thermodynamics of the early stages in homogeneous ziegler-natta polymerization: density functional...

Macromol. Theory Simul. 3,895 - 904 (1994) 895

Thermodynamics of the early stages in homogeneous Ziegler- Natta polymerization: density functional calculations on model systems TiCIzR+ and ZrClzR+

Roberto Fusco*, Luca Longo

EniChem - Istituto Guido Donegani, Via Fauser, 4 - 28100 Novara, Italy

(Received: February 18, 1994; revised manuscript of April 26, 1994)

SUMMARY The ethylene polymerization enthalpy, calculated through quantum-mechanical ab-initio

methods on model systems of homogeneous Ziegler-Natta cationic catalysts, is reported to be from two to three times greater than the experimental value of 22,3 kcal/mol. In this paper we analyze the origin of this discrepancy and show that it is mainly due to the intrinsic instability of the cationic system in vacuum. We also demonstrate that the growing polymer chain can act as a quite efficient stabilizing agent. We examined, through density functional calculations, the model systems MC12R+, where M = Ti, Zr and R = CH,, C3H,, C5H,, , C7H15 and their analogues obtained by neutralizing the positive charge with a chloride anion. On the basis of our computational results, we found that: i) for the ideal reaction of ethane with ethylene to give butane, considered as a thermodynamical model of the single insertion step, the calculated enthalpy value of 35,6 kcal/mol is in closer agreement with the experimental value and is taken as theoretical reference value; ii) the same value is obtained also for the neutral systems MC1,R independently of the nature of the metal and of the alkyl chain length; iii) for cationic systems, when R = CH, , high insertion enthalpies are obtained in agreement with the calculated values reported in literature, but, for R = C,H7 , C5Hl, and C7H15 , the insertion enthalpy remarkably decreases converging towards the theoretical reference value. We conclude that the high enthalpy value obtained for the first monomer insertion is not only a mere consequence of the computational method, but is mainly due to the weak stabilizing effect of the methyl group. A longer alkyl chain produces a stabilization of the cationic system through the inductive effect as well as through formation of agostic bonds. This leads us to formulate the hypothesis that, in real polymerization conditions, the role of a stabilizing agent, which is mainly played by the counterion in the early stages of the propagation reaction, could be performed by the growing chain as the polymerization proceeds.

Introduction

Recently, an increasing number of papers concerning theoretical calculations on model systems of homogeneous Ziegler-Natta cationic catalysts appeared in literature'-4). The calculated energy for the insertion of an ethylene molecule into the metal-carbon bond is reported to be from two to three times greater than the experimental enthalpy value of 22,3 kcal/mol per monomeric unit5). This value is in good agreement with that of 23,5 kcal/mol derived from group additivities6-8).

The reasons of this discrepancy can reside in the computational method or in the model system itself. Until now this kind of calculations was confined to the investigation of the first monomer insertion where the growing chain was simulated only by a methyl group bound to the metal atom.

In this paper we investigate the influence of the growing chain on the insertion energy of ethylene for two catalytic model systems: TiC1,R + and ZrC1,R + . Particularly we

0 1994, Hlithig & Wepf Verlag, Zug CCC 1022-1344/94/$03.00

896 R. Fusco, L. Longo

examined the intermediates with R = -CH3, -C,H,, -C,H,, , -C,H,, and their neutral analogues TiC13R and ZrCI,R, obtained by the addition of a chloride anion.

All the quantum mechanical calculations reported here were performed using the program DMo19) based on density functional theory.

Description of the model

The enthalpy of any catalytic cycle is independent of the catalytic system; therefore, we estimated its value for the ethylene polymerization from the energy difference between the energies of reagents and products for the ideal reaction of ethylene with ethane to give butane (Scheme IA) in order to test the reliability of the adopted calculation method. Then we examined the energies of the initial and final states for the first three insertion steps in both metal systems (Scheme 1 B). Furthermore, in order to investigate the influence of the cationic nature on the stability of the catalytic complexes we performed analogous calculations on similar neutral systems built saturating the positive charge with a chloride anion (Scheme IC).

