Investigating Phthalate and 1,3-Diether Coverage and Dynamics on

Article pubs.acs.org/JPCC

Investigating Phthalate and 1,3-Diether Coverage and Dynamics on the (104) and (110) Surfaces of MgCl2‑Supported Ziegler−Natta Catalysts Raffaele Credendino,† Dario Liguori,‡ Giampiero Morini,‡ and Luigi Cavallo†,* †

Chemical and Life Sciences and Engineering, Kaust Catalysis Center, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia ‡ G. Natta Research Center, LyondellBasell Polyolefins, Piazzale G. Donegani 12, 44100 Ferrara, Italy S Supporting Information *

ABSTRACT: In this work we present a systematic DFT analysis of the effect of surface coverage on the coordination properties of two industrial Lewis bases, dimethyl phthalate and 9,9-bis(methoxymethyl)fluorene, to the (104) and (110) surfaces of MgCl2. Further, we investigated several possible migration pathways for the migration of the Lewis bases on the same MgCl2 monolayer. Our study clearly shows that complete coverage of the Mg vacancies on the surface by coordinating dimethyl phthalate or 9,9-bis(methoxymethyl)fluorene is hampered by steric repulsion between vicinally coordinated donor molecules. Further, our study clearly indicates that both dimethyl phthalate and 9,9-bis(methoxymethyl)fluorene migration on the same MgCl2 monolayer on the (104) and (110) surfaces basically requires donor dissociation.

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studies were performed to shed light on the fine structure of heterogeneous ZN catalytic systems. Indeed, several studies were devoted to the characterization of these catalysts,13,15−36 which allowed us to establish a number of broadly accepted concepts. For instance, there is agreement that the activated MgCl2 primary particles are made of a limited number of Cl− Mg−Cl monolayers piled irregularly one on top of the other,37 which should present (110) and (104) lateral cuts.24,38 As represented in Figure 1, Mg2+ ions on these lateral cuts should be 4 and 5 coordinated, respectively, thus presenting 2 or 1 vacancies.38,39 Simple electrostatic considerations suggested that the (110) lateral cut should be less stable relative to the (104) lateral cut,

INTRODUCTION Heterogeneous Ziegler−Natta (ZN) catalysts are the dominant catalytic systems in the industrial production of isotactic polypropylenes. The last generation of these systems is generally based on TiCl4 adsorbed on MgCl2, with a Lewis base (LB), usually called the donor, which can be added at the moment of catalyst synthesis (in this case it is commonly called the internal donor, ID) or at the moment the catalyst is activated (in this case it is commonly labeled as the external donor, ED).1 While different MgCl2 precursors and different recipes can be used to prepare different ZN catalysts, it remains clear that varying the nature of the LB is a remarkably powerful handle to tune the performance of the final catalyst. A huge number of Lewis bases has been screened for effective donors, and among the best performing have emerged alkoxysilanes, 1,3-diethers, and aromatic esters (benzoates and phthalates in particular), with the recent addition of aliphatic esters (succinates in particular).1 Nevertheless, despite the resulting active system being extremely well performing, it remains of extreme chemical complexity and a detailed understanding of the final structure of the catalyst remains elusive. As for the role of the Lewis base, it has been shown that it can remarkably influence (i) the stereo- and regiochemistry of the synthesized polypropylene, (ii) the distribution of the molecular mass, also through an impact on the response to H2, (iii) and also the morphology of the catalytic system, since LB can influence the size of the primary crystallites of MgCl2 and/or can have an impact on the quantity and dispersion of TiCl4 in the final catalytic system.2−16 This immediately explains why remarkable © 2014 American Chemical Society

