Modeling Nonlinear Adsorption to Carbon with a Single Chemical Parameter: A Lognormal Langmuir Isotherm

Predictive models for linear sorption of solutes onto various media, e.g., soil organic carbon, are well-established; however, methods for predicting parameters for nonlinear isotherm models, e.g., Freundlich and Langmuir models, are not. Predicting nonlinear partition coefficients is complicated by the number of model parameters to fit n isotherms (e.g., Freundlich (2n) or Polanyi-Manes (3n)). The purpose of this paper is to present a nonlinear adsorption model with only one chemically specific parameter. To accomplish this, several simplifications to a log-normal Langmuir (LNL) isotherm model with 3n parameters were explored. A single sorbate-specific binding constant, the median Langmuir binding constant, and two global sorbent parameters; the total site density and the standard deviation of the Langmuir binding constant were employed. This single-solute specific (ss-LNL) model (2 + n parameters) was demonstrated to fit adsorption data as well as the 2n parameter Freundlich model. The LNL isotherm model is fit to four data sets composed of various chemicals sorbed to graphite, charcoal, and activated carbon. The RMS errors for the 3-, 2-, and 1-chemical specific parameter models were 0.066, 0.068, 0.069, and 0.113, respectively. The median logarithmic parameter standard errors for the four models were 1.070, 0.4537, 0.382, and 0.201 respectively. Further, the single-parameter model was the only model for which there were no standard errors of estimated parameters greater than a factor of 3 (0.50 log units). The surprising result is that very little decrease in RMSE occurs when two of the three parameters, σκ and qmax, are sorbate independent. However, the large standard errors present in the other models are significantly reduced. This remarkable simplification yields the single sorbate-specific parameter (ss-LNL) model.