Modified Free-Volume Theory for the Viscosity Modeling of Ionic Liquids and Deep Eutectic Solvents

Abstract

The present work presents a modification to the free volume theory (FVT) in order to obtain improved representations of the dynamic viscosity of various representative last-generation ionic fluids: pure ionic liquids (ILs) and deep eutectic solvents (DESs). Within the formalism of the current FVT approach, the barrier energy that a molecule must overcome to diffuse is proportional to the density of the fluid. We found that this barrier energy was better expressed in terms of (rather than the density) a cohesive energy between molecules of the ionic fluid, namely, the residual internal energy, which accounts for all the intermolecular forces that oppose to the breaking of bonds, including both ionic and hydrogen bonds, which are typically present in ILs and DESs. In addition, one of the characteristic parameters of the FVT approach is the length parameter, which is usually treated as a constant. However, for the present purposes, it was made density dependent. The thermodynamic potentials (residual internal energy and density) present in the resulting modified FVT model were estimated from two simple cubic equations of state of the van der Waals type: Soave−Redlich−Kwong or Peng−Robinson. The two aforementioned modifications introduced to the FVT approach were successfully verified during the representation of experimental dynamic viscosities of 3 families of imidazoliumbased ILs ([C X mim][BF 4 ], [C X mim][PF 6 ] and [C X mim][Tf 2 N]), one pyridinium-based IL ([b3mpy][BF 4 ]), one pyrrolidiniumbased IL ([bmpyr][Tf 2 N]), and one ammonium-based IL ([N1114][Tf 2 N]) over a temperature range varying from 273.15 to 353.15 K and at pressures from 1 to 3000 bar. We also considered three archetypal choline chloride-based DESs for model validation: reline, ethaline, and glyceline within a temperature range varying from 293.15 to 373.15 K and at pressures from 1 to 1000 bar.