A density functional theory approach to the development of Q-e parameters for the prediction of reactivity in free-radical copolymerizations

The Q-e scheme was developed for the interpretation of the reactivity of a monomer containing a double bond in free-radical copolymerizations. This empirical scheme has proven to be remarkably useful and continues to be the only general reactivity scheme in use today. To develop a reliable computational approach for the theoretical prediction of the Q and e values of molecules whose experimental Q and e values have not been established, we have analyzed the Q-e approach to develop a computational approach to their prediction. We then performed density-functional theory (DFT) calculations on molecules whose experimental Q and e values are available to develop a set of correlation parameters for monomers without experimental values. It has been demonstrated that for a general choice of the Q and e values of the reference monomer that both parameters Q and e should be dependent on the energetic properties of the free-radical reaction and the polar properties of the monomer and radical. To correlate the Q and e parameters with these properties, the overall quality of the calibrated correlation relationships should not be affected by the choice of the reference Q and e values. Satisfactory relationships have been found for the correlations of the Q-e parameters with DFT-calculated electronegativities and reaction free energies, suggesting that the electronegativity and reaction free energy determined by the DFT calculations reasonably reflect the polar and energetic properties, respectively, needed for Q-e parameter development. With the particular choice of the popularly used reference values of Q = 1.0 and e = -0.8 for styrene, the parameter e is dependent only on the calculated electronegativity, and the parameter Q is dominated by the calculated reaction free energy of the process of adding a radical to a C=C double bond. The explicit relationships obtained in this work can be used to predict unknown Q and e parameters based on DFT calculations.