D-optimal experimental designs for Freundlich and Langmuir adsorption isotherms

In this paper, D-optimal experimental designs are derived for three common adsorption isotherm models: the 2-parameter Freundlich, the 2-parameter Langmuir, and the 3-parameter Langmuir. For each of these liquid-solid adsorption models, the D-optimal design equations are derived from the information matrix and then solved numerically to determine the specific design values as a function of the model parameters. The variation of the design with the assumed values of the model parameters is discussed. For all three isotherms, it was determined that one support point was always at the maximum of the scaled experimental region. It was also determined that the D-optimal designs for all three isotherms were independent of the proportionality parameter in the model. For the three models and their associated D-optimal designs, the design optimality was verified using the general equivalence theorem.