Feedback and Impulse Behavior of Differential-Algebraic Equations

Mathematical Notes - A controlled linear system of differential-algebraic equations with infinitely differentiable coefficients is considered. An arbitrarily high unsolvability index and a variable...     

Aluminate and Magnesiate Complexes as Propagating Species in the Anionic Polymerization of Styrene and Dienes

The influence of MgR₂ and AlR₃ additives on alkyllithium initiators in the anionic polymerization of butadiene has been investigated in non polar solvents. A strong decrease of the diene polymerization rate in the presence of the two Lewis acids was observed, similarly to that observed in the retarded anionic polymerisation of styrene. With n,s-Bu₂Mg, the percentage of 1,2 vinyl units increases with the [Mg]/[Li] ratio. This behavior is specific to magnesium derivatives bearing secondary alkyl groups and likely results from the additional complexation of lithium species by free dialkylmagnesium and/or a 1,4- to 1,2- chain end isomerization process during chain exchanges between polybutadienyl active chains and dormant ones attached to magnesium species. These reversible exchanges also lead to the formation of one supplementary chain by initial dialkyl magnesium which acts as reversible chain transfer agent. On the contrary with the R₃Al/RLi systems the number of chains is only determined by the concentration of initial alkyllithium and no modification of the polybutadiene microstructure compared to lithium initiators (1,4 units = 80%) is noticed. Dialkyl magnesiate complexes with alkali metal derivatives (i.e. alkoxide) are also able to influence the stereochemistry of the styrene insertion during the propagation reaction. Polystyrenes with different tacticities ranging from predominantly isotactic (85% triad iso) to syndiotactic (80% triad syndio) can be obtained with these initiators.