Figure 1. Model of a MgCl2 monolayer, with indication of the (104) and (110) lateral cuts. Received: February 8, 2014 Revised: March 27, 2014 Published: March 27, 2014 8050

dx.doi.org/10.1021/jp501390e | J. Phys. Chem. C 2014, 118, 8050−8058

The Journal of Physical Chemistry C

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due to the higher unsaturation of the Mg atoms at the surface of the (110) monolayer. This general concept was supported by Busico and co-workers through periodic DFT calculations, which allowed us to quantify the relative energy of MgCl2 crystallites presenting (110) and (104) terminations.40 In agreement with this conclusion, we recently proposed that for naked MgCl2 crystallites constituted by equal amounts of MgCl2 units the crystallite presenting (110) terminations is less stable than the (104)-terminated crystallite because it has a higher number of Mg unsaturations and that crystallites of different shape and size can be put on the same scale using the density of vacancies as a correlating descriptor.41 We further demonstrated that donor coordination can completely change the stability order of the two faces, with (110) becoming more stable when covered by small prototype donors.42 These conclusions are in line with the accepted concept that the specific features of the catalytic system depend on the procedure followed to prepare the catalyst, as also evidenced by Andoni at al.35 and more recently by Thüne and coworkers.36 To complicate the picture further, it has to be considered that these catalysts also have a dynamic behavior, even at the time scale of the time needed to grow a polymer chain, including evidence that donors on the MgCl2 surface are mobile. For example, microstructural analysis of iPP from ZN catalytic systems presents stereodefects mostly concentrated into stereoblocks with a high number of stereomistakes.43 This is different from iPP obtained from classical zirconocenes, which lead to iPP chains with the stereomistakes distributed randomly along the macromolecule.44 To rationalize this finding, Busico introduced the 3-sites model, where the stereoselective behavior is altered by the mobility of ligands, such as the donor, around the active Ti species. Further, HRMAS studies by the same group showed that alkoxysilanes adsorbed on the MgCl2 surfaces can move and that the structure and polymerization performance of the catalytic system is affected by this mobility.45 Finally, the same study evidenced that the mobility of the alkoxysilane depends on the surface coverage.45 Despite the interaction of Lewis bases with the MgCl2 crystallites being studied from a theoretical point of view,42,46−50 these investigations mainly focused on the analysis of a single Lewis base adsorbed on the MgCl2 lateral cuts or their impact on stereoselectivity. We recently tried to take a step further by investigating coverage and dynamics of a typical alkoxysilane on the (110) and (104) surfaces using a periodic approach. Our calculations indicated that Mg vacancies on the surfaces cannot be completely covered by alkoxysilanes and that, in agreement with the experimental results,45 alkoxysilanes are rather mobile on the (104) surface, whereas they are firmly held in place on the (110) surface.51 A similar approach has been recently followed by Busico, Budzelaar, and coauthors, who investigated the adsorption of small probe molecules and model donors on MgCl2 surfaces using a periodic approach.52 In this work, we extend this approach to investigate the coverage and dynamic behavior of two other classic Lewis bases used in the field, namely, dimethyl phthalate (PHT) and 9,9bis(methoxymethyl)fluorene (BMF), see Chart 1. The work is presented in three sections. In the first we report on the influence of surface coverage on the adsorption of PHT and BMF. In the second section we report on the dynamical behavior of a single donor molecule adsorbed on either the (110) or the (104) lateral cut. In the third section we report on

Chart 1

the likely pathways for migration of the donors on both MgCl2 surfaces.

