Thermodynamics of the early stages in homogeneous ziegler-natta polymerization: Density functional calculations on model systems TiCl2R+ and ZrCl2R+

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 intrisnic 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 MCl₂R⁺, where M = Ti, Zr and R = CH₃, C₃H₇, C₅H₁₁, 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 MCl₃R independently of the nature of the metal and of the alkyl chain length; (iii) for cationic systems, when R = CH₃, high insertion enthalpies are obtained in agreement with the calculated values reported in literature, but, for R = C₃H₇, C₅H₁₁ 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.