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Accurate Prediction of Copolymerization Statistics in Molecular Olefin Polymerization Catalysis – on the Role of Entropic, Electronic and Steric Effects in Catalyst Comonomer Affinity Francesco Zaccaria, Christian Ehm, Peter H.M. Budzelaar, and Vincenzo Busico ACS Catal., Just Accepted Manuscript • DOI: 10.1021/acscatal.6b03458 • Publication Date (Web): 12 Jan 2017 Downloaded from http://pubs.acs.org on January 14, 2017
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Accurate Prediction of Copolymerization Statistics in Molecular Olefin Polymerization Catalysis – on the Role of Entropic, Electronic and Steric Effects in Catalyst Comonomer Affinity Francesco Zaccaria,a Christian Ehm,a,* Peter H.M. Budzelaarb and Vincenzo Busicoa a.
Dipartimento di Scienze Chimiche, Università di Napoli Federico II, Via Cintia, 80126
Napoli, Italy. b.
Department of Chemistry, University of Manitoba, Winnipeg, MB R3T 2N2, Canada
ABSTRACT: Accurate in silico prediction of copolymerization performance of olefin polymerization catalysts is demonstrated. It is shown on the example of 19 metallocene and postmetallocene group IV metal (Ti, Zr, Hf) systems that DFT (M06-2X(PCM)/TZ//TPSSTPSS/DZ) can accurately describe the copolymerization factor re, i.e. the competition of ethene and propene for insertion in metal n-alkyl bonds. Experimental re values were computationally reproduced with mean average deviation (MAD) and maximum deviations of only 0.2 and 0.5 kcal/mol, respectively. Both dispersion and solvent corrections play a crucial role in achieving this accuracy. Ethene insertion is found to be entropically favored for all catalysts due to a combination of symmetry factors and less congested insertion geometries. Enthalpic preference for either ethene or propene is catalyst dependent. The predictions are based on straightforward
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calculation of relevant insertion transition state energies; there are no indications for a shift in rate limiting step from insertion to e.g. olefin capture or chain rotation.
KEYWORDS: Catalysis, Copolymerization, LLDPE, DFT, comonomer affinity 1. INTRODUCTION Polyolefins rank among the major products of bulk chemical industries,1,2 approaching 150 million tons yearly production in 2015.3 Although ‘classical’ heterogeneous Ziegler-Natta systems are still the work-horse of commercial polyolefin production, remarkable breakthroughs in 1980s sparked a steady growth in molecular olefin polymerization catalysis. Metallocenes4 and post-metallocenes5 have opened routes to novel polymeric materials, especially copolymers of ethene and 1-alkenes, that now hold a sizable market share in the area of commodity and higher-added-value polyolefins.2, 6-12 The distinctive ‘single-center’ nature13 of molecular catalysts allows easy identification of structure/property correlations.14-15 The tailored design of novel catalysts is of great interest in olefin copolymerization, as the controlled incorporation of α-olefins (i.e. short or long chain branching) in the polyethylene chain opens routes to a variety of polymer architectures, leading to a broad range of mechanical, optical and other chemical-physical properties.16-22 Copolymerization of ethene with propene yields Ethylene/Propylene Rubbers (EPR), which are used as such or blended with other polyolefins,1 while comonomers like 1-hexene (or 1-octene) are largely employed in the production of Linear Low Density Polyethylene (LLDPE), a family of polymers with outstanding processability properties mainly used for packaging.23 Rational modelling of a polymerization process can be a challenging task, due to the complexity of the reaction pool and the high accuracy that is needed for predictions to be useful. On the one hand, prediction of stereochemistry represents a particularly successful case for
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computational modelling.24-35 On the other hand, many other catalyst properties are at least as important but more difficult to rationalize. For instance, prediction of molecular weight capability works only in simple cases where the main termination process can be easily and unambiguously identified,36-47 while prediction of catalyst activity (‘productivity’) and catalyst decay (‘catalyst mileage’) is greatly hampered by its strong dependence on reaction and activation conditions,48-53 although some progress has been made recently.54,55 Modelling catalyst performance in ethene/α-olefin copolymerization represents another challenging task. To date, a complete understanding of factors determining co-monomer incorporation degree and distribution in the polyethylene chain, which would allow catalyst performance prediction, has remained elusive. Catalyst performance differs from that in homopolymerization in significant and non-obvious ways. For example, the molecular weight in copolymerization is usually appreciably lower than that of the two corresponding homopolymerization reactions.56 For the purpose of the present work, we will focus on the more straightforward issue of comonomer incorporation. The tendency of a comonomer to insert generally depends on the last inserted monomer,1, 57 and this is usually expressed in the reactivity ratios re and rc defined as follows:
= ; =
(1)
Here, k is the kinetic constant of the specific insertion reaction indicated by the two subscripts: the first subscript denotes the last inserted monomer, while the second refers to the inserting one. For instance, kec is the kinetic constant related to insertion of the comonomer (c) after ethene (e). The product re·rc describes the tendency of the catalyst to form blocky (re·rc > 1), alternating (re·rc < 1) or random (re·rc ̴ 1) copolymers.
