Introduction

Ziegler–Natta catalyst (ZNC) has been conventionally used in petrochemical industries for the production of polymeric material, i.e., polyethylene, polyolefin1,2, and polypropylene3,4,5,6, where the two common types of ZNC used are titanium- and vanadium-based7,8. Since the 1950s, the fourth generation of ZNC has been based on titanium tetrachloride (TiCl4) on magnesium chloride (MgCl2) support. Moreover, alkyl aluminum, which is an organoaluminium compound, was also added as a co-catalyst9. Regarding the procedure, the alkylation process can reduce the Ti4+ species of the chloride ligand to form the active species of Ti3+ and Ti2+. The reduced Ti species are crucial for the formation of a complex surrounded by ethylene molecules10,11. Moreover, it is worth noting that the Ti2+ species was also found to be the active center for ethylene polymerization12,13,14,15. One of many upgrading methods for improving the performance of ZNC is the enhancement of the TiCl4 loading, in which the pretreatment process can significantly promote the amount of TiCl4 deposition on the MgCl2 surface16,17,18,19,20.

Although the amount of TiCl4 can be increased, it does not confirm that all added TiCl4 can be activated as the active Ti species. Hence, understanding the mechanism of ZNC formation, including (1) the titanation process, which introduces the TiCl4 on the MgCl2 support, and (2) the alkylation process, in which the alkyl aluminum interacts with the adsorbed TiCl4 species, is crucial and need to unravel. To do so, the density functional theory (DFT) is an effective tool that can elucidate the insight information of the thermodynamically stable structure and the electronic charge properties for describing what phenomena have probably undergone during the titanation and alkylation processes. Taniike et al21. employed the DFT calculation to define the coordination modes of titanium and other donors on the MgCl2 surface of MgCl2/TiCl4/ID/AlR3/ED in which the most stable structures of MgCl2/TiCl4/ID/AlR3/ED were illustrated. Zorve and Linnolahti22. computationally investigated the adsorption of TiCl4 on MgCl2(104) and MgCl2(110) surfaces to describe that the mononuclear TiCl4 prefers to adsorb at the defect site of MgCl2(110) surface by creating the six-coordination bond formation. On the one hand, the resemblance of a binuclear of Ti2Cl8 can be found on the MgCl2(104) surface, shedding light on how the active centers are presented. Cheng et al.23.computationally investigated the sequence of electron donors via twelve possible ZNC models, including mono-nuclear and di-nuclear TiCl4. Moreover, the effect of ethyl benzoate (EB), which is the electron donor, on perfect and defective MgCl2(110) and MgCl2(100). They found that the EB molecule prefers to adsorb on the support over the TiCl4 region, obstructing the coordination of TiCl4 on the MgCl2 surfaces.

Herein, the combined experiment and DFT calculation in which the experimental observation found some important phenomena of catalytic deactivation during the ethylene polymerization process. Meanwhile, the DFT calculation is cooperated to describe the deactivation's cause. The results obtained via this work can be used to design a better ZNC.

Results and discussion

Experimental results

Morphological properties

The effect of the pretreatment process on morphological changes of ZNC was primarily investigated via SEM analysis. The SEM images are shown in Fig. 1, while the average particle size of the catalyst and the amount of deposited Ti in ZNC bulk, measured by ICP, are summarized in Table 1. Overall, the physical appearances of unpretreated and pretreated ZNCs are not significantly different. Moreover, the average particle sizes of unpretreated ZNC (around 21 µm) and pretreated ZNC (around 36 µm) in this work are in the ranges of conventional ZNC (20 to 40 µm)24. Intriguingly, The 4.6 wt% of Ti species in unpretreated ZNC and 10.1 wt.% of pretreated ZNC indicates that the pretreating process can increase the amount of Ti deposition during titanation process, suggesting that the interaction between the MgCl2 surface and TiCl4 is significantly improved20,25.

Figure 1
figure 1

SEM images of (a)-(c) unpretreated and (d)-(f) pretreated ZNC.

