Modified Langmuir Equation for S-Shaped and Multisite Isotherm Plots

Standard isotherm equations do not estimate capacity ( Q max ) and distribution coefficient ( K d ) for complex or non-Langmuir-shaped isotherm plots. In this study, two mycotoxins, that is, aflatoxin B 1 (AfB 1 ) and cyclopiazonic acid (CPA), were mixed with kaolinite and a naturally acidic montmorillonite clay (LPHM) at 25 °C, respectively. Isotherm data gave S-type plots. The data were fitted to the models of Langmuir (LM) and multi-Langmuir (MLM); however, these models did not provide a good fit for data that displayed multisite adsorption or multiple plateaus. While a published modification of the Langmuir equation (QKLM), which defines an effective partition coefficient as a function of the surface coverage, was able to fit simple isotherm plots from all categories (H, L, S, C), it did not fit complex or multisite isotherm plots. Importantly, an equation that enables the estimation of Q max and K d for both S-shaped and multisite isotherm plots has not yet been reported. Since the LM, MLM, and QKLM did not provide adequate fitting of the data, several modifications of the LM were developed: shifted Langmuir, shifted squared Langmuir, shifted cubed Langmuir, shifted exponential Langmuir, exponential Langmuir, and shifted modified Langmuir. These equations were used to derive information about the adsorption of mycotoxins to clay and to gain insight into the molecular mechanism(s) and site(s) of adsorption. The objectives of this study were to present a series of modified Langmuir equations that can be used to estimate the Q max and K d of a specific adsorption site and to relate Q max to available adsorption area.