Scheme I:

A) CH,=CH, + C,H, __* C4H10

B) CH,=CH, + CI,M+Ri (B-i) d C12M+Ri+l C) CH,=CH2 + C13MRi (C-i) __* C13MRi+,

where:

R, = CH3 R, = C3H7 R2 = C5H11

R3 = C7H15

M = Ti, Zr

The adopted polymerization model follows the generally accepted monometallic mechanism proposed by Cossee several years ago lo) and is shown in Fig. 1. Each polymerization step is composed of two phases: coordination of the olefin to the metal atom followed by its insertion in the growing chain through cis opening of the double bond. In this paper we focus our attention to the thermodynamics of the global mechanism. Therefore we calculated AE values between steps 1 and 3, neglecting the coordination phase.

The minimum energy intermediates examined here were modelled starting from hypothetical structures based on standard geometrical values of bond distances and valence angles. A tetrahedral configuration of the metal atoms was assumed with only three coordination sites occupied by two chlorine atoms and the first carbon atom of the alkyl group. For longer alkyl chains (R = -C,H,, -C,H,, , -C,H,,) the second

Thermodynamics of the early stages in homogeneous Ziegler-Natta . . . 897

Fig. 1. Polymerization mechanism and scheme of the reaction energy path

1 Reaction coordinate

carbon atom was assumed in a skew conformation with respect to both the chlorine atoms. Tentatively three initial conformations, cis (C) , gauche (G) (G+ and G - conformations are symmetry related) and trans ( T ) , of the first carbon-carbon bond were examined and the remaining part of the alkyl chain was kept in trans-planar conformation. The final structures were obtained through a full geometry optimization, minimizing the total energy using an algorithm described in the next paragraph. All the chain atoms were explicitely included in the calculation.

Calculation method

All the energy calculations were performed using the density functional program developed by Delley et al. " - 1 3 ) , implemented in the DMo12.3 package9). The Hedin- LundqvWJanak-Morruzi-Williams 14) local correlation functionals were adopted without gradient corrected potential terms. Since all the examined systems were in closed shell configurations, spin restricted wavefunctions with default orbital occupations were selected. Double-numeric basis sets were adopted with frozen inner core orbitals. The values of the control parameters used are listed in the Appendix. All the structures were geometrically optimized using a BFGS Newton-Raphson algorithm Is).

Results

In Fig. 2 schematic representations of the calculated minimum energy structures are shown for B intermediates while their main geometrical features are reported in Rb. 1. The geometry optimization showed that the alkyl chain in the intermediates B-I, B-2 and B-3 can assume different conformations. The most stable ones correspond to the trans ( T ) , skew (S), obtained starting from G, and cis ( C ) conformations of the first carbon-carbon bond in the alkyl chain; all these structures are characterized by


8-0 B-1. 8-2. 8-3

Fig. 2. Schematic representa-

tion diates of and the their reaction main interme- conforma- tional isomers. The dashed lines represent the closest interatomic interactions between the growing

CH, y y R H j H !''!'' \ I

\ , s , 1 ,

I '\ ' \ :

cI ..,wM : : / I ,

I ,

MCI, MCI, CI

MCI2

trans skew cis chain and the metal atom

stabilizing interactions between the metal and the neighbour atoms of the growing chain, which tend to saturate the fourth vacant coordination site. Their geometries are in close agreement with those reported in ref. 3, From the examination of Tab. 2, it is apparent that S and T conformations are stabilized by 8-agostic interactions while y- agostic bonds prevail in C. The remaining part of the alkyl chain does not depart significantly from the initial trans-planar conformation. An extremely good agreement was found between the calculated geometrical structures involving Hp agostic interactions, particularly the S conformation, and X-ray data reported by Jordan et al. 16) for the (C,H,CH3)2Zr(CH,CH,R)(P(CH3)3) + complex. Experimental values of 2,16 A for the Hp-Zr distance and of 84,7" for the Zr-C,-C, angle are very close to the calculated values of 2,14 A and 87,6" reported in Tab. 1.

Tab. 1 . Main geometrical distances (in A) and angles (in degrees) of the examined intermediates

B-0 a) M-C1 M-C,

B-I b, (T) M-Cp M-Hp M-C,-Cp C,--CD-Hp

(S 1 M-Cp M-Hp M-C,-Cp C,-Cp-Hp

( C ) M-C, M-H, M-C,-Cp

Cp-C,-H, c,-cp-c,

Ti Zr

2,14 2,30 1,94 2,lO

2,21 2,42 2,30 2.50

77,6" 82,l" 112,7" 111,8O

2,38 2,71 2,02 2,14

85,2" 87,6O 113,l" 110,8"

2,19 2,38 2,25 2,40

91,3" 87,6" 1 1 3,O" 120,6" 113,5" 117,2"

a) The M-C, and M-C1 bond distances are constant in all the examined intermediates. b, For B-1 intermediates only geometrical parameters affected by agostic interactions are

reported. These are substantially analogous in B-2 and B-3 intermediates.