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Table 1 Amount of Ti content and average particle size of ZNCs.
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In order to elucidate the distribution of TiCl4 species, especially on the surface of unpretreated and pretreated ZNCs, the elemental analysis via EDX spectroscopy was performed, as shown in Fig. 2. The blue and red dots in the EDX mapping represent the elemental distribution of Ti and Mg species, respectively. It is found that the dispersions of Ti and Mg species on both unpretreated and pretreated ZNCs seem uniform. However, the Ti species on the pretreated ZNC is more condensed, while the density of Mg species on both ZNCs is comparable. Furthermore, the molar ratios of Ti/Mg on unpretreated and pretreated ZNCs are 0.3 and 1.8, respectively. The higher amount of Ti/Mg ratio found on the pretreated ZNC reveals that performing the pretreatment process successively increases the amount of the Ti species deposition in both bulk structures, elucidated by ICP, and the catalyst surface, distinguished by SEM–EDX.

Figure 2
figure 2

The SEM–EDX image representing a distribution of Ti species (blue spot) and Mg species (red spot) on (a-c) unpretreated and (d-f) pretreated ZNCs.

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The crystallinity of MgCl2 support during the titanation process

Regarding the previous section that clearly proves that pretreatment of MgCl2 can increase the amount of TiCl4 loading on the ZNC surface, the crystallinity of ZNC is another crucial factor that has to be investigated in order to confirm phase transformation of ZNC that normally takes place during the titration process26,27. Herein, the XRD patterns of clean MgCl2 support and ZNCs are illustrated in Fig. 3, showing sharp peaks at 2θ of 15ο, 30ο, 35ο, and 50ο corresponding to the Miller index of (003), (102), (104), and (110), respectively. These characteristic peaks refer to the unique character of MgCl2 in the alpha phase (α-MgCl2)20,28. After the titanation process, all mentioned peaks invincibly disappear. These results demonstrate the scenario of the phase transformation in which the α-MgCl2 undergoes the delta phase of MgCl2 (δ-MgCl2). Nevertheless, the δ-MgCl2 is realized as mainly an amorphous phase27. Hence, the crystal peak on the XRD patterns of both unpretreated and pretreated ZNCs does not clearly exhibit.

Figure 3
figure 3

The XRD patterns of clean α-MgCl2 (black) before the titanation process, unpretreated (green), and pretreated (blue) ZNCs containing TiCl4 on MgCl2 support.

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Regarding the δ-MgCl2, three facets; including (001), (104), and (110) planes, are normally considered29,30. Among them, only (104) and (110) facets significantly influence the titanation process. On the other hand, the presence of an inactive Mg center found in the δ-MgCl2(001) surface makes the (001) facet inactive for the titanation process. Hence, investigation on the ZNC, especially on the δ-MgCl2(001) surface, can be neglected, as discussed in various works28,31.

In this work, small amplitudes of ~ 32ο and ~ 50ο representing (104) (marked as a star) and (110) (marked as a triangle) facets of δ-MgCl2 support20,28 are observed. However, these signals are not strong enough to explain which facet is dominant. Therefore, consideration of the catalytic performance of ZNCs via MgCl2(104) and δ-MgCl2(110) surfaces is selected. According to these strategies, theoretical investigation via the ZNC(104) and ZNC(110) models was performed and discussed in the computational section.

The activity of ZNCs during ethylene polymerization

As mentioned, the pretreatment process can add TiCl4 species, which can further activate during the alkylation process. The TiCl4 species which is interacted with the AlEt3 reduces Ti species. Then, the reduced Ti species can attack the π electron of ethylene monomer at the initial state of ethylene polymerization32,33. In this work, the concentration of AlEt3 was varied. The ratios of Al/Ti are listed in Table 2. Moreover, the normalized catalytic activity in the function of the Al/Ti ratio is plotted in Fig. 4, in which the activity plot can be classified by two main states. For the first state, the activity of ZNC for ethylene polymerization is increased as the function of AlEt3, in which the optimum Al/Ti ratios refer to the maximum catalytic activity. The optimum Al/Ti of unpretreated and pretreated ZNCs are 120 and 140, respectively. The lower optimum value of the Al/Ti ratio on unpretreated ZNC reflects that unpretreated ZNC consumes less amount of Al to activate the Ti species. These results also confirm that the amount of Ti species, which is possible to be activated, on the unpretreated ZNC is less than that on the pretreated ZNC.

Table 2 The activity of ethylene polymerization in various Al/Ti ratios.
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Figure 4
figure 4

The plots of relative activity in the function of the Al/Ti molar ratio of unpretreated (green) and pretreated (blue) ZNCs.