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COMPUTATIONAL DETAILS As in our previous work,51 DFT static and dynamics simulations were performed using the Born−Oppenheimer scheme as implemented in the CP2K Quickstep code.53 Electronic structure calculations were carried out at the DFT level using the Perdew−Burke−Ernzerhof exchange and correlation functional.54 The CP2K program employs a mixed basis set approach with Gaussian-type orbitals (GTO) and plane waves (PWs).53 At variance from our previous work on alkoxysilanes adsorption,51 in this work we also take into account dispersion interaction55−58 using the DFTD3 scheme proposed by Grimme.59 GTO functions are used to expand the molecular orbitals and charge density in real space, whereas PWs are used for a representation of the charge density in reciprocal space. An energy cutoff of 300 Ry is used for the plane-waves basis set. A triple-ζ basis set with a double polarization function, in conjunction with the Goedecker− Teter−Hutter pseudopotentials,60 was used for all the atoms. Full geometry optimization (cell parameters and atom coordinates) was performed in the presence of 1.0 bar external pressure. The parameters a and c of the simulation cell, which would be 3.63 and 17.66 Å using the crystalline structure, are slightly larger by 0.6% and 3.7% after optimization. For the sake of simplicity, in all other calculations the simulation cell was frozen. To relax eventual stress in the simulation cell, we used the optimized a and c values. A cubic box of 14.6 × 22.4 × 30.0 Å3 was thus used to model the (104) surface, while a box of 12.7 × 18.3 × 30.0 Å3 was used to model the (110) surface. In order to model the bulk, 5 and 6 layers of MgCl2 (respectively, for (104) and (110)) were considered in the direction perpendicular to the surface. The two systems are composed of 60 and 36 units of MgCl2, respectively. In the dynamic simulation the equations of motion were integrated using a time step of 0.5 fs. The MgCl2/LB adduct was equilibrated at 300 K for 10 ps using a canonical sampling through velocity rescaling thermostat.61 The energy barriers for donor migration were evaluated by an improved tangent nudged elastic band (NEB) method,62 which allows one to find the minimum energy path (MEP) between given initial and final states of a reaction. The MEP is found by constructing a set of images (replicas) of the system (for migrations we adopted 11 replicas) between the initial and the final states. A spring interaction between adjacent images is added to ensure continuity of the path, thus mimicking an elastic band. In one case, corresponding to intralayer donor migration on the (110) surface, the energy barrier found with the NEB method was tested versus the energy barrier found using the classical cluster method, an approach validated by Ziegler and co-workers.63 These calculations were carried out 8051



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using Gaussian09 software.64 Energies, geometries, and vibrational frequencies were obtained at the PBEhPBE level65 of theory in conjunction with Ahlrichs triple-ζ basis set66 incorporating a polarization function. A cluster of 11 MgCl2 units was chosen, and all MgCl2 units were frozen. The transition state (TS) were located by the synchronous transitguided quasi-Newton approach67 (QST3 method) implemented in Gaussian09. The genuineness of the transition state was ensured by the presence of one imaginary frequency.

At variance from previous results, in the case of PHT the 110chelate geometry is favored by 3.3 kcal/mol over the 110-bridge geometry, when stacking of MgCl2 layers is considered. As shown in Figure 2, this difference is due to repulsive interaction

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RESULTS AND DISCUSSION 1. Coverage. Capping Mg2+ unsaturations on the MgCl2 surfaces with the donors, or surface coverage by the donors, is a relevant issue that controls (i) the relative stability of MgCl2 crystallites presenting different surface, which influences also adsorption of TiCl4, and (ii) the morphology of the MgCl2 crystallites, since Mg pentacoordinated (104) surfaces should dominate in the absence of the donors while Mg tetracoordinated (110) surfaces should be favored if a large excess of the donor is used. With this background, we investigated different coverages by PHT and BMF of both the (104) and the (110) surfaces. As in a previous paper,51 we define the fraction of covered surface, θ, as the ratio of the number of oxygen atoms adsorbed and the number of Mg vacancies on the surface (eq 1). nOxygen θ= nv (1)

Figure 2. Comparison between the 110-bridge coordination geometry of a single phthalate on a single (110)-terminated monolayer (a)42 and on stacked (110)-terminated multilayers (b).

between the aromatic ring of PHT and the vicinal MgCl2 layer, which forces PHT to bend away from the MgCl2 surface. While the main conclusions we derived in the past are not changed, i.e., phthalates are more flexible donors that can assume a variety of close in energy coordination geometries on the (110) surface, for the sake of simplicity in the following we only considered 110-chelate coordination for both BMF and PHT. To analyze the geometry, when two or more donors are coordinated on the MgCl2 surface, we focused attention on the average Mg−O distance between the adsorbed PHT and BMF and the surface, ⟨dMg−O⟩, see Table 1 and Figure 3. Focusing on

