive energy value. CCl4 and CHCl3 with ETot of −19.8 and −11.4 kcal/mol, respectively, are qualified to reoxidize the TiII site via a radical mechanism. Further, Bahri explored the possible interaction between AlEt3 , TiCl4 adsorbed on MgCl2 , and MgCl2 with potential poisonous agents that can be present during catalysts (including methanol, water, hydrogensulfide) as well as their influence on polymer stereospecifity and catalytic activity [206]. Results showed that the examined molecules bind strongly on both (104) and (110) facets of MgCl2 , following the order of CH3 OH > H2 O> H2 S. They also explored the effect of Mg-adsorbed poison molecule on the olefin insertion barrier at a nearby Ti-active species, and found a negligible effect on both the insertion barrier and stereoselectivity in agreement with experimental results of Terano et al. [207]. Further, these small molecules were suggested to deactivate the catalyst by forming stable complexes with the Ti-active species [203,206]. Finally, doping of Mg(OEt)2 or MgCl2 supports, by a proper amount of Lewis acid, has been lately identified as an effective way to synthesize efficient ZN catalysts with superior activity and better performance towards higher ␣-olefin (co)polymerizations, which is useful in LLDPE production. These Lewis acids are mostly based on metal halides, such as MnCl2 , ZnCl2 , NaCl, AlCl3 , or their mixture with SiCl4 - and GeCl4 -type metalloids [208–211]. Recently, Bahri et al. computationally studied FeCl3 as a support modifier to improve catalytic performance and comonomer incorporation in ethylene homopolymerization and 1-hexene/ethylene copolymerization [178,212]. They considered the three models including [Fe3 ]/TiCl2 CH3 , [Mg2 Fe]/TiCl2 CH3 and [Mg3 ]/TiCl2 CH3 . Analysis of the energy profiles of ethylene insertion into the (doped and undoped) model catalysts indicated a slightly lower insertion barrier in partially doped MgCl2 support (see Fig. 29). A Fe-doped catalyst can incorporate a higher amount of 1hexene in copolymerization of ethylene/1-hexene than an undoped one can [212], because of the lower electron density on Ti in the doped catalyst which is beneficial for higher olefin incorporation [213–215]. However, a similar effect was not reported for the isoselectivity of ZN-catalysts modified with n-butyl-phthtalate and ethylbenzoate donors [178,206].

Fig. 29. Relative energy diagram (in kcal/mol) for ethylene insertion into [Mg3 ]/TiCl2 CH3 (red); [Mg2 Fe]/TiCl2 CH3 (blue); and [Fe3 ]/TiCl2 CH3 (black) models calculated at BP86/SVP level Adapted from ref. [212].

6. Conclusions In this work, we reviewed DFT studies focused on olefin polymerization catalyzed by heterogeneous ZN systems. The evolution of DFT tools in terms of reduced computer time, better treatment of heterogeneous surfaces and reliable computational protocols match the better understanding of heterogeneous ZN catalysts since the pioneering works of the 80’s [92,133,134] and indicate DFT as a great tool to be combined with the more advanced surface science techniques [22,30,31,37,62,154,165,216–218]. The main features characterizing the transition metal catalyzed polymerization (e.g. stereoselectivity, regioselectivity and chain transfer reactions), as well as undesired side reactions, have been discussed here. Ironically, the models developed to explain the origin of stereoselectivity of heterogeneous ZN, although based on still elusive active site structure, have been successfully applied to well-defined homogeneous systems. Despite significant progress in the field, the nature of ZN active sites still remains a matter of debate and prevents a rational design at a molecular level. Although formed by a combination of four elements, namely MgCl2 , TiCl4 , a LB, and Al-alkyls, the cross-relations between these elements generate a gaming puzzle. Here we summarized several active site hypotheses developed since the seminal works based on crystallographic consideration for TiCl3 based systems. We are confident that the evolution of computational methods will continue to assist progress in understanding of this amazingly efficient catalysis. Acknowledgments G.T wish to thank the KAUST for the visiting contract KAUST2017-C0854 and the University of Naples Federico II for financial support (Ricerca di Ateneo 2017 of University of Naples Federico II, DR 409 2017). A.P. thanks the Spanish MINECO for project CTQ2014-59832-JIN. References [1] [2] [3] [4]

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