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After the optimum point, the second state takes place. The catalytic activity is significantly declined according to the function of AlEt3 loading. These results reflect the overloading of AlEt3 after the optimum Al/Ti ratio, inducing the over-reduction of Ti species from Ti+4 to Ti+, in which this Ti+ species is inactive for ethylene polymerization34,35. Interestingly, consideration of the absolute activities of unpretreated and pretreated ZNCs elucidates that the absolute activities of ethylene polymerization on unpretreated ZNC are approximately two times higher than that on the pretreated one in every Al/Ti ratio even though the amount of deposited Ti species on pretreated ZNC is higher. According to these results, there is a crucial clue as to why the increment of the Ti content decreases the catalytic activity for ethylene polymerization. To answer this question, DFT participated in the computational section.

Computational results

Adsorption of TiCl4 on MgCl2(104) and MgCl2(110) surfaces

According to the experimental observation, phase transformation of the α-MgCl2 to the δ-MgCl2 was observed during titanation process in which the structure of δ-MgCl2 probed via XRD revealed equivocal judgment on either (104) or (110) facet is dominant. Hence, the construction of both (104) and (110) surfaces was not ignored. The scenario of two concentrations of TiCl4 on δ-MgCl2(104) and δ-MgCl2(110) surfaces was scoped to represent low-concentration (L104 and L110) and high-concentration (H104 and H110) models. The most stable geometries of L104, L110, H104, and H110 are illustrated in Fig. 5. It is noted that the single molecular TiCl4 adsorption represents L104 and L110, while the bimolecular TiCl4 adsorption represents H104 and H110. Also, adsorption energy (Eads), the contact point between each bonding atom, and the adsorption height of each adsorbate are included in Table 3. All possible optimized geometries are shown in Table S1 in the supplementary document.

Figure 5
figure 5

Stable geometries of (a) L104, (b)L110, (c) H104, and (d) H110 surfaces.

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Table 3 Adsorption energies (Eads) in eV, contact points of TiCl4 on MgCl2(104) and MgCl2 (110) surfaces, and adsorption height in Å of TiCl4, including single TiCl4 molecule and TiCl4 cluster on MgCl2(104) and (110) surfaces.
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For the (104) plane, the single molecule of TiCl4 can be adsorbed with the Eads of −0.53 eV by creating three contact points: Cl1-Mg1, Cl2-Mg2, and Ti1-Cl5. In the case of bimolecular adsorption of TiCl4 on δ-MgCl2(104) surface, the interaction of the second TiCl4 molecule is strengthened in which the Eads is −0.73 eV. The two additional contact points of Cl4-Mg3 and Ti2-Cl6 are created. The more negative Eads during the second TiCl4 adsorption implies the promotional effect of the first TiCl4 molecule enhancing TiCl4 adsorption. These results agree well with the experimental observation that the existence of TiCl4 species from the pretreatment process can facilitate more amount of TiCl4 adsorption in the upcoming impregnation process25. However, adsorption of the new coming TiCl4 on H (104) seems to occur of TiCl4 clustering on the δ-MgCl2 (104) surface.

For the (110) plane, the single molecule of TiCl4 can be adsorbed with the Eads of −1.05 eV by creating the four contact points of Cl1-Mg1, Cl2-Mg2, Ti1-Cl5, and Ti1-Cl6. The most favorable adsorption site is elucidated at the defect site of the δ-MgCl2 (110) surface. The more negative Eads compared to that on the δ-MgCl2 (104) surface reveals that the interaction of TiCl4 on the δ-MgCl2 (110) surface is stronger than that on the δ-MgCl2 (104) surface because the presence of the defective site facilitates the creation of four contact points between TiCl4 and δ-MgCl2 (110) surface. Thereby, the appearance of the “defect” site is one of the most important key roles in improving TiCl4 deposition on MgCl2 support. When the concentration of TiCl4 on the δ-MgCl2 (110) surface is increased, the second TiCl4 molecule is adsorbed on the second defective site of the δ-MgCl2 (110) surface in which the Eads of the second molecule of TiCl4 is comparable to the single molecular TiCl4 adsorption. According to these results, the dispersion of the defective site on the δ-MgCl2 (110) surface is a key factor in controlling the distribution of deposited TiCl4 in which control of the distribution of the TiCl4 on δ-MgCl2 (104) is more difficult.

