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.

评估固液吸附等温线模型的常用实验程序包括改变吸附物的初始浓度，同时保持溶液体积和吸附剂质量之间的比率恒定。然而，人们可能想知道如果允许这个比率变化，实验设计是否会更有效。为此，在目前的工作中，提出了用于吸附等温线模型的精确参数估计的 D 最优设计，允许初始浓度以及溶液体积与吸附剂质量比之间的比率同时变化，以最小化行列式参数估计的协方差矩阵。观察到的一个重要结果是，最佳实验条件倾向于将初始吸附物浓度的最大允许值与溶液体积与吸附剂质量之间的比率的不同值结合起来。该结果与液固吸附研究中的常规实验程序形成对比，其中等温线是通过在初始吸附剂浓度变化时保持该比率恒定的实验来确定的。事实上，这项工作表明，当吸附物浓度保持在其最大允许值，而溶液体积与吸附剂质量之间的比率变化时，可以获得更精确的模型参数。该结果与液固吸附研究中的常规实验程序形成对比，其中等温线是通过在初始吸附剂浓度变化时保持该比率恒定的实验来确定的。事实上，这项工作表明，当吸附物浓度保持在其最大允许值，而溶液体积与吸附剂质量之间的比率变化时，可以获得更精确的模型参数。该结果与液固吸附研究中的常规实验程序形成对比，其中等温线是通过在初始吸附剂浓度变化时保持该比率恒定的实验来确定的。事实上，这项工作表明，当吸附物浓度保持在其最大允许值，而溶液体积与吸附剂质量之间的比率变化时，可以获得更精确的模型参数。