Three-parameter empirical isotherm model: Its application to sorption onto organoclays

A new three-parameter empirical isotherm model (the Song isotherm model, hereinafter) is proposed. This model satisfies the Henry's law and the Freundlich isotherm model in the low and high concentration ranges, respectively. We applied this model to the single-solute sorption of 2-chloro-, 3-cyano-, and 4-nitrophenol from water to montmorillonites organically modified with either hexadecyltrimethylammonium (HDTMA) cation or both HDTMA and tetramethylammonium (TMA) dual cations. Sorption to organoclays (i.e., organically modified clays) modified with the long-hydrocarbon chain organic cations or the short- and long-hydrocarbon chain dual organic cations usually occurs by a partition mechanism. Sorption of polar organic compounds to organoclays, however, becomes nonlinear when the solution-phase concentration covered is more than 3 orders of magnitude. The three parameters contained in the presently proposed model could be estimated from the plot, log(q/c) versus log c. The partition coefficient in the Henry's law region (K) can be estimated from the ordinale value of the asymptote in the low concentration region, the Freundlich index (n) can be estimated from the slope of the asymptote in the high concentration region, and the parameter (β) corresponding to the crossover point can be estimated from the intersection point of the two asymptotes. By performing nonlinear curve fitting to the raw data, q versus c, using the initial guesses estimated from the manipulated data, log-(q/c) versus log c, the optimum set of parameters could be determined without worrying much over the annoying local minima. The Song model was compared with other existing two- and three-parameter isotherm models. The Song model fitted our experimental data better than the Langmuir and Freundlich models and showed nearly the same goodness-of-fit as the Redlich-Peterson and dualmode models. The obvious merit of the Song model is that it provides us with the partition coefficient in the Henry's law region. The organic carbon-normalized partition coefficients in the Henry's law region were found to be about 1 order of magnitude higher than the corresponding octanol-water partition coefficients, at least for the phenolic compounds covered in this study.