ARTICLE pubs.acs.org/JPCC
Thermodynamics of Formation of Uncovered and Dimethyl Ether-Covered MgCl2 Crystallites. Consequences in the Structure of ZieglerNatta Heterogeneous Catalysts Raffaele Credendino,† Jochem T. M. Pater,‡ Andrea Correa,†,§ Giampiero Morini,‡ and Luigi Cavallo*,†,§ †
Dipartimento di Chimica, Universita di Salerno, Via ponte don Melillo, 84084, Fisciano (SA), Italy LyondellBasell Polyolefins, G. Natta Research Center, P.le G. Donegani 12, 44100, Ferrara, Italy § Dutch Polymer Institute (DPI), P.O. Box 902, 5600 AX Eindhoven, The Netherlands ‡
bS Supporting Information ABSTRACT: In this work, we report on the structure and formation energy of uncovered MgCl2 crystallites of different shapes (hexagonal and square), sizes (up to crystallites composed of 157 MgCl2 units), and edges (crystallites presenting the (104) and (110) edges). Both uncovered crystallites and crystallites covered by dimethyl ether were considered. Our results indicate that the formation energy of uncovered crystallites, irrespective of shape, size, and edges, linearly depends on the density of vacancies (measured as the ratio between the number of Mg vacancies and the number of MgCl2 units in the crystallite) and that larger crystallites that present (104) edges are favored. In the case of crystallites completely covered by dimethyl ether, our results indicate that the formation energy of crystallites, again irrespective of shape, size, and edges, inversely depends on the dimethyl ether/Mg ratio. As opposed to uncovered crystallites, in the presence of dimethyl ether, smaller crystallites presenting (110) edges are favored. The knowledge acquired with both uncovered and dimethyl ether-covered crystallites was used to achieve insight into the behavior of carbon monoxide-covered crystallites by performing calculations on a limited number of small crystallites.
1. INTRODUCTION Heterogeneous ZieglerNatta catalytic systems are still the industrial catalysts for the production of isotactic polypropylene (iPP). Their extreme efficiency (in the order of 103104 kg iPP/g Ti) and low cost have contributed to creating iPP. Over the years, these catalysts have evolved from simple TiCl3 crystals into the typically used MgCl2/TiCl4/donor systems, where the donor is a Lewis base (LB) that can be added during catalyst preparation (the so-called internal donor, ID).1,2 The donors, alkoxysilanes, 1,3-diethers,35 aromatic esters (benzoates and phthalates in particular),68 and, recently, aliphatic esters (succinates in particular), have been shown to be particularly effective.9 Catalyst activation requires the addition of alkylating reducing species (AlEt3 the most commonly used) possibly mixed with a second electron donor (the so-called external donor, ED), usually an alkoxysilane or, more recently, a diether. The resulting active system is of extreme chemical complexity, and the polypropylene obtained presents very different properties. The nature of the added Lewis bases is fundamental in terms of performance, because it can significantly impact (i) the tacticity of the obtained polypropylene from a large fraction of almost atactic polymer (as in the absence of any Lewis base) to almost exclusively highly isotactic polymers, (ii) the molecular mass distribution, that can be rather narrow or rather broad, and (iii) the response to molecular hydrogen, which clearly allows one to control the molecular masses of the produced polymers.1014 However, the Lewis bases clearly have a significant impact upon the morphology of the final r 2011 American Chemical Society
catalyst, because they can stabilize small primary crystallites of MgCl2 and/or influence the amount and distribution of TiCl4 in the final catalyst. A typical process for the preparation of MgCl2 supports with improved controlled morphology and outstanding performance consists of the precipitation of MgCl2 3 nEtOH complexes (EtOH = ethanol and n ≈ 23), from oil/molten complex emulsions by rapid cooling. This process produces spherical particles with a narrow size distribution; their reaction with TiCl4 and other catalyst components creates active forms of MgCl2 with a high degree of porosity, which are used in ZieglerNatta catalysis.1,2,15,16 The nature of these active forms and the origin of the high degree of nanoporosity of these catalysts are still unclear. Regardless of the nature of the LB, MgCl2 3 nLB complexes with n = 23 are generally crystalline and characterized by the presence of polymeric (MgCl2)x.1,2 In all cases, at the end of the process, the base content becomes very low (n < 0.3) and the final catalyst essentially consists of the disordered δ form of MgCl2.35 In this active form of MgCl2, consecutive ClMgCl sandwich layers are disorderly stacked along c according to a hexagonal or cubic sequence or rotated by 60 to each other.1,2 It is widely known that TiCl4 and the internal donor cannot be easily removed from the catalyst unless severe thermal treatments Received: February 12, 2011 Revised: May 30, 2011 Published: June 21, 2011 13322
