ABSTRACT

The linearization of adsorption equations is controversial. The estimation of fitting parameters strongly depends on the linearization method, magnitude of experimental error, and data range. Although many studies contrast linear versions of these equations with their non-linear counterparts, linearization is preferred due to its simplicity since a line could be represented with fewer experimental points than a curve. An in-depth analysis was carried out to compare the accuracy of linear and non-linear models. Although different transformations linearize Langmuir isotherms, only one form yields reliable fitting parameters. Linear transformations could also lead to a statistical bias, favoring a model that does not represent the experimental behavior. Similar observations are discussed regarding the pseudo-second-order kinetic model. Linearization of Freundlich isotherms, pseudo-first-order kinetic models, and fixed-bed adsorption models through logarithms implies that attention must be taken on the logarithm limits by properly selecting the data range. Linearization also promotes the incorrect interpretation of models due to oversimplification. The linearized van’t Hoff equation would yield a reasonable fit with fewer experimental points than the non-linear regression, which requires more data to assure convergence. In this sense, there is convincing evidence that non-linear regression is a more robust and reliable tool for adsorption modeling.

摘要

吸附方程的线性化是有争议的。拟合参数的估计很大程度上取决于线性化方法、实验误差的大小和数据范围。尽管许多研究将这些方程的线性版本与其非线性对应物进行了对比，但线性化因其简单性而成为首选，因为一条线可以用比曲线更少的实验点来表示。进行了深入分析以比较线性和非线性模型的准确性。尽管不同的变换使 Langmuir 等温线线性化，但只有一种形式会产生可靠的拟合参数。线性变换也可能导致统计偏差，有利于不代表实验行为的模型。关于准二级动力学模型讨论了类似的观察结果。通过对数对 Freundlich 等温线、准一级动力学模型和固定床吸附模型进行线性化意味着必须通过正确选择数据范围来注意对数限制。由于过度简化，线性化还促进了模型的错误解释。与非线性回归相比，线性化 van't Hoff 方程将产生合理的拟合，实验点更少，非线性回归需要更多数据来确保收敛。从这个意义上说，有令人信服的证据表明，非线性回归是一种更强大、更可靠的吸附建模工具。由于过度简化，线性化还促进了模型的错误解释。与非线性回归相比，线性化 van't Hoff 方程将产生合理的拟合，实验点更少，非线性回归需要更多数据来确保收敛。从这个意义上说，有令人信服的证据表明，非线性回归是一种更强大、更可靠的吸附建模工具。由于过度简化，线性化还促进了模型的错误解释。与非线性回归相比，线性化 van't Hoff 方程将产生合理的拟合，实验点更少，非线性回归需要更多数据来确保收敛。从这个意义上说，有令人信服的证据表明，非线性回归是一种更强大、更可靠的吸附建模工具。