Fluid Phase Equilibria 379 (2014) 96–103 Contents lists available at ScienceDirect Fluid Phase Equilibria journal h om epage: www.elsevier.com/locate/fluid Accurate prediction of the solubility parameter of pure compounds from their molecular structures Tareq A. Albahri ∗ Chemical Engineering Department, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait a r t i c l e i n f o Article history: Received 10 January 2014 Received in revised form 20 April 2014 Accepted 15 July 2014 Available online 23 July 2014 Keywords: Group contribution Neural networks QSPR Solubility parameter Structure property correlation a b s t r a c t A quantitative structure property relation (QSPR) method for predicting the solubility parameter (ı) of pure compounds is presented. Artificial neural network (ANN) model was developed and used to probe the structural groups that have significant contribution to the overall solubility of pure compounds and arrive at the set of groups that can best represent the solubility parameter for about 418 substances. The 36 atom-type structural groups listed can predict the solubility parameter of pure compounds from the knowledge of the molecular structure alone with a correlation coefficient of 0.998 and an absolute standard deviation and error of 0.109 and 0.67%, respectively. The results are further compared with those of the traditional structural group contribution (SGC) method based on multivariable regression as well as other methods in the literature. The method is very useful in predicting the solubility potential of various compounds and has advantages in terms of combined accuracy and simplicity. © 2014 Elsevier B.V. All rights reserved. 1. Introduction Food, medical and petroleum industries have recently placed more focus on the solubility of raw materials, undesirable gases etc. to improve medical drugs, reduce environmental emissions, and extract vegetable oil from plant seeds. Solubility plays key role in designing purification process like absorbers, strippers, distillation columns, extraction and leaching equipment [1]. There are many solubility scale systems in the literature includ- ing the solubility grade, aromatic character, aniline cloud point, wax number, heptane number, Kaouri-Butanol number, and the solubil- ity parameter (ı) which is perhaps the most widely applicable of all. Numerically, the solubility parameter is defined by the following equation [2]: ı =  U vap V L 1/2 (1) where, U vap is internal energy change on vaporization to the ideal gas, in cal/mol, and V L is the liquid molar volume at 25 ◦ C, in cm 3 /mol. ∗ Tel.: +965 2481 7662; fax: +965 2483 9498. E-mail address: toalbahri@gmail.com An approximation of the internal energy change yields [2]: ı =   - RT V L 1/2 (2) where,  is the heat of vaporization at 25 ◦ C, in cal/mol, R is the gas constant (1.9872 cal/mol K), and T is the absolute temperature, 298.15 K. This equation was used to calculate solubility parameter in units of (cal/cm 3 ) 1/2 . The above equation, also known as the Hildebrand [3] solu- bility parameter (ı) provides a numerical estimate of the degree of interaction between materials, and can be a good indication of solubility. Materials with similar values of ı are likely to be misci- ble. The Hildebrand solubility parameter is the square root of the cohesive energy density, which is the amount of energy needed to completely remove unit volume of molecules from their neigh- bors to infinite separation (an ideal gas), which is equal to the heat of vaporization divided by molar volume [3]. The cohesive energy density is a direct reflection of the degree of van der Waals forces holding the molecules of the liquid together. In order for a mate- rial to dissolve, these same interactions need to be overcome as the molecules are separated from each other and surrounded by the solvent. Solubility parameter provides simple predictions of phase equi- librium based on a single parameter that is readily obtained for most materials. These predictions are often useful for non-polar and slightly polar systems without hydrogen bonding. For polar molecules, more complicated 3D solubility parameters, such as http://dx.doi.org/10.1016/j.fluid.2014.07.016 0378-3812/© 2014 Elsevier B.V. All rights reserved.