A state-of-the-art theoretical method for estimating ultrasonic velocity in ionic liquid mixtures: An extension of McAllister's interaction model

McAllister's Interaction Model has been extended to predict ultrasonic velocities in eight binary mixtures of ionic liquids and water at temperatures T = 288.15 K, 298.15 K, and 308.15 K.The ionic liquids chosen for the current study are [BMim][TfO], [BMpyr][TfO], [BMpy][TfO], [BMim][dca], [HMim][dca], [BMpyr][dca], [Mpy] [MSO4], and [EEpy][ESO4]. The interactions considered in present cases have been investigated for a range of variations from three -body interactions to nine -body interactions. The experimental values of ultrasonic velocities for all the mixturesat temperatures T = 288.15 K, 298.15 K, and 308.15 Kare compared with the computed values. The differences between the experimental and theoretically predicted velocities are determined in terms of absolute percentage deviation. It is worth mentioning that McAllister's Model of interactions has been extended, for consideration, from three -body interactions to nine -body interactions among constituent molecules of binary mixtures and applied for the prediction of ultrasonic velocities in binary mixtures of water and ionic liquids for the first time. The extended Huckel theory (EHT) is used to calculate the charge distributions in eight ionic liquids and water molecules to understand the active sites available for interactions on each constituting molecule of the binary mixtures under investigation. The results we obtained complemented our decision to extend McAllister's interactions model (MAIM) to higher orders (four -body to nine -body interactions). The results obtained (using extended MAIM) report an excellent agreement with experimental velocity values for ninebody interactions for all the systems under study. It is also pointed out that McAllister's assumption that the free energies of activation are the additive quantity for viscosity investigation in organic liquid mixtures is also valid in the case of ultrasonic velocity studies for ionic liquids and water mixtures. Considering McAllister's conjecture that rather than a planar system of interactions among solvent -solute molecules, a three-dimensional approach to intermolecular interactions can be more appropriate, authors have confirmed the validity of McAlliter's conjecture by successfully investigating three-dimensional multi -body (in the present case: 9 -body) interactions in the binary mixtures of ionic liquids and water.