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The Journal of Physical Chemistry C or strongly coordinating solvents are used. Therefore, it seems that the catalyst components lose their identity and become strongly linked together, forming new complexes.1,2 These complexes are formed on the lateral sides (coordinatively unsaturated) of the structural layers of MgCl2, normally assumed to be coincident with the crystallographic faces (104) and (110).15,16,17 Periodic DFT calculations by Busico, Causa, and co-workers indicated that the various surfaces exposing 5-coordinated Mg are very similar in energy and are the lowest nontrivial surfaces. Cuts exposing 4-coordinated Mg are significantly less stable, and both kinetic and equilibrium models of crystal growth indicated that they should normally not be formed to a significant extent.18 On the experimental side, Sozzani et al. investigated MgCl2/EtOH adducts with high molar ratios, which is a possible starting composition for preparing highly productive catalysts by direct titanation. Their study indicated that primary particles can be octahedral complexes of small MgCl2 clusters with ethanol molecules that saturate all vacancies. After direct titanation, this catalyst yields highly isotactic polypropylene, suggesting that the intricate architecture of highly alcoholated and exchangeable magnesium sites is specific for building up active surfaces for catalyst insertion.15 Focusing on the crystallite morphology, Andoni et al. found that well-defined crystallites of MgCl2 3 nEtOH obtained by spin-coating have hexagonal or rectangular shapes with 120 and 90 edge angles, independent of the crystallite size. After titanation, these complexes are capable of polymerizing ethylene.16 However, a clear understanding of the relative stability of MgCl2 crystallites with different sizes, shapes, and lateral faces, both in isolated MgCl2 as well as in the presence of LB, is still missing. For this reason, we decided to investigate these aspects with a DFT approach. In particular, we model several MgCl2 crystallites investigating the effect of size, shape, and number of Mg atoms exposed on the edges, arriving to define a unique law that rationalizes their relative stability. On these crystallites, we also adsorb the most simple ether, namely, dimethyl ether, and we evaluate how the presence of an LB can change the stability of the various crystallites examined. In the present work, we focus on the simple MgCl2 support and on the effect of a prototype Lewis base, while we neglect the influence of TiCl4. The reason is two-fold. First, the computational effort of this work is already extremely demanding, because we modeled systems including up to 471 atoms. Considering that no hydrogen is present, this is close to the actual computational possibility. Second, the debate about the capability of DFT methods to correctly reproduce the MgCl2/ TiCl4 interaction is still open, and this could result in wasting considerable computational results to produce biased results. We postponed the study of the role of TiCl4 on the structure of MgCl2 crystallites until an assessment of the performance of DFT methods to describe this interaction will be available. As a final note, while this paper was in preparation,19 a valuable computational paper by Pakkanen et al. on the microstructure of uncovered and methanol-covered MgCl2 crystallites was published.20 In this paper, they showed that increasing crystallite size and the existence of high coordination numbers in the edge Mg atoms enhance crystallite stability. Further, crystallite shapes with a high proportion of (104)/(110) sites have higher stability, and the methanol addition greatly stabilizes the crystallites with a high proportion of (110) sites. However, their calculations are based on semiflexible crystallites, because only the surface atoms were relaxed in the geometric optimizations. In addition, no unique equation correlating the stability of all the crystallites, independent of shape or size, was proposed. In the present work,
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Figure 1. First-generation MgCl2 crystallites of families IIII. The number in red close to each surface Mg atom indicates its coordination number.