Alkylation of TiCl4 species on H104 and H110 surfaces

To activate the deposited TiCl4 readily for ethylene polymerization, the alkylation process must be first performed when the addition of the AlEt3 is introduced. Regarding the experimental question, why does an increment of TiCl4 deposition deteriorate the catalytic activity for ethylene polymerization? Consideration of the geometries of ZNCs, especially the high TiCl4 contents, including H104 and H110, when interacting with the AlEt3, is performed. From various possible adsorbed configurations of AlEt3, as listed in Table S2, the most stable geometries of each AlEt3-H104 and AlEt3-H110 are demonstrated in Fig. 6a and Fig. 6b. Furthermore, the electron density difference (EDD), which is depicted as the contour plot, together with Bader charge analysis values, are expressed in Fig. 6c and Fig. 6d.

Figure 6
figure 6

The geometries of AlEt3 adsorption on (a) ZNC(104) and (b) ZNC(110).

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The red region corresponds to the negative Bader charge value representing electron accumulation. In contrast, the blue region with the positive Bader charge refers to electron depletion. For the alkylation on the H104 surface, the AlEt3 prefers to adsorb on TiCl4 by creating the interaction of Al-Cl3 with the Eads of −0.47 eV and the adsorption height of 2.54 Å. For alkylation of the H110 surface, adsorption of AlEt3 takes place via the connection of the Al species of AlEt3 to the Cl4 species of the adsorbed TiCl4 with an Eads of −0.58 eV and the adsorption height of 2.46 Å.

The appearance of a negative Bader charge of the adsorbed AlEt3 species corresponding to the positive Bader charge of surfaces, including H104 and H110 surfaces, elucidates the scenario of electron transfer from catalyst surfaces to adsorbed AlEt3 molecule. Moreover, the less negative Bader charge of the AlEt3 molecule on the H104 surface compared to the H110 surface agrees well with the weaker interaction of AlEt3 on the H104 surface.

Intriguingly, the change of Bader charge of Ti1 species during the formation of H104 higher TiCl4 and adsorption of AlEt3 demonstrate sharing electron around the first and second TiCl4 molecule on only ZNC (104) surface due to agglomeration of TiCl4. Focusing on the Bader charge of the Ti1 species in L104 (denoted as + 0.46 |e|) and H104 (denoted as −0.29 |e|), which is reported in Table S3, changing of the Bader charge when the formation of the TiCl4-TiCl4 cluster exhibits that there is electron transfer between the first species of TiCl4 and the second species of TiCl4. These results elucidate that there is an interaction between two TiCl4 species, confirming the clustering of TiCl4-TiCl4 on H104. This agglomeration is not observed during the transformation of L110 to H110.

The presence of TiCl4-TiCl4 cluster has negative effects, not only weakening the interaction between AlEt3 and deposited TiCl4 but the presence of TiCl4-TiCl4 cluster prevents dispersion of TiCl4, making only one species of TiCl4-TiCl4 cluster can be activated via interacting with the first AlEt3 whereas the other is still inactive because of the steric hindrance of the adsorbed AlEt3 hindering the further alkylation process. As a result, there is only one active species readily available for ethylene polymerization. On the other hand, the good dispersion of TiCl4 species supports activation of the adsorbed TiCl4 species in the upcoming alkylation process because the good distribution of TiCl4 species on the special defective site overcomes the steric effect of AlEt3. Thereby, the activity of the H110 is possibly higher than that of H104. The results obtained by DFT calculation suggest that the increment of TiCl4 loading does not always enhance the activity of ZNC, but the increment of the TiCl4 contents on the (110) plane of ZNC is more important in enhancing the performance of the ZNC. In contrast, an increment of TiCl4 deposition on the (104) plane of ZNC promotes the enlargement of the TiCl4-TiCl4 cluster, lowering the activity of ZNC.

