Propagation rate coefficient of acrylic acid: theoretical investigation of the solvent effect

The free-radical polymerization propagation rate coefficient (k_p) of acrylic acid (AA) was calculated using transition state theory and ab initio quantum chemistry in order to shed light on the very strong solvent effects observed experimentally. Calculations were performed using a gas-phase reaction simulation, and the contribution of solvent then taken into account using the Polarizable Continuum Model for two solvents—water and toluene. The frequency factor (A) for AA propagation was insensitive to both varying the level of quantum theory applied as well as introducing a solvent field into the calculations. The activation energy (E_a) decreased substantially (∼10 kJ mol⁻¹) upon introduction of the water solvent field relative to the gas phase; however, the toluene solvent field had little impact on E_a. From analyzing transition state (TS) bond lengths and angles, as well as electronic density, this variation in E_a was attributed to greater resonance stabilization of the TS in the polar solvent, as well as more substantial mixing of reactant molecular orbitals, assisting in the transfer of electrons from the alkene to the radical. This provides a partial explanation to the marked variation in aqueous-phase k_p of water-soluble monomers seen experimentally with changes in monomer and electrolyte concentrations, which alters the hydrogen bonding patterns in solution.