in addition to complete geometric optimization of the whole crystallites, we propose an equation law that unifies the stability of all the crystallites, whether uncovered or covered by an electron donor and independent of shapes, sizes, or edges. We believe this results in a deeper comprehension of the behavior of MgCl2 catalysts and offers a model to predict the relative stability of the crystallite. Indeed, we used this knowledge to achieve insight into the behavior of carbon monoxide-covered crystallites by performing a limited number of calculations.
2. MODELS AND COMPUTATIONAL DETAILS Models. To model the MgCl2 crystallites, we cut from an infinite R-MgCl2 monolayer crystallite with hexagonal and squared shapes; see Figure 1. Within this choice, three crystallite families can be defined. Family I is hexagonal and is characterized by 4-coordinated Mg atoms on the edges, thus corresponding to hexagonal crystallites presenting (110) lateral cuts; see Figure 1. Family II is also hexagonal, but it is characterized by 5-coordinated Mg atoms on the edges, thus corresponding to hexagonal crystallites presenting (104) lateral cuts. Family III is squared (in the sense that the same number of Mg atoms are exposed on all the edges) and is characterized by alternating edges presenting 4- and 5-coordinated Mg atoms, thus corresponding to squared crystallites presenting both the (110) and the (104) lateral cuts; see Figure 1. For each crystallite family, we considered different generations, G, with G1 corresponding to the smallest crystallite. Depending on the specific generation number, crystallites of family I present Mg atoms at the corners with a coordination number of 3 (generations 4, 7, and 9), 4 (generations 1, 3, and 6), and 5 (generations 2, 5, and 8); see Figure 1. Independent of the generation, all the crystallites of families II and III are characterized by 4-coordinated Mg atoms at the corners, whereas crystallites of family I are characterized by 3-, 4-, and 5-coordinated Mg atoms at the corners; see Figure 1. In the case of family I, we considered crystallites up to G9, for a total of 157 MgCl2 units, 13323
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whereas in the case of families II and III, we considered crystallites up to G4, for a total of 91 and 71 MgCl2 units, respectively. Independent of the family, all the crystallites present two dangling Cl atoms (see Figure 1) to preserve the (MgCl2)n stoichiometry. These dangling Cl atoms were positioned on opposite sides of the crystallite to build structures with no dipole moment. Because preliminary geometry optimizations were performed with no symmetry constrain on family I, the G2 crystallite resulted in a C2h symmetric structure, and all family I crystallites have been optimized under C2h symmetry, with the C2-symmetry axis shown in Figure 1. The only exception is the G3 crystallite, which is Ci symmetric. Within this choice, the dangling MgCl bonds are not forced on the symmetry axis. The possibility to exploit symmetry enabled the analysis of the family I crystallites up to G9 (471 atoms) in a reasonable amount of computer time. In the case of families II and III crystallites, no symmetry constrain was used because this would have forced the MgCl dangling bonds on the symmetry axis. For this reason, the computational cost to calculate families II and III is quite higher than that for family I, and thus for families II and III, we arrived up to G4 only (273 and 213 atoms, respectively). The average dimension of the crystallites considered ranges from 10 to 40 Å. For example, the average dimension of the G4 crystallites of families I and II, measured as the average value of the distance between Mg atoms on opposite edges, is 17 and 27 Å, respectively. Crystallites of this dimension are close in size to crystallites in the industrially relevant catalysts.1,2 Within this framework, we modeled MgCl2 crystallites with n unsaturated Mg atoms on the edges, evaluating the formation energy with respect to separated MgCl2 units and several properties, such as dimensions, surface area, distribution, and crystallite growth equation. In the final section, we also investigated the stability of G1G4 family I and of G1 and G2 family II crystallites covered by carbon monoxide. Computational Details. All of the DFT calculations were carried out using the TURBOMOLE package, version 6.1.21 Energies and geometries have been obtained at the BP86 level of theory.2224 The electronic configuration of the atoms was described by a triple-ζ basis set (TURBOMOLE basis set TZVP).25 The formation energy, Ef, of a crystallite composed by n MgCl2 units is calculated according to eq 1 Ef ¼