Conclusion

The issue of how the MgCl2 support pretreatment improves the amount of TiCl4 deposition on the ZNC catalyst yields a low-performance ZNC is investigated. Overall, the phase transformation from α-MgCl2 to δ-MgCl2 was observed during the titanation process. Also, the δ-MgCl2 (104) and δ-MgCl2 (110) are dominant surfaces. Although the pretreatment process can increase the amount of TiCl4 loading, the absolute catalytic activity for the unpretreated ZNC is still higher. The DFT calculation participated in unraveling why the higher content of TiCl4 deposition lowering deactivated the ZNC. It is demonstrated that the pretreatment process could enhance the adsorption of further TiCl4 species, but the clustering of TiCl4-TiCl4 cluster, especially on the H104 surface, is also easily facilitated. However, the presence of a TiCl4-TiCl4 cluster is not observed on the H110 surface. The presence of the TiCl4-TiCl4 cluster has a negative effect in terms of blocking the second alkylation process, whereas the first alkylation process can be done normally. Hence, only one TiCl4 species can be activated even though two TiCl4 were introduced. On the other hand, two species of TiCl4 on H110 can be fully activated via the alkylation process. The results obtained by DFT calculation suggest that the key point for enhancing the activity in ZNC is not always the amount of TiCl4 loading but controlling either the presence of MgCl2(110) or other special support that can prevent the formation of the TiCl4-TiCl4 cluster is more crucial for improving the performance of a better ZNC.

Methodology

Experimental details

Catalyst preparation

All preparations were carried out under the purified N2 atmosphere (supplied by Linde (Thailand) Ltd.). Firstly, the MgCl2 mixture was produced. The 2 g of anhydrous MgCl2 (purchased from Merck Ltd.) were suspended in 150 mL of n-heptane. Then, 12.30 mL of ethanol (EtOH) was added. This process is called the EtOH adduct process26,36,37. Subsequently, the mixture was homogenized at 120 ℃ for 2 h under a continuously refluxed condition. This precursor is indispensable for synthesizing ZNC in the upcoming step.

The two types of ZNCs, including (1) unpretreated and (2) pretreated ZNCs, were synthesized. For the unpretreated ZNC, the 11.50 mL of TiCl4, which was dissolved in 1 M of toluene, was added to 40 ℃ of the MgCl2 mixture. The titanation process was carried out by introducing the TiCl4 into the MgCl2 mixture, in which the molar ratio of Ti and Mg was controlled at 5:1. For the pretreated ZNC, the 2.30 mL of TiCl4 solution was firstly introduced into the MgCl2 mixture to pretreat the MgCl2 surface in order to dealcoholize the MgCl2•nEtOH adduct in which the equivalent molar ratio of Ti and Mg species was regulated. After that, the TiCl4 solution was introduced again to the dealcoholized MgCl2 through the same condition as the unpretreated ZNC.

When the titanation process was complete, all unpretreated and pretreated ZNCs were continually heated at 120 °C for 2 h before cooling down to room temperature. Finally, pretreated and unpretreated ZNCs were washed several times with the distilled hexane in order to eliminate impurities and excess TiCl4 before drying at 110 ℃ under a vacuum overnight. The dried ZNCs were safely stored under an Ar atmosphere.

Characterizations

The Ti content in each ZNC sample was measured via the inductively coupled plasma atomic emission spectroscopy (ICP-AES) by Perkin Elmer equipped with a 2100-DV inductively coupled plasma (ICP). The 0.01 g of each catalyst were dissolved in 5 mL of hydrochloric acid before being diluted with 100 mL of deionized water. The morphology and particle size were revealed through the secondary electron detector of scanning electron microscopy (SEM) performed on a Hitachi-S3400N model. In addition, the elemental analysis of Ti and Mg on ZNC was determined by the energy-dispersive X-ray spectroscopy (EDX) on the Apollo X model with the Edex 2371 series. Moreover, the crystallinity and phase transformation of MgCl2 support before and after the titanation process were analyzed by the powder X-ray diffraction (XRD), Bruker D8 Advance, with a diffraction angle (2θ) of 10° to 60°. The scanning speed was set as 0.5 s/step.

