Model of phase distribution of hydrophobic organic chemicals in cyclodextrin–water–air–solid sorbent systems as a function of salinity, temperature, and the presence of multiple CDs

Environmental and other applications of cyclodextrins (CD) often require usage of high concentration aqueous solutions of derivatized CDs. In an effort to reduce the costs, these studies also typically use technical grades where the purity of the CD solution and the degree of substitution has not been reported. Further, this grade of CD often included high levels of salt and it is commonly applied in high salinity systems. The mathematical models for water and air partitioning coefficients of hydrophobic organic chemicals (HOC) with CDs that have been used in these studies under-estimate the level of HOC within CDs. This is because those models (1) do not take into account that high concentrations of CDs result in significantly lower levels of water in solution and (2) they do not account for the reduction in HOC aqueous solubility due to the presence of salt. Further, because they have poor knowledge of the CD molar concentration in their solutions, it is difficult to draw comparisons between studies. Herein is developed a mathematical model where cyclodextrin is treated as a separate phase whose relative volume is calculated from its apparent molar volume in solution and the CD concentration of the solution. The model also accounts for the affects of temperature and the presence of salt in solution through inclusion of modified versions of the Van’t Hoff and Setschenow equations. With these capabilities, additional equations have been developed for calculating HOC phase distribution in air–water–CD–solid sorbent systems for a single HOC and between water and CD for a system containing multiple HOCs as well as multiple types of cyclodextrin.