ECr nEMg ECr¥ n
ð1Þ
where ECr¥, ECr, and EMg are the total energies of the infinite perfect crystal, of a defined crystallite, and of a free MgCl2 molecule, respectively, and n is the number of MgCl2 units in the crystallite. In the case of crystallites covered by dimethyl ether or carbon monoxide, the formation energy of the covered crystallite is calculated according to eq 2 Ef ¼
ECr=LB nEMg νELB ECr¥ n
ð2Þ
where ECr/LB is the total energy of the crystallite with all of the Mg vacancies completely saturated with dimethyl ether or carbon monoxide molecules, while ELB is the energy of the free Lewis base (dimethyl ether or carbon monoxide), respectively, and ν is the number of adsorbed Lewis base molecules. Within our model, the formation energy defined by eqs 1 and 2 represents the energy gain associated with the assembling of the uncovered and covered crystallites starting from monomeric MgCl2 units and free donor molecules. In the case of the
Figure 2. Optimized geometry of the uncovered family I G7 crystallite (Mg, white; Cl, green). The dashed and dotted lines indicate the position of the Cl and Mg atoms in the bulk of the ideal crystal.
uncovered crystallites, this definition sets a lower bound to Ef, which is the value of a MgCl2 unit in the bulk of a perfect and infinite MgCl2 crystal, Ef(bulk). In other words, for a crystallite of finite dimension, such as those considered in the present work, Ef(crystallite) > Ef(bulk), and Ef(crystallite) slowly converges to Ef(bulk) with the size of the crystallite.
3. RESULTS AND DISCUSSION Naked MgCl2 Crystallites. On the structural side, all of the crystallites substantially preserve a planar/sandwich shape after geometric optimization, although some deviations occur at the corners; see Figure 2. Indeed, the crystallites with a high number of vacancies on the Mg atoms at the corners tend to distort and shrink the flat geometry in order to pull these highly unsaturated Mg atoms toward the bulk of the layer, in order to maximize interaction with the electronic cloud of the nearby chlorine atoms. This kind of deformation, with the cations pulled inside the bulk of the MgCl2 layer, was already indicated by Parrinello and coworkers in the case of Mg atoms at the surface of an infinite (110) monolayer.26 The optimized structure of the family I G7 crystallite, shown in Figure 2, clearly illuminates these deformations and indicates that there is a regular alternation of corners moving in opposite directions from the main plane of the crystallite. Data relative to the optimized crystallites are reported in Table 1. For each crystallite, we report the number of MgCl2 units, nMg, the number of Mg vacancies, v, the energy of formation per unit of MgCl2, Ef, and the density of Mg vacancies, Fv, defined as Fv = v/nMg. The density of Mg vacancies Fv is defined between 0 for the infinite crystal without vacancies and 4 for the one isolated unit of MgCl2 with four vacancies. The first result is that family I crystallites are much easier to assemble than those of family II. Indeed, the G1 crystallite of family I can be assembled with 7 MgCl2 units, whereas the G1 of family II requires 19 MgCl2 units. In addition, 91 MgCl2 units can be assembled as a family I or II crystallite, but in the case of family I, this corresponds to a crystallite of generation 7. In the case of family II, it corresponds to a crystallite of generation 4; see Table 1. Incidentally, the family I G7 crystallite presents 40 Mg vacancies, whereas the similarly sized family II G4 crystallite presents only 34 Mg vacancies; see Table 1. Moving to the formation energy per MgCl2 unit, Ef, as expected, there is a regular stabilization trend with increasing generation numbers, because more MgCl2 units present a 6-coordinated Mg atom as in the bulk. Again, the G7 and G4 crystallites of families I and II allow for a direct comparison between the two families, and the Ef of Table 1 indicates that the family II crystallite is more stable than the family I crystallite by 3.6 kJ mol1 per MgCl2 unit. These results are in line with recent theoretical work, where it was shown that increasing crystallite size enhances crystallite stability and that crystallite shapes with a high proportion of (104)/(110) 13324