Polymerization reaction testing

The 0.01 g of ZNC was introduced into a stainless-steel autoclave reactor. Then, the AlEt3 cocatalyst (donated by Thai Polyethylene Co. Ltd.) was added to the reactor. The hexane was then injected until the final volume reached 30 mL (note that the concentrations of AlEt3 were varied in which the molar ratio of Al:Ti was set as 80:1, 110:1, 120:1, 140:1, 170:1, and 200:1). When all components were added, the reactor was vacuumed by evacuating the under vacuum condition for 10 min. The reaction was begun by ramping the temperature up to 70 ℃ in a heated water bath. Then, the reactor was soaked in the water bath. When the temperature was at equilibrium. The slurry polymerization of ethylene was taken place by feeding 7 bars of ethylene gas into the reactor continuously for 10 min. The reaction was terminated by (1) cooling the system down to room temperature and (2) adding 3.0 M of hydrochloric acid dissolved in methanol in order to precipitate the produced polymer. Finally, the solid phase samples, including ZNC and precipitated polymer, were washed using purified ethanol before drying at 110 ℃ until the weight became stable. The catalytic activity and relative activity are calculated in Eq. 1 and Eq. 2, respectively.

$$ {\text{Catalytic activity}} = \frac{{{\text{obtained PE polymer}} ({\text{kg}})}}{{({\text{Ti in the catalyst (mol)}}) \times ({\text{Reaction time (s)}})}} $$
(1)
$$ {\text{Relative activity = }}\frac{{\text{Catalytic activity}}}{{\text{Maximum activity}}} $$
(2)

Computational details

Catalyst modeling and parameters

All stable geometries and electronic properties were performed using DFT calculation, which was implemented through the Vienna ab initio simulation package (VASP 5.4.4)38,39,40,41. The projector augmented wave (PAW) of the generalized gradient approximation (GGA) proposed by Perdew, Burke, and Ernzerhof (PBE) functional was employed in the calculation42. The structural optimization was performed through the conjugate gradient method43 until the energy convergence was lower than 10−6 eV and the force convergence was less than 0.01 eV/Å. Moreover, the Van der Waals dispersion force is considered by applying the DFT–D3 method proposed by Grimme et al.44 During the optimization, the 3 × 3 × 1 Monkhorst–Pack k-mesh Brillouin-zone integration45 was used. The VESTA package46 was used to visualize all models. The interaction between the catalyst surface and the adsorbed molecule was characterized by the adsorption energy (Eads) calculated by Eq. 3.

$$ \Delta {\text{E}}_{{{\text{ads}}}} { = }\Delta {\text{E}}_{{{\text{complex}}}} {\text{ {-} }}\Delta {\text{E}}_{{{\text{adsorbent}}}} { + }\Delta {\text{E}}_{{{\text{adsorbate}}}} $$
(3)

The parameters: \(\Delta\)Ecomplex, \(\Delta\)Eadsorbent, and \(\Delta\)Eadsorbate are the calculated energies of the complex system (molecule-adsorbed surface), clean surface and adsorbed molecule (TiCl4 as well as AlEt3 species) are considered. The partial charge accumulation or depletion during the adsorption process (Δρads) of AlEt3 on TiCl4/MgCl2 catalyst was calculated based on the Bader charge analysis47,48,49,50 defined in Eq. 4.

$$ \rho_{{{\text{ads}}}} { = }\rho_{{\text{surface - TEA}}} {\text{ {-} }}\rho_{{{\text{surface}}}} {\text{ {-} }}\rho_{{{\text{AlEt}}_{{3}} }} $$
(4)

The parameters: \(\rho_{{\text{surface - TEA}}}\), \(\rho_{{{\text{surface}}}}\), and \(\rho_{{\text{surface - TEA}}}\) denote partial charge densities of adsorbed surface, catalyst surface, and an isolated molecule, respectively. The geometry of an isolated molecule (either TiCl4 or AlEt3) and the clean MgCl2 supports were constructed, as shown in Fig. 7. The stable MgCl2 surfaces of (110) and (104), including their possible active sites, are shown in Fig. 7a,b), respectively. Also, the four atomic layers of MgCl2(110) and MgCl2(104) surfaces were constructed.

Figure 7
figure 7

Structural geometries of (a) MgCl2(104), (b) MgCl2(110) with their possible adsorption sites, (c) TiCl4, and (d) AlEt3.

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Interaction between the periodic boundary was avoided by adding ~ 20 Å vacuum region along the z-axis of the slab model. All possible adsorption sites include (1) atop the site of Mg (A-Mg), (2) atop the site of Cl (A-Cl), (3) bridge between Cl and Cl (B-Cl-Cl), (4) bridge site between Mg and Cl (B-Mg-Cl), and (5) the hollow site (H). During optimization, the bottom two layers of MgCl2 surfaces were fixed to their bulk lattice parameter, while the rest of the layers and adsorbed species of TiCl4 and AlEt3 were fully relaxed.