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The copolymerization ratio re indicates the tendency of the catalytic system to incorporate an α-olefin in the homo-polyethylene chain. It can be expressed in terms of a Gibbs free energy via:
= =
‡ ‡ ∆ ∆
(2)
The underlying assumption here is that ethene and α-olefin coordination are reversible and that olefin complexes lie energetically below the different insertion TS. Therefore, the CurtinHammett principle applies and selectivity ratios are solely determined by TS energy differences. 58
Insertion of ethene is almost always favoured, with re values ranging from 50 (poor incorporator). In order for computational prediction to be useful in catalyst pre-screening, predicted re values should not be off by more than a factor of ~2, corresponding to less than 0.5 kcal/mol in ∆∆G‡ at 50 °C. Early attempts to reproduce/predict re for a number of rac-dimethylsilylenebis(indenyl) catalysts significantly overestimated the preference for ethene over propene insertion.56 It remained unclear if this was due to the computational method and/or oversimplified chemical models. More recently, an improved model, including counterion effects in combination with a higher level of theory led to a somewhat better agreement between experiment and theory.59 The authors suggested that introduction of dispersion corrections rather than anion contributions might be the key factor for the improvement in accuracy, which however was still not good enough for reliable prediction. These conclusions are in line with experimental results showing that a change of anion does not decisively impact comonomer reactivity ratios for racMe2Si(Ind)2ZrCl2.60 Notwithstanding the pronounced effect of solvent polarity on activity, reactivity ratios for different olefins are largely independent of solvent polarity,61 further
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underlining that weakly coordinating anions likely play at most a very limited role in determining copolymerization statistics. In the framework of a broader project on structure/property correlation in molecular olefin polymerization catalysis, we recently identified a suitable computational protocol for effective modelling of olefin polymerization.62-63 In the present manuscript, we show that the protocol can also be successfully applied to the study of reactivity ratios for a large variety of metallocene and non-metallocene catalysts in the copolymerization of ethene with α-olefins. In particular, this paper will focus on the re parameter, which is especially important in the context of LLDPE production.23 2. COMPUTATIONAL METHODS All the geometries were fully optimized by using the Gaussian 09 software package64 in combination with the OPTIMIZE routine of Baker65 and the BOpt software package.66 Following the protocol proposed in Refs. 62-63, all relevant minima and transition states were fully optimized at the TPSSTPSS level of theory67 employing correlation-consistent polarized valence double-ζ Dunning [cc-pVDZ-(PP)] basis sets,68-74 from the EMSL basis set exchange library75-76 (small-core pseudopotential for Zr and Hf77-80). All calculations were performed at the standard Gaussian 09 quality settings [Scf=Tight and Int(Grid=Fine)]. All structures represent either true minima (as indicated by the absence of imaginary frequencies) or transition states (exactly one imaginary frequency corresponding to the reaction coordinate). Final single-point energies were calculated at the M06-2X level of theory81 employing triple-ζ Dunning basis sets.68-74 Solvent effects (heptane or toluene) were included with the polarizable continuum model approach (PCM).82 Enthalpies and Gibbs free energies were then obtained from TZ single-point energies and thermal corrections from the TPSSTPSS/cc-pVDZ-(PP) vibrational analyses; entropy
