Group contribution method for evaluation of volumetric properties of ionic liquids using experimental data recommended by mathematical gnostics

The volumetric properties of 81 different ionic liquids (ILs) have been modeled as a function of temperature and pressure using an extended version of the group contribution method previously reported by our group (Jacquemin et al. J. Chem. Eng. Data 2008, 53, 716–726). Prior to correlating collected data from the literature using this model, the mathematical gnostics was used to critically analyze experimental density data sets as a function of temperature (from 217–473 K) and pressure (from 0.1–207 MPa) to be then able to recommend one data set for each IL. In addition, recommended density data sets were then fitted as a function of temperature and pressure using a series of mathematical equations reported in the literature. These fitting equations were then assessed through the comparison of the calculated mechanical coefficients with the limited directly measured experimental data reported in the literature. Among these recommended data sets, 5399 density data points for 54 different ILs were then used as the training data set to determine the temperature and pressure dependences on the effective molar volume of 31 different cations and 24 different anions. Then 2522 density data points for 27 other ILs were used as a test data set to determine the accuracy of this method. In light of this analysis, excellent agreement was observed between calculated and recommended literature data within the whole temperature and pressure ranges investigated herein as stated by the overall relative average absolute deviation (RAAD) for each volumetric property, which was lower than 0.31% and 3.5% in the case of the density and isobaric thermal expansion coefficient of pure ILs, respectively. Finally, this model was further assessed with other methods reported in the literature in the case of the evaluation of the density of binary mixtures of two ILs as a function of temperature at atmospheric pressure. This analysis demonstrates that the proposed method shows a good ability to evaluate the density even in the case of mixture of ILs with a RAAD lower than 0.25%