The average adsorption energy per donor molecule, Ead, is calculated as in eq 2 −Ead =

Table 1. Average Mg−O Distance, ⟨dMg−O⟩ in Angstroms, and Average Adsorption Energy, Ead in kcal/mol, for the (104)-Bridge and (110)-Chelate Adsorption of PHT and BMF on MgCl2

EMg/D − EMg − nD·E D nD

(2)

(104)/PHT

where EMg/D is the energy of the system composed by a donor molecule adsorbed on the MgCl2 surface, EMg and ED are the energies of the uncovered MgCl2 system and of the free donor, respectively, and nD is the number of donor molecules adsorbed. Since previous work indicated that the only achievable coordination geometry for phthalates and 1,3-diethers on the (104) lateral cut of a MgCl2 monolayer is the so-called 104bridge geometry,42 we focused on this geometry when coverage of the (104) is considered. In the case of the (110) lateral cut of a MgCl2 monolayer, instead, previous work indicated that two geometries are possible. One of them, called 110-chelate, presents both O atoms of the donor coordinated to the same Mg atom, while in the other, called 110-bridge, the two O atoms of the donor coordinate to vicinal Mg atoms. In the case of 1,3-diethers, the 110-bridge coordination geometry was found remarkably higher in energy than the 110-chelate geometry, more than 10 kcal/mol, due to the inability of the 1,3-diether skeleton to stretch enough to coordinate to two vicinal Mg atoms, which are 6 Å apart. Differently, in the case of the more flexible phthalate, the 110-bridge geometry was found to be slightly lower in energy, by 2.2 kcal/mol, relative to the 110-chelate geometry. For this reason, we started this analysis with a comparison of the 110-chelate and the 110-bridge geometries for BMF and PHT when a single donor is coordinated on a multilayers (110) surface. Consistently with previous results,42 for BMF the 110-bridge geometry is of remarkably high energy, 11.3 kcal/mol higher than the 110chelate geometry, even in the presence of stacked MgCl2 layers.

coverage θ 0.17 0.33 0.50 0.67 0.83 1.00 θ 0.17 0.33 0.50 0.67 0.83 1.00

⟨dMg−O⟩ 2.14 ± 0.06 2.30 ± 0.34 2.49 ± 0.64 2.73 ± 0.79 2.89 ± 0.91 3.12 ± 1.00 (110)/PHT

(104)/BMF Ead 34.5 34.9 36.3 28.3 31.6 30.8

⟨dMg−O⟩

Ead

± ± ± ± ± ±

24.3 24.3 25.7 20.5 14.8 14.1

2.13 2.91 2.64 3.67 4.20 5.36

0.01 1.52 1.20 2.19 2.39 2.55

⟨dMg−O⟩ 2.23 2.25 2.26 2.59 3.08 3.21

± 0.01 ± 0.01 ± 0.04 ± 0.85 ± 1.29 ± 1.07 (110)/BMF

Ead 30.3 27.1 26.2 21.4 20.4 14.1

⟨dMg−O⟩

Ead

± ± ± ± ± ±

30.1 30.3 29.7 29.8 19.3 14.7

2.14 2.16 2.17 2.17 2.19 2.56

0.06 0.02 0.04 0.07 0.07 0.73

PHT adsorption on the (104) surface, the ⟨dMg−O⟩ value of 2.14 Å at the lowest coverage of the MgCl2 surface (corresponding to θ = 0.17, which is one molecule adsorbed), increases to a value of 3.10 Å at θ = 1 (corresponding to a completely covered (104) surface). The sizable increase of the value of ⟨dMg−O⟩ at high surface coverage suggests that donors coordinated next to each other interact repulsively. Noticeably, at θ values around 0.5 a sharp increase is observed in the value of ⟨dMg−O⟩. Nonetheless, all oxygen atoms remain clearly coordinated to the surface. Similar behavior is found for BMF, with the ⟨dMg−O⟩ of 2.23 Å at the lowest coverage, rising at 8052



