Prediction of Partitioning between Complex Organic Mixtures and Water: Application of Polyparameter Linear Free Energy Relationships

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Abstract
Equilibrium partitioning between nonaqueous phase liquids (NAPLs) and water is a governing process for contaminants leaching from NAPLs. Conventional prediction methods, such as Raoult's law and single-parameter linear free energy relationship (SP-LFER), are inaccurate for compounds with polar functional groups. Therefore, this study introduces a polyparameter linear free energy relationship (PP-LFER) approach as a more general tool to predict NAPL−water partitioning coefficients. Our approach was evaluated using 441 experimental partitioning data from 30 references. Experimental fuel−water partitioning coefficients were generally well reproduced by existing PP-LFERs for pure solvents using either a volume−fraction weighted sum of partitioning coefficients K (linear model, R2 = 0.983, root-mean-squared error [rmse] = 0.23) or a volume−fraction weighted sum of log K (log linear model, R2 = 0.976, rmse = 0.28). Using the linear model, estimations were, in most cases, within a factor of 2 from the experimental values, regardless of the type of compounds and the presence of a fuel additive. In contrast, the log linear model considerably underestimated partitioning coefficients in the presence of strong solute−solvent hydrogen bonding. For coal tar−water partitioning coefficients (Kcoal tar/w), new PP-LFER equations were calculated based on experimental log Kcoal tar/w values of 35 compounds. The resulting regression equation was log Kcoal tar/w = 0.40(±0.33) + 0.34(±0.32)E + 0.61(±0.57)S − 0.55(±0.61)A − 5.07(±0.61)B + 3.22(±0.35)V with the rmse equal to 0.21, where E, S, A, B, and V are Abraham's solute descriptors. Partitioning coefficients for phenol and alcohols, calculated by the above equation, were much closer to the experimental values than to those estimated by the SP-LFER approach with octanol−water partitioning coefficients. The values of the coefficients also provide insight into the properties of coal tar in terms of molecular interactions with solutes. Consequently, using the approaches presented in this study, complex organic mixture−water partitioning coefficients of a wide range of organic compounds with varying polarity can be reasonably estimated.