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corrections were scaled by a factor of 0.67 to account for decreased entropy in the condensed phase.83-85 The growing chain was modelled by an n-propyl group, and only primary insertions were considered. 3. RESULTS AND DISCUSSION UNBRIDGED METALLOCENES
a)
TiPh2
ZrCl2
1-Ti
Hf Cl2
1-Zr
1-Hf
BRIDGED METALLOCENES
b)
Si
ZrCl2
tBu
tBu
ZrCl2
ZrCl2
tBu 2-Zr
Si
Si
ZrCl2
4a-Zr
Si
Si
TiCl2 N tBu 6-Ti
Si
HfCl2
Si
ZrCl2
CGC
3b-Zr
4a-Hf
4d-Zr
c)
tBu 3a-Zr
4b-Zr
Si
ZrCl2
4e-Zr
d)
ZrCl2
5-Zr
KETIMIDE
TiCl2
TiCl2
TiCl2
N tBu
7-Ti
ZrCl2
4f-Zr
O iPr
ZrCl2
4c-Zr
PHENOXY
iPr
Si
ZrCl2
TiCl2
N tBu
N tBu
tBu
tBu
tBu
8a-Ti
8b-Ti
8c-Ti
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Figure 1. Pre-catalysts included in this study. Copolymerization performances of pre-catalysts vary depending on the ancillary ligand scaffold, its substitution pattern and the metal center. To test the reliability of the computational protocol, we selected systems to cover a broad range of catalyst structural types (Figure 1, Table 1) in combination with the industrially relevant comonomers propene and 1-hexene: a) Ti, Zr and Hf bis-cyclopentadienyls, which typically exhibit poor comonomer incorporation; b) 11 ansa-metallocenes, ranging from poor incorporators (2-Zr, 3a-Zr) to good ones (4cZr, 4d-Zr); c) The prototypical Constrained Geometry Catalyst (CGC: 6-Ti), one of the first examples of commercially relevant molecular catalysts for olefin copolymerization, due to its distinctive combination of high stability, activity, comonomer incorporation and molecular weight capabilities at high polymerization temperature (up to 160 °C);7 d) Several Ti-based non-metallocenes that are reported to copolymerize ethene and 1hexene with good activity and molecular weight capability, ranging from quite good (7Ti) to poor (8c-Ti) comonomer incorporation. Experiment vs. computational prediction Table 1 lists experimental and predicted ∆∆G‡ values for the selected 19 catalysts (24 different conditions). Experimental re values ranging from 1.8 to 48 have been reported. This translates to a ∆∆G‡(ec-ee) preference for ethene insertion of 0.4 to 2.5 kcal/mol, i.e. only a 2.1 kcal/mol spread, emphasizing that modelling this process presents significant challenges due to the accuracy that is needed for the results to be useful. At the same time, accurate experimental determination of re
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is nontrivial. Incorporation can be straightforwardly determined from accurate high-resolution 13
C-NMR spectra,60, 86 but extraction of meaningful re and rc values is not always simple.87
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Table 1. Experimental and calculated preference (∆∆G‡) for ethene over comonomer insertion. Entry
Abbr.
CA
∆∆G‡(ec-ee) (kcal/mol) Solv.
T (°C)
re
Ref. Exp.
Calc.
