Piecewise linear regression: A statistical method for the analysis of experimental adsorption data by the intraparticle-diffusion models

The film-diffusion and the intraparticle-diffusion models are widely used to analyze the mechanism of adsorption. The plots of these models often have a multi-linear nature, and in general, the graphical method is employed to analyze the data in which the linear segments are determined visually. This method suffers from subjectivity and therefore its estimated diffusion parameters are not very reliable. An alternative statistical method, piecewise linear regression (PLR) is presented and applied to experimental data. The results demonstrate that the use of PLR is practical and leads to diffusion estimates that may be quite different from the graphical method. PLR also determined the exact time periods for each diffusion regime, which opens new possibilities for analyzing and understanding the mechanism of diffusion. In order to encourage the testing and application of PLR, an easy to use Microsoft® Excel™ spreadsheet is made available.