D-optimal experimental designs for precise parameter estimation of adsorption equilibrium models: initial concentration and solvent volume to adsorbent mass ratio as independent variables

A usual experimental procedure for evaluation of solid–liquid adsorption isotherm models consists in varying the initial concentration of adsorbate, while keeping constant the ratio between the solution volume and adsorbent mass. However, one may wonder whether the experimental design can be more efficient if this ratio is allowed to vary. For this reason, in the present work, D-optimal designs for precise parameter estimation of adsorption isotherm models are proposed, allowing both the initial concentration and the ratio between the solution volume and the adsorbent mass ratio to vary simultaneously in order to minimize the determinant of the covariance matrix of parameter estimates. An important result observed was that the optimal experimental conditions tend to combine the maximum allowed value of the initial adsorbate concentration with different values of the ratio between the solution volume and the adsorbent mass. This result is in contrast with the usual experimental procedures in liquid–solid adsorption studies, where isotherms are determined with experiments that keep this ratio constant while the initial adsorbent concentration is varied. In fact, this work shown that more precise model parameters can be obtained when the adsorbate concentration is kept at its maximum allowed value, while the ratio between the solution volume and the adsorbent mass is varied.