∆
1
1-Ti
P
Tol
50
19.5
1.9
1.8
-0.1
88
2
1-Zr
P
Tol
50
48.0
2.5
2.3
-0.2
88
3
1-Hf
P
Tol
50
13.5
1.6
1.5
-0.1
87
4
2-Zr
P
Tol
50
24.0
2.0
1.7
-0.3
88
5
3a-Zr
P
Tol
50
25.6
2.1
1.6
-0.5
87
6
3b-Zr
P
Tol
50
14.0
1.7
1.8
0.1
89
7
4a-Hf
P
Tol
25
3.0
0.7
0.7
0.0
90
8
4a-Zr
P
Hep
50
5.4
1.1
1.0
-0.1
56
9
4a-Zr
P
Tol
30
4.5
0.9
0.9
0.0
60
10
4b-Zr
P
Hep
50
5.4
1.1
1.3
0.2
56
11
4b-Zr
P
Tol
30
4.2
0.9
1.3
0.4
60
12
4c-Zr
P
Hep
50
1.8
0.4
0.3
-0.1
56
13
4d-Zr
P
Hep
50
2.0
0.5
0.9
0.4
56
14
4d-Zr
P
Tol
30
2.5
0.6
0.8
0.2
60
15
4e-Zr
P
Hep
50
4.5
1.0
1.2
0.2
56
16
4f-Zr
P
Hep
50
4.5
1.0
1.4
0.4
56
17
5-Zr
P
Tol
50
6.6
1.2
1.7
0.5
88
18B
6-Ti
P
Tol
50
1.4
0.2
0.8
0.6
91
19
6-Ti
P
Tol
90
3.8
1.0
0.9
-0.1
90
20
6-Ti
P
Tol
140
4.3
1.2
1.0
-0.2
90
21
6-Ti
H
Tol
20
4.0
0.8
0.5
-0.3
92
22
7-Ti
H
Tol
40
2.6
0.6
0.6
0.0
93
23
8a-Ti
H
Tol
25
4.5
0.9
0.5
-0.4
94
24
8b-Ti
H
Tol
25
5.1
1.0
0.6
-0.4
94
25
8c-Ti
H
Tol
25
7.4
1.2
1.0
-0.2
94
MAD
0.2
Activator: methylaluminoxane (MAO), except for entry 20 (modified MAO, modification not specified in original reference). Comonomer: P = propene, H = 1-hexene. B not included in MAD as re value differs significantly from entries 19 and 20, for a detailed discussion, see main text.
A
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3.0
2.5
2.0
1.5
1.0
0.5 y = 1.0658x - 0.1203 R² = 0.7885
0.0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
Figure 2. Experimental (ordinate) vs. predicted (abscissa) ∆∆G‡(ec-ee) (kcal/mol, E/P polymerization). Ti species (○), Zr (∆), Hf (□). Unbridged metallocenes in red, bridged metallocenes in blue and CGC in green. DFT calculations (M06-2X(PCM)/TZ//TPSSTPPSS/DZ) were performed using the naked cation approach. Coussens and Linnolahti recently showed that modelling of weakly coordinating anions can be reasonably neglected after the first chain growth step.59 Inspection of Table 1 shows that experimental ∆∆G‡(ec-ee) values are reproduced with an average and maximum deviation of only 0.2 and 0.5 kcal/mol, which is in line with expectations for our method62-63 and represents a remarkably good agreement in this field. The high quality of the predictions data is illustrated in Figure 2 by the slope and intercept (close to 1 and 0 respectively) obtained by linear regression analysis on experimental vs calculated ∆∆G‡(ec-ee) values for ethene/propene (E/P) polymerization (entries 1-17, 19-20 in Table 1). Deviations are
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small and randomly distributed around zero. Ti, Zr and Hf systems appear to be modelled similarly well. The deviations are not much higher than experimental errors and discrepancies. In ethene/1-hexene copolymerization re appears to be modelled nearly as well. 3.0 2.5 2.0 1.5 1.0 0.5 0.0
Figure 3. Predicted ∆∆G‡(ec-ee) (kcal/mol) for E/P copolymerization under a uniform set of conditions (323 K, 1 bar, toluene). Comparing catalysts It is difficult to compare the intrinsic copolymerization capabilities of various catalysts based on the literature data in Table 1 since these have been collected at different temperatures, in different solvents. Figure 3 summarizes the predicted performance of catalysts for E/P copolymerization under a uniform set of conditions (323 K, 1 bar, toluene; see also Table S2), allowing a more meaningful comparison. Unbridged metallocenes and sterically overcrowded (tert-butyl substituents) 3b-Zr are poor incorporators, while CGC, 4a-Hf and 4c-Zr are seen to be better at comonomer incorporation.
