Modeling Nonlinear Adsorption with a Single Chemical Parameter: Predicting Chemical Median Langmuir Binding Constants

Procedures for accurately predicting linear partition coefficients onto various sorbents (e.g., organic carbon, soils, clay) are reliable and well established. However, similar procedures for the prediction of sorption parameters of nonlinear isotherm models are not. The purpose of this paper is to present a procedure for predicting nonlinear isotherm parameters, specifically the median Langmuir binding constants, K̃L, obtained utilizing the single-chemical parameter log-normal Langmuir isotherm developed in the accompanying work. A reduced poly parameter linear free energy relationship (pp-LFER) is able to predict median Langmuir binding constants for graphite, charcoal, and Darco granular activated carbon (GAC) adsorption data. For the larger F400 GAC data set, a single pp-LFER model was insufficient, as a plateau is observed for the median Langmuir binding constants of larger molecular volume sorbates. This volumetric cutoff occurs in proximity to the median pore diameter for F400 GAC. A log-linear relationship exists between the aqueous solubility of these large compounds and their median Langmuir binding constants. Using this relationship for the chemicals above the volumetric cutoff and the pp-LFER below the cutoff, the median Langmuir binding constants can be predicted with a root-mean square error for graphite (n = 13), charcoal (n = 11), Darco GAC (n = 14), and F400 GAC (n = 44) of 0.129, 0.307, 0.407, and 0.424, respectively.