Designing experiments to differentiate between adsorption isotherms using T-optimal designs

T-optimal experimental designs are developed to distinguish between the 3-parameter Guggenheim–Anderson–deBoer (GAB) and 2-parameter Brunauer–Emmett–Teller (BET) adsorption isotherms. The results show that the designs are not dependent on one of the GAB model parameters (the monolayer capacity, which is a linear scaling factor), but are dependent on the other two, which determine the curvature and shape of the isotherms. Further analysis of the designs show that for the range of model parameters considered, misspecification of the model parameters can reduce the efficiency of the experimental design to 30% or less: proper selection of the model parameters at which the design is developed within the model-parameter space can increase the maximum–minimum design efficiency to nearly 55%. The experimental replication inherent in T-optimal designs is then used in combination with a statistical lack-of-fit analysis to illustrate the role of experimental variability on the ability to distinguish between the two isotherm models.