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unrealistic, considering the increased congestion at the surface, as also indicated by the increase in ⟨dMg−O⟩ at high θ. Inspection of the optimized geometries indeed indicates that at high θ several donors are completely dissociated from the MgCl2 surface; still they are stuck to each other forming a condensed layer above the MgCl2 surface, see Figure S1, Supporting Information. Considering that remarkably reduced interaction is occurring between the donors and the MgCl2 layer, the only reason for the increase in Ead is in a stabilizing interaction between the donor molecules, which can only be ascribed to the empirical dispersion term added to the DFT energy. To have a better understanding of this point and to investigate also the impact of basis set, we evaluated Ead of PHT on the (110) layer without including the dispersion term in the energy evaluation, column TZV2P in Table 2, as well as with Table 2. Average Adsorption Energy, Ead in kcal/mol, for the (104)-Chelate Adsorption of PHT on MgCl2 Using Different Computational Approaches Figure 3. Top view of the (104) and (110) surfaces covered by PHT and BMF, a and b, respectively.

⟨dMg−O⟩ of 3.2 Å at θ = 1. The clearly high values of ⟨dMg−O⟩ at high coverage, definitely larger than a long Mg−O bond, together with the large standard deviation indicate that at high coverage not all donors can coordinate to the surface, and there are several O atoms simply unable to bind to the MgCl2 surface. Moving to the (110) surface, the impact of surface coverage is rather similar to what was found for the (104) surface, although effects are more pronounced. Both donors prefer to adopt a chelate geometry instead of bridge or zip ones on the (110) surface due to the large distance of 6 Å between the closest unsaturated Mg atoms on the (110) surface. For this reason, only the adsorption energy of the chelate geometry is reported in Table 1. For PHT, the average distance ⟨dMg−O⟩ is rather stable up to θ = 0.5, around 2.6 Å, while it increases to 5.4 Å when θ = 1. Again, the remarkable increase of ⟨dMg−O⟩ at high θ values indicates extreme congestion on the surface at high coverage and actually indicates that several of the O atoms have detached from the surface. Comparable behavior is predicted for BMF, which starts with a ⟨dMg−O⟩ of 2.1 Å at θ = 0.17 and arrives at a ⟨dMg−O⟩ of 2.6 Å at θ = 1. Congestion of donors on the surface becomes so high that at θ > 0.67 further added donors are not able to chelate the unsaturated Mg atoms on the surface, which explains the very high values for ⟨dMg−O⟩. Moving to the adsorption energy per donor molecule, Ead, the average Ead values reported in Table 1 highlight that surface coverage has a large impact on the Ead values, which mirrors the trend in the ⟨dMg−O⟩ values. As for the (104) surface, the Ead of an isolated PHT, θ = 0.17, is 34.5 kcal/mol. If surface coverage increases to θ = 0.33, with two PHT molecules coordinated on different MgCl2 layers the value of Ead increases to 0.4 kcal/ mol, probably due to a weak attractive dispersive interaction between the adsorbed donors. A similar trend is achieved when a third PHT molecule, corresponding to θ = 0.50, is coordinated to the third MgCl2 layer. This suggests that up to one-half of the unsaturated Mg2+ ions on the surface can be capped by PHT molecules without a remarkable effect on the donor adsorption energy. The rather stable ⟨dMg−O⟩ up to θ = 0.50 also indicates that up to this coverage interaction between the adsorbed donors is scarce. Surprisingly, beyond θ = 0.50, adsorption of additional phthalate molecules results in even better Ead, which is