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Table 1. Formation Energy and Structural Data of Naked MgCl2 Crystallites family I generation 1
2
3
4
5
6
7
8
9
nMg 7
19
31
43
55
73
91
109
157
v
16
22
28
28
34
40
40
52
10
Fv 1.429 0.842 0.710 0.651 0.509 0.466 0.440 0.367 0.331 ECr þ67.4 þ34.0 þ28.5 þ25.6 þ18.8 þ18.4 þ16.6 þ13.0 þ12.0 family II generation 1
2
3
4
nMg
19
37
61
91
v
16
22
28
34
Fv
0.842
0.595
0.459
0.374
ECr
33.4
21.8
16.6
12.9
Figure 3. Graphic plot of the crystallite formation energy, Ef, of the uncovered crystallites and of the crystallites covered by dimethyl ether or carbon monoxide.
family III generation 1
2
3
4
nMg
10
31
49
71
v Fv
12 1.200
22 0.710
30 0.612
34 0.479
ECr
51.1
28.5
22.6
19.1
sites have higher stability.20 However, so far, no unique law relating the stability of the various crystallites has been proposed, and this is what we decide to try next. Inspection of Table 1 indicates that the simple total number of vacancies is not a sufficient parameter to compare the relative stability of all of the crystallites. In fact, family I G4 and G5 crystallites present 28 vacancies, but this total number of vacancies is distributed among 43 and 55 MgCl2 units, respectively, which explains why the G5 crystallite, with an Ef of þ18.8 kJ mol1 is more stable than the G4 crystallite with an Ef of þ25.6 kJ mol1. For this reason, we examined whether the density of vacancies Fv could represent a better parameter to place all of the crystallites on a unique scale of stability. The plot of the Ef versus Fv is reported in Figure 3. Visual inspection of Figure 3 clearly shows the excellent linear correlation between Ef and Fv, indicating that Fv is indeed an excellent parameter to place the relative stability of rather different crystallites on a single scale. Equation 3, with a R2 = 0.99, quantifies this correlation. Ef ¼ þ 45:44Fv kJ mol1
ð3Þ
The slope of the line, þ45.44 kJ 3 mol1, represents the energy needed to generate one vacancy per MgCl2 unit. The excellent correlation between Ef and Fv illuminates that the crystallites’ stability is dominated essentially by the number of vacancies per MgCl2 unit, while it depends marginally on the shape or on the type of Mg exposed on the edges. Focusing on practical consequences, our results indicate that, in line with previous
considerations8,18 based on thermodynamics, crystallites of the same average size prefer to adopt a family II hexagonal shape because this minimizes the number of Mg vacancies and that larger crystallites are preferred over smaller ones for the same reason. Before discussing crystallites of different shape, we remark that a linear correlation with the total number of vacancies would be obtained if the total energy of the crystallite, Etot, rather than the total energy of the crystallite normalized per the number of MgCl2 units, Ef, were considered. However, as discussed in the Computational Details section, Ef has the advantage of that it can be directly compared with the energy of a MgCl2 unit in the bulk of a perfect and infinite MgCl2 crystal, which also represents a bound to Ef. Differently, Etot increases linearly with the crystallite size and does not allow defining the energy of a MgCl2 unit in the perfect crystal. To test to which extent eq 3 can be used to calculate the relative stability of different crystallites, we calculated Ef for a series of rectangular crystallites, presenting both the (104) and the (110) edges, in which new MgCl2 units for one additional layer are adsorbed on the (110) face at each generation