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Origins of the improved computational accuracy The reported considerable improvement in the prediction of re values (relative to earlier attempts)56,
59
can be traced to the choice of method and in particular to electronic energy
corrections. Optimization was performed at a relatively low level of theory [TPSSTPSS/ccpVDZ-(PP), fine grid] within the ‘naked-cation’ approximation, while dispersion and solvent corrections were added afterwards via single point energy corrections at the M06-2X(PCM)/ccpVTZ-(PP) level. The increased accuracy of our data compared to the results reported by Coussens and Linnolahti56 can be traced back to our use of sufficiently large basis sets for the final energy evaluation: it was shown earlier that the def2-SVP basis set is not large enough to achieve the accuracy needed here, but unfortunately calculations including an anion are not feasible with better basis sets, yet.62-63 For all catalysts in this paper, conventional insertion transition states (TSs) were found, although in some cases, locating these TSs proved challenging due to the flatness of the Potential Energy Surface (PES) around the TS. Earlier work on co-polymerization statistics hypothesized that the disagreement between computational and experimental copolymerization factors might be traced back to either chemical origins or computational accuracy.56, 59 Counterion effects or shift of the rate limiting step to olefin capture or chain rotation have been mentioned as possible chemical origins. Coussens and Linnolahti showed that the counterion effect has no marked influence after the first insertion. The good agreement with experiment obtained here without modeling the ‘tricky’ counterion seems to confirm this observation and indicates that it can be extended to other classes of olefin polymerization catalysts as well. Furthermore, the accuracy of the data implies that it is indeed the more accurate computational method that resolved the discrepancies between computation and experiment. At least as far as re
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is considered, a change in rate limiting step appears not to play a role for the catalysts in the test set. However, this is not necessarily true for insertion after an α-olefin (rc). Indeed, we are currently testing the reliability of the protocol for the prediction of rc and exploring possible shifts in the rate limiting step: this will be addressed in a forthcoming paper.
Influence of solvent and dispersion corrections Figure 4 illustrates the importance of solvent corrections. While experimental (blue line) and solvent corrected (green) ∆∆G‡(ec-ee) values give nearly identical shapes in the radar plot, uncorrected ∆∆G‡(ec-ee) values are significantly off in most cases as can be easily seen by different shape of the red line (see also Table S3). While solvent corrections for silyl-bridged bis(indenyl) metallocenes are small (≈ 0.3 kcal/mol), they can become substantial for other catalyst classes (≈ 0.6 kcal/mol for bis(cyclopentadienyl) metallocenes) or higher olefins (≈ 1.0 kcal/mol in 1-hexene copolymerization).
1-Ti 8c-Ti 2.5 8b-Ti 2.0 8a-Ti 1.5 1.0 7-Ti 0.5 0.0 6-Ti -0.5 6-Ti -1.0
1-Zr 1-Hf 2-Zr 3a-Zr 3b-Zr 4a-Hf
6-Ti
4a-Zr
5-Zr
4a-Zr
4f-Zr 4e-Zr
4b-Zr 4b-Zr 4d-Zr
4c-Zr 4d-Zr
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Figure 4. Influence of solvent corrections on predicted vs. experimental ∆∆G‡(ec-ee)
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(kcal/mol)
values. Blue line experimental value, red line uncorrected M06-2X, green line solvent corrected M06-2X. Considering the accuracy that is needed to usefully model copolymerization, solvent corrections are therefore essential. Recently, Coussens and Linnolahti concluded that solvation effects modelled with the polarizable continuum model do not significantly affect relative insertion barriers for ethene and propene polymerization for a bis(cyclopentadienyl) Zrcatalyst.59 Our broader test set leads to a slightly different conclusion, in the sense that this appears to be only true with the silyl bridged metallocene class of catalysts. Experimentally, copolymerization ratios appear to be somewhat sensitive to the choice of solvent, with heptane usually giving better co-monomer incorporation.61 Our model appears to capture this (Table 2), although the calculated effect is small (
