The three-parameter (K, b, and n) Song isotherm model was slightly modified to make it possible to obtain analytical integration of the spreading pressure integral. The modified Song model (MSM) allows more efficient and accurate calculation of the ideal adsorbed solution theory (IAST). The MSM also satisfies the Henry's law and the Freundlich model at low and high concentrations, respectively, and reverts to the Langmuir and the linear models when n equals zero and one, respectively. Approximate values of each parameter could be estimated from a plot of log (q/c) versus log c; the partition coefficient in the Henry's law region (K) and the Freundlich index (n) can be estimated from the ordinate value of the low-concentration asymptote and the slope of the high-concentration asymptote, respectively, and the parameter (b) can be estimated from the solution-phase concentration of the intersection point of the two asymptotes. The MSM was fitted to the single-solute sorption of 2-chloro-, 3-cyano-, and 4-nitrophenol onto montmorillonites modified with either HDTMA cation or TMA/HDTMA dual cations. The ideal adsorbed solution theory (IAST) combined with either dual-mode model, Khan model or MSM as a single-solute isotherm model was used to predict three bisolute and one trisolute sorption to organoclays. The Sheindorf-Rebhun-Sheintuch (SRS) and Murali-Aylmore (M-A) were also used to predict bisolute sorption to organoclays. The IAST predictions were generally in good agreement with the multisolute sorption data. The advantages of MSM over other three-parameter models were fully discussed.
Keywords: Competition modelling; ideal adsorbed solution theory (IAST); modified Song isotherm model; organoclay; spreading pressure.