step, thus resulting in an elongation of the (104) lateral face. This situation could mimic the growth of a crystal along the direction that maximizes the adsorption energy of new units and maximizes the extent of the more stable lateral face. The formation energy per MgCl2 unit of these crystallites calculated with eq 3, Ef(eq 3), is plotted versus the formation energy per MgCl2 unit calculated by DFT, Ef(DFT), in Figure 4. The excellent linear correlation between Ef(eq 3) and Ef(DFT), R2 = 0.96, further supports our conclusion that the density of Mg vacancies is the best parameter to describe the relative stability of MgCl2 crystallites and indicates that eq 3 can be used to predict and compare the stability of differently shaped crystallites. MgCl2 Crystallites Covered by Dimethyl Ether. In this section, we report on the relative stability of different MgCl2 crystallites if the Mg vacancies are saturated by LB. Considering the size of the systems to calculate, we were forced to use the smallest LB that still preserves the basic features of industrially used LB, so we selected Me2O as the representative LB. In the 13325
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Figure 4. Plot of the predicted and of the DFT-calculated Ef for a series of rectangular MgCl2 crystallites.
Table 2. Formation Energy and Structural Data of MgCl2 Crystallites Covered by Me2O Molecules family I generation 1
Figure 5. Optimized geometry of the family I G2 crystallite covered by Me2O: (A) view parallel to the basal plane, (B) view of a corner when covered by Me2O, and, for comparison, (C) view of the same corner in the uncovered crystallite.
case of 3-, 4-, and 5-coordinated Mg atoms, we coordinated three, two, and one Me2O molecules, which means that all of the Mg atoms of the crystallite are 6-coordinated. The optimized geometry of the family I G2 crystallite is reported in Figure 5. The presence of the Lewis base stabilizes the Mg vacancies, significantly reducing the out-of-plane distortion of crystallites (see Figure 5); even at the edges of the optimized structure are definitely flat and thus similar to the bulk. Deformations at the corners of the crystallites are similarly smaller in the presence of the LB; compare views B and C of Figure 5). Of course, the family II uncovered crystallites, which are already less deformed than the family I crystallites, present an optimized structure strongly similar to the bulk when the edges are covered by Me2O. The results from the geometry optimizations on the Me2Ocovered crystallites are reported in Table 2. In this case, Fv is replaced by FLB, which indicates the density number of Me2O molecules per Mg atom or, also, the Me2O/Mg molar ratio. The first result emerging from Table 2 is that the stability of the crystallites, measured by Ef, decreases with increasing the generation number. This is in qualitative agreement with calorimetric analysis results shown by Sozzani.15 On the basis of the results for the uncovered MgCl2 crystallites, we examined the
2
3
4
5
6
nMg
7
19
31
43
55
73
nLB
10
16
22
28
28
34
FLB
1.429
0.842
0.710
0.651
0.509
0.466
Ef
65.6
42.7
36.5
31.4
28.5
25.8
family II generation 1
2
3
nMg
19
37
61
nLB
16
22
28
FLB Ef
0.842 42.7
0.595 30.5
0.459 23.1
possible correlation between the crystallite energy, in this case, Ef, and the number of vacancies, in this case, the LB number density FLB, that would allow the placement of the different crystallite families on the same scale. The excellent linear correlation between Ef and FLB, R2 = 0.94 (see Figure 3), indicates that, as Fv, FLB is indeed an excellent descriptor to place on the same scale as all the clusters, independent of their shape or size. Equation 4 quantifies the linear correlation between Ef and FLB. Ef ¼ 39:65FLB kJ mol1
ð4Þ
1
The slope of eq 4, 39.65 kJ mol , corresponds to the average energy gain associated with the overall process 13326
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Table 3. Formation Energy and Structural Data of MgCl2 Crystallites Covered by CO Molecules family I generation 1
2
3
4
5
nMg
7
19
31
43
nLB
10
16
22
28
28
FLB Ef
1.429 þ18.6
0.842 þ8.7
0.710 þ7.2
0.651 þ6.5
0.509 þ3.9
