Stokes shift dynamics in (non-dipolar ionic liquid + dipolar solvent) binary mixtures: a semi-molecular theory.

A semi-molecular theory for studying composition dependent Stokes shift dynamics of a dipolar solute in binary mixtures of (non-dipolar ionic liquid + common dipolar solvent) is developed here. The theory provides microscopic expressions for solvation response functions in terms of static and dynamic structure factors of the mixture components and solute-solvent static correlations. In addition, the theory provides a framework for examining the interrelationship between the time dependent solvation response in and frequency dependent dielectric relaxation of a binary mixture containing electrolyte. Subsequently, the theory has been applied to predict ionic liquid (IL) mole fraction dependent dynamic Stokes shift magnitude and solvation energy relaxation for a dipolar solute, C153, in binary mixtures of an ionic liquid, trihexyltetradecylphosphonium chloride ([P(14,666)][Cl]) with a common dipolar solvent, methanol (MeOH). In the absence of suitable experimental data, necessary input parameters have been obtained from approximate methods. Dynamic shifts calculated for these mixtures exhibit a linear increase with IL mole fraction for the most part of the mixture composition, stressing the importance of solute-IL dipole-ion interaction. Average solvation rates, on the other hand, show a nonlinear IL mole fraction dependence which is qualitatively similar to what has been observed for such binary mixtures with imidazolium (dipolar) ILs. These predictions should be re-examined in suitable experiments.