Thermodynamics of the early stages in homogeneous Ziegler-Natta . . .

Tab. 2. Calculated energies of examined structures

899

System E/(kcal/mol) System E/(kcal/mol)

A- 1 A-2 A-3

B-0

B-1

B-2

B-3

c - 0 c- 1 c-2

C2H4

C2H6 C4H10

TiCI,CH$

TiCI,C,Hq

TiCl,C,H:,

TiC12C7H &

TiCl,CH, TiCl,C3H7 TiCI,C,H

- 596,l -748,3

- 1 380,O

-447,9 ZrC1,CH;

- 1 096,5 ZrCI2C,Hq - 1 094,7 - 1 107,4

- 1731,5 ZrCI,C,H:, - 1 729,l - 1745,2

-2363,9 ZrCI2C7H 7, -2361,5 - 2 377,6

-748,l ZrCl,CH, - 1 319,4 ZrC13C3H7 -2011,3 ZrC13C,H,

-478,5

( T ) -1121,7 ( S ) - 1 122,l (C) - 1 129,l

( T ) -1756,3 (S) -1756,2 (C) -1766,O

( T ) -2388,5 ( S ) -2388,l (C) -2398,4

-773,2 - 1403,3 - 2 035,l

In C-1 and C-2 intermediates the fourth coordination site is occupied by a third chlorine atom: this prevents the formation of agostic bonds and consequently only the Tconformation of the first carbon-carbon bond of the alkyl chain was examined. The energy values calculated for all the examined intermediates are reported in Tab. 2.

The energies of A-1 , A-2 and A-3 structures were calculated with the aim to estimate the AE for the single step of the global catalytic cycle for the ideal reaction of ethylene with ethane to give butane. The resulting value, obtained using the same ab-initio method, was 35,6 kcal/mol and must be compared with the experimental one of 22,3 kcal/mol.

The B intermediates refer to the catalytic reactions. B-0 is the starting catalytic system; B-I, B-2 and B-3 correspond, respectively, to the insertions of the first, the second and the third monomeric units and AEi (i = 1 , 2, 3) denote the relative insertion energies. AEi values can be obtained in different ways depending on the choice of the reference conformations. Of course they must be calculated as energy differences between homologous conformations as reported in Tab. 3.

Discussion

The enthalpy values AE, , referred to ethylene insertion on catalytic model systems where R = CH, , are confirmed to be from two to three times greater than the experimental value: the entity of the discrepancy depends on the nature of the metal and on the choice of the reference conformation in the final state.

900

Tab. 3. Calculated insertion energies (in kcal/mol)

R. Fusco, L. Longo

Experimental Reference

TiCl,R+ ( T ) ( S 1 (0

( S ) (0

ZrC12R+ ( T )

TiC1,R ZrC1,R

3 -30 E 1

-40 Y

L a -50

-60

-70

-22,3 -35,6

-52,4 - 38,9 - 50,7 - 38,2 -63,3 -41,7

-47,O - 3 8 3 - 4 7 3 - 37,9 - 5 4 3 - 40,7

-35,2 -35,7 - 34,O - 3 5 7

0.4 1 2 3

-60 1

c 0.9 1

0.8

0.7

0.6

-36,3 - 36,3 - 36,3

-36,l -35,8 -36.3

Ti

\ L-. 0 1 2 3

Zr

\ -.-. -70 I 0 . 5 1

0 1 2 3 0 1 2 3 Step Step

Fig. 3. Fig. 4.

Fig. 3. reference conformations data are reported

Fig. 4. conformations data are reported

Insertion energy plots for titanium and zirconium systems. T (El), S ( 0 ) and C (W)

Metal charge plots for titanium and zirconium systems. T ( O ) , S ( o ) and C ( W ) reference


The theoretical value of 35,6 kcal/mol for the polymerization energy per monomeric unit, calculated for the ideal reaction of ethylene with ethane to give butane (system A), is about 14 kcal/mol greater than the experimental one and we suppose that this is caused by an intrinsic error in the computational method. The same reference value of 35,6 kcal/mol is obtained by analyzing, through an analogous procedure, the hypothetical polymerization reaction for neutral systems obtained saturating the positive charge of the catalyst by addition of a third chloride anion to the vacant site of the metal atom (system C). This value is found to be substantially constant irrespective of the chain length and of the metal. This leads us to suppose that the further energy differences between the reference value and those obtained for the charged systems can be originated by the intrinsic cationic nature of the catalyst.