55
relationship between Ef and the number density Fv or FLB of Mg vacancies or adsorbed molecules, we limited the analysis only to the smallest clusters of families I and II (see Table 3), and from there, we extrapolated trend lines to describe the behavior of larger crystallites. The excellent linear correlation between Ef and FLB also for CO-covered crystallites, R2 = 0.94 (see Figure 3), indicates that FLB is indeed an excellent descriptor to place on the same scale all the clusters, independent of their shape or size. Equation 6 quantifies the linear correlation between Ef and FLB. Ef ¼ þ 16:97FLB kJ mol1
ð6Þ
1
family II generation 1
2
nMg
19
37
nLB
16
22
FLB
0.842
0.595
Ef
þ7.7
þ4.8
corresponding to the formation of a vacancy on a Mg atom, followed by the adsorption of a single Me2O molecule. The chemical meaning of the linear correlation between Ef and FLB is that the stability of the covered crystallites is controlled by the density of donor molecules (or LB/Mg molar ratio) adsorbed per Mg atom. Thus, LB favors the formation of smaller crystallites.15 However, of paramount relevance is the fact that, in the presence of an LB, the crystallites with the largest number of Mg vacancies are favored, because coordination of a higher number of LBs is possible. Differently, in the absence of an LB, the crystallites with the smallest number of Mg vacancies are favored. This implies that, in the absence of an LB, the large family II crystallites, characterized by (104) edges, are favored, whereas in the presence of an LB, the small family I crystallites, characterized by (110) edges, are favored. Because the plots of Figure 3 report the potential energy, while coordination of a donor is at the end controlled by the free energy change, we performed a test calculation in which we compared the potential energy associated with coordination of 10 Me2O molecules on the (MgCl2)7 crystallite with the free energy of coordination as obtained from standard vibrational analysis. This test has been limited to one of the smallest systems due to the associated computational cost. The potential energy change per Me2O molecule, calculated as indicated in eq 5, amounts to 93 kJ/mol, whereas the corresponding free energy value is 37 kJ/mol. Of course, the strong reduction in the free energy of Me2O coordination is due to the loss in the translational and rotational degrees of freedom of Me2O after coordination. Nevertheless, even in terms of free energy, Me2O coordination remains clearly favored. Ead ¼
EðMgCl2 Þ7 ðMe2 OÞ10 EðMgCl2 Þ7 10EMe2 O 10
ð5Þ
MgCl2 Crystallites Covered by Carbon Monoxide. In this section, we report on the relative stability of different MgCl2 crystallites if the Mg vacancies are saturated by CO. Considering that the results of the previous sections indicate a clear
The slope of eq 6, þ16.97 kJ mol , corresponds to the average energy change associated with the overall process corresponding to the formation of a vacancy on a Mg atom, followed by the adsorption of a CO molecule. The positive slope in the case of CO indicates that the coordination ability of CO is less than that of Me2O. Actually, the positive slope suggests that CO can cover the present Mg vacancies but cannot induce the formation of smaller crystallites. Nevertheless, more relevant is the conclusion that an excellent correlation also for CO-covered crystallites indicates that the approach we have developed can be used in a predictive way to compare different donors by a limited amount of calculations on a limited number of smaller crystallites. Finally, also in this case, we compared the potential and the free energies of CO coordination to the (MgCl2)7 crystallite, using an approach consistent with that of eq 5, used to calculate the potential and free energies of Me2O coordination. In the case of CO, the potential energy change per CO molecule amounts to 34 kJ/mol, whereas the corresponding free energy value is þ7 kJ/mol, which indicates that CO adsorption on MgCl2 is almost a thermoneutral process. This is qualitatively consistent with the experimental evidence that CO adsorption requires a small CO pressure.27
