Studies of the kinetics of polymerization of ε-caprolactone (CL) by salen-aluminum catalysts comprising ligands with similar steric profiles but different electron donating characteristics (R = OMe, Br, or NO2) were performed using high initial monomer concentrations (2 M < [CL]0 < 2.6 M) in toluene-d8 at temperatures ranging from 20 to 90 °C. Saturation behavior was observed, enabling determination of monomer equilibrium constants (Keq) and catalytic rate constants (k2) as a function of R and temperature. While Keq varied only slightly with the electron donating properties of R (Hammett ρ = +0.16(8)), k2 showed a more significant dependence reflected by ρ = +1.4(1). Thermodynamic parameters ΔG° (associated with Keq) and ΔG(‡) (associated with k2) were determined, with the former being ∼0 kcal/mol for all catalysts and the latter exhibiting the trend R = OMe > Br > NO2. Density functional theory (DFT) calculations were performed to characterize mechanistic pathways at a microscopic level of detail. Lowest energy transition-state structures feature incipient bonding of the nucleophile to the lactone carbonyl that is approaching the metal ion, but a distinct CL adduct is not an energy minimum on the reaction pathway, arguing against Keq being associated with coordination of monomer according to the typical coordination-insertion mechanism. An alternative hypothesis is presented associating Keq with "nonproductive" coordination of substrate in a manner that inhibits the polymerization reaction at high substrate concentrations.
Aluminum
alkoxide complexes (2) of salen ligands with
a three-carbon linker and para substituents having variable electron-withdrawing
capabilities (X = NO2, Br, OMe) were prepared, and the
kinetics of their ring-opening polymerization (ROP) of ε-caprolactone
(CL) were investigated as a function of temperature, with the aim
of drawing comparisons to similar systems with two-carbon linkers
investigated previously (1). While 1 and 2 exhibit saturation kinetics and similar dependences of their
ROP rates on substituents X (invariant Keq, similar Hammett ρ = +1.4(1) and 1.2(1) for k2, respectively), ROP by 2 was significantly
faster than for 1. Theoretical calculations confirm that,
while the reactant structures differ, the transition state geometries
are quite similar, and by analyzing the energetics of the involved
distortions accompanying the structural changes, a significant contribution
to the basis for the rate differences was identified. Using this knowledge,
a simplified computational method for evaluating ligand structural
influences on cyclic ester ROP rates is proposed that may have utility
for future catalyst design.
A new variational theorem is formulated which has as its Euler equations and natural boundary conditions all of the differential equations and boundary conditions of the boundary value problem under consideration. Other variational theorems, including the classical theorems of Helmholtz, follow from this fundamental theorem. Conditions under which the theorems obtained are minimum or maximum principles are discussed and application to non-Newtonian flow in a tube is made.
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