Additional proofs of the validity of this hypothesis were obtained examining the behaviour of the cationic catalytic systems where R = C,H,, C,H,, and C,H,, . The decrease of the enthalpy value for further monomer insertions (Fig. 3) and the parallel decrease of the metal charge (Fig. 4) show that long alkyl chains produce a more effective stabilization of the cation as a consequence of inductive effects and of the formation of agostic bonds. The enthalpy values appear to converge towards the reference value with increasing chain length (Fig. 3). The higher energy values and the faster convergence observed for the titanium system can be explained in terms of a greater electron affinity of this metal compared with zirconium. This observation adds another piece of evidence to the hypothesis of the stabilizing effect of long alkyl chains to the cationic system.

All these considerations strongly suggest that, in vacuum, the high insertion energy values are peculiar to the early stages of polymerization and that the enthalpy converges towards the reference value as the reaction proceeds. A hypothesis about the role that this behaviour could play in the initial stages of polymerization is suggested by the following considerations. In the real polymerization conditions many species are able to coordinate the catalyst; the most important ones are the olefin and the counterion. As suggested by the perturbation theory of chemical reactions 17,1*), while the catalyst- olefin interaction is expected to be mainly ruled by the LUMO-HOMO (lowest unoccupied molecular orbital-highest occupied molecular orbital) energy difference, the catalyst-counterion interaction should be dominated by Coulombian forces and, therefore, strongly affected by the metal charge. The LUMO of the catalytic system coincides with an unoccupied d orbital of the metal atom as shown in Fig. 5. The LUMO energy increases with the chain length as demonstrated by the plots reported in Fig. 6. Comparing the charge plots reported in Fig. 4 with the LUMO plots, it is apparent that, as the polymerization proceeds, the metal charge decreases while the LUMO energy becomes closer to the HOMO energy of the olefin (- 165,4 kcal/mol calculated by the DMol program): therefore, the coordinative preference of the catalyst shifts from the counterion towards the olefin. We think that this behaviour could play an important role in the initial phase of the polymerization reaction. This consideration could offer a key to interpret the experimental behaviour of CpzTiR+ system (Cp: cyclopentadienyl; R = -CH, , -CH,CH,) which show an increasing catalytic activity for longer alkyl chains 19).


Fig. 5. Titanium systems show the same orbital shape and are not reported

LUMO plots of B-0, B-1 (C), B-1 (S) and B-1 (T) intermediates for zirconium systems.

- 1 ~ ~ 1 Zr

Step Step

Fig. 6. reference conformations data are reported

LUMO energy plots for titanium and zirconium systems. T (a), S ( +) and C (W)


Appendix

The values of the main control parameters of the DMol program for both self-consistent-field (SCF) calculation and BFGS (Broydon-Fletcher-Goldfarb-Shanno) energy minimization algorithms used in this work are listed here.

SCF parameters

The numerical integration parameters used are the following: - default functional form of the partition function:

- minimum and maximum allowed values of the harmonic generator used in the angular IPA = 5

sampling: IOMIN = 1 IOMAX = 6 - numerical threshold on the angular part of the wavefunctions: THRES = lo-’ - radial distribution limit distance of sampling points around each nucleus in atomic units: RMAXP = 12,O - radial points number scaling factor: SP = 1,2

Flow parameters: - convergency threshold in eV

- charge mixing coefficient: FASCF = lo-’ - spin mixing coefficient: FBSCF = lo-’ - charge smearing parameter in Hartrees (Ha): SMEAR =

SCFTOL = lo-’

Minimization parameters

- energy threshold in Ha: ETOL =

- maximum Cartesian gradient threshold in Ha/Bohr:

- RMS gradient threshold in Ha/Bohr: GRTOL = 1 , O - - stop parameter for a single line search in eV:

MAXGRTOL = 1,s. 1 0 - ~

LINTOL =

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thermodynamics of the early stages in homogeneous ziegler-natta polymerization: density functional...

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