4. CONCLUSIONS In this paper, we have investigated the structure and the stability of uncovered and Me2O- and CO-covered MgCl2 crystallites of different shapes and sizes. The main conclusions that emerged from our work are the following: (1) The relative stability of the uncovered MgCl2 crystallites does not depend upon the shape, size, and type of edges, but it almost exclusively depends on the density of Mg vacancies, Fv (measured as the ratio between the total number of Mg vacancies and the total number of MgCl2 units in the crystallite). The stability of these crystallites, again irrespective of size, shape, and type of edges, is linearly (inversely) dependent on Fv. This implies that large crystallites presenting (104) edges are favored in the case of uncovered crystallites. (2) The relative stability of MgCl2 crystallites covered with Me2O does not depend upon the shape, size, and type of edges, but it almost exclusively depends on the density of the adsorbed Me2O molecules, FLB (measured as the ratio between the total number of adsorbed Me2O molecules and the total number of MgCl2 units in the crystallite; this also corresponds to the Me2O/Mg molar ratio). The stability of these crystallites, again irrespective of size, shape, and type of edges, is linearly (directly) dependent on FLB. This implies that small crystallites presenting (110) edges are favored in the presence of the LB. 13327
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The Journal of Physical Chemistry C (3) Using the knowledge acquired in points 1 and 2 has enabled us to extrapolate data for larger crystallites and to compare CO with Me2O adsorption, with a limited number of calculations on small CO-covered crystallites. These results indicate a method for systematic and easy comparison of the effect of different donors on MgCl2 crystallite sizes and shapes. (4) The strong correlation between FLB and the stability of crystallites implies a very localized behavior of MgCl2, at least as far as energies are concerned. This suggests that clusters of limited size are good enough to model MgCl2 when donors or active Ti species are coordinated to the support. These conclusions illuminate and rationalize the known fact that the performance of ZieglerNatta catalytic systems strongly depends on the catalyst preparation recipe. In fact, in the absence of any LB, such as in the simple mechanical milling of MgCl2, it is reasonable to expect large crystallites presenting (104) edges, whereas in the presence of an LB, smaller crystallites presenting (110) edges should be formed. Of course, the formation of crystallites with different edges can have a significant impact on the nature of the Ti-active species.
’ ASSOCIATED CONTENT
bS
Supporting Information. Cartesian coordinates and energies of all the species discussed; equations describing the growth of the various families of MgCl2 crystallites; and average diameter of crystallites, vdW surface area, specific surface area, correlation between vacancy density, and diameter or weight percent of LB are reported. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
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’ ACKNOWLEDGMENT 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. This work is part of the Research Programme of the Dutch Polymer Institute, Eindhoven, The Netherlands, Project #707. ’ REFERENCES (1) Cecchin, G.; Morini, G.; Pelliconi, A. Macromol. Symp. 2001, 173, 195. (2) Albizzati, E.; Giannini, U.; Collina, G.; Noristi, L.; Resconi, L. In Polypropylene Handbook; Moore, E. P., Ed.; Hanser: Munich, 1996; p 11. (3) Di Noto, V.; Pavanello, L.; Viviani, M.; Storti, G.; Bresadola, S. Thermochim. Acta 1991, 189, 223. (4) Di Noto, V.; Bresadola, S.; Zannetti, R.; Viviani, M.; Valle, G.; Bandoli, G. Z. Kristallogr. 1992, 201, 161. (5) Di Noto, V.; Cecchin, G.; Zannetti, R.; Viviani, M. Macromol. Chem. Phys. 1994, 195, 3395. (6) Giunchi, G.; Allegra, G. J. Appl. Crystallogr. 1984, 17, 172. (7) Dorrepaal, J. J. Appl. Crystallogr. 1984, 17, 483. (8) Pasquini, N., Ed. Polyrpopylene Handbook: Product, Technology, Market, 2nd ed.; Hanser: Munich, 2005. 13328
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