θ

DZVP

TZV2P

TZV2P-VdW

0.17 0.33 0.50 0.67 0.83 1.00

33.6 32.2 31.6 26.6 25.3 17.3

22.0 20.8 21.0 17.4 17.4 9.7

34.5 34.9 36.3 28.3 31.6 30.8

the smaller double-ζ quality basis set used in our previous work on alkoxysilane adsorption, column DZVP in Table 2. For the sake of readability, we replicate in Table 2 the already discussed TZV2P plus dispersion Ead of Table 1, column TZV2P+VdW in Table 2. The values included in Table 2 suggest that without the dispersion term Ead is drastically reduced at high θ, with both the DZVP and the TZV2P basis sets, indicative of the unability of PHT to completely cover the surface. On the other hand, the TZV2P Ead are remarkably lower than the corresponding DZVP Ead, which can be ascribed to a reduced basis set superposition error with the higher quality triple-ζ basis set. On the other hand, comparison between the TZV2P and the TZV2P+VdW Ead clearly shows the remarkable relevance of the dispersion term in determining the strength of the interaction between the MgCl2 surface and the donor. In conclusion, the values of Table 2 suggest that dispersion interactions are relevant in determining the overall adsorption ability of donors, but this correction should be only included at low coverage. Indeed, at high coverage adsorption energies including dispersion interactions are basically meaningless, due to missing dispersion interactions between the donor molecules and the solvent.68−70 As a final test, we also evaluated the basis set superposition error, BSSE, for a single PHT molecule adsorbed on the (110) lateral cut, θ = 0.17. This test was performed with the TZV2P basis set, which is the basis set used through the whole work. According to the procedure proposed by Boys and Bernardi,71 in the case considered the BSSE amounts to 1.4 kcal/mol only, indicating that the Ead values are substantially converged with respect to the basis set. The trend in the adsorption energy of BMF basically replicates that calculated for PHT up to θ values of 0.5. At this low coverage, it is possible to have BMF molecules well separated, so that the impact of donor−donor interaction on 8053



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the adsorption energy is minimal on both the (104) and the (110) surfaces. Differently from PHT, for BMF there is a clear reduction in adsorption energy at θ greater than 0.5, indicating that donor adsorption on the surface is disfavored, despite the overstabilizing attractive dispersion interaction between donor molecules, not balanced by dispersion interaction between the donors and the solvent. This can be easily ascribed to the higher bulkiness of BMF compared to PHT, which prevents BMF from adopting a stable enough disordered structure, such as that shown for PHT in Figure S1, Supporting Information. In summary, the geometric and energy analysis we performed suggests that complete coverage of the MgCl2 surface by coordinated donor molecules is prevented by repulsive interaction between donor molecules that are coordinated on vicinal Mg atoms. Further, the small Ead at high coverage of the surfaces, together with an unfavorable entropic term, which is not considered in this work, results in low and even unfavorable adsorption free energies, suggesting that total coverage of the MgCl2 surfaces is impossible to achieve. 2. Coordination Stability. In this section we report on the dynamic behavior of one BMF or PHT molecule coordinated to the (110) or (104) MgCl2 surface. Also in this case we considered the (104)-bridge and the (110)-chelate coordination modes. The value of the Mg−O distances along the DFT molecular dynamics simulations is reported in Figure 4. Analysis of Figure 4 clearly indicates that within the 10 ps long simulations both PHT and BMF remain strongly coordinated on both surfaces with an average distance Mg−O on the (104) surface of 2.12 ± 0.09 Å for PHT and 2.20 ± 0.12 Å for BMF (Figure 4) and of 2.16 ± 0.09 Å for PHT and 2.21 ± 0.09 Å for BMF on the (110) surface. Despite the quite similar standard deviations, in the case of adsorption on the (104) surface there are peaks that reach values around 2.5 and 2.7 Å, respectively, for PHT and BMF. Nevertheless, also with these large fluctuations the donors remain coordinated to the surface. Quite interesting is the behavior of the Mg−Cl bonds that are in the trans position to the Mg−O bonds. Focusing on the (104) surface, the average value of the ⟨dMg−Cl⟩ distances trans to the Mg−O bonds are 3.54 ± 0.35 and 3.60 ± 0.44 Å, respectively, for PHT and BMF, which are values clearly longer than the value of the ⟨dMg−Cl⟩ distance in the case of an uncovered Mg atom on the (104) surface, 2.57 ± 0.10 Å, and of the ⟨dMg−Cl⟩ distance in a hexacoordinated Mg atom in the bulk, 2.70 ± 0.10 Å. Switching to the (110) surface, the value of the average ⟨dMg−Cl⟩ distances trans to the Mg−O bonds are, respectively, 2.65 ± 0.11 and 2.75 ± 0.12 Å, which are again clearly longer than the value of the ⟨dMg−Cl⟩ distance, 2.48 ± 0.09 Å, if an uncovered Mg atom on the (110) surface is considered and clearly closer to the ⟨dMg−Cl⟩ distance in a Mg atom in the bulk, 2.70 ± 0.10 Å. The tendency of unsaturated Mg atoms on the surface to be pulled toward the bulk of the crystal was already remarked by Parrinello and co-workers.72 Concluding this part, our calculations suggest that PHT and BMF adsorption on both surfaces is quite stable also from a dynamic viewpoint and that difficulties in the coordination of the donors can only start at high coverage. Further, these conclusions lead to the hypothesis that the possible incomplete coverage of the surfaces by the donors could originate vacancies on the surface. On these vacancies, also the weakly coordinating TiCl4 could adsorb, since it would not compete with the more strongly binding donors.

