Initial behavior of intraparticle diffusion model used in the description of adsorption kinetics

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Activated lignin-chitosan extruded blends for efficient adsorption of methylene blue (2017, neutral): “temperature, adsorbent particle size 3 and solute concentration, and), which make it complicated for prediction or control [28].”
Adsorption of sulfamethoxazole and 17β-estradiol by carbon nanotubes/CoFe2O4 composites (2015, background): “6a), thus indicating that two or more steps take place [50].”
Linear and nonlinear kinetic and isotherm adsorption models for arsenic removal by manganese ferrite nanoparticles (2019, methodology): “Hence, the behavior of initial adsorption has been analyzed based on the commonly known as the Weber and Morris equation [27] or intraparticle diffusion model (IPD) [28].”
Tetracycline adsorption by H3PO4-activated carbon produced from apricot nut shells: A batch study (2016, methodology): “The two mentioned models cannot identify the diffusion mechanism; therefore, we used the intra-particle diffusion model proposed by Morris and Weber (Wu et al., 2009).”
In-depth Insights into Mathematical Characteristics, Selection Criteria and Common Mistakes of Adsorption Kinetic Models: A Critical Review (2021, methodology): “However, most of the intercepts reported in the literature were positive, showing a rapid adsorption in a short time.([82]) The graphic method was generally used to analyze the kinetic data.”