Figure 4. Time evolution of the Mg−O distances for PHT and BMF coordination to the (104) and (110) surfaces.

3. Migration. Next, we studies the donor mobility on the MgCl2 surfaces by investigating suitable mechanisms for intralayer migration of PHT and BMF on the (110) and (104) surfaces. Specifically, we investigated the migration pathways shown in Figure 5. Taking in account our previous results on alkoxysilane migration,51 we considered only intralayer pathways. On the (104) surface we considered two different pathways to migrate a 104-bridge coordinated donor. The first consists in a stepwise movement, with both coordinated oxygen atoms moving from one Mg to the near, through a high-energy intermediate with both oxygen atoms coordinated to the same Mg atom, see Figure 5, while the second pathway consists of a rotation around one Mg−O bond, thus requiring rupture and formation of only one Mg−O bond, 8054



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mol roughly, which is comparable to the energy required to completely dissociate one of the O atoms of the 104-bridgecoordinated monomer to give a monocoordinated species, Ead = 17.4 kcal/mol for PHT and Ead = 11.0 kcal/mol for BMF. Despite the barrier of roughly 15 kcal/mol being higher than the barrier of about 8 kcal/mol we found for alkoxysilane migration on the (104) surface, BMF and PHT migration on the (104) surface is a process easily accessible at the high temperatures used during polymerization. A similar conclusion is achieved when migration on the (110) surface is considered, since the barrier for conversion of both the BMF and the PHT 110-chelate geometry into the 110-bridge geometry occurs with barriers around 15 kcal/mol. Again, migration barriers of this magnitude are accessible during the catalytic process. Comparison with alkoxysilane migration indicates a sharp difference with PHT and BMF, since for alkoxysilane migration on the (110) lateral we calculated barriers of roughly 30 kcal/mol. The reason for this sharp difference can be connected to the complete inability of alkoxysilanes to interact with two vicinal Mg atoms on the (110) lateral cut. The NEB localized transition state for (104)/PHT along the stepwise migration pathway, see Figure 7a, shows that the PHT

Figure 5. Possible migration pathways for PHT and BMF coordinated on the (104) and (110) surfaces.

see again Figure 5. For the sake of simplicity, we tested the first mechanism for PHT and the second for BMF. For donor migration from the 110-chelate geometry on the (110) surface, we considered only a stepwise mechanism, with the intermediate structure consisting of the 110-bridge geometry, see again Figure 5. The NEB energy profile corresponding to PHT and BMF migrations on the (104) and (110) surfaces along various

Figure 7. Geometry of the NEB approximated transition state for PHT and BMF migration on the (104) and (110) surface.

is placed on top of one of the Mg atoms. The moving oxygen atom is above the layer plane, with a distance of 3.37 Å with respect to the Mg atom in the starting geometry and a distance of 2.27 Å with respect to the Mg atom in the final geometry. The transition state for intralayer migration along the (104)/ BMF pathway is quite similar to that proposed for alkoxysilane migration,51 with a movement consisting of rotation of the donor around one Mg−O bond, acting as a pivotal point. According to this mechanism, only one Mg−O bond is broken during migration, see Figure 7b. The Mg−O bond distances in the approximated transition state, around 4.6 Å, are quite longer relative to the same distance in the initial and final geometries, 2.2 Å. Focusing on the transition state geometry for donor migration on the (110) surface, the considered intralayer

Figure 6. NEB energy profile for PHT and BMF migration on the (104) and (110) layers.

pathways is shown in Figure 6. The reaction coordinate, γ, is defined as in eq 3 i f γ = dMg − O − dMg − O

diMg−O

(3)

f

where and d Mg−O are the distances of the O atoms from the Mg atoms to which the donor coordinates in the initial and final geometry, respectively. We start discussing intralayer migration on the (104) surface. As appears clearly in Figure 6, migration of both PHT and BMF occurs with relatively low energy barriers, around 15 kcal/ 8055



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migration pathway considered requires the breaking of only one the Mg−O bonds from the starting geometry 110-chelate geometry. In the transition state geometry the moving O atoms are almost midway between the starting and the final geometries, see Figure 7. The capability of PHT and BMF to stretch enough to interact with two vicinal Mg atoms, evidenced by the structures reported in Figure 7, explains the low barrier we calculated for their migration on the (110) lateral cut.

CONCLUSIONS In this work we studied the effect of the amount of donor molecules adsorbed to unsaturated Mg atoms on the (104) and (110) surfaces of MgCl2, the dynamics behavior of one donor molecule coordinated on the two MgCl2 surfaces, and finally likely pathways for intralayer migration of the donor. The principal conclusions of our work can be summarized as follows. (1) Increasing the surface coverage by increasing the amount of coordinated donor results in a reduction of the average coordination ability of the donor. Specifically, dimethyl phthalate and 9,9-bis(methoxymethyl)fluorene adsorbed on vicinal sites on the MgCl2 surface interact repulsively, resulting in a clear reduction of the donor coordination ability. This conclusion holds both for the (104) and the (110) surfaces, and coverages greater than 50% are difficult to achieve. One consequence is that complete coverage of the MgCl2 surface by the phthalates and 1,3diethers, consistent with our previous work on alkoxysilane adsorption, is difficult. (2) Molecular dynamics simulation of a single phthalate and 9,9-bis(methoxymethyl)fluorene molecule 104-bridge or 110-chelate coordinated indicated that these are quite stable systems, even when the quite stretched 104-bridge coordination mode is considered. (3) Intralayer migration of both phthalate and 9,9-bis(methoxymethyl)fluorene on the (104) lateral cut is not energetically expensive and requires partial donor dissociation from the surface. This conclusion is consistent with our previous work on alkoxysilane migration. However, differently from alkoxysilane, which was found to be hardly mobile on the (110) lateral cut, we found that phthalates and 1,3-diethers are highly mobile on the (110) lateral cut. ASSOCIATED CONTENT

S Supporting Information *

Coordinates and energy of all the minimum energy discussed in the text. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS L.C. thanks ENEA (www.enea.it) and the HPC team for support and for using ENEA-GRID and the HPC facilities CRESCO (www.cresco.enea.it) Portici (Naples), Italy. 8056



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